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In the hidden variable theory, Bohm proved a connection between the Schrödinger and Hamilton–Jacobi equations and showed the existence of classical paths, for which the generalized Bohr quantization condition is valid. In this paper we prove similar properties, starting from the equivalence between the Schrödinger and wave equations in the case of the conservative bound systems. Our approach is based on the equations and postulates of quantum mechanics without using any additional postulate. Like in the hidden variable theory, the above properties are proven without using the approximation of geometrical optics or the semiclassical approximation. Since the classical paths have only a mathematical significance in our analysis, our approach is consistent with the postulates of quantum mechanics. [ABSTRACT FROM AUTHOR]

We present in this paper a comprehensive account of an explicitly spin-free coupled cluster theory for treating energy differences of open-shell states relative to a closed-shell ground state, where the open-shell states of interest are dominated by a few simple configuration state functions. We develop a valence-universal coupled cluster formalism to achieve this via a novel cluster expansion ansatz for the valence part of the wave operator, where the orbital relaxation and the correlation relaxation accompanying ionization/excitation from the ground state are taken care of to all orders in compact, efficient, and explicitly spin-free manner. The essential difference of our proposed ansatz from the ordinary and the normal-ordered cluster ansatz in vogue is that (a) we allow the valence cluster operators to be connected among themselves with spectator valence lines only and (b) we use suitable combinatoric factors accompanying powers of cluster operators thus connected, which are equal to the number of ways the operators can be joined, leading to the same excitation (the automorphic factor). We emphasize that such an ansatz does not generate terms (diagrams) with chains of cluster operators joined among themselves via spectator lines only. Barring only a few, almost all the terms in the working equations determining the cluster amplitudes involve contraction of the Hamiltonian with the cluster operators via at least one nonspectator line, leading to what we call a “strongly connected” series. The structure of the working equation is remarkably similar to the single-reference closed-shell equation, with a few additional terms. The presence of contractions among cluster operators via spectator lines introduces the additional physical effects of orbital and correlation relaxation using low-body cluster operators. As an illustrative application of the new multireference coupled cluster (CC) theory, we consider in this paper computation of ionization potentials (IPs) of one-valence problem with only one active orbital. The numerical applications are made for both the core- and the inner- and outer-valence IPs for several molecular systems. The numerical values demonstrate the superiority of the relaxation-inducing CC theory, as compared to the normal-ordered ansatz. [ABSTRACT FROM AUTHOR]

Based on a recently developed quantum dissipation formulation [R. X. Xu and Y. J. Yan, J. Chem. Phys. 116, 9196 (2002)], we present a reduced Liouville-space approach to evaluate the response and correlation functions of dissipative systems. The weak system-bath interaction is treated properly for its effects on the initial state, the evolution, and the correlation between coherent driving and non-Markovian dissipation. Numerical demonstration shows this correlated effect cannot be neglected even in the calculation of linear response quantities that do not explicitly depend on external fields. Highlighted in this paper is also the proper choice of theory among various formulations in the weak system-bath interaction regime. [ABSTRACT FROM AUTHOR]

The Nakajima­Zwanzig generalized quantum master equation (GQME) provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a, possibly anharmonic, quantum bath. In this equation, a memory kernel superoperator accounts for the influence of the bath on the dynamics of the system. In a previous paper [Q. Shi and E. Geva, J. Chem. Phys. 119, 12045 (2003)] we proposed a new approach to calculating the memory kernel, in the case of arbitrary system-bath coupling. Within this approach, the memory kernel is obtained by solving a set of two integral equations, which requires a new type of two-time system-dependent bath correlation functions as input. In the present paper, we consider the application of the linearized semiclassical (LSC) approximation for calculating those correlation functions, and subsequently the memory kernel. The new approach is tested on a benchmark spin-boson model. Application of the LSC approximation for calculating the relatively short-lived memory kernel, followed by a numerically exact solution of the GQME, is found to provide an accurate description of the relaxation dynamics. The success of the proposed LSC­GQME methodology is contrasted with the failure of both the direct application of the LSC approximation and the weak coupling treatment to provide an accurate description of the dynamics, for the same model, except at very short times. The feasibility of the new methodology to anharmonic systems is also demonstrated in the case of a two level system coupled to a chain of Lennard­Jones atoms. [ABSTRACT FROM AUTHOR]

Using the multiexciton density matrix theory of excitation energy transfer in chromophore complexes developed in a foregoing paper [J. Chem. Phys. 118, 746 (2003)], the computation of ultrafast transient absorption spectra is presented. Beside static disorder and standard mechanisms of excitation energy dissipation the theory incorporates exciton exciton annihilation (EEA) processes. To elucidate signatures of EEA in intensity dependent transient absorption data the approach is applied to the B850 ring of the LH2 found in rhodobacter sphaeroides. As main indications for two-exciton population and resulting EEA we found (i) a weakening of the dominant single-exciton bleaching structure in the transient absorption, and (ii) an intermediate suppression of long-wavelength and short-wavelength shoulders around the bleaching structure. The suppression is caused by stimulated emission from the two-exciton to the one-exciton state and the return of the shoulders follows from a depletion of two-exciton population according to EEA. The EEA-signature survives as a short-wavelength shoulder in the transient absorption if orientational and energetic disorder are taken into account. Therefore, the observation of the EEA-signatures should be possible when doing frequency resolved transient absorption experiments with a sufficiently strongly varying pump-pulse intensity. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

It is well known that the group of operators that commutes with the Hamiltonian operator can be used to facilitate the calculation of energy levels. Due to numerical errors in the computation of Hamiltonian matrix elements, it may happen that the matrix representation of a group operator does not commute with the Hamiltonian matrix although the group operator does commute with the Hamiltonian operator. We demonstrate that it is possible, even in this case, to use the single-symmetry and multisymmetry symmetry-adapted Lanczos (SAL) methods to efficiently compute energy levels. The two SAL methods are applied to the calculation of the bend levels of methane using the G[SUB6] symmetry group and polyspherical angles. We show that although potential matrix elements are corrupted by quadrature error, it is nonetheless possible to take advantage of the full symmetry of the polyspherical basis. For a CX[SUB3]Y-type molecule the symmetry-adapted method of this paper would enable one to exploit all of the symmetry of the molecule. [ABSTRACT FROM AUTHOR]

