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Molecular chirality has traditionally been viewed as a binary property where a molecule is classified as either chiral or achiral, yet in recent decades, mathematical methods for quantifying chirality have been explored. Here, we use toy molecular systems to systematically compare the performance of two state-of-the-art chirality measures: (1) the Continuous Chirality Measure (CCM) and (2) the Chirality Characteristic (χ). We find that both methods exhibit qualitatively similar behavior when applied to simple molecular systems such as a four-site molecule or the polymer double-helix, but we show that the CCM may be more suitable for evaluating the chirality of arbitrary molecules or abstract structures such as normal vibrational modes. We discuss a range of considerations for applying these methods to molecular systems in general, and we provide links to user-friendly codes for both methods. We aim for this paper to serve as a concise resource for scientists attempting to familiarize themselves with these chirality measures or attempting to implement chirality measures in their own work. [ABSTRACT FROM AUTHOR]

The article discusses the debate surrounding the mechanism of sum frequency generation (SFG) signals emitted by liquid benzene. The authors argue that the main signal comes from local modes generated by symmetry breaking, while another paper challenges this view and suggests that the dominant mechanism is the interfacial electric quadrupole. The authors refute this argument, stating that their previous paper considered both symmetry breaking and the electric quadrupole in their calculations, while the opposing paper did not properly examine the effect of symmetry breaking. The authors present evidence of symmetry breaking through computational evaluations and the reversal of symmetry breaking at the silica-benzene interface. They recommend that the opposing authors consider these evidences before drawing their conclusion. [Extracted from the article]

Stimulated Raman Adiabatic Passage (STIRAP) and its variants, such as M-type chainwise-STIRAP, allow for efficiently transferring the populations in a multilevel system and have widely been used to prepare molecules in their rovibrational ground state. However, their transfer efficiencies are generally imperfect. The main obstacle is the presence of losses and the requirement to make the dynamics adiabatic. To this end, in the present paper, a new theoretical method is proposed for the efficient and robust creation and detection of deeply bound molecules in three-level Λ-type and five-level M-type systems via "Invariant-based shortcut-to-adiabaticity." In the regime of large detunings, we first reduce the dynamics of three- and five-level molecular systems to those of effective two- and three-level counterparts. By doing so, the major molecular losses from the excited states can be well suppressed. Consequently, the effective two-level counterpart can be directly compatible with two different "Invariant-based Inverse Engineering" protocols; the results show that both protocols give a comparable performance and have a good experimental feasibility. For the effective three-level counterpart, by considering a relation among the four incident pulses, we show that this model can be further generalized to an effective Λ-type one with the simplest resonant coupling. This generalized model permits us to borrow the "Invariant-based Inverse Engineering" protocol from a standard three-level Λ-type system to a five-level M-type system. Numerical calculations show that the weakly bound molecules can be efficiently transferred to their deeply bound states without strong laser pulses, and the stability against parameter variations is well preserved. Finally, the detection of ultracold deeply bound molecules is discussed. [ABSTRACT FROM AUTHOR]

Nonequilibrium molecular dynamics simulations have been performed for a system of 512 four-site models representing n-butane molecules. The results are compared to simulations previously reported for 125 molecules to check a recently reported number dependence in such simulations. A small system size dependence was observed at low shear rates, but the rheological behavior is not affected. Considerably greater certainty is obtained using larger systems. [ABSTRACT FROM AUTHOR]

Ytterbium monohydroxide is a promising molecule in the search for new physics. It is well known that levels of opposite parity, separated by energy split, the so-called l-doublets, define the experimental electric field strength required for molecule polarization. In addition, in our previous paper [Phys. Rev. A 105, L050801 (2022)], we have shown that the value of l-doubling directly influences the sensitivity of linear triatomic molecules toward the P , T -odd effects. In our work [J. Chem. Phys. 155, 164301 (2021)], we have calculated the value of l-doubling for YbOH molecules with the approximation of fixed O–H bond length. Taking the importance of this property into account, in the present study, we consider the additional degree of freedom corresponding to ligand (OH) deformation. [ABSTRACT FROM AUTHOR]

This paper demonstrates the performance of our previously suggested property-energy consistent method on the example of the generation of effective basis sets, pecS-1 and pecS-2, suited for the calculation of hydrogen, carbon, nitrogen, and oxygen chemical shifts. The new basis sets were successfully approbated in the GIAO-DFT calculations of the chemical shifts of 35 molecules using six different functionals. The pecS-1 basis set demonstrated very good accuracy, which makes this small basis set an effective means for the large-scale computations. At the same time, the pecS-2 basis set also gave very accurate results, thus putting it on a par with the other commensurate basis sets suited for the chemical shifts calculations. [ABSTRACT FROM AUTHOR]

The theory of adiabatic electron transport in a correlated condensed-matter system is rooted in a seminal paper by Niu and Thouless [J. Phys. A: Math. Gen. 17, 2453 (1984)]; I adopt here an analogous logic in order to retrieve the known expression for the adiabatic electronic flux in a molecular system [L. A. Nafie, J. Chem. Phys. 79, 4950 (1983)]. Its derivation here is considerably simpler than those available in the current quantum-chemistry literature; it also explicitly identifies the adiabaticity parameter, in terms of which the adiabatic flux and the electron density are both exact to first order. It is shown that the continuity equation is conserved to the same order. For the sake of completeness, I also briefly outline the relevance of the macroscopic electronic flux to the physics of solids and liquids. [ABSTRACT FROM AUTHOR]

Theoretical analysis and computer simulations (Monte Carlo and numerical integration of differential equations) indicate that the statistical effect of a small number of reacting molecules is affected by transfer of reagent molecules between nanoreactors (droplets in this study). As a model reaction, a simple reversible association A + B ⇆ C was chosen, which was studied previously without reagent transfer processes. For sufficiently fast exchange of reactant molecules and a sufficiently high number of nanoreactors, the studied systems virtually do not differ from large volume systems if overall kinetics and thermodynamics of the chemical process are concerned. However, if either reagent molecule exchange is not fast or the number of exchanging nanoreactors is low, then the stochastic effect is clearly visible, influencing the kinetics of reaching reaction equilibrium. In systems with a low number of nanoreactors, the apparent (average) equilibrium constant is affected as well. The distribution of reactant molecules in the nanoreactors is governed by stochastic processes, dependent on stochastic rate constants of all processes, chemical as well as physical (transfer of molecules outside and into droplets). When accumulation of reactant molecules in the continuous phase cannot be neglected, then the partition coefficients of reactants between the continuous and dispersed phases have to be taken into account. Distributions of reactant molecules described in the paper for systems composed of few nanoreactors can be especially important for some biochemical processes in living cells or devised corresponding artificial reactors. If the reactant molecules predominate in a continuous phase, then the kinetics and overall conversion of reversible association may be significantly affected by the presence of the dispersed phase and its catalytic behavior can be observed. It has been shown that Monte Carlo simulations, applying a devised simple algorithm, give reliable results, allowing theoretical studies of nanoscale-droplet systems. [ABSTRACT FROM AUTHOR]

In liquid water, there is a natural tendency to form aggregates that consist of water molecules linked by hydrogen bonds. Such spontaneously formed aggregates are surrounded by a "sea" of disordered water molecules, with both forms remaining in equilibrium. The process of creating water aggregates also takes place in the solvation water of proteins, but in this case, the interactions of water molecules with the protein surface shift the equilibrium of the process. In this paper, we analyze the structural properties of the solvation water in antifreeze proteins (AFPs). The results of molecular dynamics analysis with the use of various parameters related to the structure of solvation water on the protein surface are presented. We found that in the vicinity of the active region responsible for the binding of AFPs to ice, the equilibrium is clearly shifted toward the formation of "ice-like aggregates," and the solvation water has a more ordered ice-like structure. We have demonstrated that a reduction in the tendency to create "ice-like aggregates" results in a significant reduction in the antifreeze activity of the protein. We conclude that shifting the equilibrium in favor of the formation of "ice-like aggregates" in the solvation water in the active region is a prerequisite for the biological functionality of AFPs, at least for AFPs having a well-defined ice binding area. In addition, our results fully confirm the validity of the "anchored clathrate water" concept, formulated by Garnham et al. [Proc. Natl. Acad. Sci. U. S. A. 108, 7363 (2011)]. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study of the theory of entangled two-photon emission/absorption (E2P-EA) between a many-level cascade donor and a many-level acceptor (which could be quantum dots or molecules) using second-order perturbation theory and where the donor–acceptor pair is in a homogeneous but dispersive medium. To understand the mechanism of E2P-EA, we analyze how dipole orientation, radiative lifetime, energy detuning between intermediate states, separation distance, and entanglement time impact the E2P-EA rate. Our study shows that there are quantum interference effects in the E2P-EA rate expression that lead to oscillations in the rate as a function of entanglement time. Furthermore, we find that the E2P-EA rate for a representative system consisting of two quantum dots can be comparable to one-photon emission/absorption (OP-EA) when donor and acceptor are within a few nm. However, the E2P-EA rate falls off much more quickly with separation distance than does OP-EA. [ABSTRACT FROM AUTHOR]

The Dirac–Coulomb equation with positive-energy projection is solved using explicitly correlated Gaussian functions. The algorithm and computational procedure aims for a parts-per-billion convergence of the energy to provide a starting point for further comparison and further developments in relation with high-resolution atomic and molecular spectroscopy. Besides a detailed discussion of the implementation of the fundamental spinor structure, permutation, and point-group symmetries, various options for the positive-energy projection procedure are presented. The no-pair Dirac–Coulomb energy converged to a parts-per-billion precision is compared with perturbative results for atomic and molecular systems with small nuclear charge numbers. Paper II [D. Ferenc, P. Jeszenszki, and E. Mátyus, J. Chem. Phys. 156, 084110 (2022).] describes the implementation of the Breit interaction in this framework. [ABSTRACT FROM AUTHOR]

Heavy-atom alkaline earth monofluoride molecules are considered as prospective systems to study spatial parity or spatial parity and time-reversal symmetry violating effects such as the nuclear anapole moment or the electron electric dipole moment. A comprehensive and highly accurate theoretical study of the electronic structure properties and transition energies in such systems can simplify the preparation and interpretation of the experiments. However, almost no attempts to calculate quantum electrodynamics (QED) effects' contribution into characteristics of these neutral heavy-atom molecules have been performed. Recently, we have formulated and implemented such an approach to calculate QED contributions to transition energies of molecules [L. V. Skripnikov, J. Chem. Phys. 154, 201101 (2021)]. In this paper, we perform a benchmark theoretical study of the transition energies in the Ba+ cation and BaF molecule. The deviation of the calculated values from the experimental ones is of the order 10 cm−1 and is more than an order of magnitude better than the "chemical accuracy," 350 cm−1. The achievement of such an agreement has been provided, in particular, by the inclusion of the QED effects. The latter appeared to be not less important than the high-order correlation effects beyond the coupled cluster with single, double, and perturbative triple cluster amplitude level. We compare the role of QED effects for transition energies with heavier molecules—RaF and E120F, where E120 is the superheavy Z = 120 homolog of Ra. [ABSTRACT FROM AUTHOR]

The variational approach detailed in the previous paper (Paper I) for the treatment of the Renner–Teller effect in linear tetra-atomic molecules including all degrees of freedom and couplings between angular momenta is applied for HCCH+. The accurate six-dimensional potential energy surfaces of the X 2Πu electronic state, presented in Paper I is incorporated in the variational treatment in order to obtain all rovibronic levels including the spin-orbit coupling for 1/2≤J≤7/2 and up to 2600 cm-1 above the global zero point energy. The “pure” stretching levels are calculated up to 11 000 cm-1 from the stretching zero point energy. The calculated rovibronic energies are compared with previous theoretical and experimental data. The mean agreement with the zero kinetic energy photoelectron measurements of Tang et al. [J. Chem. Phys. 125, 133201 (2006)] is of 16.7 cm-1. The Renner–Teller parameters have been determined at νtrans=690.0 cm-1, εtrans=0.30, νcis=715.0 cm-1, and εcis=-0.063. A detailed analysis of the rovibronic Hund’s cases is presented and the rotational structures of some vibronic bands recorded by Yang and Mo [J. Phys. Chem. A 110, 11001 (2006)] are given. [ABSTRACT FROM AUTHOR]

