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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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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 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]

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]

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]

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]

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]

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 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]

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]

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]