Most of the numerical simulation in quantum (bilinear) control have used one of the monotonically convergent algorithms of Krotov (introduced by Tannor et al.) or of Zhu and Rabitz. However, until now no explicit relationship has been revealed between the two algorithms in order to understand their common properties. Within this framework, we propose in this paper a unified formulation that comprises both algorithms and that extends to a new class of monotonically convergent algorithms. Numerical results show that the newly derived algorithms behave as well as (and sometimes better than) the well-known algorithms cited above. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Expanding the set of stable, accurate, and scalable methods for simulating molecular quantum dynamics is important for accelerating the computational exploration of molecular processes. In this paper, we adapt the signed particles Monte Carlo algorithm for solving the transient Wigner equation to scenarios of chemical interest. This approach was used in the past to study electronic processes in semi-conductors, but to the best of our knowledge, it had never been applied to molecular modeling. We present the algorithm and demonstrate its excellent performance on harmonic and double well potentials for electronic and nuclear systems. We explore the stability of the algorithm, discuss the choice of hyper-parameters, and cautiously speculate that it may be used in quantum molecular dynamics simulations. [ABSTRACT FROM AUTHOR]

Quantum molecular dynamics requires an accurate representation of the molecular potential energy surface from a minimal number of electronic structure calculations, particularly for nonadiabatic dynamics where excited states are required. In this paper, we employ pseudospectral sampling of time-dependent Gaussian basis functions for the simulation of non-adiabatic dynamics. Unlike other methods, the pseudospectral Gaussian molecular dynamics tests the Schrödinger equation with N Dirac delta functions located at the centers of the Gaussian functions reducing the scaling of potential energy evaluations from O(N²) to O(N). By projecting the Gaussian basis onto discrete points in space, the method is capable of efficiently and quantitatively describing the nonadiabatic population transfer and intra-surface quantum coherence. We investigate three model systems: the photodissociation of three coupled Morse oscillators, the bound state dynamics of two coupled Morse oscillators, and a two-dimensional model for collinear triatomic vibrational dynamics. In all cases, the pseudospectral Gaussian method is in quantitative agreement with numerically exact calculations. The results are promising for nonadiabatic molecular dynamics in molecular systems where strongly correlated ground or excited states require expensive electronic structure calculations. [ABSTRACT FROM AUTHOR]

The formulation of quantum statistical mechanics based on the path centroid variable in Feynman path integration is generalized to a phase space perspective, thereby including the momentum as an independent dynamical variable. By virtue of this approach, operator averages and imaginary time correlation functions can be expressed in terms of an averaging over the multidimensional phase space centroid density. The imaginary time centroid-constrained correlation function matrix for the phase space variables is then found to define the effective thermal width of the phase space centroid variable. These developments also make it possible to rigorously analyze the centroid molecular dynamics method for computing quantum dynamical time correlation functions. As a result, the centroid time correlation function as calculated from centroid molecular dynamics is shown to be a well-defined approximation to the exact Kubo transformed position correlation function. This analysis thereby clarifies the underlying role of the equilibrium path centroid variable in the quantum dynamical position correlation function and provides a sound theoretical basis for the centroid molecular dynamics method. [ABSTRACT FROM AUTHOR]

Following a previous Communication [J. Chem. Phys. 99, 5615 (1993)], which reported several initial state-selected total reaction probabilities for the title reaction for J=0, we present in this paper the methodologies of the previous calculation and show results of new calculations. In particular, the present calculations are extended to all angular momentum J>=0 and obtained reaction cross sections for a range of energies using the centrifugal sudden (CS) approximation. The computed cross sections are used to obtain the state-specific thermal rate constants for both the ground and the excited vibrations of H2. The dynamics calculation, in which the nonreactive OH bond is frozen, includes explicitly five degrees of freedom in the time-dependent quantum dynamics treatment. The comparison of the present accurate cross sections with other approximate theoretical calculations shows discrepancies. The computed rate constants (from the ground rotation state) are larger than experimental measurements at low temperatures, the v=0 rate is larger than the corresponding experimental rate by a factor of 1.8, and the ratio of v=1 to v=0 rate is a factor of 4.8 greater than the experimental ratio at 300 K. The calculated reaction rates are also compared to those of other theoretical calculations and the differences are discussed in the text. [ABSTRACT FROM AUTHOR]

Potential energy surfaces have been determined for the A’ and A‘ states of the He(1S)+CH(X 2Π) system. The interaction energies were computed using a Hartree–Fock singles and doubles CI treatment; convergence of the calculation with respect to both basis set and configuration set was investigated. The surfaces have been represented quantitatively by standard Legendre polynomial expansions and qualitatively by novel pairwise additive potentials. With the pairwise additive models, successful fits require that the centers of force be orbital based as opposed to the typical nucleus-based form. Comparison of the surfaces would suggest that the final fitted surfaces are accurate to a few tenths of a kcal/mol up to 5–10 kcal/mol. In the following paper, the dynamical consequences of the small differences between all the surfaces will be assessed by quantum dynamics calculations of cross sections and their subsequent comparison to experiment. [ABSTRACT FROM AUTHOR]

We discuss an effective numerical method for obtaining the best trajectory to be used in the classical path approach. The method is based upon a time dependent variational method, which yields from first principles the classical path equations. In its simplest formulation the classical path equations contain an optimal momentum determined self-consistently. A variational method, which satisfies detailed balance is also discussed. [ABSTRACT FROM AUTHOR]

