Related papers: High-order geometric integrators for representatio…
Density functional theory with linear combination of atomic orbitals (LCAO) basis sets is useful for studying large atomic systems, especially when it comes to computationally highly demanding time-dependent dynamics. We have implemented…
Quantum dynamics (e.g., the Schr\"odinger equation) and classical dynamics (e.g., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. The difference between both worlds is due to the…
We introduce new Langevin-type equations describing the rotational and translational motion of rigid bodies interacting through conservative and non-conservative forces, and hydrodynamic coupling. In the absence of non-conservative forces…
The explicit split-operator algorithm has been extensively used for solving not only linear but also nonlinear time-dependent Schr\"{o}dinger equations. When applied to the nonlinear Gross-Pitaevskii equation, the method remains…
We design a quantum molecular dynamics method for strongly correlated electron metals. The strong electronic correlation effects are treated within a real-space version of the Gutzwiller variational approximation (GA), which is suitable for…
Application of the time-dependent variational principle to a linear combination of frozen-width Gaussians describing the nuclear wavefunction provides a formalism where the total energy is conserved. The computational downside of this…
The combined quantum electron-nuclear dynamics is often associated with the Born-Huang expansion of the molecular wave function and the appearance of nonadiabatic effects as a perturbation. On the other hand, native multicomponent…
We present a new implicit asymptotic preserving time integration scheme for charged-particle orbit computation in arbitrary electromagnetic fields. The scheme is built on the Crank-Nicolson integrator and continues to recover full-orbit…
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…
Experiments indicate that collective coupling of molecular ensembles to confined optical modes can modify excited-state dynamics and photochemical reactivity. To describe such cavity-induced effects at atomic resolution, semi-classical…
Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. In this paper we present a method to construct symplectic-momentum integrators for…
The long-time behaviour of splitting integrators applied to nonlinear Schr\"odinger equations in a weakly nonlinear setting is studied. It is proven that the energy is nearly conserved on long time intervals. The analysis includes all…
Solving the time-dependent Schr\"odinger equation (TDSE) is pivotal for modeling non-adiabatic electron dynamics, a key process in ultrafast spectroscopy and laser-matter interactions. However, exact solutions to the TDSE remain…
We propose to measure nonadiabaticity of molecular quantum dynamics rigorously with the quantum fidelity between the Born-Oppenheimer and fully nonadiabatic dynamics. It is shown that this measure of nonadiabaticity applies in situations…
Incorporating nuclear quantum effects into nonadiabatic dynamics remains a significant challenge. Herein we introduce new nonadiabatic dynamics approaches based on the recently developed constrained nuclear-electronic orbital (CNEO) theory.…
We study the semiclassical Ehrenfest trajectories in open quantum systems. We first derive in explicit form the Fokker-Planck equation that governs the time evolution of the mixing measure for a Gaussian mixture. Then, we embed the…
We present an approach for carrying out non-adiabatic molecular dynamics simulations of systems in which non-adiabatic transitions arise from the coupling between the classical atomic motions and a quasi-continuum of electronic quantum…
We present a program package for the simulation of ultrafast vibration-induced autoionization dynamics in molecular anions in the manifold of the adiabatic anionic states and the discretized ionization continuum. This program, called…
In this work we introduce a geometric integrator for molecular dynamics simulations of physical systems in the canonical ensemble. In particular, we consider the equations arising from the so-called density dynamics algorithm with any…
We present a time-reversible Born-Oppenheimer molecular dynamics scheme, based on self-consistent Hartree-Fock or density functional theory, where both the nuclear and the electronic degrees of freedom are propagated in time. We show how a…