Assessment of time-dependent density functional theory with the restricted excitation space approximation for excited state calculations of large systems

Abstract

The restricted excitation subspace approximation is explored as a basis to reduce the memory storage required in linear response time-dependent density functional theory (TDDFT) calculations within the Tamm-Dancoff approximation. It is shown that excluding the core orbitals and up to 70% of the virtual orbitals in the construction of the excitation subspace does not result in significant changes in computed UV/vis spectra for large molecules. The reduced size of the excitation subspace greatly reduces the size of the subspace vectors that need to be stored when using the Davidson procedure to determine the eigenvalues of the TDDFT equations. Furthermore, additional screening of the twoelectron integrals in combination with a reduction in the size of the numerical integration grid used in the TDDFT calculation leads to significant computational savings. The use of these approximations represents a simple approach to extend TDDFT to the study of large systems and make the calculations increasingly tractable using modest computing resources.

Broadband X-Ray Absorption Spectra from Time-Dependent Kohn-Sham Calculations

“…S1d compares the oxygen K-edge LR-TDDFT spectrum for methionine using this reduced excitation space, versus the one that is computed using the full excitation space. This results in very little change to the spectrum, consistent with LR-TDDFT results reported by Besley and co-workers, 57,59 and with the general validity of core/valence separation for K-edge excitations. 34 The TDA (eq.…”

“…This LR-TDDFT formalism has been adapted for the calculation of core excitation spectra using frozen occupied orbitals, 6,33,[57][58][59] i.e., core/valence separation. We will compare this LR-TDDFT approach to the TKDS approach, for benchmark purposes and to highlight advantages of the latter formalism.…”

TD-DFT simulations of K-edge resonant inelastic X-ray scattering within the restricted subspace approximation

“…The convergence of the RIXS spectrum with respect to the truncation used in the RSA is found to be rapid, as also observed for UV-vis transitions. 29 Moreover, the RSA enables a consistent description of both coreand valence-excited states. This set of states can be used, in future applications, to simulate full RIXS planes and intermediate-state interference can be treated intrinsically.…”

“…As the excitation energy is tuned beyond the core-ionization threshold, the scattering cross-section is overtaken by the non-resonant emission process. Furthermore, restricting the virtual space in TD-DFT has been proposed early on as a means for tackling states for adsorbed molecules as well as molecules in solution, [41][42][43] and it has been shown to also be a suitable route to obtaining excited states energies, 29 geometries 44 and vibrational frequencies 45 of large systems. Virtual space restriction has also been successfully used in RIXS simulations at the L-edge of transition metal complexes within the multi-configurational Kohn-Sham ROCIS method.…”

“…26,27 In contrast, the application of standard linear-response time-dependent DFT (LR-TD-DFT) to RIXS has been largely unexplored and remains limited to a few isolated instances. 28 In this work we investigate the applicability of LR-TD-DFT within the Restricted Subspace Approximation 29 (RSA) to K-edge RIXS spectroscopy. A consistent description of both core-and valence-excited states is achieved by a pragmatic truncation of the orbital spaces, thus enabling computations of RIXS crosssections in a near black-box fashion.…”