Variational basis-set formulations of the quantum mechanical reactive scattering problem lead to large, dense sets of equations. In previous work, we showed that the generalized minimal residual (GMRes) algorithm is sometimes competitive in terms of computer time with direct methods for these dense matrices, even when complex-valued boundary conditions are used, leading to non-Hermitian matrices. This paper presents a preconditioning scheme to accelerate convergence and improve performance. We block the potential energy coupling into a series of distortion blocks, and we employ the outgoing wave variational principle with nonorthogonal basis functions, including both dynamically adapted Green’s functions for the distortion blocks and also square integrable functions. The coefficient matrix of the resulting linear system couples the blocks. We have found that preconditioners formed from diagonal blocks of the coefficient matrix corresponding to the distortion blocks and vibrational blocks are effective at accelerating the iterative method in every test case, by factors of 2.9–20, with an average speedup of a factor of 6.5. The storage requirements and computational efficiency of the new scheme compare favorably to those for preconditioners based on banded matrices of variable bandwidth. The new preconditioners yield converged transition probabilities in less computer time than a direct solver even in cases which do not converge in a reasonable amount of time without preconditioning, and the average speedup compared to the direct solution is a factor of 7.6. [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 experiments by Zafiropulos et al. [Phys. Rev. Lett. 61, 1485 (1988)] indicate that K2 photodissociation through the B 1Πu state results in fluorescence polarization which is strongly dependent on excitation wavelength. To understand these results, we have studied the K2 system quantum mechanically using a half-collision analysis derived from the generalized form of multichannel quantum defect theory. This analysis factors the transition amplitudes into separate terms representing absorption and final state interactions. An approximation called the adiabatic(a→c)/recoil(c→e) approximation is developed for the half-collision matrix which reproduces quantitatively the exact half-collision results projected from the close-coupled wave function. This specific approximation applies to the homonuclear molecule K2 because of the very long range of the excited state potential, which varies as 1/R3. The quantum mechanical expression for the polarization as a function of initial rotational quantum number J0 and total energy E is found to be extremely simple in this approximation, depending only on J0 and the single-channel P, Q, and R phase shifts for the adiabatic reference states corresponding to the B 1Πu state at short distance. In the high J limit, the quantum expression is in exact agreement with a semiclassical expression which is derived in the accompanying paper by Kleiber et al. [ABSTRACT FROM AUTHOR]

We discuss the achievability of optimal control of the evolution of an unbounded quantum system by the action of external fields. Previous work has established that the evolution of a quantum system with a nondegenerate discrete and bounded spectrum of states can, in principle, be fully controlled, i.e., that the system wave function can be guided by external fields to approach arbitrarily closely a selected target state wave function. The optimal control of the evolution of a quantum system with a discrete and bounded spectrum of states has also been studied, using a method of analysis that depends on the localized character of bound state wave functions and the fact that the spectrum of states is bounded. In this paper, we examine whether it is possible to control, partially or fully, the evolution of an unbounded quantum system. We show that optimal control of the evolution of an unbounded quantum system is possible, in the sense that it is possible to minimize the difference between the product function formed at time t0 from a localizing function and a continuum wave function and a similarly defined target function at time tf.We have not been able to establish that such optimal control is equivalent to full control, i.e., that the difference between the initial and target functions can be made arbitrarily small, which would require showing that the set of control functions is complete with respect to the function space of the system. Our analysis establishes the existence of external fields that can optimally guide the unbounded system evolution in the absence of other constraints than the Schrödinger equation of motion, but does not provide an algorithm for the construction of such fields. The relationship between optimal control of the evolution of a quantum system and the existence of chaotic dynamics in the continuum domain is briefly discussed. We argue that the optimally controlled system cannot have chaotic dynamics even if the bare system... [ABSTRACT FROM AUTHOR]

This paper presents a new, quantum mechanical, time dependent approach to the photodissociation of triatomic molecules in Jacobi coordinates. The algorithm is based on a nested interaction representation, designed to make the representation of the time evolving wave packet as compact as possible. The new equations of motion are solved numerically using a synthesis of grid techniques: the fast Fourier transform (FFT) method is used in Cartesian-like coordinates, and the discrete variable representation (DVR) method in the angular or bending coordinate. A variant on the short iterative Lanczos (SIL) procedure is used for the temporal propagation of the wave packet. Rotational state distributions obtained from this new algorithm are presented for the single surface photodissociation of ClCN and for the two surface photodissociation of ICN. The ClCN results are in good agreement with the semiclassical results of Barts and Halpern [J. Phys. Chem. 93, 7346 (1989)] and in excellent agreement with the time independent quantum results of Schinke [J. Chem. Phys. 92, 2397 (1990)]. Rotational state distributions for the two electronic surface photodissociation of ICN are in good agreement with the time independent quantum results of Guo and Schatz [J. Chem. Phys. 92, 1634 (1990)] and illustrate the flexibility of the method for dealing with nonadiabatic processes. The numerical efficiency of the method is comparable with standard time independent techniques, but has the attractive feature of yielding final state distributions at all energies from a single wave packet propagation. [ABSTRACT FROM AUTHOR]

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]

In this work, we examine the efficiency of the recently developed [P. Piecuch et al., J. Chem. Phys. 99, 6732 (1993)] state-selective (SS) multi-reference (MR) coupled-cluster (CC) method for calculation of molecular properties. In our earlier papers, we demonstrated that the SSMRCC method with inclusion of single, double, and internal and semi-internal triple excitations [SSCCSD(T) approach] is capable of providing an accurate description of the ground-state potential energy surfaces. In this paper, we present the dipole moment and polarizability values of the HF molecule at equilibrium and stretched geometries calculated using finite field technique and SSCCSD(T) ansatz. The calculations use double zeta quality basis sets with and without polarization functions. Molecular orbital basis sets include both relaxed and nonrelaxed orbitals. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

