Exponential Integrator Methods in Time-Dependent Density Functional Calculations

The integrating factor and exponential time differencing methods are implemented and tested within one-dimensional time-dependent density functional theory. Popular time propagation methods used in physics are also tested and compared to these exponential integrator methods. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven by nonlinear potentials using fourth-order Runge–Kutta-type exponential integrators. 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.