Quantum dynamics of molecules poses a variety of computational challenges that are
presently at the forefront of research efforts in numerical analysis in a number of application …

Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous
Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the …

This overview is devoted to splitting methods, a class of numerical integrators intended for
differential equations that can be subdivided into different problems easier to solve than the …

We provide a comprehensive survey of splitting and composition methods for the numerical
integration of ordinary differential equations (ODEs). Splitting methods constitute an …

Time-dependent electronic structure methods are growing in popularity as tools for modeling
ultrafast and/or nonlinear processes, for computing spectra, and as the electronic structure …

The computation of the semiclassical Schrödinger equation presents major challenges
because of the presence of a small parameter. Assuming periodic boundary conditions, the …

Several different numerical propagation techniques for explicitly time-dependent
Hamiltonians are discussed and compared, with the focus on models of pump-probe …

The finite-difference time-domain (FDTD) method is a widely used numerical technique for
solving Maxwell's equations. FDTD has also been applied to numerically solve the …

Cheap and easy to implement fourth-order methods for the Schrödinger equation with time-
dependent Hamiltonians are introduced. The methods require evaluations of exponentials of …

In mixed quantum-classical nonadiabatic molecular dynamics methods, the anchoring of the
electronic wave function to a single nuclear geometry results in both quantitative and …