Unraveling Water Solvation Effects with Quantum Mechanics/Molecular Mechanics Semiclassical Vibrational Spectroscopy: The Case of Thymidine

We introduce a quantum mechanics/molecular mechanics semiclassical method for studying the solvation process of molecules in water at the nuclear quantum mechanical level with atomistic detail. We employ it in vibrational spectroscopy calculations because this is a tool that is very sensitive to the molecular environment. Specifically, we look at the vibrational spectroscopy of thymidine in liquid water. We find that the C═O frequency red shift and the C═C frequency blue shift, experienced by thymidyne upon solvation, are mainly due to reciprocal polarization effects, that the molecule and the water solvent exert on each other, and nuclear zero-point energy effects. In general, this work provides an accurate and practical tool to study quantum vibrational spectroscopy in solution and condensed phase, incorporating high-level and computationally affordable descriptions of both electronic and nuclear problems.

Calculating Multidimensional Optical Spectra from Classical Trajectories

Multidimensional optical spectra are measured from the response of a material system to a sequence of laser pulses and have the capacity to elucidate specific molecular interactions and dynamics whose influences are absent or obscured in a conventional linear absorption spectrum. Interpretation of complex spectra is supported by theoretical modeling of the spectroscopic observable, requiring implementation of quantum dynamics for coupled electrons and nuclei. Performing numerically correct quantum dynamics in this context may pose computational challenges, particularly in the condensed phase. Semiclassical methods based on calculating classical trajectories offer a practical alternative. Here I review the recent application of some semiclassical, trajectory-based methods to nonlinear molecular vibrational and electronic spectra.

Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Semiclassical propagation of Wigner functions

We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are discussed. The propagator of the Wigner function based on van Vleck's approximation replaces the Liouville propagator by a quantum spot with an oscillatory pattern reflecting the interference between pairs of classical trajectories. Employing phase-space path integration instead, caustics in the quantum spot are resolved in terms of Airy functions. We apply both to two benchmark models of nonlinear molecular potentials, the Morse oscillator and the quartic double well, to test them in standard tasks such as computing autocorrelation functions and propagating coherent states. The performance of semiclassical Wigner propagation is very good even in the presence of marked quantum effects, e.g., in coherent tunneling and in propagating Schrodinger cat states, and of classical chaos in four-dimensional phase space. We suggest options for an effective numerical implementation of our method and for integrating it in Monte-Carlo-Metropolis algorithms suitable for high-dimensional systems.

Symmetrized correlation function for liquidpara-hydrogen using complex-time pair-product propagators

We present a simple and efficient method for calculating symmetrized time correlation functions of neat quantum fluids. Using the pair-product approximation to each complex-time quantum mechanical propagator, symmetrized correlation functions are written in terms of a double integral for each degree of freedom with a purely positive integrand. At moderate temperatures and densities, where the pair-product approximation to the Boltzmann operator is sufficiently accurate, the method leads to quantitative results for the early time part of the correlation function. The method is tested extensively on liquid para-hydrogen at 25 K and used to obtain accurate quantum mechanical results for the initial 0.2 ps segment of the symmetrized velocity autocorrelation function of this system, as well as the incoherent dynamic structure factor at certain momentum transfer values.

Nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation method revisited: Applications to Tully’s three model systems

The nonadiabatic surface hopping Herman-Kluk (HK) semiclassical initial value representation (SC-IVR) method for nonadiabatic problems is reformulated. The method has the same spirit as Tully's surface hopping technique [J. Chem. Phys. 93, 1061 (1990)] and almost keeps the same structure as the original single-surface HK SC-IVR method except that trajectories can hop to other surfaces according to the hopping probabilities and phases, which can be easily integrated along the paths. The method is based on a rather general nonadiabatic semiclassical surface hopping theory developed by Herman [J. Chem. Phys. 103, 8081 (1995)], which has been shown to be accurate to the first order in h and through all the orders of the nonadiabatic coupling amplitude. Our simulation studies on the three model systems suggested by Tully demonstrate that this method is practical and capable of describing nonadiabatic quantum dynamics for various coupling situations in very good agreement with benchmark calculations.

SEMICLASSICAL INITIAL VALUE TREATMENTS OF ATOMS AND MOLECULES

This review describes some developments in the theory and application of the semiclassical initial representation for the treatment of the dynamical and static properties of atoms and molecules. The theoretical basis of initial value treatments for the propagator is discussed. A variety of useful alternative initial value expressions for the propagator and other quantities are presented as generalizations of the well-known Herman-Kluk approximation. Special emphasis is given to treatments that involve integration over only half the phase space variables. The recent development of semiclassical initial value expressions that are exact for specific, desired systems is reviewed and some of the implications are described.