By using the evolution equations for heat and mass fluxes which have been derived from the kinetic equation for the Wigner distribution function of a quantum gas mixture, a quantum effect in mass and heat transport is discussed in this paper. We show that there are transport coefficients associated with mass and heat transport which are proportional to h2 and the curvatures of the external force applied to the system. These quantum effect terms should become observable at low temperatures if the field gradients are comparable to the temperature gradient or the concentration gradients in magnitude. In the case of charge carriers, one of the field gradients can be related to the charge density if the external field is electric, and the quantum effect should be noticeable at low temperatures if the charge density gradient is comparable to the temperature gradient or the concentration gradients of neutral species in magnitude. The said quantum effect means that heat and mass can be driven by second-order gradients (e.g., the curvature) of the external field. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Classical transition state theory (TST) provides the rigorous basis for the application of molecular dynamics (MD) to infrequent events, i.e., reactions that are slow due to a high energy barrier. The TST rate is simply the equilibrium flux through a surface that divides reactants from products. In order to apply MD to infrequent events, corrections to the TST rate that account for recrossings of the dividing surface are computed by starting trajectories at the dividing surface and integrating them backward and forward in time. Both classical TST and conventional MD invoke the adiabatic approximation, i.e., the assumption that nuclear motion evolves on a single potential energy surface. Many chemical rate processes involve multiple potential energy surfaces, however, and a number of ‘‘surface-hopping’’ MD methods have been developed in order to incorporate nonadiabatic transitions among the potential energy surfaces. In this paper we generalize TST to processes involving multiple potential energy surfaces. This provides the framework for a new method for MD simulation of infrequent events for reactions that evolve on multiple potential energy surfaces. We show how this method can be applied rigorously even in conjunction with phase-coherent surface-hopping methods, where the probability of switching potential energy surfaces depends on the history of the trajectory, so integrating trajectories backward to calculate the recrossing correction is problematic. We illustrate this new method by applying it in conjunction with the ‘‘molecular dynamics with quantum transitions’’ (MDQT) surface-hopping method to a one-dimensional two-state barrier crossing problem. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In a recent Letter [Chem. Phys. Lett. 221, 482 (1994)], we demonstrated that the dynamics of reduced density matrices for systems in contact with dissipative harmonic environments can be obtained in an iterative fashion by multiplication of a propagator tensor. The feasibility of iterative procedures in reduced dimension spaces arises from intrinsic features of the dissipative influence functional in Feynman’s path integral formulation of quantum dynamics. Specifically, the continuum of frequencies characteristic of broad condensed phase spectra disrupts phase coherence to a large extent, such that the dynamics of an augmented reduced density tensor becomes Markovian. In a preceding article [J. Chem. Phys. 102, 4600 (1995)] we examined in detail the formal properties of the tensor propagator. In the present paper we show that the tensor propagator can be further decomposed into a product of small rank tensors, resulting in an extremely simple and efficient numerical scheme that scales almost linearly with the dimension of the augmented reduced density tensor. Numerical application to a model electron transfer reaction is presented. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Trajectory-based Gaussian basis sets have been tremendously successful in describing highdimensional quantum molecular dynamics. In this paper, we introduce a pseudospectral Gaussianbased method that achieves accurate quantum dynamics using efficient, real-space sampling of the time-dependent basis set. As in other Gaussian basis methods, we begin with a basis set expansion using time-dependent Gaussian basis functions guided by classical mechanics. Unlike other Gaussian methods but characteristic of the pseudospectral and collocation methods, the basis set is tested with N Dirac delta functions, where N is the number of basis functions, rather than using the basis function as test functions. As a result, the integration for matrix elements is reduced to function evaluation. Pseudospectral Gaussian dynamics only requires O(N) potential energy calculations, in contrast to O(N²) evaluations in a variational calculation. The classical trajectories allow small basis sets to sample high-dimensional potentials. Applications are made to diatomic oscillations in a Morse potential and a generalized version of the Henon-Heiles potential in two, four, and six dimensions. Comparisons are drawn to full analytical evaluation of potential energy integrals (variational) and the bra-ket averaged Taylor (BAT) expansion, an O(N) approximation used in Gaussian-based dynamics. In all cases, the pseudospectral Gaussian method is competitive with full variational calculations that require a global, analytical, and integrable potential energy surface. Additionally, the BAT breaks down when quantum mechanical coherence is particularly strong (i.e., barrier reflection in the Morse oscillator). The ability to obtain variational accuracy using only the potential energy at discrete points makes the pseudospectral Gaussian method a promising avenue for on-the-fly dynamics, where electronic structure calculations become computationally significant. [ABSTRACT FROM AUTHOR]

When a nonadiabatic system that has an ionic state (large dipole moment) and a covalent state (small dipole moment) is located in a strong laser field, the crossing point of the two potential energy curves is forced to oscillate due to the oscillating laser field and to meet wavepackets moving on the potential curves many times. This leads to additional transitions between the two states, and under favorable conditions, the wavepacket may be confined in a spatial region rich in nonadiabatic interaction. In this paper, taking the LiF molecule system in a continuous-wave driving field as a prototypical example, the dynamical origins of the wavepacket confinement are theoretically investigated. [ABSTRACT FROM AUTHOR]

In their comment, Sanz and Miret-Artés (SMA) describe previous trajectory-based formalisms based on the quantum Hamilton-Jacobi (QHJ) formalism. In this reply, we highlight our unique contributions: the identification of the smallness of the quantum force in the complex QHJ and its solution using complex trajectories. SMA also raise the question of how the term locality should be used in quantum mechanics. We suggest that at least certain aspects of nonlocality can depend on the method used to solve the problem. [ABSTRACT FROM AUTHOR]

The photodesorption of CO from TiO2(110) by femtosecond pulses is investigated with the Surrogate Hamiltonian approach. The aim of the study is to resolve the relaxation mechanism and forecast the lifetime of the exited state based on a microscopic description of the excitation and relaxation processes. The parameters characterizing the system are obtained from ab initio and Density Functional Theory-calculations with one parameter estimated from physical considerations and convergence studies. Two electronic states are considered and the relaxation is assumed to be due to the interaction of the excited adsorbate with electron hole pairs in the surface. Desorption probabilities and velocity distributions of the desorbing molecules are calculated and an exited state lifetime is predicted. Throughout this paper atomic units, i.e., ℏ = me = e = a0 = 1, have been used unless otherwise stated. [ABSTRACT FROM AUTHOR]