This paper presents new results for the modeling of isolated line shapes from the Doppler to the collisional regime, thus including the effects of confinement (Dicke narrowing) and of the speed dependence of collisional parameters. They are obtained within a classical description of the time evolution of the autocorrelation function of the optical transition moment, combined with the use of the Keilson and Storer model for the changes in the radiator translational velocity. A purely numerical solution to the subsequent differential equations, which uses discretized grids for the radiating-molecule velocity vector, is first described. An alternative approach, using projections onto generalized Laguerre polynomials (for the velocity modulus) and spherical harmonics (for the velocity orientation), is also presented. A first test of these approaches is made in the particular case of the Q(1) Raman line of the fundamental band of pure H2 at room temperature (others will be presented in paper II). It is shown that the two models lead to exactly the same results, as expected, and to satisfactory agreement with measured values of the linewidth at various densities. [ABSTRACT FROM AUTHOR]

Previous work testing density functionals for use in calculating high-spin–low-spin energy differences, ΔEHL, for iron(II) spin-crossover transitions has tended to conclude that only properly reparametrized hybrid functionals can predict ΔEHL since it seems to depend critically on a correct description of the electron pairing energy governed by the exchange term. Exceptions to this rule are the previous three papers (I, II, and III in the present series of papers) where it was found that modern generalized gradient approximations (GGAs) and meta-GGAs could do as well as hybrid functionals, if not better, for this type of problem. In the present paper, we extend these previous studies to five more molecules which are too large to treat with high-quality ab initio calculations, namely, the series [Fe(L)(‘NHS4’)], where NHS4=2.2′-bis(2-mercaptophenylthio)diethylamine dianion, and L=NH3, N2H4, PMe3, CO, and NO+. Since we know of no reliable experimental estimate of ΔEHL, we content ourselves with a comparison against the experimentally determined ground-state spin symmetry including, in so far as possible, finite-temperature effects. Together with the results of Papers I, II, and III, this paper provides a test of a large number of functionals against the high-spin/low-spin properties of a diverse set of Fe(II) compounds, making it possible to draw some particulary interesting conclusions. Trends among different classes of functionals are discussed and it is pointed out that there is at least one functional, namely, the OLYP generalized gradient approximation, which is able to give a reasonably good description of the delicate spin energetics of Fe(II) coordination compounds without resorting to hybrid functionals which require the relatively more expensive calculation of a Hartree–Fock-type exchange term. [ABSTRACT FROM AUTHOR]

Dichroism experiments with 150 fs time resolution on anthracene in benzyl alcohol are presented as a function of viscosity from 14.4 cP (274 K) to 2.7 cP (329 K). These measurements test a qualitative prediction of the viscoelastic picture of liquid dynamics, specifically that earlier “inertial” dynamics have a viscosity independent rate, whereas later “diffusive” dynamics have a rate directly proportional to viscosity. This paper focuses on two components of the dichroism decay that are assigned to rotational motion. A third component is assigned to electronic-state solvation and is analyzed in a companion paper [J. Chem. Phys. 115, 4231 (2001)]. The longest component is due to rotational diffusion and is very well described by a hydrodynamic model with slip boundary conditions. A fast decay component in the subpicosecond region is found and shown to have a viscosity-independent rate. It is assigned to inertial rotation by comparison to the computer simulations of Jas et al. [J. Chem. Phys. 107, 8800 (1997)]. Inertial rotation extends out to at least 1 ps, longer than the range commonly assumed for inertial dynamics. Over much of this range, the inertial rotation is not free-rotor-like, but is strongly modified by interaction with the solvent. The inertial rotation also accounts for the “missing” anisotropy found when the rotational diffusion fits are extrapolated to zero time. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Quantum annealers are an alternative approach to quantum computing, which make use of the adiabatic theorem to efficiently find the ground state of a physically realizable Hamiltonian. Such devices are currently commercially available and have been successfully applied to several combinatorial and discrete optimization problems. However, the application of quantum annealers to problems in chemistry remains a relatively sparse area of research due to the difficulty in mapping molecular systems to the Ising model Hamiltonian. In this paper, we review two different methods for finding the ground state of molecular Hamiltonians using Ising model-based quantum annealers. In addition, we compare the relative effectiveness of each method by calculating the binding energies, bond lengths, and bond angles of the H 3 + and H2O molecules and mapping their potential energy curves. We also assess the resource requirements of each method by determining the number of qubits and computation time required to simulate each molecule using various parameter values. While each of these methods is capable of accurately predicting the ground state properties of small molecules, we find that they are still outperformed by modern classical algorithms and that the scaling of the resource requirements remains a challenge. [ABSTRACT FROM AUTHOR]

The phase diagram (pressure versus temperature) of the pure fluid is typically envisioned as being featureless apart from the presence of the liquid-vapor coexistence curve terminating at the critical point. However, a number of recent authors have proposed that this simple picture misses important features, such as the Widom line, the Fisher-Widom line, and the Frenkel line. In our paper, we discuss another way of augmenting the pure fluid phase diagram, lines of zero thermodynamic curvature R = 0 separating regimes of fluid solid-like behavior (R > 0) from gas-like or liquid-like behavior (R < 0). We systematically evaluate R for the 121 pure fluids in the NIST/REFPROP (version 9.1) fluid database near the saturated vapor line from the triple point to the critical point. Our specific goal was to identify regions of positive R abutting the saturated vapor line ("feature D"). We found the following: (i) 97/121 of the NIST/REFPROP fluids have feature D. (ii) The presence and character of feature D correlates with molecular complexity, taken to be the number of atoms Q per molecule. (iii) The solid-like properties of feature D might be attributable to a mesoscopic model based on correlations among coordinated spinning molecules, a model that might be testable with computer simulations. (iv) There are a number of correlations between thermodynamic quantities, including the acentric factor →, but we found little explicit correlation between → and the shape of a molecule. (v) Feature D seriously constrains the size of the asymptotic fluid critical point regime, possibly resolving a long-standing mystery about why these are so small. (vi) Feature D correlates roughly with regimes of anomalous sound propagation. [ABSTRACT FROM AUTHOR]

This paper introduces a theory to interpret future experiments to simultaneously observe angular distribution of spin-resolved Auger and photoelectrons from a molecule belonging to one of the 32 point groups. The Auger electrons are emitted in the decay of the vacancy created by photoionization. We show that the desired correlation can be completely characterized by 12 parameters which are coefficients of trigonometric functions of the spherical angles of spin quantization directions of two outgoing electrons. The expressions for the parameters themselves, although reduced to the simplest possible forms by using the symmetry properties of the molecular point group to maximum advantage, depend upon bipolar harmonics involving the propagation directions of the Auger and photoelectrons. The angular and spin correlation function thus obtained is completely general and can be readily specialized to any experimental geometry used to observe the ejected electrons. In particular, it is found that for a linear experimental arrangement with spins oriented longitudinally to the respective propagation vectors of the two electrons moving out in opposite directions, the parameters become geometry independent with their number reducing to three, which are now coefficients of the first three Legendre polynomials. Correlation between the spin-quantization directions of Auger and photoelectrons is, on the other hand, described by six parameters which do not depend upon the experimental arrangement. Directional correlation between the two outgoing electrons has also been studied without observing their spins. These angular and/or spin correlation functions are shown to take particularly simpler forms for Auger and photoelectrons emitted from linear molecules. We have applied the procedures developed in this paper to study directional correlation between photoelectrons from 2a1 orbital in a Td molecule and the Auger electrons emitted in the decay of the consequent vacancy. [ABSTRACT FROM AUTHOR]

In an earlier paper [A. D. Becke, J. Chem. Phys. 96, 2155 (1992)], Kohn–Sham density-functional calculations of the total atomization energies of the 55 molecules of the Gaussian-1 database of Pople and co-workers [J. Chem. Phys. 90, 5622 (1989); 93, 2537 (1990)] were reported. We found that the local-spin-density exchange-correlation approximation with a ‘‘gradient correction’’ for exchange gave an average deviation from experiment of only 3.7 kcal/mol. In the present work we assess the role of gradient corrections for dynamical correlation, and we enlarge our earlier survey to include 42 atomic and molecular ionization potentials and 8 proton affinities as well. We conclude that gradient corrections for correlation do not improve atomization energies, but are vitally important in electron nonconserving processes such as ionization. [ABSTRACT FROM AUTHOR]

Recent state-resolved experiments have shown that rotational energy transfer in collisions of vibrationally excited spherical top molecules is remarkably selective with respect to the fine structure components of the rovibrational states. In a recent paper [J. Chem. Phys. 93, 8731 (1990)], these results were rationalized on the basis of symmetry arguments and the Harter–Patterson theory of spectral clustering. The present paper provides numerical evidence for those assertions. Matrix elements of an atom–spherical top interaction potential are calculated using numerically accurate wave functions from spectroscopic Hamiltonians and using the approximate wave functions given by the Harter–Patterson theory. Agreement between the two calculations is satisfactory and both confirm the propensity rules derived previously, suggesting that the proposed mechanism does in fact operate in these systems. [ABSTRACT FROM AUTHOR]

In this paper we report theoretical studies of angle-resolved photoelectron spectroscopy (ARPES) and of circular dichroism in photoelectron angular distribution (CDAD) for ionization in molecules oriented in a single |JKJMJ> rotational eigenstate. These processes have been investigated also as two of the possible alternatives to photodissociation to determine orientational distribution function of rotationally state selected, oriented molecules. Expressions are derived which can be used to calculate ARPES and CDAD for such molecular species from ab initio methods or to analyze these experimentally observed spectra for extracting information about the degree of orientation of the molecular framework. These formulas are put in their simplest possible forms using the transformation properties of the molecular point group to their full advantage. The ionization amplitude is thus shown to decompose into a sum of transitions each involving the final state wave function belonging to an irreducible representation of the point group of the target molecule. It is found that, similar to the case of photodissociation, one can determine the rotational quantum number J purely from experimental photoionization data.Expressions developed herein are used to study ARPES and CDAD for ionization in a1 orbital of those rotationally state selected and oriented spherical top molecules which transform according to the Td point symmetry group. In this case, the detection-integrated cross section, singly differential in molecular orientation, is found to be independent of the photoionization dynamics and directly gives the molecular orientational function. The other ARPES and CDAD formulas are shown to depend upon the dynamics through the integrated partial cross section σ, the angularly asymmetry parameter β, the phase shift of the continuum waves representing the photoelectron, and the phase of the dipole transition amplitudes. The formulation presented in this paper sets a... [ABSTRACT FROM AUTHOR]

In this paper, we report a series of transformations for the construction of a Hamiltonian model for nonrigid polyatomic molecules in the framework of the Hougen–Bunker–Johns formalism (HBJ). This model is expressed in normal mode coordinates for small vibrations and in a specific coordinate ρ to describe the large amplitude motion. For the first time, a general procedure linking the "true" curvilinear coordinates to ρ is proposed, allowing the expression of the potential energy part in the same coordinate representation as the kinetic energy operator, whatever the number of atoms. A Lie group-based method is also proposed for the derivation of the reference configuration in the internal axis system. This work opens new perspectives for future high-resolution spectroscopy studies of nonrigid, medium-sized molecules using HBJ-type Hamiltonians. Illustrative examples and computation of vibrational energy levels on semirigid and nonrigid molecules are given to validate this method. [ABSTRACT FROM AUTHOR]

We investigate different approaches to derive the proper Floquet-based quantum–classical Liouville equation (F-QCLE) for laser-driven electron-nuclear dynamics. The first approach projects the operator form of the standard QCLE onto the diabatic Floquet basis and then transforms to the adiabatic representation. The second approach directly projects the QCLE onto the Floquet adiabatic basis. Both approaches yield a form that is similar to the usual QCLE with two modifications: (1) The electronic degrees of freedom are expanded to infinite dimension and (2) the nuclear motion follows Floquet quasi-energy surfaces. However, the second approach includes an additional cross derivative force due to the dual dependence on time and nuclear motion of the Floquet adiabatic states. Our analysis and numerical tests indicate that this cross derivative force is a fictitious artifact, suggesting that one cannot safely exchange the order of Floquet state projection with adiabatic transformation. Our results are in accord with similar findings by Izmaylov et al., [J. Chem. Phys. 140, 084104 (2014)] who found that transforming to the adiabatic representation must always be the last operation applied, although now we have extended this result to a time-dependent Hamiltonian. This paper and the proper derivation of the F-QCLE should lay the basis for further improvements of Floquet surface hopping. [ABSTRACT FROM AUTHOR]

