Bridging the Gap Between Variational and Perturbational DFT-based Methods for Calculating Excited States
Obtaining the excited electronic states and their properties is a vital part of simulating photochemical reactions. The most precise wavefunction-based methods scale poorly with the system size, which sparkled the development of density functional theory (DFT)-based perturbational methods like Linear-Response Time-Dependent DFT also known as TDDFT. It is affordable, but comes with certain drawbacks, as it fails to describe the charge transfer and Rydberg states. On top of that, the multi-electron excitations cannot be simulated by TDDFT due to the adiabatic approximation. Variational DFT-based methods are a promising alternative which should alleviate the aforementioned issues.1 However, they require a good initial guess as well as some sort of verification procedure to ensure that the resulting excited state is the one we need.
A restricted-open Kohn--Sham delta self-consistent field (ROKS-ΔSCF) approach allows for direct calculation of unmixed singlet and triplet excited electronic states without the need for spin purification.2 With a proper initial guess, i.e. the fractional occupation numbers which can be obtained e.g. from a TDDFT calculation, and a molecular orbital tracking procedure to rectify the root flipping during the diagonalization, even distinctly multi-reference states with no clearly dominant contribution can be targeted and converged which, to our best knowledge, has not been achieved before.3 The previously developed method for calculating the transition dipole moments4 has been extended to the multi-reference states as well. Moreover, we conducted a large-scale benchmark and demonstrated that the excited electronic states converged with our ROKS-ΔSCF method are indeed the targeted ones in every case by comparing the electron density differences and transition dipole moments with both TDDFT and the second-order algebraic diagrammatic construction method.
[1] Nicola Bogo, Christopher J. Stein, Physical Chemistry Chemical Physics, 2024, 26, 21575-21588
[2] Eva Vandaele, Momir Mališ, Sandra Luber, Journal of Chemical Physics 2022, 156, 130901
[3] Andrey Sinyavskiy, Momir Mališ, Sandra Luber, in revision
[4] Momir Mališ, E. Vandaele, Sandra Luber, Journal of Chemical Theory and Computation 2022, 18, 4082