# Molecular dynamics simulations

- Non-adiabatic molecular dynamics
- Classical Monte Carlo methods
- Quantum Monte Carlo methods
- Global and local optimization methods for molecular structures predictions

The field of molecular simulations comprises theoretical and/or computational methods for modeling physical and chemical properties of molecules and their assemblies via computational approaches. They naturally split into two basic sub-families, molecular dynamics methods and Monte Carlo methods. The former are based on the numerical solution of dynamical equations of motion of the system, and the latter employ various ensembles approaches of statistical physics. A couple of other branches of computational science, like molecular structures optimizations or molecular interactions modeling, are tightly connected with the field of molecular simulations as well.

## Non-adiabatic molecular dynamics

Molecular dynamics methods mean numerical integration of sets of dynamical equations of motion for representative sets of initial conditions and using the integrated trajectories in subsequent calculations of various properties of the system under study. Usually, the electronic degrees of freedom are included via adiabatic potential energy surface, and jumps between different electronic states are not considered. However, this may be a rather strong restriction in many interesting situations, photochemistry, or high-energy collisions being well known examples. If electronic jumps have to be included, methods of non-adiabatic molecular dynamics become necessary. As a computationally practicable approach, classical equations of motion are solved for atomic nuclei, and quantum Schrödinger equation is used for electrons. In our work, we use one of such semiclassical approaches, based on the Ehrenfest, a mean-field approach with the inclusion of quantum decoherence, in simulations of non-adiabatic processes in ionic rare-gas clusters. Specific directions of our research in this field are, for example, post-excitation dynamics of ionic rare-gas clusters and the dynamics of elementary collision processes in rare-gas plasmas.

## Classical Monte Carlo methods

Classical Monte Carlo methods employ the machinery of Markovian chains in computational implementations of ensemble methods of classical statistical physics. The principal focus of our work lies in parallel implementations of sophisticated approaches with accelerated convergence, like parallel-tempering approaches and multidimensional multiple histogram methods. One of the aims of our work consists in the parallelization of such calculations and in connecting our simulation programs with quantum chemistry methods for electronic structure calculations. Presently, molecular clusters (water clusters with dopants) represent the main object of our research.

## Quantum Monte Carlo methods

The Monte Carlo methods are, among others, well suited for numerical solving of the stationary Schrodinger equation for systems of many bosons (and after some modifications also for fermions). They can be used, to give a few examples, in evaluations of multidimensional integrals in the variational approach (variational Monte Carlo), simulations of relaxation of many-particle wave function to the ground state one by mimicking diffusion in imaginary time (diffusion Monte Carlo), or by employing Feynman’s path-integral approach for evaluating quantum canonical ensemble averages via classical Monte Carlo approaches (path-integral Monte Carlo). In our work, the former two approaches are used to study zero-temperature properties of selected atomic clusters and the latter for simulations at non-zero temperatures. Main attention is presently paid to clusters of ionized helium.

## Global and local optimization methods for molecular structures predictions

The first step toward understanding physical and chemical properties of a molecular system consists usually in recognizing their geometric structure. It means that global and local minima (structural isomers) and saddle points (transition structures) are to be found on (usually) the ground-state potential energy surface. The minima provide us at least with the qualitative information of how the system will behave under various situations and at not too high temperatures, the saddle points then give us some idea about transition processes between various structural isomers of the system. In our work, we use stochastic algorithms, either evolutionary or Monte Carlo based, for structural calculations on atomic and molecular clusters. Genetic algorithms, swarm-intelligence approaches, simulated annealing, and the Monte Carlo basin-hopping method are examples of the methodologies we use.

Web pages of the subgroup Molecular dynamics.