A general method for implementing vibrationally adiabatic mixed quantum-classical simulations

Abstract

An approach for carrying out vibrationally adiabatic mixed quantum-classical molecular dynamics simulations is presented. An appropriate integration scheme is described for the vibrationally adiabatic equations of motion of a diatomic solute in a monatomic solvent and an approach for calculating the adiabatic energy levels is presented. Specifically, an iterative Lanczos algorithm with full reorthogonalization is used to solve for the lowest few vibrational eigenvalues and eigenfunctions. The eigenfunctions at one time step in a mixed quantum-classical trajectory are used to initiate the Lanczos calculation at the next time step. The basis set size is reduced by using a potential-optimized discrete variable representation. As a demonstration the problem of a homonuclear diatomic molecule in a rare gas fluid (N 2 in Ar͒ has been treated. The approach is shown to be efficient and accurate. An important advantage of this approach is that it can be straightforwardly applied to polyatomic solutes that have multiple vibrational degrees-of-freedom that must be quantized.

Calculations of Differential Cross Sections Using Mixed Quantum/Classical Theory of Inelastic Scattering

“…To our best knowledge, this relatively straightforward approach (with integer values of l within the mixed quantum/classical framework), has not been tried in the past, neither by Billing ,,− nor by his followers. − , Application of eqs and to the N 2 ( j =0) + Na system is reported in section below.…”

Vibrational Quantum Decoherence in Liquid Water

“…Solvent quantum decoherence D(t) results from the growing divergence between the paths followed by the classical bath interacting with the two different quantum states. These trajectories are obtained by vibrationally adiabatic quantum−classical molecular dynamics (QCMD) simulations, where the vibration of the water OH stretch is described quantum mechanically while all other degrees of freedom are described classically 20 (we note that while imaginary time path integral and ring polymer molecular dynamics techniques 21 account for some nuclear quantum effects, they cannot describe quantum decoherence). Simulations are performed in the microcanonical ensemble with a 1 fs time step.…”

“…These trajectories are obtained by vibrationally adiabatic quantum–classical molecular dynamics (QCMD) simulations, where the vibration of the water OH stretch is described quantum mechanically while all other degrees of freedom are described classically (we note that while imaginary time path integral and ring polymer molecular dynamics techniques account for some nuclear quantum effects, they cannot describe quantum decoherence). The simulation box contains a single HOD molecule immersed in 255 D 2 O molecules.…”

“…Intermolecular interactions are modeled by the SPC/E potential, and all water molecules are rigid except for the OH stretch vibration of HOD, which is described by the Morse potential D OH [1 – exp­(−α­( r – r OH ))] 2 with D OH = 132.7 kcal/mol, α = 2.131 Å –1 , and r OH = 0.98 Å (these values were adapted from ref and optimized to reproduce the ν = 0 → ν = 1 and ν = 1 → ν = 2 transition energies in D 2 O , ). The ground and first excited vibrational states are determined by a discrete variable representation of the vibrational Hamiltonian with a potential-optimized grid, following the procedure introduced in ref (see the SI). The Hellmann–Feynman forces between the quantum oscillator in its ground or excited eigenstate and the classical bath are used to propagate the trajectory.…”

Recent Advances in Development and Applications of the Mixed Quantum/Classical Theory for Inelastic Scattering

“…The great work of Billing was so influential that at the end of 1990s and beginning of 2000s quite a few theory groups around the world decided to give a try to the mixed quantum/classical approach, applying it to a broad variety of problems, including nonadiabatic phenomena, 44 ro-vibrational excitation, 45 femtosecond spectroscopy, 46 collision-induced dissociation, 47 photodissociation, 48 and solvent effect. 49 Some of the results obtained at that time were quite encouraging but because those systems, processes, and collision conditions were so diverse, it was hard to come out with general conclusions about accuracy, generality, and numerical efficiency of the method. To our best knowledge, no one else pursued a focused systematic study of the method, and after the death of Billing in 2003, 50 these activities gradually declined.…”