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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]

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]

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 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 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]

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]

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]

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]

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]

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]