We investigate the secondary (β-) relaxations of an asymmetric binary glass former consisting of a spirobichroman derivative (SBC; Tg = 356 K) as the high-Tg component and the low-Tg component tripropyl phosphate (TPP; Tg = 134 K). The main relaxations are studied in Paper I [B. Potzschner et al., J. Chem. Phys. 146, 164503 (2017)]. A high Tg contrast of ΔTg = 222 K is put into effect in a non-polymeric system. Component-selective studies are carried out by combining results from dielectric spectroscopy (DS) for mass concentrations cTPP ≤ 60% and those from different methods of 2H and 31P NMR spectroscopy. In the case of NMR, the full concentration range (10% ≤ cTPP ≤ 100%) is covered. The neat components exhibit β-relaxation (β 1 (SBC) and β 2 (TPP)). The latter is rediscovered by DS in the mixtures for all concentrations with unchanged time constants. NMR spectroscopy identifies the β-relaxations as being alike to those in neat glasses. A spatially highly restricted motion with angular displacement below ±10° encompassing all molecules is involved. In the lowtemperature range, where TPP shows the typical 31PNMRecho spectra of the α2-process, very similar spectral features are observed for the (deuterated) SBC component by 2H NMR, in addition to its "own" β 1-process observed at high temperatures. Apparently, the small TPP molecules enslave the large SBC molecules to perform a common hindered reorientation. The temperature dependence of the spin-lattice relaxation time of both components is the same and reveals an angular displacement of the SBC molecules somewhat smaller than that of TPP, though the time constants τβ2 are the same. Furthermore, T1 (T) of TPP in the temperature region of the β 2-process is absolutely the same as in the mixture TPP/polystyrene investigated previously. It appears that the manifestations of the β-process introduced by one component are essentially independent of the second component. Finally, at cTPP ≤ 20% one finds indications that the β 2-process starts to disintegrate. More and more TPP molecules get immobilized upon decreasing cTPP. We conclude that the β-process is a cooperative process. [ABSTRACT FROM AUTHOR]

In this paper, we present new ideas for computing rovibrational energy levels of molecules composed of two components and apply them to H2O-Cl-. When both components are themselves molecules, Euler angles that specify their orientation with respect to an axis system attached to the inter-monomer vector are used as vibrational coordinates. For H2O-Cl-, there is only one set of Euler angles. Using Euler angles as intermolecular vibrational coordinates is advantageous because in many cases coupling between them and coordinates that describe the shape of the monomers is unimportant. The monomers are not assumed to be rigid. In the most efficient calculation, vibrational wavefunctions of the monomers are used as contracted basis functions. Energy levels are calculated using the Lanczos algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we present a new approach to study the probability distribution of the radius of gyration of freely jointed chains. In this approach, we study the joint distribution PN(Rg2,Rvector G), where Rg is the radius of gyration and Rvector G is the vector from the first bead to the center of the chain. We derive an iteration relation between the probability distributions of chains with lengths N and N+1. When the chain length is large, the iteration relation can be approximated by an evolution equation with integral determining condition. The equation is solved to obtain the probability distribution function, which yields the known result obtained by Fixman [J. Chem. Phys. 36, 306 (1962)] using the integral method. We hope the iteration method in this paper could be used to study the probability distribution of the structure factor of polymer molecules. [ABSTRACT FROM AUTHOR]

The (VA+, Ve, e⁁) vector correlation method, combining imaging and time-of-flight resolved electron-ion coincidence techniques, is used to probe dissociative photoionization (DPI) of CO induced by vacuum ultra violet linearly or circularly polarized synchrotron radiation in the 26–33 eV photon excitation energy range. It provides original information about both the photoionization dynamics of the CO molecule and the dissociation dynamics of the CO+ molecular ions. The explored region corresponds to valence and inner-valence CO+ ionic states, which involve doubly or multiply excited electronic configurations. In this paper I we identify up to 17 DPI reaction pathways by the position of the intermediate CO+ molecular states in the Franck–Condon region and the (C++O) or (O++C) dissociation limits to which they correlate. For these processes we report the laboratory frame βC+/O+ and βe asymmetry parameters as well as the relative branching ratios in selected binding energy bands. The I(χ,θe,φe) molecular frame photoelectron angular distributions for selected PI processes will be reported in a companion paper II and compared with multichannel Schwinger configuration interaction ab initio calculations of these observables. [ABSTRACT FROM AUTHOR]

Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived. [ABSTRACT FROM AUTHOR]

In this paper, we examine decay and fragmentation of core-excited and core-ionized water molecules combining quantum chemical calculations and electron-energy-resolved electron–ion coincidence spectroscopy. The experimental technique allows us to connect electronic decay from core-excited states, electronic transitions between ionic states, and dissociation of the molecular ion. To this end, we calculate the minimum energy dissociation path of the core-excited molecule and the potential energy surfaces of the molecular ion. Our measurements highlight the role of ultra-fast nuclear motion in the 1 a 1 − 1 4 a 1 core-excited molecule in the production of fragment ions. OH+ fragments dominate for spectator Auger decay. Complete atomization after sequential fragmentation is also evident through detection of slow H+ fragments. Additional measurements of the non-resonant Auger decay of the core-ionized molecule (1 a 1 − 1 ) to the lower-energy dication states show that the formation of the OH+ + H+ ion pair dominates, whereas sequential fragmentation OH+ + H+ → O + H+ + H+ is observed for transitions to higher dication states, supporting previous theoretical investigations. [ABSTRACT FROM AUTHOR]

As of yet, unexamined aluminum bearing molecules may help elucidate aluminum chemistry and associated refractory atom reactions in the interstellar medium. The flexibility of modern quantum chemistry in the construction and analysis of novel molecules makes it perfectly suited to analyze molecules of astrochemical significance. In this paper, high level ab initio electronic structure calculations using the coupled cluster CCSD(T) and explicitly correlated coupled cluster CCSD(T)-F12 methods with large basis sets extrapolated to the complete basis set limit have been performed on the various [Al,N,C,O] isomers. The anharmonic rotational and vibrational spectroscopic parameters for all isomers are produced with these same levels of theory via quartic force fields and vibrational perturbation theory in order to aid in their potential laboratory or even astrophysical identification. The most stable isomer is determined here to be the aluminum isocyanate radical with linear equilibrium geometry AlNCO (X1Σ+). The NCO antisymmetric stretch of AlNCO has an intensity of 1500 km/mol, which should greatly aid in its infrared detection in the region around 2305 cm−1. Additionally, the AlOCN isomer is relatively low lying, possesses a 5.12 D dipole moment, and has a notable kinetic stability, making it a viable candidate for astronomical observation. All isomers are characterized by small frequencies, which indicates that these are floppy molecules. Isomers with a terminal aluminum atom are especially floppy, with bending modes less than 100 cm−1. [ABSTRACT FROM AUTHOR]

The paper presents the results of large-scale molecular dynamics simulations of the irreversible bimolecular reaction A+B→C+B for the simple liquid composed of mechanically identical soft spheres. The systems with the total number of molecules corresponding to 107–109 are considered. The influence of the concentration of a quencher (B) on the surviving probability of A and the reaction rate is analyzed for a wide range of the concentrations and for two significantly different reduced densities. It is shown that the quencher concentration dependence effect (QCDE) is, in fact, a composition of two QCDE effects: the short-time QCDE that increases the reaction rate and the long-time QCDE that decreases it. The paper also analyzes the influence of the concentration on the steady-state rate constant, kSS, obtained by integrating the surviving probability. The excess in kSS due to finite quencher concentration changes the sign from negative to positive while going from low to high concentrations. Generally, the excess is extremely weak. It attains a 1% level only if the concentration is very high. [ABSTRACT FROM AUTHOR]

Obtaining ultracold samples of dipolar molecules is a current challenge which requires an accurate knowledge of their electronic properties to guide the ongoing experiments. In this paper, we systematically investigate the ground state and the lowest triplet state of mixed alkali dimers (involving Li, Na, K, Rb, Cs) using a standard quantum chemistry approach based on pseudopotentials for atomic core representation, Gaussian basis sets, and effective terms for core polarization effects. We emphasize on the convergence of the results for permanent dipole moments regarding the size of the Gaussian basis set, and we discuss their predicted accuracy by comparing to other theoretical calculations or available experimental values. We also revisit the difficulty to compare computed potential curves among published papers, due to the differences in the modelization of core-core interaction. [ABSTRACT FROM AUTHOR]

As discussed in the companion paper [J. B. Witkoskie and J. S. Cao, J. Chem. Phys. 121, 6361 (2004), preceding paper], quantitative extraction of information from single molecule experiments by several proposed indicators is difficult since the experiments only observe certain characteristics of the system, even though the indicators can contain all available information. This paper shows how one can circumvent the shortcomings of these indicators by combining information extracted from indicators with a numerical Bayesian statistical approach. The Bayesian approach determines the relative probability of various models reproducing the entire sequence of the single molecules trajectory, instead of' binning and averaging over the data, which removes much of this information. [ABSTRACT FROM AUTHOR]

This paper presents a density functional study of multisite amphiphile molecules with the number of sites in the amphiphile ranging from 2 to 12. The molecular sites of the amphiphiles are fixed with either a freely jointed or rigid rod geometry. The difference between these two geometries is explored in detail. The paper studies the lamellar phase of these amphiphiles, as well as structures (such as monolayers and bilayers) against spherical hard bodies. The hard body surface can be tuned from solvophilic to neutral to solvophobic, and the phase behavior associated with these different arrangements is explored. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We report on a new implementation and first numerical tests of the fourth-order algebraicdiagramatic construction [ADC(4)] propagator method for K-shell ionization in molecules. The theory, which has been presented in a preceding paper (paper I) [J. Chem. Phys. 115, 10621 (2001)], is based on an intermediate state representation (ISR) or non-Dyson reformulation of the general ADC approach and uses the core-valence separation approximation to specialize the method to the case of core-level ionization. The ISR form offers the possibility to go beyond the finite perturbation-theoretical expressions of the previous (strict) ADC(4) scheme, and several such modifications are considered. The general aim of the present development is to establish a practical "frozen" orbital method that can be applied equally well to systems with and without equivalent core levels. A set of small model calculations has been carried out on the 1s ionization in CO and N[sub 2] allowing us to compare the ADC results with those of large-scale configuration interaction treatments and analyze the performance of several ADC(4) modifications in describing the 1s ionization energies as a function of the bond lengths. These studies clearly demonstrate the need for improving the previous (strict) ADC(4) scheme. In the theoretical description of the C1s and N1s ionization, the proposed modifications lead to a substantial improvement, whereas in the case of the O1s ionization further developments appear to be necessary. In another set of calculations using reasonably large basis sets, the improved ADC(4) method is applied to the vibrational structure in the CO C1s and N[sub 2] N1s ionization spectra. The results are in very good agreement with the findings of recent high-resolution measurements. An interesting feature is the different behavior of the g and u components of the N1s ionization energy curves of N[sub 2] leading to different vibrational line intensity distributions. [ABSTRACT FROM AUTHOR]

We theoretically investigate a possibility that the symmetry of the repetitively branched structure of light-harvesting dendrimers creates the energy gradient descending toward inner generations (layers of pigment molecules) of the dendrimers. In the first half of this paper, we define a model system using the Frenkel exciton Hamiltonian that focuses only on the topology of dendrimers and numerically show that excitation energy tends to gather at inner generations of the model system at a thermal equilibrium state. This indicates that an energy gradient is formed in the model system. In the last half, we attribute this result to the symmetry of the model system and propose two symmetry-origin mechanisms creating the energy gradient. The present analysis and proposition are based on the theory of the linear chain (LC) decomposition [S. Koda, J. Chem. Phys. 142, 204112 (2015)], which equivalently transforms the model system into a set of one-dimensional systems on the basis of the symmetry of dendrimers. In the picture of the LC decomposition, we find that energy gradient is formed both in each linear chain and among linear chains, and these two mechanisms explain the numerical results well. [ABSTRACT FROM AUTHOR]

The observed increase in the steric effect of the reaction Ca(1D)+CH3F(JKM=111) →CaF(2Π)+CH3 with increasing energy has been tentatively ascribed to a reorientation of the initially oriented CH3F axis, due to anisotropic long-range forces [M. H. M. Janssen, D. H. Parker, and S. Stolte, J. Phys. Chem. 95, 8142 (1991)]. Here we present ab initio calculations and use these to construct a long-range potential. To this potential we fit an isotropic model potential and two anisotropic model potentials. On the long-range potential and on the model potentials we perform classical trajectory calculations, and we compare the two methods presented in the preceding paper [G. C. Groenenboom and A. J. H. M. Meijer, J. Chem. Phys. 101, 7592 (1994)] for the extraction of the steric effect. We conclude that already the attractive isotropic model presented in this paper can account for the observed energy dependence of the steric effect for this reaction via a ‘‘trapping’’ mechanism. We show that although reorientation is possible, it contributes little to the positive energy dependence of the steric effect. [ABSTRACT FROM AUTHOR]

