Background

The time dependent density functional theory (TDDFT)

Reference
E. Runge and E. K. U. Gross, 'Density-Functional Theory for Time-Depndent Systems', Phys. Rev. Lett. 52, 997 (1984)

A brief description of TDDFT and FPSEID²¹

To describe many-body interaction of electrons in condensed matters, one of popular approximation is the density functional theory (DFT) in which the many-body interaction was represented by exchange-correlation potential as a functional of the electron charge density. The one-to-one relation between the charge density and external potential for electrons given in the system was derived. On the other hand, the TDDFT expanded the one-to-one relation for the time-varying charge density and the time-varying external potential that enabled us to numerically trace the dynamics of electrons under time-varying external potential, for instance, high-speed ion motion, optical field, dynamical electronic field, and so on. Furthermore, the time-varying charge density causes modulation in the classical force field on ions (with some levels of approximation) that enables us to play Newton’s dynamics of ions under electronic excitations.The FPSEID²¹ code can perform molecular dynamics simulation of periodic (extended) systems under electronic excitation by optical field as described in the velocity gauge (introduction of the vector potentials) within the scheme of the local density approximation (LDA) as well as the generalized gradient approximation (GGA) employing the norm-conserving pseudopotentials and the plane-wave basis set. The time-evolution of electron wavefunction (time-dependent Kohn-Sham orbitals) was numerically obtained by the split-operator scheme. All details were published in [O. Sugino and Y. Miyamoto, ‘Density-functional approach to electron dynamics: stable simulation under a self-consistent field’, Phys. Rev. B59, 2579 (1999)] and [Y. Miyamoto, ‘Direct treatment of interaction between laser-field and electrons for simulating laser processing of metals’, Scientific Reports, 11, 14626 (2021)]
   Note that the code works within hybrid scheme of parallel computing with use of MPI and OPENMP, but it is recommended to run with option of 'OMP_NUM_THREAD=1' which suits many HPC systems. The parallelization is made for band-index, while G-vector parallelization for the plane-wave basis has not been implemented.