We extend the statistical associating fluid theory of quantum corrected Mie potentials (SAFT-VRQ Mie), previously developed for pure fluids [Aasen et al., J. Chem. Phys. 151, 064508 (2019)], to fluid mixtures. In this model, particles interact via Mie potentials with Feynman–Hibbs quantum corrections of first order (Mie-FH1) or second order (Mie-FH2). This is done using a third-order Barker–Henderson expansion of the Helmholtz energy from a non-additive hard-sphere reference system. We survey existing experimental measurements and ab initio calculations of thermodynamic properties of mixtures of neon, helium, deuterium, and hydrogen and use them to optimize the Mie-FH1 and Mie-FH2 force fields for binary interactions. Simulations employing the optimized force fields are shown to follow the experimental results closely over the entire phase envelopes. SAFT-VRQ Mie reproduces results from simulations employing these force fields, with the exception of near-critical states for mixtures containing helium. This breakdown is explained in terms of the extremely low dispersive energy of helium and the challenges inherent in current implementations of the Barker–Henderson expansion for mixtures. The interaction parameters of two cubic equations of state (Soave–Redlich–Kwong and Peng–Robinson) are also fitted to experiments and used as performance benchmarks. There are large gaps in the ranges and properties that have been experimentally measured for these systems, making the force fields presented especially useful. [ABSTRACT FROM AUTHOR]

Basing on the earlier works on the hierarchical equations of motion for quantum transport, we present in this paper a first principles scheme for time-dependent quantum transport by combining time-dependent density functional theory (TDDFT) and Keldysh's non-equilibrium Green's function formalism. This scheme is beyond the wide band limit approximation and is directly applicable to the case of non-orthogonal basis without the need of basis transformation. The overlap between the basis in the lead and the device region is treated properly by including it in the self-energy and it can be shown that this approach is equivalent to a lead-device orthogonalization. This scheme has been implemented at both TDDFT and density functional tight-binding level. Simulation results are presented to demonstrate our method and comparison with wide band limit approximation is made. Finally, the sparsity of the matrices and computational complexity of this method are analyzed. [ABSTRACT FROM AUTHOR]

Expressions for reaction rate constants in multidimensional chemical systems are derived by applying semiclassical approximation to the quantum path integrals of the ImF formulation of reaction rate theory. First, the transverse degrees of freedom orthogonal to the reaction coordinate are treated within the steepest descent approximation, after which the semiclassical approximation is applied to the remaining reaction coordinate. Thus derived, the semiclassical expressions account for the multidimensional nature of quantum effects and accurately incorporate nuclear quantum effects such as multidimensional tunneling and zero point energies. The obtained expressions are applicable in the broad temperature range from the deep tunneling to high-temperature regimes. The present paper provides derivation of the semiclassical instanton expressions proposed by Kryvohuz [J. Chem. Phys. 134, 114103 (2011)]. [ABSTRACT FROM AUTHOR]

Following the calculation of optimal energy transfer in thermal environment in our first paper [J. L. Wu, F. Liu, Y. Shen, J. S. Cao, and R. J. Silbey, New J. Phys. 12, 105012 (2010)], full quantum dynamics and leading-order 'classical' hopping kinetics are compared in the seven-site Fenna-Matthews-Olson (FMO) protein complex. The difference between these two dynamic descriptions is due to higher-order quantum corrections. Two thermal bath models, classical white noise (the Haken-Strobl-Reineker (HSR) model) and quantum Debye model, are considered. In the seven-site FMO model, we observe that higher-order corrections lead to negligible changes in the trapping time or in energy transfer efficiency around the optimal and physiological conditions (2% in the HSR model and 0.1% in the quantum Debye model for the initial site at BChl 1). However, using the concept of integrated flux, we can identify significant differences in branching probabilities of the energy transfer network between hopping kinetics and quantum dynamics (26% in the HSR model and 32% in the quantum Debye model for the initial site at BChl 1). This observation indicates that the quantum coherence can significantly change the distribution of energy transfer pathways in the flux network with the efficiency nearly the same. The quantum-classical comparison of the average trapping time with the removal of the bottleneck site, BChl 4, demonstrates the robustness of the efficient energy transfer by the mechanism of multi-site quantum coherence. To reconcile with the latest eight-site FMO model which is also investigated in the third paper [J. Moix, J. L. Wu, P. F. Huo, D. F. Coker, and J. S. Cao, J. Phys. Chem. Lett. 2, 3045 (2011)], the quantum-classical comparison with the flux network analysis is summarized in Appendix C. The eight-site FMO model yields similar trapping time and network structure as the seven-site FMO model but leads to a more disperse distribution of energy transfer pathways. [ABSTRACT FROM AUTHOR]

Most of today's molecular-dynamics simulations of materials are based on the Born-Oppenheimer approximation. There are many cases, however, in which the coupling of the electrons and nuclei is important and it is necessary to go beyond the Born-Oppenheimer approximation. In these methods, the non-adiabatic coupling vectors are fundamental since they represent the link between the classical atomic motion of the nuclei and the time evolution of the quantum electronic state. In this paper we analyze the calculation of non-adiabatic coupling vectors in a basis set of local orbitals and derive an expression to calculate them in a practical and computationally efficient way. Some examples of the application of this expression using a local-orbital density functional theory approach are presented for a few simple molecules: H3, formaldimine, and azobenzene. These results show that the approach presented here, using the Slater transition-state density, is a very promising way for the practical calculation of non-adiabatic coupling vectors for large systems. [ABSTRACT FROM AUTHOR]