This paper develops theoretical expressions to study angular distribution and spin polarization of those Auger electrons which are emitted in the decay of a vacancy created by the absorption of a photon in a rotating linear molecule. Identical expressions except, of course, for different decay amplitudes, in both the Hund’s coupling schemes (a) and (b), are obtained for the differential Auger current emitted in the transition J→Jf measured by an electron spectrometer sensitive to spin detection. The structure of these angular distributions is exactly the same as that of the spin-resolved photoelectrons from unoriented atoms and molecules. The present paper thus puts the angle- and spin-resolved Auger and photoelectron spectroscopies on the same footing wherein identical geometrical and kinematical analysis is applicable. The four parameters needed to completely characterize such distributions depend, in the present case, on rotational orientation and/or alignment of the photoexcited molecule, in addition to its Auger decay amplitudes. The use of parity-adapted molecular states separates the Auger spectra into even and odd partial wave components of the ejected electron continuum in both of the coupling schemes. Our analysis shows that the integrated Auger current is spin resolved provided it is produced in the decay of oriented vacancies. We further find that Auger electrons which leave the molecular ion in Jf=0 state may have nonzero degree of spin polarization if they follow absorption of only circularly polarized light. In this case, both the angular distribution and spin polarization of emitted electrons become totally independent of Auger dynamics. Thus, angle- and spin-resolved Auger electron spectroscopy can be used to produce polarized electrons, to determine rotational orientation and alignment of linear molecules, to study their structure and dynamics, and to prepare ions of such molecules in selective ro-vibronic states. [ABSTRACT FROM AUTHOR]

If a set of solvent molecules are sufficiently weakly interacting, then their net effect on a solute is simply the sum of their individual effects. The shift and broadening of any solute quantum state would then be determined solely by the statistics of this sum (the local field at the solute). However, when the solvent–solvent interaction is comparable to that felt by the solute, the problem of ascertaining solvent effects on solute states becomes one of understanding how a band of collective solvent states couples to a solute. In this paper we show that a nonlinear liquid theory for band structure can be used to understand phenomena such as inhomogeneous broadening from precisely this solvent–band perspective. Inhomogeneous broadening in this language arises from configuration-to-configuration fluctuations in the solvent’s Green’s function, the size of which one can now evaluate. [ABSTRACT FROM AUTHOR]

The semiclassical determination of the specific density of quantum states, ρ(E;J), at energy E with fixed total angular momentum J is discussed for small molecules. Monte Carlo integration allows the accurate numerical determination of the phase space volume of systems with J>0 and arbitrary anharmonicity. The corresponding semiclassical number of states can be corrected for the effects of zero point motion in analogy to the well-known Whitten–Rabinovitch procedure. In this paper, the procedures are tested by comparison with rigid rotor harmonic oscillator models, while a comparison with recent exact quantum calculations on H+3 and HD+2 is described in the following paper. We conclude that, if the intramolecular potential is known or assumed, this numerical semiclassical procedure is a viable and simple way to get state densities of a much improved accuracy. [ABSTRACT FROM AUTHOR]

In Part I of this paper, we started from a dipole array model of elastic light scattering, and found the longwave asymptotic formulas for all 16 elements of the orientation averaged Mueller scattering matrix. However, the Perrin symmetry of the scattering matrix was not obvious from the formulas obtained in Part I. In this paper, Part II, we carry the analysis further, finding the molecular parameter identities which result in the Perrin symmetries. The formulas we present provide a very practical method for model calculations in the longwave limit. After evaluation of ten sums over pairs of the dipolar subunits of the model, the orientation averaged Mueller scattering matrix, as a function of scattering angle, is given by simple trigonometric polynomials. For models containing several hundred subunits the computation is easily carried through by a desktop computer. We verify the asymptotic formulas by numerical comparison with our analytic orientation averaging program PMAT2. We use a helical model with spherical subunits, in which the first Born approximation gives excellent results for the dipole elements (symmetry DSE). In this same model the first, second, and third Born approximations are utterly worthless for calculating the helicity-retardation elements M13 and M23 and their transposes, but fourth Born gives nearly the exact result. These observables therefore use four bounces to feel out the helicity of the array, and may be more sensitive to structural variations than the traditional circular difference observable M14, which responds after only two bounces. [ABSTRACT FROM AUTHOR]

The MP2-R12 method (Mo\ller–Plesset second-order perturbation theory with terms linear in the interelectronic coordinate r12) in the approximations A and B as outlined in paper I of this series is applied to the ground states of the molecules H2, LiH, HF, H2O, NH3, CH4, Be2, N2, F2, C2H2, and CuH in their experimental equilibrium geometry, and to the van der Waals interaction between two He atoms. In all cases MP2 correlation energies are obtained that are supposed to differ by at most a few percent from the basis set limit. For CH4 the dependence of the energy on the symmetric stretching coordinate is studied, which together with other information leads to a recommended bond length of 1.086 Å for the CH bond length. For He2 and F2 the canonical and localized descriptions are compared. The latter is superior for the K-shell contributions, otherwise there is a little difference. For He2 in the localized representation rather good results for the dispersion interaction are obtained. The potential curve of Be2 is significantly improved in MP2-R12 as compared to conventional MP2. The examples C2H2 and CuH show that the method is not limited to very small systems. [ABSTRACT FROM AUTHOR]

We have recorded the high resolution (150 MHz) excitation spectra of NO2 molecules cooled in a supersonic jet in two energy ranges: 16 000–19 362 cm-1 [‘‘yellow’’ range, see R. Georges, A. Delon, and R. Jost, J. Chem. Phys. 103, 1732 (1995), hereafter referred to as paper I] and 23 326–23 945 cm-1 (‘‘blue’’ range). In this paper we are interested mainly in the rovibronic properties of about 1500 rotational levels (N=1, K=0, J=1/2, and J=3/2) observed in these two ranges. Among these levels about 480 are observed via the so-called extra lines, i.e., the lines which are observable because of rovibronic couplings between bright levels (N=1, K=0, 2B2 vibronic character) and nearby dark levels. These rovibronic couplings result mainly from second order spin–orbit and orbit–rotation interactions which have been evidenced previously by Zeeman effect and anticrossing experiments [A. Delon, P. Dupré, and R. Jost, J. Chem. Phys. 99, 9482 (1993)]. By comparing the average matrix element of rovibronic interactions occuring for N=1, K=0 (J=1/2 and J=3/2), and for N=3, K=0 (J=5/2 and J=7/2) we can exclude a significant contribution from Coriolis interactions.A model of small random matrices constructed by using the properties of the above mentioned rovibronic Hamiltonian (density of states, selection rules, and matrix elements) allowed us to reproduce the observed statistical properties of the rovibronic states: average number of extra lines per vibronic band, distribution of intensities, Fourier transform analysis, next-neighbor spacing distribution, hierarchical tree analysis, and intensity and energy correlations between J=1/2 and J=3/2 lines. All these properties confirm that the second-order spin–orbit interaction is responsible for most of the observed extra lines for low rotational levels N=1 and N=3, K=0. As a result, the average reduced rovibronic matrix element is 0... [ABSTRACT FROM AUTHOR]

A detailed theoretical framework is developed for studying sequential emission of a photoelectron and an Auger electron from a rotating linear molecule with information on momenta and spin-polarization of the departing particles. Identical expressions, except, of course, for different dynamical amplitudes, in both the Hund’s coupling schemes (a) and (b) are obtained for the three different correlation functions considered in this paper. The use of the parity adapted wave functions for the molecular states involved results in, among other things, the presence of only a finite number of harmonics for each of the directions included in the correlation function. Several specific photon-propagation, electron-detection configurations are suggested for which the general correlation functions derived herein become particularly simple. The correlation between the Auger and the photoelectrons is shown to become, under specific conditions, completely isotropic for all bound molecular orbitals, whatever may be their symmetries, from which pair of electrons comes out. This analysis is independent of any dynamical calculations which can be performed in a hierarchy of approximations beginning from semiempirical phenomenological models to sophisticated ab initio methods. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In a recent communication [N. Makri, J. Chem. Phys. 148, 101101 (2018)], it was shown that the locality of interactions in many systems of interest allows a decomposition of the path integral and its evaluation via sequential linking of the paths of relatively small "modules" (e.g., chemical groups or monomers). The present paper describes the modular path integral methodology for simulating dynamical properties by propagating the density matrix in real time. The procedure is first presented for the simple topology of a single-file arrangement of units interacting via nearest neighbor couplings and subsequently extended to the calculation of two-particle correlations in arrays that may also contain some long-range interactions, to the treatment of systems with side chains or cyclic structures, to the simulation of internal dynamics in long organic molecules, and to the modifications required for coupling of one or several units of a system to dissipative environments. Illustrative applications to the dynamics of interacting two-level-systems are presented. [ABSTRACT FROM AUTHOR]

Chemistry is governed by the principle of quantum mechanics as expressed by the Schrödinger equation (SE) and Dirac equation (DE). The exact general theory for solving these fundamental equations is therefore a key for formulating accurately predictive theory in chemical science. The free-complement (FC) theory for solving the SE of atoms and molecules proposed by one of the authors is such a general theory. On the other hand, the working theory most widely used in chemistry is the chemical formula that refers to the molecular structural formula and chemical reaction formula, collectively. There, the central concepts are the local atomic concept, transferability, and from-atoms- to-molecule concept. Since the chemical formula is the most successful working theory in chemistry ever existed, we formulate our FC theory to have the structure reflecting the chemical formula. Our basic postulate is that as far as the SE is the principle of chemistry, its solutions for chemistry should have the structure that can be related to the chemical formulas. So, in this paper, we first formulate a theory that designs the wave function to reflect the structure of the chemical formula. We call this theory chemical formula theory (CFT). In the CFT, we place the valence ground and excited states of each atom at each position of the chemical formula of the molecule and let them interact using their free valences to form the ground and excited states of the molecule. The principle there is the variational principle so that the ground and excited states obtained satisfy the orthogonality and Hamiltonian-orthogonality relations. Then, we formulate the exact FC theory starting from the initial functions produced by the CFT. This FC theory is referred to as free-complement chemical- formula theory (FC-CFT), which is expected to describe efficiently the solution of the SE by the above reason. The FC-CFT wave function is modified from that of CFT. Since this modification is done by the exact SE, its analysis may give some insights to chemists that assist their chemistry. Thus, this theory would be not only exact but also conceptually useful. Furthermore, the intermediate theory between CFT and FC-CFT would also be useful. There, we use only integratable functions and apply the variational principle so that we refer to this theory as FC-CFT-variational (FC-CFT-V). It is an advanced theory of CFT. Since the variational method is straightforward and powerful, we can do extensive chemical studies in a reasonable accuracy. After finishing such studies, if we still need an exact level of solutions, we add the remaining functions of the FC-CFT and perform the exact calculations. Furthermore, when we deal with large and even giant molecules, the inter-exchange (iExg) theory for the antisymmetry rule introduced previously leads to a large simplification. There, the inter-exchanges between distant electron pairs fade away so that only Coulombic interactions survive. Further in giant systems, even an electrostatic description becomes possible. Then, the FC-CFT for exactly solving the SE would behave essentially to order N for large and giant molecular systems, though the pre-factor should be very large and must be minimized. [ABSTRACT FROM AUTHOR]

Fluctuating hydrodynamics (FHD) provides a framework for modeling microscopic fluctuations in a manner consistent with statistical mechanics and nonequilibrium thermodynamics. This paper presents an FHD formulation for isothermal reactive incompressible liquid mixtures with stochastic chemistry. Fluctuating multispecies mass diffusion is formulated using a Maxwell–Stefan description without assuming a dilute solution, and momentum dynamics is described by a stochastic Navier–Stokes equation for the fluid velocity. We consider a thermodynamically consistent generalization for the law of mass action for non-dilute mixtures and use it in the chemical master equation (CME) to model reactions as a Poisson process. The FHD approach provides remarkable computational efficiency over traditional reaction-diffusion master equation methods when the number of reactive molecules is large, while also retaining accuracy even when there are as few as ten reactive molecules per hydrodynamic cell. We present a numerical algorithm to solve the coupled FHD and CME equations and validate it on both equilibrium and nonequilibrium problems. We simulate a diffusively driven gravitational instability in the presence of an acid-base neutralization reaction, starting from a perfectly flat interface. We demonstrate that the coupling between velocity and concentration fluctuations dominates the initial growth of the instability. [ABSTRACT FROM AUTHOR]

