The effect of sampling techniques used in the multiconfigurational Ehrenfest method

In this paper, we compare and contrast basis set sampling techniques recently developed for use in the ab initio multiple cloning method, a direct dynamics extension to the multiconfigurational Ehrenfest approach, used recently for the quantum simulation of ultrafast photochemistry. We demonstrate that simultaneous use of basis set cloning and basis function trains can produce results which are converged to the exact quantum result. To demonstrate this, we employ these sampling methods in simulations of quantum dynamics in the spin boson model with a broad range of parameters and compare the results to accurate benchmarks

Simulation of ultrafast photodynamics of pyrrole with a multiconfigurational Ehrenfest method

We report the first results of ab initio multiconfigurational Ehrenfest simulations of pyrrole photodynamics. We note that, in addition to the two intersections of 11A2 and 11B1 states with the ground state 11A1, which are known to be responsible for N–H bond fission, another intersection between the 12A2 and 12B1 states of the resulting molecular radical becomes important after the departure of the H atom. This intersection, which is effectively between the two lowest electronic states of the pyrrolyl radical, may play a significant role in explaining the branching ratio between the two states observed experimentally. The exchange of population between the two states of pyrrolyl occurs on a longer scale than that of N–H bond fission

Fully Atomistic Simulations of Protein Unfolding in Low Speed Atomic Force Microscope and Force Clamp Experiments with the Help of Boxed Molecular Dynamics

The results of Boxed Dynamics (BXD) fully atomistic simulations of protein unfolding by Atomic Force Microscope (AFM), in both force clamp (FC) and velocity clamp (VC) modes are reported. In AFM experiments the unfolding occurs on time scale which is too long for standard atomistic Molecular Dynamics (MD) simulations, which are usually performed with the addition of forces which exceed those of experiment by many orders of magnitude. BXD can reach the time scale of slow unfolding and sample the very high free energy unfolding pathway, reproducing the experimental dependence of pulling force against extension and extension against time. Calculations show the presence of the pulling force ‘humps’ previously observed in the Velocity Clamp (VC) AFM experiments and allow the identification of intermediate protein conformations responsible for them. Fully atomistic BXD simulations can estimate the rate of unfolding in the Force Clamp (FC) experiments up to the time scale of seconds

Ultrafast X-ray Scattering from Molecules

We present a theoretical framework for the analysis of ultrafast X-ray scattering experiments using nonadiabatic quantum molecular dynamics simulations of photochemical dynamics. A detailed simulation of a pump-probe experiment in ethylene is used to examine the sensitivity of the scattering signal to simulation parameters. The results are robust with respect to the number of wavepackets included in the total expansion of the molecular wave function. Overall, the calculated scattering signals correlate closely with the dynamics of the molecule

A two-layer approach to the coupled coherent states method

In this paper a two-layer scheme is outlined for the coupled coherent states (CCS) method, dubbed two-layer CCS (2L-CCS). The theoretical framework is motivated by that of the multiconfigurational Ehrenfest (MCE) method, where different dynamical descriptions are used for different subsystems of a quantum mechanical system. This leads to a flexible representation of the wavefunction, making the method particularly suited to the study of composite systems. It was tested on a 20-dimensional asymmetric system-bath tunnelling problem, with results compared to a benchmark calculation, as well as existing CCS, MP/SOFT and CI expansion methods. The two-layer method was found to lead to improved short and long term propagation over standard CCS, alongside improved numerical efficiency and parallel scalability. These promising results provide impetus for future development of the method for on-the-fly direct dynamics calculations

Coupled-coherent-states approach for high-order harmonic generation

In this paper, we report a version of the coupled-coherent-states method which is able to accurately compute the high-order harmonic generation (HHG) spectrum of an electron in a laser field in one dimension by the use of trajectory-guided grids of Gaussian wave packets. It is shown that by periodic reprojection of the wave function and dynamically altering the basis set size, the method can account for a wave function which spreads out to cover a large area in phase space while still keeping computational expense low and ensuring the preservation of coherence of the wave function. The HHG spectra obtained show good agreement with those from a time-dependent Schrödinger equation solver. We show also that the part of the wave function which is responsible for HHG moves along a periodic orbit which is far from that of classical motion. Although this paper is a proof of principle and therefore focused on a simple one-dimensional system, future generalizations for the multielectron case are discussed

Basis set generation for quantum dynamics simulations using simple trajectory-based methods

Methods for solving the time-dependent Schrödinger equation generally employ either a global static basis set, which is fixed at the outset, or a dynamic basis set, which evolves according to classical-like or variational equations of motion; the former approach results in the well-known exponential scaling with system size, while the latter can suffer from challenging numerical problems, such as singular matrices, as well as violation of energy conservation. Here, we suggest a middle road: building a basis set using trajectories to place time-independent basis functions in the regions of phase space relevant to wave function propagation. This simple approach, which potentially circumvents many of the problems traditionally associated with global or dynamic basis sets, is successfully demonstrated for two challenging benchmark problems in quantum dynamics, namely, relaxation dynamics following photoexcitation in pyrazine, and the spin Boson model

Boxed molecular dynamics: Decorrelation time scales and the kinetic master equation

A number of methods proposed in the past few years have been aimed at accelerating the sampling of rare events in molecular dynamics simulations. We recently introduced a method called Boxed Molecular Dynamics (BXD) for accelerating the calculation of thermodynamics and kinetics (J. Phys. Chem. B 2009, 113, 16603 -16611). BXD relies upon confining the system in a series of adjacent "boxes" by inverting the projection of the system velocities along the reaction coordinate. The potential of mean force along the reaction coordinate is obtained from the mean first passage times (MFPTs) for exchange between neighboring boxes, simultaneously providing both kinetics and thermodynamics. In this paper, we investigate BXD in the context of its natural relation to a kinetic master equation and show that the BXD first passage times (FPTs) include different time scales-a fast short time decay due to correlated dynamical motion and slower long time decay arising from phase space diffusion. Correcting the FPTs to remove the fast correlated motion yields accurate thermodynamics and master equation kinetics. We also discuss interrelations between BXD and a recently described Markovian milestoning technique and use a simple application to show that, despite each method producing distinct nonstatistical effects on time scales on the order of dynamical decorrelation, both yield similar long-time kinetics. © 2011 American Chemical Society