Efficient electron dynamics with the planewave-based real-time time-dependent density functional theory: absorption spectra, vibronic electronic spectra, and coupled electron-nucleus dynamics.

The electron dynamics with complex third-order Suzuki-Trotter propagator (ST(3)) has been implemented into a planewave (PW) based density functional theory program, and several applications including linear absorption spectra and coupled electron-nucleus dynamics have been calculated. Since the ST(3) reduces the number of Fourier transforms to less than half compared to the fourth-order Suzuki-Trotter propagator (ST(4)), more than twice faster calculations are possible by exploiting the ST(3). We analyzed numerical errors of both the ST(3) and the ST(4) in the presence∕absence of an external field for several molecules such as Al(2), N(2), and C(2)H(4). We obtained that the ST(3) gives the same order of numerical errors (10(-5) Ry after 100 fs) as the ST(4). Also, the time evolution of dipole moments, hence the absorption spectrum, is equivalent for both ST(3) and ST(4). As applications, the linear absorption spectrum for an ethylene molecule was studied. From the density difference analysis, we showed that the absorption peaks at 6.10 eV and 7.65 eV correspond to the π → 4a(g) and π → π* excitation bands, respectively. We also investigated the molecular vibrational effect to the absorption spectra of an ethylene molecule and the dynamics of a hydrogen molecule after the σ → σ* transition by formulating coupled electron-nucleus dynamics within the Ehrenfest regime. The trajectory of nuclei follows the excited state potential energy curve exactly.