The mass-action law, which predicts the rates of chemical reactions, is widely used for modeling the kinetics of the chemical reactions and their stationary states, also for complex chemical reaction networks. However, violations of the mass-action equations have been reported in various cases: in confined systems with a small number of molecules, in non-ideally-stirred systems, when the reactions are limited by the diffusion, at high concentrations of reactants, or in chemical reaction networks with marginally stable mass-action equations. In this paper, I describe a new mechanism, leading to the violation of the mass-action equations, that takes place at a low concentration of at least one of the reactants; in this limit, the reaction rates can be easily inferred from the chemical reaction network. I propose that this mechanism underlies the replication stability of the hypercycles, a class of chemical reaction networks hypothetically connected with abiogenesis. I provide two simple examples of chemical reaction networks in which the mechanism leading to the violation of the mass-action law is present. I study the two chemical reaction networks by means of a simulation performed with a cellular automaton model. The results have a general validity and represent a limitation of the validity of the mass-action law, which has been overlooked up to now in the studies about the chemical reaction networks. [ABSTRACT FROM AUTHOR]

The hard/soft-acid/base (HSAB) principle indicates that hard acids prefer binding to hard bases (often forming bonds with substantial ionic character) while soft acids prefer binding to soft bases (often forming bonds with substantial covalent character). Though the HSAB principle is a foundational concept of the modern theory of acids and bases, the theoretical underpinnings of the HSAB principle remain murky. This paper examines the exchange reaction, wherein two molecules, one the product of reacting a hard acid and a soft base and the other the product of reacting a soft acid with a hard base, exchange substituents to form the preferred hard–hard and soft–soft product. A simple derivation shows that this reaction is exothermic, proving the validity of the HSAB principle. The analysis leads to the simple and conceptually appealing conclusion that the HSAB principle is a driven by simple electron transfer effects. [ABSTRACT FROM AUTHOR]

External non-uniform magnetic fields acting on molecules induce non-collinear spin densities and spin-symmetry breaking. This necessitates a general two-component Pauli spinor representation. In this paper, we report the implementation of a general Hartree-Fock method, without any spin constraints, for non-perturbative calculations with finite non-uniform fields. London atomic orbitals are used to ensure faster basis convergence as well as invariance under constant gauge shifts of the magnetic vector potential. The implementation has been applied to investigate the joint orbital and spin response to a field gradient—quantified through the anapole moments—of a set of small molecules. The relative contributions of orbital and spin-Zeeman interaction terms have been studied both theoretically and computationally. Spin effects are stronger and show a general paramagnetic behavior for closed shell molecules while orbital effects can have either direction. Basis set convergence and size effects of anapole susceptibility tensors have been reported. The relation of the mixed anapole susceptibility tensor to chirality is also demonstrated. [ABSTRACT FROM AUTHOR]

We present an inverse-design method, the poor man's materials optimization, that is designed to identify materials within a very large class with optimized values for a pre-chosen property. The method combines an efficient genetic-algorithm-based optimization, an automatic approach for generating modified molecules, a simple approach for calculating the property of interest, and a mathematical formulation of the quantity whose value shall be optimized. In order to illustrate the performance of our approach, we study the properties of organic molecules related to those used in dye-sensitized solar cells, whereby we, for the sake of proof of principle, consider benzene as a simple test system. Using a genetic algorithm, the substituents attached to the organic backbone are varied and the best performing molecules are identified. We consider several properties to describe the performance of organic molecules, including the HOMO-LUMO gap, the sunlight absorption, the spatial distance of the orbitals, and the reorganisation energy. The results show that our method is able to identify a large number of good candidate structures within a short time. In some cases, chemical/physical intuition can be used to rationalize the substitution pattern of the best structures, although this is not always possible. The present investigations provide a solid foundation for dealing with more complex and technically relevant systems such as porphyrins. Furthermore, our "properties first, materials second" approach is not limited to solar-energy harvesting but can be applied to many other fields, as briefly is discussed in the paper. [ABSTRACT FROM AUTHOR]

In continuation of our recent paper on vibrational quadratic response functions for vibrational configuration interaction wave functions, we present in this paper a derivation and implementation of the pure vibrational cubic response function for vibrational configuration interaction wave functions. In addition, we present combined electronic and vibrational cubic response functions derived from sum-over-states expressions in the Born-Oppenheimer framework and a discussion of complicating issues. The implementation enables analytic calculation of the pure vibrational cubic response function via response theory, which constitutes a part of the vibronic cubic response function. [ABSTRACT FROM AUTHOR]

In view of the initial success of the complete active space (CAS) based size-extensive state-specific multireference perturbation theory (SS-MRPT) [J. Phys. Chem. A 103, 1822 (1999)] for relatively diverse yet simple chemically interesting systems, in this paper, we present the computation of the potential energy curves (PEC) of systems with arbitrary complexity and generality such as HF, H2O, H2S, C2, and N2 molecules. The ground states of such systems (and also low-lying singlet excited states of C2) possess multireference character making the description of the state difficult with single-reference (SR) methods. In this paper, we have considered the Mo\ller–Plesset (MP) partitioning scheme [SS-MRPT(MP)] method. The accuracy of energies generated via SS-MRPT(MP) method is tested through comparison with other available results. Comparison with FCI has also been provided wherever available. The accuracy of this method is also demonstrated through the calculations of NPE (nonparallelism error) and the computation of the spectroscopic constants of all the above mentioned systems. The quality of the computed spectroscopic constants is established through comparison with the corresponding experimental and FCI results. Our numerical investigations demonstrate that the SS-MRPT(MP) approach provides a balanced treatment of dynamical and non-dynamical correlations across the entire PECs of the systems considered. [ABSTRACT FROM AUTHOR]

In this paper we test a nondirect product discrete variable representation (DVR) method for solving the bend vibration problem and compare it with well-established direct product DVR and finite basis representation approaches. [ABSTRACT FROM AUTHOR]

This article is a continuation of our previous paper on schemes of energy decompositions of molecular systems in the real space [D. R. Alcoba et al., J. Chem. Phys. 122, 074102 (2005)] now using correlated state functions. We study, according to physical arguments, the appropriate management of the density cumulant arising from the second-order reduced density matrix at correlated level, whose contributions can be assigned to one-center or to two-center terms in the energy partitioning. Our treatments are applied within two physical space partitioning schemes: the Bader partitioning into atomic basins and the fuzzy atom procedure. The results obtained in selected molecules are analyzed and discussed in detail. [ABSTRACT FROM AUTHOR]

In this paper the authors show how the multiconfiguration time-dependent Hartree-Fock (MCTDHF) method can be used for the calculation of electronic properties of molecules associated with the population of excited states. In contrast to other methods for correlated electron dynamics, such as configuration interaction, MCTDHF does not rely on a solution of the electronic Schrödinger equation prior to the propagation. The authors apply this approach to the calculation of vertical excitation energies, transition dipole moments, and oscillator strengths for two test molecules, lithium hydride and methane. [ABSTRACT FROM AUTHOR]

We consider a monodispersed Rayleigh droplet beam of water droplets doped with proteins. An intense infrared laser is used to align these droplets. The arrangement has been proposed for electron- and x-ray-diffraction studies of proteins which are difficult to crystallize. This paper considers the effect of thermal fluctuations on the angular spread of alignment in thermal equilibrium, and relaxation phenomena, particularly the damping of oscillations excited as the molecules enter the field. The possibility of adiabatic alignment is also considered. We find that damping times in a high-pressure gas cell as used in x-ray-diffraction experiments are short compared with the time taken for molecules to traverse the beam and that a suitably shaped field might be used for electron-diffraction experiments in vacuum to provide adiabatic alignment, thus obviating the need for a damping gas cell. [ABSTRACT FROM AUTHOR]

Modern spectroscopical techniques allow the efficient experimental investigation of highly excited vibrational states in molecular systems. On the theoretical side, powerful computational methods have also been developed for the calculation of the corresponding energy levels and wave functions, and their interpretation. In this paper we use a combination of two such methods, namely, the distribution of zeroes in the Husimi function and energy-level correlation diagrams, to discuss a classification scheme, for the lowest hundred vibrational levels of the LiNC/LiCN floppy molecular system, based on their dynamical characteristics. [ABSTRACT FROM AUTHOR]

The interaction of formic acid (HCOOH) with solid water, deposited on tungsten at 80 K, was investigated. We have prepared and annealed formic acid (FA)/water interfaces (FA layers on thin films of solid water and H2O adlayers on thin FA films). Metastable impact electron spectroscopy and ultraviolet photoemission spectroscopy (He I and II) were utilized to study the electron emission from the 10a′ to 6a′ molecular orbitals (MOs) of FA, and the 1b1, 3a1, and 1b2 MOs of H2O. These spectra were compared with results of density-functional theory calculations on FA-H2O complexes reported in Ref. 14 [A. Allouche, J. Chem. Phys. 122, 234703(2005), (preceding paper)]. Temperature programmed desorption was applied for information on the desorption kinetics. Initially, FA is adsorbed on top of the water film. The FA spectra are distorted with respect to those from FA monomers; it is concluded that a strong interaction exists between the adsorbates. Even though partial solvation of FA species takes place during annealing, FA remains in the top layer up to the desorption of the water film. When H2O molecules are offered to FA films at 80 K, no water network is formed during the initial stage of water exposure; H2O molecules interact individually via H bonds with the formic acid network. Experiment and theory agree that no water-induced deprotonation of the formic acid molecules takes place. [ABSTRACT FROM AUTHOR]

The Hamilton dynamics of a molecule in a translationally and/or rotationally symmetric field is kept rigorously constrained in its phase space. The relevant dynamical laws should therefore be extracted from these constrained motions. An internal space that is induced by a projection of such a limited phase space onto configuration space is an intrinsically curved space even for a system of zero total angular momentum. In this paper we discuss the general effects of this curvedness on dynamics and structures of molecules in such a manner that is invariant with respect to the selection of coordinates. It is shown that the regular coordinate originally defined by Riemann is particularly useful to expose the curvature correction to the dynamics and statisitcal properties of molecules. These effects are significant both qualitatively and quantitatively and are studied in two aspects. One is the direct effect on dynamics: A trajectory receives a Lorentz-like force from the curved space as though it was placed in a magnetic field. The well-known problem of the trapping phenomenon at the transition state is analyzed from this point of view. By showing that the trapping force is explicitly described in terms of the curvature of the internal space, we clarify that the physical origin of the trapped motion is indeed originated from the curvature of the internal space and hence is not dependent of the selection of coordinate system. The other aspect is the effect of phase space volume arising from the curvedness: We formulate a general expression of the curvature correction of the classical density of states and extract its physical significance in the molecular geometry along with reaction rate in terms of the scalar curvature and volume loss (gain) due to the curvature. The transition state theory is reformulated from this point of view and it is applied to the structural transition of linear chain molecules in the so-called dihedral angle model. It is shown that the curvature effect becomes large roughly linearly with the size of molecule. [ABSTRACT FROM AUTHOR]