A comparison between different semiclassical approximations for optical response functions in nonpolar liquid solutions

The temporal behavior of optical response functions (ORFs) reflects the quantum dynamics of an electronic superposition state, and as such lacks a well-defined classical limit. In this paper, we consider the importance of accounting for the quantum nature of the dynamics when calculating ORFs of different types. To this end, we calculated the ORFs associated with the linear absorption spectrum and the nonlinear two-pulse photon-echo experiment, via the following approaches: (1) the semiclassical forward-backward approach; (2) an approach based on linearizing the path-integral forward-backward action in terms of the difference between the forward and backward paths; (3) an approach based on ground state nuclear dynamics. The calculations were performed on a model that consists of a two-state chromophore solvated in a nonpolar liquid. The different methods were found to yield very similar results for the absorption spectrum and "diagonal" two-pulse photon echo (i.e., the homodyne-detected signal at time t=t(0) after the second pulse, where t(0) is the time interval between the two pulses). The different approximations yielded somewhat different results in the case of the time-integrated photon-echo signal. The reasons for the similarity between the predictions of different approximations are also discussed.

A Bohmian total potential view to quantum effects. I. Methodology and simple model systems

The coherent-state wave packet dynamics of several model systems is analyzed in terms of Bohm's total potential. The quantum dynamics has been obtained by solving the time-dependent Schrodinger equation, and a method for obtaining the total potential from it, involving just matrix algebra, has been proposed. Contrary to what one may expect, it is shown that the time- and state-dependent features of the total potential admit a rationale, classical-like description of quantum effects, leading to a unified picture of them, which is not critically dependent, as for the key features, on the classical potential. An outstanding feature is found to be the relation of the state system's density amplitude and sharpness (in its dependence with position) with quantum effects. Sharp density profiles and low densities cause the total potential to strongly depart from the classical value, in both time regimes and position ranges, which provide a clearer, more deterministic view to quantum dynamics. Free motion as well as scattering processes by square and Eckart barriers have been analyzed by means of careful inspection of several time dependent snapshots. The result is an insightful picture of processes involving tunneling and antitunneling, including their dynamical variants, as well as resonances and quantization.

SEMICLASSICAL DESCRIPTION OF MOLECULAR DYNAMICS BASED ON INITIAL-VALUE REPRESENTATION METHODS

Recent progress in the development of semiclassical methods to describe quantum effects in molecular dynamics is reviewed. Focusing on rigorous semiclassical methods that are based on the initial-value representation of the semiclassical propagator, we discuss several promising schemes that have been developed in the past few years to extend the applicability of semiclassical approaches to complex molecular systems. In particular, integral-filtering techniques and forward-backward methods are surveyed. Furthermore, recently proposed approaches that allow the semiclassical description of nonadiabatic molecular dynamics are discussed. The potential and efficiency of these methods is illustrated by selected applications.

Time-dependent quantum methods for large systems

This review focuses on time-dependent methods suitable for simulating the quantum dynamics of processes in large clusters and condensed-phase environments. A number of mean field, quantum-classical, and quantum statistical approximations that avoid the conventional exponential scaling with the number of degrees of freedom are reviewed. In addition, rigorous semiclassical and path integral approaches are described that are feasible in certain physical situations. Select chemical applications illustrating the capabilities of these methods are discussed.

Time-dependent probability of quantum tunneling in terms of the quasisemiclassical method

In view of the rapid progress in experiments of the tunneling dynamics in the time domain, we develop a quasisemiclassical method that is aimed at a study of the proton-transfer dynamics in a large system such as tropolone and its interesting derivatives, to which not only full quantum mechanics, but even a standard semiclassical theory is never easy to apply. In our very tractable method for multidimensional systems, the tunneling paths are generated in terms of the generalized classical mechanics, but the quantum phases arising from the action integral, the Maslov index, and the semicalssical amplitude factor as well in the semiclassical kernels are entirely neglected. This approach is called the quasisemiclassical method. One of the technical issues involved in the general semiclassical scheme is how to locate points from which a tunneling path emanates. Hence the studies of such tunneling points and the quasisemiclassical method should be examined collectively. We test several ways of determining the tunneling point, including those already proposed in the literature and a newly proposed one. It is shown numerically that the quasisemiclassical method with an appropriate choice of tunneling points reproduces the full quantum mechanical tunneling probability reasonably well. This case study indicates that the present conventional approach is promising to the study of large systems. The role of tunneling points in the initial process of tunneling is also discussed.

Semiclassical calculation of chemical reaction dynamics via wavepacket correlation functions

Calculation of chemical reaction dynamics is central to theoretical chemistry. The majority of calculations use either classical mechanics, which is computationally inexpensive but misses quantum effects, such as tunneling and interference, or quantum mechanics, which is computationally expensive and often conceptually opaque. An appealing middle ground is the use of semiclassical mechanics. Indeed, since the early 1970s there has been great interest in using semiclassical methods to calculate reaction probabilities. However, despite the elegance of classical S-matrix theory, numerical results on even the simplest reactive systems remained out of reach. Recently, with advances both in correlation function formulations of reactive scattering as well as in semiclassical methods, it has become possible for the first time to calculate reaction probabilities semiclassically. The correlation function methods are contrasted with recent flux-based methods, which, although providing somewhat more compact expressions for the cumulative reactive probability, are less compatible with semiclassical implementation.