This paper shows how a compact finite difference Hessian approximation scheme can be proficiently implemented into semiclassical initial value representation molecular dynamics. Effects of the approximation on the monodromy matrix calculation are tested by propagating initial sampling distributions to determine power spectra for analytic potential energy surfaces and for 'on the fly' carbon dioxide direct dynamics. With the approximation scheme the computational cost is significantly reduced, making ab initio direct semiclassical dynamics computationally more feasible and, at the same time, properly reproducing important quantum effects inherent in the monodromy matrix and the pre-exponential factor of the semiclassical propagator. [ABSTRACT FROM AUTHOR]

Mixed quantum/classical (MQC) simulations treat the majority of a system classically and reserve quantum mechanics only for a few degrees of freedom that actively participate in the chemical process(es) of interest. In MQC calculations, the quantum and classical degrees of freedom are coupled together using pseudopotentials. Although most pseudopotentials are developed empirically, there are methods for deriving pseudopotentials using the results of quantum chemistry calculations, which guarantee that the explicitly-treated valence electron wave functions remain orthogonal to the implicitly-treated core electron orbitals. Whether empirical or analytically derived in nature, to date all such pseudopotentials have been subject to the frozen core approximation (FCA) that ignores how changes in the nuclear coordinates alter the core orbitals, which in turn affects the wave function of the valence electrons. In this paper, we present a way to go beyond the FCA by developing pseudopotentials that respond to these changes. In other words, we show how to derive an analytic expression for a pseudopotential that is an explicit function of nuclear coordinates, thus accounting for the polarization effects experienced by atomic cores in different chemical environments. We then use this formalism to develop a coordinate-dependent pseudopotential for the bonding electron of the sodium dimer cation molecule and we show how the analytic representation of this potential can be used in one-electron MQC simulations that provide the accuracy of a fully quantum mechanical Hartree-Fock (HF) calculation at all internuclear separations. We also show that one-electron MQC simulations of Na2+ using our coordinate-dependent pseudopotential provide a significant advantage in accuracy compared to frozen core potentials with no additional computational expense. This is because use of a frozen core potential produces a charge density for the bonding electron of Na2+ that is too localized on the molecule, leading to significant overbinding of the valence electron. This means that FCA calculations are subject to inaccuracies of order ∼10% in the calculated bond length and vibrational frequency of the molecule relative to a full HF calculation; these errors are fully corrected by using our coordinate-dependent pseudopotential. Overall, our findings indicate that even for molecules like Na2+, which have a simple electronic structure that might be expected to be well-treated within the FCA, the importance of including the effects of the changing core molecular orbitals on the bonding electrons cannot be overlooked. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical and experimental study of nuclear magnetic resonance technique for sign-sensitive determination of the dipolar couplings of rare spins-1/2 to spin-1 with a strong quadrupolar interaction. The technique is based on low-power transition-selective single-quantum decoupling of spin-1 in the presence of high-power decoupling of abundant (proton) spins. Single-transition operator formalism is employed to calculate the time evolution of the density matrix in the presence of low-power irradiation of spin-1. Generally, the sign of dipolar coupling is unavailable from intrinsically symmetric shapes of dipolar-coupled spectra. Asymmetric dipolar multiplets, resulted from selective decoupling, reveal both the signs and magnitudes of the heteronuclear dipolar couplings. The approach is used to develop the experimental strategy for sign-sensitive measurements of short- and long-range heteronuclear dipolar couplings in highly ordered anisotropic samples. The technique is demonstrated for 13C-2H and 13C-14N spin pairs and for 13C-2H2 three-spin system in liquid crystals. [ABSTRACT FROM AUTHOR]

Time-resolved photoelectron spectroscopy can obtain detailed information about the dynamics of a chemical process on the femtosecond timescale. The resulting signal from such detailed experiments is often difficult to analyze and therefore theoretical calculations are important in providing support. In this paper we continue our work on the competing pathways in the photophysics and photochemistry of benzene after excitation into the 'channel 3' region [R. S. Minns, D. S. N. Parker, T. J. Penfold, G. A. Worth, and H. H. Fielding, Phys. Chem. Chem. Phys. 12, 15607 (2010)] with details of the calculations shown previously, building on a vibronic coupling Hamiltonian [T. J. Penfold and G. A. Worth, J. Chem. Phys. 131, 064303 (2009)] to include the triplet manifold. New experimental data are also presented suggesting that an oscillatory signal is due to a hot band excitation. The experiments show that signals are obtained from three regions of the potential surfaces, three open channels, which are assigned with the help of simulations showing that following excitation into vibrationally excited-states of S1 the wavepacket not only crosses through the prefulvenoid conical intersection back to the singlet ground state, but also undergoes ultrafast intersystem crossing to low lying triplet states. The model is, however, not detailed enough to capture the full details of the oscillatory signal due to the hot band. [ABSTRACT FROM AUTHOR]

The hierarchical equations of motion (HEOM) method has recently been widely applied to many problems of quantum dynamics in condensed phase. It is now well known that the auxiliary density operators (ADOs) in the HEOM formalism contain system-bath correlations that are important in calculating various dynamical properties, yet quantitative relations to explicitly calculate such correlations from the ADOs are still scarce. This paper extends a previous study [Q. Shi et al., J. Chem. Phys. 130, 164518 (2009)] in investigating the physical meaning of ADOs to general spectral densities and lower temperature cases. Using the path-integral technique, we derive exact relations between the expectation values of the collective bath coordinate and the ADOs, which could be very useful in investigating the correlated system-bath dynamics directly with the HEOM formalism. Numerical examples concerning the evolution of the expectation values of the collective bath coordinate are also presented. [ABSTRACT FROM AUTHOR]

