A Semiclassical Framework for Mixed Quantum Classical Dynamics

Abstract

Semiclassical (SC) approximations for quantum dynamic simulations in complex chemical systems range from rigorously accurate methods that are computationally expensive to methods that exhibit near-classical scaling with system size but are limited in their ability to describe quantum effects. In practical studies of high-dimensional reactions, neither extreme is the best choice: frequently a high-level quantum mechanical description is only required for a handful of modes, while the majority of environment modes that do not play a key role in the reactive event of interest are well served with a lower level of theory. In this feature, we introduce modified Filinov filtration as a powerful tool to construct mixed quantum-classical SC theories where different subsystems can be quantized to different extents without introducing ad hoc intersubsystem interaction terms. We demonstrate that these Filinov-based SC methods can systematically tune between quantum and classical limit SC behavior, offering a practical way forward to accurate and computationally efficient simulations of high-dimensional quantum processes.

Which Algorithm Best Propagates the Meyer–Miller–Stock–Thoss Mapping Hamiltonian for Non-Adiabatic Dynamics?

“…Further work includes integrating the Cayley transform to extend these findings to stable NRPMD simulations . Additionally, one can apply the MInt algorithm to related dynamical methods such as forward–backward IVR. , Further development of the MInt algorithm would be of great interest. For example, as the adiabatic form of the Meyer–Miller Hamiltonian is known, extension of the MInt algorithm to the adiabatic representation may be possible.…”

“…Calculation of the monodromy matrix is not needed for algorithm propagation, only to determine symplecticity and if the theoretical framework requires it. For example, in some SC-IVR methods, the phase-factor can be calculated using elements of the monodromy matrix, where utilizing a symplectic algorithm can improve the stability, aiding convergence and partially mitigating the “sign” problem. ,, …”

“…For example, in some SC-IVR methods, the phase-factor can be calculated using elements of the monodromy matrix, where utilizing a symplectic algorithm can improve the stability, aiding convergence and partially mitigating the "sign" problem. 1,82,83 The symplecticity criterion, eq 8, is a much stricter condition than the conservation of volume phase-space (Liouville's theorem), which only requires the monodromy matrix determinant to be unity. 1,80,84 Volume phase-space preservation is a consequence of symplecticity, but this relationship does not necessarily hold the other way around, 79 i.e., volume phase-space preservation is necessary but not sufficient for symplecticity.…”

A Linearized Semiclassical Dynamics Study of the Multiquantum Vibrational Relaxation of NO Scattering from a Au(111) Surface

“…SC methods are, broadly, based on a stationary phase approximation to the exact path integral formulation of the real-time propagator and are capable of describing almost all quantum effects: zero-point energy, nuclear tunneling, interference, and nonadiabatic effects. 46,47 In the SC framework, a hierarchy of methods that differ by the extent to which quantum effects are captured exists. Recently, the mixed quantum classical (MQC)−SC method was introduced to filter phase contributions from different degrees of freedom to different extents, allowing for sensitive control of how much each degree of freedom in a complex system is quantized.…”

Investigating the Spectroscopy of the Gas Phase Guanine–Cytosine Pair: Keto versus Enol Configurations

“…Current computational and theoretical vibrational studies of DNA bases are limited to static (harmonic-like) approximations or low-dimensional models as a result of the system intrinsic complexity. ,,, These approximations fall short when dealing with hydrogen-bonded systems, and a higher accuracy is necessary if one wants to assign nucleobase pair experimental spectra, where there are a pletora of tautomers. − To overcome these limitations, we employ semiclassical dynamics, an active area of research, , and specifically the divide-and-conquer semiclassical initial value representation (DC SCIVR) method to compute the vibrational power spectra of the guanine–cytosine dimer . DC SCIVR is an acknowledged method, capable of accounting for anharmonicity and reproducing quantum effects, such as zero-point energy (zpe), overtones, and combination bands, using a single classical trajectory. − This allows us to limit the computational effort even when investigating the 29 atom guanine–cytosine pair.…”