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When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon…
We present a simple algorithm to switch between $N$-body time integrators in a reversible way. We apply it to planetary systems undergoing arbitrarily close encounters and highly eccentric orbits, but the potential applications are broader.…
Nonadiabatic dynamical processes are one of the most important quantum mechanical phenomena in chemical, materials, biological, and environmental molecular systems, where the coupling between different electronic states is either inherent…
The Constrained Adiabatic Trajectory Method (CATM) is reexamined as an integrator for the Schr\"odinger equation. An initial discussion places the CATM in the context of the different integrators used in the literature for time-independent…
Nonadiabatic ring-polymer molecular dynamics employs the mapping approach to describe nonadiabatic effects within the ring-polymer ansatz. In this paper, it is generalized to allow for the nuclear and electronic degrees of freedom to be…
A general theoretical framework is derived for the recently developed multi-state trajectory (MST) approach from the time dependent Schr\"odinger equation, resulting in equations of motion for coupled nuclear-electronic dynamics equivalent…
Non-adiabatic chemical reactions involving continuous circularly polarized light (cw CPL) have not attracted as much attention as dynamics in unpolarized/linearly polarized light. However, including circularly (in contrast to linearly)…
The recent improvement in experimental capabilities for interrogating and controlling molecular systems with ultrafast coherent light sources calls for the development of theoretical approaches that can accurately and efficiently treat…
We investigate two well-known approaches for extending the fewest switches surface hopping (FSSH) algorithm to periodic time-dependent couplings. The first formalism acts as if the instantaneous adiabatic electronic states were standard…
We introduce a high-performance simulation framework that permits the semi-independent, task-based solution of sets of partial differential equations, typically manifesting as updates to a collection of `patches' in space-time. A hybrid…
Ring Polymer Surface-Hopping (RPSH) has been recently introduced as a well-tailored method for incorporating nuclear quantum effects (NQEs), such as zero-point energy and tunneling, into non-adiabatic molecular dynamics simulations. The…
Trajectory surface hopping (TSH) is one of the most widely used quantum-classical algorithms for nonadiabatic molecular dynamics. Despite its empirical effectiveness and popularity, a rigorous derivation of TSH as the classical limit of a…
We present two types of meta-algorithm that can greatly improve the accuracy of existing algorithms for integrating the equations of motion of dynamical systems. The first meta-algorithm takes an integrator that is time-symmetric only for…
Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we…
This study introduces the FSSH-2 scheme, a redefined and numerically stable adiabatic Fewest Switches Surface Hopping (FSSH) method for mixed quantum-classical dynamics. It reformulates the standard FSSH hopping probability without…
The application of nonlinear control schemes to electro-hydraulic actuators often requires several alterations in the design of the controllers during their implementation. This is to overcome challenges that frequently arise in such…
Intersystem crossing is a radiationless process that can take place in a molecule irradiated by UV-Vis light, thereby playing an important role in many environmental, biological and technological processes. This paper reviews different…
We demonstrate an approach to the numerical solution of nonlinear stochastic differential equations with Markovian switching. Such equations describe the stochastic dynamics of processes where the drift and diffusion coefficients are…
We present a new method, called SISYPHUS (Stochastic Iterations to Strengthen Yield of Path Hopping over Upper States), for extending accessible time-scales in atomistic simulations. The method proceeds by separating phase space into…
In the study of non-adiabatic chemical processes such as photocatalysis and photosynthesis, non-adiabatic molecular dynamics (NAMD) is an indispensable theoretical tool, which requires precise potential energy surfaces (PESs) of ground and…