Core vacancies created on opposite sides of a molecule operate against each other in polarizing the environment between them. Consequently, the relaxation energy associated with the simultaneous creation of these two core holes turns out to be smaller than the sum of the relaxation energies associated with each individual single core vacancy created independently. The corresponding residual, termed interatomic relaxation energy, is sensitive to the environment. In the present paper we explore how the interatomic relaxation energy depends on the length and type of carbon chains bridging two core ionized nitrile groups (-C≡N). We have uncovered several trends and discuss them with the help of simple electrostatic and quantum mechanical models. Namely, the absolute value of the interatomic relaxation energy depends strongly on the orbital hybridization in carbons being noticeably larger in conjugated chains (sp and sp2 hybridizations) possessing highly mobile electrons in delocalized π-type orbitals than in saturated chains (sp3 hybridization) where only σ bonds are available. The interatomic relaxation energy decreases monotonically with increasing chain length. The corresponding descent is determined by the energetics of the molecular bridge, in particular, by the HOMO-LUMO gap. The smallest HOMO-LUMO gap is found in molecules with the sp2-hybridized backbone. Here, the interatomic relaxation energy decreases slowest with the chain length. [ABSTRACT FROM AUTHOR]

In this paper we further explore and develop the quantum continuum mechanics (QCM) of Tao et al. [Phys. Rev. Lett. 103, 086401 (2009)] with the aim of making it simpler to use in practice. Our simplifications relate to the non-interacting part of the QCM equations, and primarily refer to practical implementations in which the groundstate stress tensor is approximated by its Kohn-Sham (KS) version. We use the simplified approach to directly prove the exactness of QCM for one-electron systems via an orthonormal formulation. This proof sheds light on certain physical considerations contained in the QCM theory and their implication on QCM-based approximations. The one-electron proof then motivates an approximation to the QCM (exact under certain conditions) expanded on the wavefunctions of the KS equations. Particular attention is paid to the relationships between transitions from occupied to unoccupied KS orbitals and their approximations under the QCM. We also demonstrate the simplified QCM semianalytically on an example system. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the emission characteristics of a molecule placed in the gap of a nanoparticle dimer configuration. The emission process is described in terms of a local field enhancement factor and the overall quantum yield of the system. The molecule is represented as a dipolar source, with fixed length and fed by a constant current. We first describe the coupled dimer-molecule system and compare these results to a single sphere-molecule system. Next, the effect of dimer size is investigated by changing the radius of the nanoparticles. We find that when the radius increases, a saturation effect occurs that trends towards the case of a radiating dipole between two flat interfaces, which we refer to as a parallel plate waveguide geometry. An analytical solution for the parallel plate waveguide geometry is presented and compared to the results for the spherical dimer configuration. We use this approximation as a reference solution, and also, it provides useful guidelines to understand the physical mechanism behind the energy transfer between the molecule and the dimer. We find that the emission intensity undergoes a quenching effect only when the inter-nanoparticle gap distance of the dimer is very small, meaning that strong coupling prevails over energy engaged in the heating process unless the molecule is extremely close to the metal surface. [ABSTRACT FROM AUTHOR]

This paper is the first of a two-part series dealing with quantum-mechanical (density-functional-based) studies of helium-mediated deposition of catalytic species on the rutile TiO2(110)-(1×1) surface. The interaction of helium with the TiO2(110)-(1×1) surface is first evaluated using the Perdew-Burke-Ernzerhof functional at a numerical grid dense enough to build an analytical three-dimensional potential energy surface. Three (two prototype) potential models for the He-surface interaction in helium scattering calculations are analyzed to build the analytical potential energy surface: (1) the hard-corrugated-wall potential model; (2) the corrugated-Morse potential model; and (3) the three-dimensional Morse potential model. Different model potentials are then used to study the dynamics upon collision of a 4He300 cluster with the TiO2(110) surface at zero temperature within the framework of a time-dependent density-functional approach for the quantum fluid [D. Mateo, D. Jin, M. Barranco, and M. Pi, J. Chem. Phys. 134, 044507 (2011)] and classical dynamics calculations. The laterally averaged density functional theory-based potential with an added long-range dispersion interaction term is further applied. At variance with classical dynamics calculations, showing helium droplet splashing out of the surface at impact, the time evolution of the macroscopic helium wave-function predicts that the helium droplet spreads on the rutile surface and leads to the formation of a thin film above the substrate. This work thus provides a basis for simulating helium mediated deposition of metallic clusters embedded within helium nanodroplets. [ABSTRACT FROM AUTHOR]

The switching of single cyclooctadiene molecules chemisorbed on a Si(100) surface between two stable conformations, can be achieved with a scanning tunneling microscope [Nacci et al., Phys. Rev. B 77, 121405(R) (2008)]. Recently, it was shown by quantum chemical and quantum dynamical simulations that major experimental facts can be explained by a single-mode model with switching enforced by inelastic electron tunneling (IET) excitations and perturbed by vibrational relaxation [Nacci et al., Nano Lett. 9, 2997 (2009)]. In the present paper, we extend the previous theoretical work in several respects: (1) The model is generalized to a two-mode description in which two C2H4 units of COD can move independently; (2) contributions of dipole and, in addition, (cation and anion) resonance-IET rates are considered; (3) the harmonic-linear vibrational relaxation model used previously is generalized to anharmonic vibrations. While the present models highlight generic aspects of IET-switching between two potential minima, they also rationalize specific experimental findings for COD/Si(100): (1) A single-electron excitation mechanism with a linear dependence of the switching rate on tunneling current I, (2) the capability to switch both at negative and positive sample biases, and (3) a crossover temperature around ∼60 K from an IET-driven, T-independent atom tunneling regime, to classical over-the-barrier isomerization with exponential T-dependence at higher temperatures for a bias voltage of +1.5 V and an average tunneling current of 0.73 nA. [ABSTRACT FROM AUTHOR]

The multi-configuration electron-nuclear dynamics (MCEND) method is a nonadiabatic quantum dynamics approach to the description of molecular processes. MCEND is a combination of the multi-configuration time-dependent Hartree (MCTDH) method for atoms and its antisymmetrized equivalent MCTDHF for electrons. The purpose of this method is to simultaneously describe nuclear and electronic wave packets in a quantum dynamical way, without the need to calculate potential energy surfaces and diabatic coupling functions. In this paper we present first exemplary calculations of MCEND applied to the LiH molecule, and discuss computational and numerical details of our implementation. [ABSTRACT FROM AUTHOR]

