Dmitrii V. Shalashilin

Time dependent quantum propagation in phase space

Numerical solutions of the quantum time-dependent integro-differential Schrodinger equation in a coherent state Husimi representation are investigated. Discretization leads to propagation on a grid of nonorthogonal coherent states without the need to invert an overlap matrix, with the further advantage of a sparse Hamiltonian matrix. Applications are made to the evolution of a Gaussian wave packet in a Morse potential. Propagation on a static rectangular grid is fast and accurate. Results are also presented for a moving rectangular grid, guided at its center by a mean classical path, and for a classically guided moving grid of individual coherent states taken from a Monte Carlo ensemble.

Multidimensional quantum propagation with the help of coupled coherent states

A previous initial value coupled coherent state (CCS) representation is applied to Gaussian wave packet propagation on multidimensional Henon Heiles potentials. Solutions of the time-dependent integro-differential Schrodinger equation are obtained in a basis of trajectory guided Frozen Gaussian Coherent States, with Monte Carlo sampling to ensure a unique capability for propagating multidimensional wave functions. Results, which are obtained for up to 14 D, are compared with those derived by the Herman–Kluk semiclassical initial value representation (IVR) wave packet method.

A first-principles potential energy surface for Eley–Rideal reaction dynamics of H atoms on Cu(111)

We have performed first-principles total-energy calculations of low-dimensional sections of the electronically adiabatic potential energy surface (PES) that are relevant for the Eley–Rideal (ER) reaction of H atoms on a rigid Cu(111) surface. These calculations were performed within density-functional theory using a plane-wave and pseudopotential method and the generalized gradient approximation for the exchange-correlation energy. The calculated energy points for various configurations of one and two atoms on the Cu(111) surface were used to construct a model PES that can be used in ER reaction dynamics calculations.

Eley–Rideal and hot-atom reactions of H(D) atoms with D(H)-covered Cu(111) surfaces; quasiclassical studies

Quasiclassical molecular dynamics studies are made of H or D atoms incident from the gas phase onto D or H-covered Cu(111) surfaces. Two detailed model potential energy surfaces are used, both based on the results of extensive total energy calculations using the density functional method. The incident H (D) atoms can react directly to form HD via the Eley–Rideal mechanism, or trap onto the surface. These trapped hot atoms can react with the adsorbates to form HD or can eventually dissipate enough energy through collisions with the adsorbates to become immobile. We also observe the formation of D2 (H2). Probabilities for these various processes, as well as the rotational, vibrational, and translational energy distributions of the products are computed and compared with experiment. Hot-atom pathways to product formation are shown to make significant contributions. One of the potentials gives excellent agreement with experiment, while the other is less successful.

On-the-fly ab initio molecular dynamics with multiconfigurational Ehrenfest method

In this article we report the formalism and first implementation of the ab initio multiconfigurational Ehrenfest (AI-MCE) method for simulation of ultrafast nonadiabatic dynamics, which uses the MOLPRO electronic structure program to calculate the potential energy surfaces on the fly. The approach is tested on the benchmark of the excited ππ∗ state dynamics of ethylene producing the dynamics which agree with previous simulations by ab initio multiple spawning technique. The AI-MCE seems to be robust, stable and efficient.

Nonadiabatic dynamics with the help of multiconfigurational Ehrenfest method: Improved theory and fully quantum 24D simulation of pyrazine

This article proposes an improved version of recently developed multiconfigurational Ehrenfest approach to quantum dynamics. The idea of the approach is to use frozen Gaussians (FG) guided by Ehrenfest trajectories as a basis set for fully quantum propagation. The method is applied to simulation of nonadiabatic dynamics of pyrazine and shows that nonadiabatic dynamics on two coupled electronic states S(2) and S(1), which determines pyrazine absorption spectrum, can be simulated with the help of a basis comprised of very small number of trajectory guided basis functions. For the 24 dimensional (24D) model, good results were obtained with the basis of only 250 trajectories guided FG per electronic state. The efficiency of the method makes it particularly suitable for future application together with direct dynamics, calculating potentials on the fly.

Quantum mechanics with the basis set guided by Ehrenfest trajectories: Theory and application to spin-boson model

In this article a method of numerical solution of the Schrodinger equation is proposed. The approach corrects the Ehrenfest approximation by using several trajectories/configurations with their amplitudes coupled within and across configurations, thus making the method formally exact. Accurate results are obtained for the spin-boson model with up to 2000 bath modes treated on fully quantum level without approximations.

Ab initio multiple cloning algorithm for quantum nonadiabatic molecular dynamics

We present a new algorithm for ab initio quantum nonadiabatic molecular dynamics that combines the best features of ab initio Multiple Spawning (AIMS) and Multiconfigurational Ehrenfest (MCE) methods. In this new method, ab initio multiple cloning (AIMC), the individual trajectory basis functions (TBFs) follow Ehrenfest equations of motion (as in MCE). However, the basis set is expanded (as in AIMS) when these TBFs become sufficiently mixed, preventing prolonged evolution on an averaged potential energy surface. We refer to the expansion of the basis set as cloning, in analogy to the spawning procedure in AIMS. This synthesis of AIMS and MCE allows us to leverage the benefits of mean-field evolution during periods of strong nonadiabatic coupling while simultaneously avoiding mean-field artifacts in Ehrenfest dynamics. We explore the use of time-displaced basis sets, trains, as a means of expanding the basis set for little cost. We also introduce a new bra-ket averaged Taylor expansion (BAT) to approximate the necessary potential energy and nonadiabatic coupling matrix elements. The BAT approximation avoids the necessity of computing electronic structure information at intermediate points between TBFs, as is usually done in saddle-point approximations used in AIMS. The efficiency of AIMC is demonstrated on the nonradiative decay of the first excited state of ethylene. The AIMC method has been implemented within the AIMS-MOLPRO package, which was extended to include Ehrenfest basis functions.

Formation and dynamics of hot-precursor hydrogen atoms on metal surfaces: Trajectory simulations and stochastic models

The results of a theoretical study of H atoms colliding with a Cu(111) surface are presented. The metal is treated as a five-layer slab of 150 atoms, and all dynamics are classical. The formation of trapped “hot-precursor” atoms on the surface is examined, as well as the nature of their motion on the surface and their energy and momentum dissipation. Connections are made with recent Eley–Rideal experiments, for which hot-atom precursors may play an important role. To facilitate future simulations of Eley–Rideal and hot-atom reactions on metals, simple stochastic models are developed to describe hot-atom energy dissipation. A Fokker–Planck equation is used to model the hot-atom energy distribution. Quasi-Langevin terms, which simulate fluctuation and dissipation consistent with this Fokker–Planck description, are developed for the hot-atom equations of motion. These quasi-Langevin terms are different from the hydrodynamic forms used for Brownian-type motion.

Real time quantum propagation on a Monte Carlo trajectory guided grids of coupled coherent states: 26D simulation of pyrazine absorption spectrum.

In this work we apply the coupled coherent states technique of quantum molecular dynamics to simulation of the absorption spectrum of pyrazine. All 24 vibrational modes are taken into account. The nonadiabatic coupling obetween the S(1) and S(2) electronic states is treated by a mapping approach that adds two extra degrees of freedom to the effective vibronic Hamiltonian. The results are in a good agreement with experiment and with previous calculations by quantum multiconfigurational time dependent Hartree and semiclassical Herman-Kluk methods.