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

Abstract

Articles you may be interested inA time-dependent density-functional theory and complete active space self-consistent field method study of vibronic absorption and emission spectra of coumarin J. Chem. Phys. 141, 014306 (2014) 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 fourthorder 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.

Linear scaling density matrix real time TDDFT: Propagator unitarity and matrix truncation

“…Where possible, in order to more confidently assign peaks of our calculated absorption spectra to particular electronic transitions, we have followed the procedure in Ref. 26 whereby a sinusoidal electric field tuned to a particular excitation mode is applied. A resulting electronic resonance is set up, allowing us to examine the difference between ground state charge density and excited state charge density and thereby infer the electronic transition.…”

Real-Time Propagation via Time-Dependent Density Functional Theory Plus the Hubbard U Potential for Electron–Atom Coupled Dynamics Involving Charge Transfer

“…The dynamics of atomic systems are typically modeled within the Born–Oppenheimer approximation (BOA), which presumes that atomic velocities are negligibly slow compared with the electronic relaxation speed; thus, the electronic state is believed to be in the ground state of a given instantaneous atomic configuration, whereas the atoms follow the classical path of the potential energy surface (PES). Methods that extend beyond the BOA have been tried by theorists, and one area of progress from this perspective is the real-time propagation of the time-dependent density functional theory (rtp-TDDFT). − In this theory, the Kohn–Sham orbitals evolve through a real-time evolution operator and the forces on atoms at any point in time may be calculated according to the gradient of the total energy of the instantaneous electron density. People have suggested using the rtp-TDDFT to model electron–atom coupled dynamics and to calculate the absorption spectra, which, in principle, can include the vibrational excitations.…”

Real-Space and Real-Time Propagation for Correlated Electron–Nuclear Dynamics Based on Exact Factorization

“…On the other hand, for extended molecular systems, such quantum chemical calculations are impractical especially for excited state molecular dynamics simulations. Instead, there is a framework, namely the real-time time-dependent density functional theory (RT-TDDFT), − which propagates electronic density in terms of Kohn–Sham (KS) orbitals with time-dependent external potentials. By treating electron–nuclear potentials with moving nuclear trajectory boldR true7pt ( t ) = { R 1 false( t false) , ... , R ν false( t false) , ··· } as a source of time-dependence where ν is a nuclear index, one can derive Ehrenfest-type equations of motion as i false| normalΦ̇ R  ( t ) false⟩ = Ĥ ( t ; R  ) false| Φ R  false( t false) false⟩ and boldF ν E h = prefix− normal∇ ν E [ ρ R  false( t false...…”