Role of Core Electrons in Quantum Dynamics Using TDDFT

Abstract

The explicit simulation of time dependent electronic processes requires computationally onerous routes involving the temporal integration of motion equations for the charge density. Efficiency optimization of these methods typically relies on increasing the integration time-step and on the reduction of the computational cost per step. The implicit representation of inner electrons by effective core potentials-or pseudopotentials-is a standard practice in localized-basis quantum-chemistry implementations to improve the efficiency of ground-state calculations, still preserving the quality of the output. This article presents an investigation on the impact that effective core potentials have on the overall efficiency of real time electron dynamics with TDDFT. Interestingly, the speedups achieved with the use of pseudopotentials in this kind of simulation are on average much more significant than in ground-state calculations, reaching in some cases a factor as large as 600×. This boost in performance originates from two contributions: on the one hand, the size of the density matrix, which is considerably reduced, and, on the other, the elimination of high-frequency electronic modes, responsible for limiting the maximum time-step, which vanish when the core electrons are not propagated explicitly. The latter circumstance allows for significant increases in time-step, that in certain cases may reach up to 3 orders of magnitude, without losing any relevant chemical or spectroscopic information.

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

“…43,44 ) are employed. If excitations out of core orbitals or other high energy excitations are not of interest, then a frozen core approximation, 45 or else a more general active-space implementation, 34 can be used remove the highest-frequency components. On the other hand, these high-lying excitations are actually attractive targets for a real-time implementation due to the iterative nature of LR-TDDFT algorithms, whose cost scales with the number of excited states that are needed and thus becomes very expensive for high-energy excitations.…”

Chemical Reactivity and Spectroscopy Explored From QM/MM Molecular Dynamics Simulations Using the LIO Code

“…The later varies with the type of atoms in the QM zone and can be extended by using better propagators and/or freezing the inner electron density through the use of pseudopotentials. For a more detailed discussion please refer to Foglia et al ( 2017 ). Table 2 illustrates the performance of TDDFT calculations comparing the full electron scheme with a pseudopotential approach.…”

“… Effective core potentials and full-electron calculations were carried out with CEP and DZVP basis sets, respectively. Data from Foglia et al ( 2017 ) . …”

“…The use of pseudopotentials, recently made available in the code (Foglia et al, 2017 ), is fundamental to perform real time TDDFT simulations with transition metals and heavy atoms. The time-propagation of the core electrons, with high characteristic frequencies, demands integration time-steps that may be orders of magnitude below those required for the integration of the valence density.…”

Periodic DFT Calculations—Review of Applications in the Pharmaceutical Sciences

“…In most cases, the electrons of the inner shells (core electrons) are tightly bound and are not involved in the chemical binding. In most organic molecules, binding is solely due to the valence electrons [47]. This separation means that in a large number of cases the atom can be reduced to an ionic core that interacts with the valence electrons.…”