Nonadiabatic Dynamics for Electrons at Second-Order: Real-Time TDDFT and OSCF2

Abstract

We develop a new model to simulate nonradiative relaxation and dephasing by combining real-time Hartree-Fock and density functional theory (DFT) with our recent open-systems theory of electronic dynamics. The approach has some key advantages: it has been systematically derived and properly relaxes noninteracting electrons to a Fermi-Dirac distribution. This paper combines the new dissipation theory with an atomistic, all-electron quantum chemistry code and an atom-centered model of the thermal environment. The environment is represented nonempirically and is dependent on molecular structure in a nonlocal way. A production quality, O(N(3)) closed-shell implementation of our theory applicable to realistic molecular systems is presented, including timing information. This scaling implies that the added cost of our nonadiabatic relaxation model, time-dependent open self-consistent field at second order (OSCF2), is computationally inexpensive, relative to adiabatic propagation of real-time time-dependent Hartree-Fock (TDHF) or time-dependent density functional theory (TDDFT). Details of the implementation and numerical algorithm, including factorization and efficiency, are discussed. We demonstrate that OSCF2 approaches the stationary self-consistent field (SCF) ground state when the gap is large relative to k(b)T. The code is used to calculate linear-response spectra including the effects of bath dynamics. Finally, we show how our theory of finite-temperature relaxation can be used to correct ground-state DFT calculations.

Self-consistent predictor/corrector algorithms for stable and efficient integration of the time-dependent Kohn-Sham equation

“…The proposed algorithms were implemented in the Q-Chem program, 51 building upon the initial TDKS implementation in Q-Chem that was reported by Nguyen and Parkhill. 36 These algorithms are available starting from v. 5.0 of the code. Most calculations reported here use either the PBE 52 or the LRC-ωPBEh 53 density functional, and the 6-31G(d) basis set, although other functionals and basis sets are briefly considered to demonstrate that these results are indeed representative.…”

“…while retaining numerical stability and energy-conserving dynamics. Although the MMUT algorithm requires only a single Fock matrix construction per time step, whereas the self-consistent approaches require more than one, the MMUT approach is restricted to the use of time steps no larger than 0.2-0.5 a.u., 35,[39][40][41] and sometimes as small as 0.05 a.u., [36][37][38] and overall the PC algorithms prove to be a net "win," reducing the average number of Fock builds per unit of simulation time. For most applications, the cost of TDKS calculations in Gaussian basis sets is overwhelmingly dominated by the cost of Fock matrix construction, so this reduction in the number of Fock builds translates directly into speedup of the simulations.…”

“…Following the pulse, the molecule evolves from the ground state into a superposition of states, and if the external field is weak, then this superposition will be dominated by the ground eigenstate, with an excited-state contribution that is dominated by states around 12 eV. In practical applications, the MMUT algorithm requires that much smaller time steps be used, [35][36][37][38][39][40][41] and for good reason: our results demonstrate that this algorithm is no longer stable for ∆t ≥ 0.2 a.u. at the PBE/6-31G(d) level (Fig.…”

“…It is electron dynamics that is propagated, and often the time step ∆t for this propagation is as small as 0.05 a.u. (≈1 as), [36][37][38] although somewhat larger time steps (as large as 0.5 a.u.) have been used in some applications.…”

“…Unlike the LR approach, where the energy spectrum is obtained iteratively starting with the lowest excited state, in RT-TDDFT the entire broad-band spectrum is obtained at once, with resolution that improves upon further time propagation. The RT approach has been implemented in various DFT codes including Octopus, 31 Siesta, 20 Qbox, 32 Gaussian, 33,34 NWChem, 35 and Q-Chem, 36 and has been formulated using real-space grids, 20,31 plane waves, 32 and Gaussian-type orbitals. [33][34][35][36] We focus exclusively on Gaussian-type orbitals in this work.…”