The extrapolation method for determining benchmark quality full configuration-interaction energies described in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] is applied to the molecules H2O and N2. As in the neon atom case, discussed in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] remarkably accurate scaling relations are found to exist between the correlation energy contributions from various excitation levels of the configuration-interaction approach, considered as functions of the size of the correlating orbital space. The method for extrapolating a sequence of smaller configuration-interaction calculations to the full configuration-interaction energy and for constructing compact accurate configuration-interaction wave functions is also found to be effective for these molecules. The results are compared with accurate ab initio methods, such as many-body perturbation theory, coupled-cluster theory, as well as with variational calculations wherever possible. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This paper reports a theory for the dielectric relaxation of dimeric mesogenic molecules in a nematic liquid crystal phase. Liquid crystal dimers consist of two mesogenic groups linked by a flexible chain. Recent experimental studies [D. A. Dunmur, G. R. Luckhurst, M. R. de la Fuente, S. Diez, and M. A. Perez Jubindo, J. Chem. Phys. 115, 8681 (2001)] of the dielectric properties of polar liquid crystal dimers have found unexpected results for both the static (low frequency) and variable frequency dielectric response of these materials. The theory developed in this paper provides a quantitative model with which to understand the observed experimental results. The mean-square dipole moments of α,ω-bis[(4-cyanobiphenyl-4′-yl]alkanes in a nematic phase have been calculated using both the rotational isomeric state model and a full torsional potential for the carbon-carbon bonds of the flexible chain. The orienting effect of the nematic phase is taken into account by a parametrized potential of mean torque acting on the mesogenic groups and the segments in the flexible chain. Results of calculations using the full torsional potential are in excellent agreement with experimental results for comparable systems. The probability density peq(βA,βB) for the orientation of the mesogenic groups (A,B) along the nematic director is also calculated. The resultant potential of mean torque is a surface characterized by four deep energy wells or sites equivalent to alignment of the terminal groups A and B approximately parallel and antiparallel to the director; of course, the reversal of the director leads to equivalent sites. This potential energy surface provides the basis for a kinetic model of dielectric relaxation in nematic dimers. Solution of the Fokker-Planck equation corresponding to this four-site model gives the time dependence of the site populations, and hence the time-correlation functions for the total dipole moment along the director. In this model the end-over-end rotation of the molecule, corresponding to simulataneous reversal of both mesogenic groups, is excluded because the activation energy is too large. Results are presented for a number of cases, in which a dipole is located on one or both of the mesogenic groups, and additionally where the groups differ in size. For the latter, under particular conditions, the correlation function exhibits a biexponential decay, which corresponds to two low frequency absorptions in the dielectric spectrum. This is exactly what has been observed for nonsymmetric nematic dimers having different groups terminating a flexible chain. Experimental results over a range of temperature for the nonsymmetric dimer α-[(4-cyanobiphenyl)-4′-yloxy]-ω-(4-decylanilinebenzylidene-4′-oxy)nonane can be fitted precisely to the theory, which provides new insight into the orientational and conformational dynamics of molecules in ordered liquid crystalline phases. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper, I consider theoretical models of the decay via photobleaching of a sample of surface-immobilized fluorescent molecules excited by a spatially varying laser intensity profile. I show that, with mild restrictions on the photobleaching mechanism, the fluorescence decay measured in a nonuniform excitation profile is always nonexponential. Under the same conditions, the fluorescence decay can always be approximated by a discrete sum of exponentials. A particular example is given in which a homogeneous population of fluorophores with a single (intensity-dependent) photobleaching lifetime, when illuminated by a Gaussian laser, exhibits power law fluorescence decay at long times. These results indicate that the observation of multiple exponentials in single molecule or ensemble photobleaching lifetime measurements can arise solely as an artifact of a spatially varying laser profile and is not necessarily indicative of heterogeneity in molecular internal states, conformation, or local environment. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This paper aims at presenting a general and compact matrix expression of the exact kinetic energy operator in polyspherical coordinates adapted to the study of semirigid molecules. The internal coordinates of an N atom system are expressed by a set of N-1 relative position vectors. The operator can be applied to whatever the set of vectors (Jacobi, Radau, valence, satellite, etc., or a combination of these vectors), and whatever the number of atoms. It includes the rotation and the Coriolis coupling. Such a formulation gives the opportunity to develop a general code for calculating the ro-vibrational spectra in a curvilinear description including all the vibrational, rotational, and Coriolis couplings. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The cage effect is generally invoked when discussing the delay in the decay of time correlation functions of dense fluids. In an attempt to examine the role of caging more closely, we consider the spread of the displacement distributions of Brownian particles. These distributions are necessarily biased by the presence of neighbouring particles. Accommodation of this bias by those neighbours conserves the displacement distribution locally and presents a collective mechanism for exploring configuration space that is more efficient than the intrinsic Brownian motion. Caging of some particles incurs, through the impost of global conservation of the displacement distribution, a delayed, non-local collective process. This non-locality compromises the efficiency with which configuration space is explored. Both collective mechanisms incur delay or stretching of time correlation functions, in particular the particle number and flux densities. This paper identifies and distinguishes these mechanisms in existing data from experiments and computer simulations on systems of particles with hard sphere interactions. [ABSTRACT FROM AUTHOR]

The reaction-diffusion master equation is a stochastic model often utilized in the study of biochemical reaction networks in living cells. It is applied when the spatial distribution of molecules is important to the dynamics of the system. A viable approach to resolve the complex geometry of cells accurately is to discretize space with an unstructured mesh. Diffusion is modeled as discrete jumps between nodes on the mesh, and the diffusion jump rates can be obtained through a discretization of the diffusion equation on the mesh. Reactions can occur when molecules occupy the same voxel. In this paper, we develop a method for computing accurate reaction rates between molecules occupying the same voxel in an unstructured mesh. For large voxels, these rates are known to be well approximated by the reaction rates derived by Collins and Kimball, but as the mesh is refined, no analytical expression for the rates exists. We reduce the problem of computing accurate reaction rates to a pure preprocessing step, depending only on the mesh and not on the model parameters, and we devise an efficient numerical scheme to estimate them to high accuracy. We show in several numerical examples that as we refine the mesh, the results obtained with the reaction-diffusion master equation approach those of a more fine-grained Smoluchowski particle-tracking model. [ABSTRACT FROM AUTHOR]

In a recent paper, Theophilou [J. Chem. Phys 149, 074104 (2018)] proved that in molecules and solids, a set of spherically symmetric densities determines uniquely the external potential. Here an alternative derivation of Theophilou's new theorem is presented. A somewhat more general version is also proved via constrained search. Euler equations and Kohn-Sham equations are derived for spherically symmetric densities. [ABSTRACT FROM AUTHOR]

The paper presents a simple model to mimic orientational disorder in molecular solids. The model is based on the concept of split molecule, an object which is a superposition of two molecules in orientations which are supposed to mimic orientational distribution. The split molecule is characterized by a disorder angle, an extra parameter which labels disorder states and allows one to calculate free energy of the crystal. The model is simple for applications illustrated by numerical calculations for charge-transfer crystals A-TCNB and N-TCNB, the family of solids where the onset of orientational disorder is responsible for structural phase transitions. [ABSTRACT FROM AUTHOR]

We report a series of full close-coupling calculations of integral cross sections for fine structure resolved, rotationally inelastic transitions of CH induced by collisions with He. These calculations use the necessary two CH(X 2Π)+He potential energy surfaces as determined by a variety of ab initio techniques described in the preceeding paper. The calculated N=1→N=2-7 cross sections confirm a previous prediction of preferential population of final state levels in which the electronic wave function of the CH molecule is antisymmetric with respect to reflection in the plane of rotation of the molecule. A generally good overall agreement is found between the energy-dependent cross sections determined in earlier experiments of Macdonald and Liu and appropriate averages of the calculated cross sections. However, small, systematic, qualitative discrepancies persist between theory and experiment. Diagnostic calculations were carried out to identify the cause of these discrepancies. These calculations explored the influence of restrictions in basis set, configuration interaction, and functional forms used in fitting the potential energy surfaces. They also explored the consequences of the dynamical approximations of CH as a rigid rotor and the independence of the CH spin–orbit constant on the approach of the He partner. All these diagnostic calculations generally confirm the anticipated marginal influence of these approximations. [ABSTRACT FROM AUTHOR]

It is only relatively recently that it has become possible to use spectroscopy to track the solvation of a molecule as one proceeds from small solute-plus-solvent clusters, through bulk liquids, and into cryogenic matrices. One of the more surprising findings of such studies is that, in a number of noteworthy instances—such as with benzene dissolved in Ar—the solvent shifts of spectral lines in even apparently sizable clusters seem not to go smoothly into the bulk results. In this and the following paper we consider just what level of theoretical treatment is necessary in order to be able to account for the solvent shift of electronic spectra consistently in environments ranging from clusters to the bulk. As we discuss in some detail, neither continuum dielectric approaches nor sums of pair potentials can adequately describe the solvation. What we propose here, instead, is that the effects of nonpolar solvents can be treated fully microscopically by a model incorporating both local repulsive effects and longer-ranged dielectric effects. The latter contribution, resulting from the solvent’s polarizability, is formulated in terms of the so-called polarization modes of the solvent, which change with the detailed arrangement of the solute’s environment. We illustrate the ideas by showing that one can understand the optical spectroscopy of benzene in liquid Ar more or less quantitatively by using this model, and we point out some connections with analogous time-dependent solvation studies. The application of this same approach to clusters is described in the succeeding paper. [ABSTRACT FROM AUTHOR]

New phase rules have been derived for the rotationally inelastic diffraction scattering of an atom with a homonuclear diatomic molecule. The phase rules are obtained by applying semiclassical complex angular momentum techniques to the infinite order sudden approximation. The new phase rules are of three types, which are denoted weak coupling, intermediate coupling, and strong coupling. Higher-order terms have been derived for each type of phase rule. A systematic computational study of the accuracy of the phase rules has been carried out for a deformed inverse power potential energy of the form ε[r(γ)/r]n, n≥3, where r(γ)=r0+r2P2(cos γ). Additional calculations are reported for the Ne–D2 and He–N2 collision systems, using more realistic interaction potential energies. [ABSTRACT FROM AUTHOR]

An optimized integration scheme for calculating vibrational–rotational partition functions by the Fourier path-integral method, as presented in the previous paper [R. Q. Topper and D. G. Truhlar, J. Chem. Phys. XX, ▪▪▪▪ (19▪▪)] is applied to a three-dimensional test case involving the coupled vibrational and rotational motions of a diatomic HCl molecule in Cartesian coordinates. Converged partition functions are calculated by the new Fourier path-integral Monte Carlo scheme and by standard variational methods, and the two sets of results are compared. We obtain good agreement (∼2%) between the two methods over a range of a factor of 20 in temperature. [ABSTRACT FROM AUTHOR]

Recent research has demonstrated that optimal electromagnetic fields capable of producing selective vibrational excitation in molecules can be designed employing linear quadratic control methods using a cost functional that balances the energy distribution in the molecule, the fluence of the optical field, and a final cost to insure the desired excitation. Practical computations of molecular control theory for large molecules especially with anharmonic potentials become difficult to obtain due to the increased dimensionality and the accompanying uncertainty in the Hamiltonian. In this paper we reduce the complexity of the problem by treating a portion of the molecule including the target and optical dipoles in full detail, while the remainder of the molecule is modeled as an external disturbance of bounded energy. The optimal control field now minimizes the cost functional which is simultaneously maximized with respect to the energy constrained external disturbance to assure robustness. This optimal design process is commensurate with taking the most pessimistic view of the disturbance. This conservative view was born out in the numerical calculations such that practical laboratory studies should reach results much improved over the worst case design. As an illustration we investigate disturbances of varying energy content for a truncated 20 atom molecular chain where the uncontrolled remainder of the chain is the source of the system disturbance. The sensitivity of the system with respect to the disturbance was found to be strongly dependent on the distance of the disturbance to the target bond and the dipole arrangement. In addition, in the range of physically reasonable disturbance energy the optimal field could be accurately predicted from an asymptotic expansion involving only the reference undisturbed case. Although the present paper takes advantage of linear system techniques, the same robust optimal control procedure can be generalized to nonlinear... [ABSTRACT FROM AUTHOR]

The neutral C6H6–(CH3OH)n clusters, which have been spectroscopically characterized in Paper I, serve here as precursors for the study of intracluster ion chemistry initiated by resonant two-photon ionization. Resonant enhancement allows ion chemistry product yields to be determined as a function of cluster size by selective excitation of a single size cluster with the laser. Most of the work presented here uses one-color resonant ionization via the 610 transition of the C6H6 chromophore in the cluster. No ion chemistry is observed for the 1:n clusters with n≤2. At n=3, dissociative electron transfer (DET) to form C6H6+M+3 (M=CH3OH) is observed with a product yield of 6%. The remaining 94% of ionic products result from fragmentation of the 1:3 cluster by loss of a single CH3OH molecule. The unprotonated M+3 product ion is unusual in that electron bombardment or photoionization of pure methanol clusters yields exclusively protonated methanol cluster ions. The attachment of a C6H6 molecule to the methanol cluster provides an extremely gentle photoionization mechanism which produces M+3 with little enough internal energy to preclude its breakup to M2H++CH2OH (or CH3O ). The opening of this product channel at n=3 is consistent with estimates of the ionization potential of Mn clusters which predict an endothermic ET reaction at n=2 which becomes exothermic at n=3.Despite the increasingly exothermic DET and dissociative proton transfer product channels, larger clusters (n≥4) continue to predominantly undergo unreactive fragmentation. For the 1:4 and 1:5 clusters, in addition to DET products, dissociative proton transfer (DPT) products are also observed. The MnH+ product arises from proton transfer from C6H+6, while Mn-1H+ probably occurs by DPT within the M+n cluster following loss of C6H6 in DET. Scans of the 1:2–1:5 clusters through their 610110 transitions yield a broader set of products which reflect the 5 kcal/mol increase in the... [ABSTRACT FROM AUTHOR]