The dynamical properties of liquid water play an important role in many processes in nature. In this paper, we focus on the infrared (IR) absorption spectrum of liquid water based on the linearized semiclassical initial value representation (LSC-IVR) with the local Gaussian approximation (LGA) [J. Liu and W. H. Miller, J. Chem. Phys. 131, 074113 (2009)] and an ab initio based, flexible, polarizable Thole-type model (TTM3-F) [G. S. Fanourgakis and S. S. Xantheas, J. Chem. Phys. 128, 074506 (2008)]. Although the LSC-IVR (LGA) gives the exact result for the isolated three-dimensional shifted harmonic stretching model, it yields a blueshifted peak position for the more realistic anharmonic stretching potential. By using the short-time information of the LSC-IVR correlation function; however, it is shown how one can obtain more accurate results for the position of the stretching peak. Due to the physical decay in the condensed phase system, the LSC-IVR (LGA) is a good and practical approximate quantum approach for the IR spectrum of liquid water. The present results offer valuable insight into future attempts to improve the accuracy of the TTM3-F potential or other ab initio-based models in reproducing the IR spectrum of liquid water. [ABSTRACT FROM AUTHOR]

Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave functions are critical to ascertaining new physics. One such wave function is the multi-Slater-Jastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In this paper we describe a method for working with these wave functions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized. The computational cost scales quadratically with particle number making this scaling no worse than the single determinant case and linear with the total number of excitations. Additionally, we implement this method and use it to compute the ground state energy of a water molecule. [ABSTRACT FROM AUTHOR]

Biomolecular simulations with atomistic detail are often required to describe interactions with chemical accuracy for applications such as the calculation of free energies of binding or chemical reactions in enzymes. Force fields are typically used for this task but these rely on extensive parameterisation which in cases can lead to limited accuracy and transferability, for example for ligands with unusual functional groups. These limitations can be overcome with first principles calculations with methods such as density functional theory (DFT) but at a much higher computational cost. The use of electrostatic embedding can significantly reduce this cost by representing a portion of the simulated system in terms of highly localised charge distributions. These classical charge distributions are electrostatically coupled with the quantum system and represent the effect of the environment in which the quantum system is embedded. In this paper we describe and evaluate such an embedding scheme in which the polarisation of the electronic density by the embedding charges occurs self-consistently during the calculation of the density. We have implemented this scheme in a linear-scaling DFT program as our aim is to treat with DFT entire biomolecules (such as proteins) and large portions of the solvent. We test this approach in the calculation of interaction energies of ligands with biomolecules and solvent and investigate under what conditions these can be obtained with the same level of accuracy as when the entire system is described by DFT, for a variety of neutral and charged species. [ABSTRACT FROM AUTHOR]

An efficient time-dependent importance sampling method is developed for the Monte Carlo calculation of time correlation functions via the initial value representation (IVR) of semiclassical (SC) theory. A prefactor-free time-dependent sampling function weights the importance of a trajectory based on the magnitude of its contribution to the time correlation function, and global trial moves are used to facilitate the efficient sampling the phase space of initial conditions. The method can be generally applied to sampling rare events efficiently while avoiding being trapped in a local region of the phase space. Results presented in the paper for two system-bath models demonstrate the efficiency of this new importance sampling method for full SC-IVR calculations. [ABSTRACT FROM AUTHOR]

Fewest-switches surface hopping (FSSH) is a popular nonadiabatic dynamics method which treats nuclei with classical mechanics and electrons with quantum mechanics. In order to simulate the motion of a wave packet as accurately as possible, standard FSSH requires a stochastic sampling of the trajectories over a distribution of initial conditions corresponding, e.g., to the Wigner distribution of the initial quantum wave packet. Although it is well-known that FSSH does not properly account for decoherence effects, there is some confusion in the literature about whether or not this averaging over a distribution of initial conditions can approximate some of the effects of decoherence. In this paper, we not only show that averaging over initial conditions does not generally account for decoherence, but also why it fails to do so. We also show how an apparent improvement in accuracy can be obtained for a fortuitous choice of model problems, even though this improvement is not possible, in general. For a basic set of one-dimensional and two-dimensional examples, we find significantly improved results using our recently introduced augmented FSSH algorithm. [ABSTRACT FROM AUTHOR]

Internal conversion is an inherently quantum mechanical process. To date, 'on the fly' computation of internal conversion rates is limited to harmonic approximations, which would seem to be especially unsuitable, given that the typical transition to the ground electronic state occurs at energies which are far from the harmonic limit. It is thus of interest to study the applicability of the semiclassial initial value representation (SCIVR) approach which is in principle amenable to on the fly studies even with 'many' degrees of freedom. In this paper we study the applicability of the Herman-Kluk (HK) SCIVR to a model system with two coupled and anharmonic degrees of freedom. We find that (a) the HK SCIVR is a good approximation to the exact quantum dynamics; (b) computation of the first order correction to the HK-SCIVR approximation corroborates the accuracy; (c) by studying a large parameter range, we find that the harmonic approximation is mostly unsatisfactory; and (d) for the specific model used, the coupling between the modes was found to be relatively unimportant. These results imply that the HK-SCIVR methodology is a good candidate for on the fly studies of internal conversion processes of 'large' molecules. [ABSTRACT FROM AUTHOR]

In this paper, we present a theoretical approach to construct a fluctuating quantum model of the CO vibration in heme-CO proteins and its interaction with external laser fields. The methodology consists of mixed quantum-classical calculations for a restricted number of snapshots, which are then used to construct a parametrized quantum model. As an example, we calculate the infrared absorption spectrum of carboxy-hemoglobin, based on a simplified protein model, and found the absorption linewidth in good agreement with the experimental results. [ABSTRACT FROM AUTHOR]