Exponential Integrators in Time-Dependent Density Functional Calculations

Abstract

The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn--Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches, are compared to these exponential integrator methods in order to judge the relative merit of the computational schemes. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven primarily by a nonlinear potential. For cases of dynamics driven by a time-dependent external potential, the accuracy of the exponential integrator methods are less enhanced but still match or outperform the best of the conventional methods tested.

References in corpus (10)

• A real-space, rela-time method for the dielectric function
• Calculation of the optical response of C60 and Na8 using time-dependent density functional theory and local orbitals
• A Krylov subspace algorithm for evaluating the phi-functions appearing in exponential integrators
• Attosecond streaking of correlated two-electron transitions in helium
• A brief compendium of time-dependent density-functional theory
• Explicit exponential Runge-Kutta methods of high order for parabolic problems
• Charge-transfer in time-dependent density-functional theory via spin-symmetry-breaking
• A Chebychev propagator with iterative time ordering for explicitly time-dependent Hamiltonians
• Explicit schemes for time propagating many-body wavefunctions
• Spectral-based Propagation Schemes for Time-Dependent Quantum Systems with Application to Carbon Nanotubes

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• Numerical integration of quantum time evolution in a curved manifold
• INQ, a modern GPU-accelerated computational framework for (time-dependent) density functional theory
• Time-dependent Hole States in Multiconfigurational Time-Dependent Hartree-Fock Approaches: Applications in Photoionization of Water Molecule
• Implementation of a time-dependent multiconfiguration self-consistent-field method for coupled electron-nuclear dynamics in diatomic molecules driven by intense laser pulses