The third-order nonlinear optical response of one-dimensional molecular aggregates of arbitrary size is calculated using equations of motion for single-exciton and two-exciton variables. These equations map the system onto the dynamics of N(N+1)/2 coupled nonlinear oscillators, where N is the number of molecules in the aggregate. The scaling of the generalized third-order hyperpolarizability γ(3) with N is analyzed in detail. The complete wave vector and frequency dependence of γ(3) is maintained and cooperative radiative decay (superradiance) is incorporated. Comparison is made with the density-matrix approach which provides a fully time-ordered expression. [ABSTRACT FROM AUTHOR]

This work presents a systematic investigation of binary nucleation rates for sulfuric acid and water and the effect of temperature on these rates at isothermal, subsaturated conditions. The results from nucleation rate measurements for the sulfuric acid (H2SO4) –water system are discussed and compared to those previously presented for methanesulfonic acid (MSA)–water [B. E. Wyslouzil, J. H. Seinfeld, R. C. Flagan, and K. Okuyama, J. Chem. Phys. (submitted)]. Experiments were conducted at relative humidities (Rh) ranging from 0.006

The analytical infinite order sudden (IOS) quantum theory of triatomic photodissociation, developed in paper I, is applied to study the indirect photodissociation of NOCl through a real or virtual intermediate state. The theory uses the IOS approximation for the dynamics in the final dissociative channels and an Airy function approximation for the continuum functions. The transition is taken as polarized in the plane of the molecule; symmetric top wave functions are used for both the initial and intermediate bound states; and simple semiempirical model potentials are employed for each state. The theory provides analytical expressions for the photofragment yield spectrum for producing particular final fragment ro-vibrational states as a function of the photon excitation energy. Computations are made of the photofragment excitation spectrum of NOCl in the region of the T1(13A″) ←S0(11A′) transition for producing the NO fragment in the vibrational states nNO=0, 1, and 2. The computed spectra for the unexcited nNO==0 and excited nNO=2 states are in reasonable agreement with experiment. However, some discrepancies are observed for the singly excited nNO=1 vibrational state, indicating deficiencies in the semiempirical potential energy surface. Computations for two different orientations of the in-plane transition dipole moment produce very similar excitation spectra. Calculations of fragment rotational distributions are performed for high values of the total angular momentum J, a feature that would be very difficult to perform with close-coupled methods. Computations are also made of the thermally averaged rotational energy distributions to simulate the conditions in actual supersonic jet experiments. © 1997 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Both the vibrational energy relaxation and pure dephasing of a polar solute in polar liquids are theoretically studied and particularly the role of the long-range Coulomb interaction between the solute and the polarization modes of the polar liquid is focused on in this paper. If the linear coupling potential between the vibrational displacement and the solvent polarization mode is taken into account and assuming that the anharmonic contribution to the pure dephasing is the dominant mechanism, the vibrational relaxation rates are shown to be related to the dielectric friction. However the pure dephasing of a perfect harmonic oscillator is an effect arising from the nonlinear (with respect to the vibrational coordinate) vibrational coupling potential, and the relationship between the pure dephasing rate and the frequency-dependent friction is no longer valid. By expanding the bare electric field of the polar solute in terms of the multipoles, the vibrational coupling potential is obtained as a power series summation with respect to the vibrational displacement. Each expansion coefficient is found to be associated with the interaction of the projected multipole fields with the solvent polarization. A few simple cases are discussed in detail with an emphasis on the connection between the vibrational relaxation rates and solvation dynamics of static multipoles in polar liquids. [ABSTRACT FROM AUTHOR]

In this paper we extend our previous study (F. Schneider, F. Di Giacomo, and F. A. Gianturco, J. Chem. Phys. 104, 5153) on the topology of the electronic states of the neutral H2O molecule in C2v symmetry by examining the lowest ten potential energy surfaces of the water molecular cation in its doublet states. The relevant electronic energy surfaces of H2O+ are shown as 2D contour maps where possible reaction pathways for several low-lying potential energy surfaces of H2O+ are clearly seen and therefore can be discussed and analyzed in some detail. The present results were obtained using ab initio multireference configuration interaction calculations at 184 nuclear arrangements, as described in our previous paper dealing with the neutral H2O. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper, we present the implementation of the ‘‘conductorlike screening model’’ (COSMO) into the density functional program DMol. The electronic structure and geometry of the solute are described by a density functional method (DFT). The solute is placed into a cavity which has the shape of the solute molecule. Outside of the cavity, the solvent is represented by a homogeneous dielectric medium. The electrostatic interaction between solute and solvent is modeled through cavity surface charges induced by the solvent. The COSMO theory, based on the screening in conductors, allows for the direct determination of the surface charges within the SCF procedure using only the electrostatic potentials. This represents the major computational advantage over many of other reaction field methods. Since the DMol/COSMO energy is fully variational, accurate gradients with respect to the solute coordinates can be calculated for the first time, without any restriction on the shape of the cavity. The solvation energies and optimized molecular structures are calculated for several polar solutes. In addition, the trends in basicity of amines and the relative stabilities of molecular conformers are studied. Our results suggest that for neutral solutes, agreement between calculated and experimental solvation energies of better than about 2 kcal/mol can be achieved. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Interaction site models are used quite extensively to describe molecular fluids. However, theories for these fluids are not as well developed or tested as compared to those for simple fluids. With this in mind, it appears useful to develop analytical expressions for the thermodynamic properties of fluids whose molecules are composed of hard-sphere interactions sites, since these systems can serve as a convenient reference state for perturbation theories for molecular fluids. In an effort to achieve this goal and advance our understanding of molecular fluids, in this paper, we present an analysis of the Chandler–Silbey–Ladanyi (CSL) equations, a diagrammatically proper set of integral equations for interaction site fluids, with the specific aim of solving them analytically. First, we rewrite the CSL equations to explicitly account for the presence of equivalent sites. We find that the mathematical structure of the resulting CSL equations remains the same as that of the original CSL equations, subject to slight modifications in some of the matrices which appear in these equations. Subsequently, we apply the Wiener–Hopf factorization technique to the CSL equations with the Percus–Yevick (PY) closure for a general fluid composed of hard-sphere interaction sites. We then analytically solve these equations for symmetric n-atomic tangent hard-sphere molecules (n≤4: spheres, diatomics, triangles, and tetrahedrals), which results in analytical expressions for the equation of state and other thermodynamic properties of the fluid. Finally, we compare the predictions of the analytical equation of state with those of other theories as well as with those of Monte Carlo simulations of these systems. The CSL equations with the PY closure are found to provide fair predictions for the equation of state of the fluids under investigation. More specifically, the CSL–PY equations tend to perform better for smaller molecules and at lower... [ABSTRACT FROM AUTHOR]

In a previous paper, we described a fast and reliable numerical method for obtaining the optical absorption spectrum of a fluid of nonpolar linearly polarizable molecules. The fluid is modeled by a generalization of the microscopic classical Yvon–Kirkwood equations, which yields the same dynamic response as the much-studied quantum Drude oscillator model. Numerical results were presented based on a linear closure relation to the central Ornstein–Zernike analog equation. In the present paper, we consider a nonlinear closure which includes but goes beyond the previously studied linear closure. We display the absorption spectrum, as implied by the renormalized polarizability and the dynamic dielectric constant, for both hard sphere and Lennard-Jones fluids. Comparison with available simulation results shows that the nonlinear closure performs well over a wide density range, and in particular corrects the poor low-density behavior of the linear theory. © 1994 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present the DEC-RIMP2-F12 method where we have augmented the Divide Expand-Consolidate resolution-of-the-identity second-order Møller-Plesset perturbation theory method (DEC-RIMP2) [P. Baudin et al., J. Chem. Phys. 144, 054102 (2016)] with an explicitly correlated (F12) correction. The new method is linear-scaling, massively parallel, and it corrects for the basis set incompleteness error in an efficient manner. In addition, we observe that the F12 contribution decreases the domain error of the DEC-RIMP2 correlation energy by roughly an order of magnitude. An important feature of the DEC scheme is the inherent error control defined by a single parameter, and this feature is also retained for the DEC-RIMP2-F12 method. In this paper we present the working equations for the DEC-RIMP2-F12 method and proof of concept numerical results for a set of test molecules. [ABSTRACT FROM AUTHOR]

Our paper [J. Chem. Phys. 97, 4616 (1992) (SJ92)] and Gwaltney and Bartlett’s comments to it [J. Chem. Phys. 99, ▪▪▪ (1993) (GB93)] show that discrepancies in the literature between ab initio and experimental intensities are mainly due to inaccuracies in the computed dipole moment. SJ92 and GB93 find that the most accurate transformation between intensity and dipole moment is the one outlined by SJ92, however GB93’s intensities are more accurate than those presented in Table II in SJ92. This high accuracy is not common in the literature, particularly not for overtones and combination bands. [ABSTRACT FROM AUTHOR]

In this paper, the linear response (LR) theory for the variant of internally contracted multireference coupled cluster (ic-MRCC) theory described by Hanauer and Köhn [J. Chem. Phys. 134, 204211 (2011)] has been formulated and implemented for the computation of the excitation energies relative to a ground state of pronounced multireference character. We find that straightforward application of the linear-response formalism to the time-averaged ic-MRCC Lagrangian leads to unphysical second-order poles. However, the coupling matrix elements that cause this behavior are shown to be negligible whenever the internally contracted approximation as such is justified. Hence, for the numerical implementation of the method, we adopt a Tamm-Dancoff-type approximation and neglect these couplings. This approximation is also consistent with an equation-of-motion based derivation, which neglects these couplings right from the start. We have implemented the linear-response approach in the ic-MRCC singles-and-doubles framework and applied our method to calculate excitation energies for a number of molecules ranging from CH2 to p-benzyne and conjugated polyenes (up to octatetraene). The computed excitation energies are found to be very accurate, even for the notoriously difficult case of doubly excited states. The ic-MRCC-LR theory is also applicable to systems with open-shell ground-state wavefunctions and is by construction not biased towards a particular reference determinant. We have also compared the linear-response approach to the computation of energy differences by direct state-specific ic-MRCC calculations. We finally compare to Mk-MRCC-LR theory for which spurious roots have been reported [T.-C. Jagau and J. Gauss, J. Chem. Phys. 137, 044116 (2012)], being due to the use of sufficiency conditions to solve the Mk- MRCC equations. No such problem is present in ic-MRCC-LR theory. [ABSTRACT FROM AUTHOR]

With shear interest in nanoporous materials, the ultraconfining interlayer spacing of calcium- silicate-hydrate (C-S-H) provides an excellent medium to study reactivity, structure, and dynamic properties of water. In this paper, we present how substrate composition affects chemo-physical properties of water in ultraconfined hydrophilic media. This is achieved by performing molecular dynamics simulation on a set of 150 realistic models with different compositions of calcium and silicon contents. It is demonstrated that the substrate chemistry directly affects the structural properties of water molecules. The motion of confined water shows a multi-stage dynamics which is characteristic of supercooled liquids and glassy phases. Inhomogeneity in that dynamics is used to differentiate between mobile and immobile water molecules. Furthermore, it is shown that the mobility of water molecules is composition-dependent. Similar to the pressure-driven self-diffusivity anomaly observed in bulk water, we report the first study on composition-driven diffusion anomaly, the self diffusivity increases with increasing confined water density in C-S-H. Such anomalous behavior is explained by the decrease in the typical activation energy required for a water molecule to escape its dynamical cage. [ABSTRACT FROM AUTHOR]

The paper deals with a reaction-diffusion problem that arises in developmental biology when describing the formation of the concentration profiles of signaling molecules, called morphogens, which control gene expression and, hence, cell differentiation. The mean local accumulation time, which is the mean time required to reach the steady state at a fixed point of a patterned tissue, is an important characteristic of the formation process. We show that this time is a sum of two times, the conditional mean first-passage time from the source to the observation point and the mean local accumulation time in the situation when the source is localized at the observation point. [ABSTRACT FROM AUTHOR]

We show how the path-integral formulation of quantum statistical mechanics can be used to construct practical ab initio techniques for computing the chemical potential of molecules adsorbed on surfaces, with full inclusion of quantum nuclear effects. The techniques we describe are based on the computation of the potential of mean force on a chosen molecule and generalize the techniques developed recently for classical nuclei. We present practical calculations based on density functional theory with a generalized-gradient exchange-correlation functional for the case of H2O on the MgO (001) surface at low coverage. We note that the very high vibrational frequencies of the H2O molecule would normally require very large numbers of time slices (beads) in path-integral calculations, but we show that this requirement can be dramatically reduced by employing the idea of thermodynamic integration with respect to the number of beads. The validity and correctness of our path-integral calculations on the H2O/MgO(001) system are demonstrated by supporting calculations on a set of simple model systems for which quantum contributions to the free energy are known exactly from analytic arguments. [ABSTRACT FROM AUTHOR]

A new electron-methanol molecule pseudopotential is developed and tested in the present paper. The formal development of the potential is based on quantum mechanical calculations on the electron-methanol molecule model in the static exchange approximation. The computational model includes a steep confining potential that keeps the otherwise unbound excess electron in the vicinity of the methanol molecule. Using the Phillips–Kleinman theorem we introduce a smooth pseudowave function of the excess electron with the exact eigenenergy and correct asymptotic behavior. The nonlocal potential energy operator of the model Hamiltonian is then replaced to a local potential that reproduces the ground-state properties of the excess electron satisfactorily. The pseudopotential is then optimized in an analytically simple functional form to fit this approximate local potential in conjunction with the point charges and the geometry of a classical, all-site methanol-methanol interaction potential. Of the adjustable parameters, the parameters for the carbon and the methyl hydrogen atoms are optimized, while those for the oxygen and the hydroxyl hydrogen are taken from a previous electron-water molecule pseudopotential. A polarization term is added to the potential a posteriori. The polarization parameters are chosen to reproduce the experimental position of the optical absorption spectrum of an excess electron in mixed quantum-classical molecular dynamics simulations. The energetic, structural and spectroscopic properties of the solvated electron in a methanol bath are simulated at 300 K and compared with previous solvated electron simulations and available experimental data. [ABSTRACT FROM AUTHOR]

In this paper, a new solvation model is proposed for simulations of biomolecules in aqueous solutions that combines the strengths of explicit and implicit solvent representations. Solute molecules are placed in a spherical cavity filled with explicit water, thus providing microscopic detail where it is most needed. Solvent outside of the cavity is modeled as a dielectric continuum whose effect on the solute is treated through the reaction field corrections. With this explicit/implicit model, the electrostatic potential represents a solute molecule in an infinite bath of solvent, thus avoiding unphysical interactions between periodic images of the solute commonly used in the lattice-sum explicit solvent simulations. For improved computational efficiency, our model employs an accurate and efficient multiple-image charge method to compute reaction fields together with the fast multipole method for the direct Coulomb interactions. To minimize the surface effects, periodic boundary conditions are employed for nonelectrostatic interactions. The proposed model is applied to study liquid water. The effect of model parameters, which include the size of the cavity, the number of image charges used to compute reaction field, and the thickness of the buffer layer, is investigated in comparison with the particle-mesh Ewald simulations as a reference. An optimal set of parameters is obtained that allows for a faithful representation of many structural, dielectric, and dynamic properties of the simulated water, while maintaining manageable computational cost. With controlled and adjustable accuracy of the multiple-image charge representation of the reaction field, it is concluded that the employed model achieves convergence with only one image charge in the case of pure water. Future applications to pKa calculations, conformational sampling of solvated biomolecules and electrolyte solutions are briefly discussed. [ABSTRACT FROM AUTHOR]

Long-range-corrected hybrids, which incorporate all of the long-range exact exchange interaction, improve performance for a host of molecular properties. The long-range portion of exact exchange is both computationally and formally problematic in solids, and screened hybrids therefore eliminate it. While screened hybrids give similar results to their parent global hybrids for many molecular properties, one may worry that they perform poorly for those properties that are improved by the long-range-correction procedure. In this paper, we show that at least for the Heyd–Scuseria–Ernzerhof (HSE) screened hybrid, this is not the case; for many properties improved by long-range-correction, screened hybrids and global hybrids deliver essentially the same results. We suggest that this is because screened hybrids and global hybrids have fundamentally the same many-electron self-interaction error. We also introduce some small revisions to our computational implementation of the HSE screened hybrid, and we recommend these revisions for future applications of HSE. [ABSTRACT FROM AUTHOR]

Using the mean first passage time analysis, we have recently developed a kinetic model for the thermal unfolding of a native protein in a barrierless way. A protein was considered as a random heteropolymer consisting of hydrophobic and hydrophilic beads with all the bonds and bond angles equal and constant. As a crucial idea of the model the overall potential around a folded part (cluster) of the protein in which a protein residue performs a chaotic motion was considered to be a combination of three potentials: effective pairwise, average dihedral, and confining. However, the hydrogen bonding of water molecules was not taken into account explicitly. In this paper we improve that model by combining it with a probabilistic approach to water hydrogen bonding. Thus, an additional contribution due to the disruption of hydrogen bond networks around the interacting particles (a cluster of native residues and a residue in the protein unfolded part) appears in the overall potential field around a cluster. The overall potential as a function of the distance from the cluster center has a double well shape. This allows one to determine the rates with which the cluster emits and absorbs residues by using the mean first passage time analysis. Due to a sufficiently large temperature increase or decrease, the emission rate becomes larger than the absorption rate in the whole range of cluster sizes. This leads to the unfolding of the protein in a barrierless way reminiscent of spinodal decomposition. Knowing the cluster emission and absorption rates as functions of temperature and cluster size, one can find the threshold temperatures of cold and hot barrierless denaturation as well as the corresponding unfolding times. The extended model is then applied to the unfolding of bovine pancreatic ribonuclease, consisting of 124 residues whereof 43 are hydrophobic (neutral beads are considered to be hydrophobic as well) and 81 hydrophilic. [ABSTRACT FROM AUTHOR]

This is the second paper in a series of investigations on spin-orbit coupling (SOC) effects in dihydrides of third-row transition elements. The dissociation path of rhenium dihydride was explored using the multiconfiguration self-consistent-field method followed by diagonalization of SOC matrices, in which the Stevens–Basch–Krauss–Jasien–Cundari (SBKJC) basis sets were employed after adding one set of polarization functions for each atom. The most stable rhenium dihydride has a linear structure and its ground state is 6Σg+. Both C2v and Cs dissociation paths into a Re atom and a hydrogen molecule (Re(6S)+H2(1Σg+)) were explored on the potential energy curves of low-lying states. A relatively high energy barrier was obtained along the C2v path and two conical intersections were found at the H–Re–H angles of 29.8° and 96.1° along the C2v path. Since it was revealed that the geometrical deformation to Cs symmetry at the H–Re–H angle of 29.8° does not provide explicit lowering of the energy barrier for the dissociation, even after considering nonadiabatic couplings (NACs) in the neighborhood of the conical intersections, it can be concluded that the most feasible path is hopping from the lowest 6A1 state to the lowest 6B2 state at the H–Re–H angle of 96.1° followed by hopping from the lowest 6B2 state back to the lowest 6A1 state at the H–Re–H angle of 29.8°, where the latter crossing point is the highest in energy along this path. Thus, when the molecular system can reach the areas of these crossing points, the molecular system hops from one of the states to another owing to NAC or SOC effects; especially, SOC effects become important at the crossing point with C2v symmetry. [ABSTRACT FROM AUTHOR]

Anharmonicities of vibrational modes allow controlling state-to-state transitions and encoding quantum information bits into vibrational eigenstates. Resonances between different transitions hinder the control. In this paper all resonances that can occur in a two-qubit system are identified and studied. Computational experiments are carried out using optimal control theory and numerical propagation of vibrational wave packets. Useful insight is obtained into the mechanisms of negative effect of these resonances onto the control tasks. A set of general criteria is derived for evaluation of candidate molecules for practical realization of vibrational two-qubit system. Several simple strategies for avoiding such resonances by choosing suitable vibrational characteristics (mode frequencies and anharmonicities) are proposed. [ABSTRACT FROM AUTHOR]

Fock space multireference coupled-cluster (FSMRCC) method emerged as an efficient tool to describe the electronic structure of nearly degenerate cases. Development of linear response has been one of the challenging problems in FSMRCC due to the multiple-root nature of the effective Hamiltonian. A response from any of the roots would span the space for getting the properties. Hence, all roots perturbed by the external field would proliferate the excited states. We recently developed the FSMRCC method for the efficient evaluation of analytic response properties using a constrained variation approach. In this paper, we present analytic dipole moments and polarizabilities of H2O, O3, and CH+ molecules in low-lying excited states along with brief discussion of singlet triplet decoupling of (1,1) sector of FSMRCC resulting from spin adaptation. [ABSTRACT FROM AUTHOR]

A new milestoning procedure using Voronoi tessellations is proposed. In the new procedure, the edges of Voronoi cells are used as milestones, and the necessary kinetic information about the transitions between the milestones is calculated by running molecular dynamics (MD) simulations restricted to these cells. Like the traditional milestoning technique, the new procedure offers a reduced description of the original dynamics and permits to efficiently compute the various quantities necessary in this description. However, unlike traditional milestoning, the new procedure does not require to reinitialize trajectories from the milestones, and thereby it avoids the approximation made in traditional milestoning that the distribution for reinitialization is the equilibrium one. In this paper we concentrate on Markovian milestoning, which we show to be valid under suitable assumptions, and we explain how to estimate the rate matrix of transitions between the milestones from data collected from the MD trajectories in the Voronoi cells. The rate matrix can then be used to compute mean first passage times between milestones and reaction rates. The procedure is first illustrated on test-case examples in two dimensions and then applied to study the kinetics of protein insertion into a lipid bilayer by means of a coarse-grained model. [ABSTRACT FROM AUTHOR]

Recently single photon emission has been observed for systems in which multiple excitons are generated by pulsed excitation. When fast pair annihilation of excitons takes place, finally a single exciton remains and single photon can be emitted. Its efficiency depends on the competition among pair annihilation, unimolecular nonradiative, and radiative processes. The efficiency of single photon emission is usually studied by measuring the correlation of emitted photons after pulsed excitation by the Hanbury-Brown and Twiss method. The photon correlation measured in this method is different from that calculated by taking into account all pairs of emitted photons, which was presented in a previous paper. We calculate the former rigorously for the first time in the case of multiple excitations and compare it with the latter. We also calculate correlation of arrival times of two photons by the Hanbury-Brown and Twiss method. These results should be useful for the analysis of the antibunching measurement by the Hanbury-Brown and Twiss method. [ABSTRACT FROM AUTHOR]

The variational approach detailed in the previous paper (Paper I) for the treatment of the Renner–Teller effect in linear tetra-atomic molecules including all degrees of freedom and couplings between angular momenta is applied for HCCH+. The accurate six-dimensional potential energy surfaces of the X 2Πu electronic state, presented in Paper I is incorporated in the variational treatment in order to obtain all rovibronic levels including the spin-orbit coupling for 1/2≤J≤7/2 and up to 2600 cm-1 above the global zero point energy. The “pure” stretching levels are calculated up to 11 000 cm-1 from the stretching zero point energy. The calculated rovibronic energies are compared with previous theoretical and experimental data. The mean agreement with the zero kinetic energy photoelectron measurements of Tang et al. [J. Chem. Phys. 125, 133201 (2006)] is of 16.7 cm-1. The Renner–Teller parameters have been determined at νtrans=690.0 cm-1, εtrans=0.30, νcis=715.0 cm-1, and εcis=-0.063. A detailed analysis of the rovibronic Hund’s cases is presented and the rotational structures of some vibronic bands recorded by Yang and Mo [J. Phys. Chem. A 110, 11001 (2006)] are given. [ABSTRACT FROM AUTHOR]

For electronically degenerate states of linear tetra-atomic molecules, a new method is developed for the variational treatment of the Renner–Teller and spin-orbit couplings. The approach takes into account all rotational and vibrational degrees of freedom, the dominant couplings between the corresponding angular momenta as well as the couplings with the electronic and electron spin angular momenta. The complete rovibrational kinetic energy operator is expressed in Jacobi coordinates, where the rovibrational angular momenta J⁁N have been replaced by J⁁-L⁁ez-S⁁ and the spin-orbit coupling has been described by the perturbative term ASO×L⁁ez·S⁁z. Attention has been paid on the electronic wave functions, which require additional phase for linear tetra-atomic molecules. Our implemented rovibrational basis functions and the integration of the different parts of the total Hamiltonian operator are described. This new variational approach is tested on the electronic ground state X 2Πu of HCCH+ for which new six-dimensional potential energy surfaces have been computed using the internally contracted multireference configuration interaction method and the cc-pV5Z basis set. The calculated rovibronic energies and their comparisons with previous theoretical and experimental works are presented in the next paper. [ABSTRACT FROM AUTHOR]