State-Specific Configuration Interaction for Excited States

Abstract

We introduce and benchmark a systematically improvable route for excited-state calculations, labeled state-specific configuration interaction (ΔCI), which is a particular realization of multiconfigurational self-consistent field and multireference configuration interaction. Starting with a reference built from optimized configuration state functions, separate CI calculations are performed for each targeted state (hence, state-specific orbitals and determinants). Accounting for single and double excitations produces the ΔCISD model, which can be improved with second-order Epstein-Nesbet perturbation theory (ΔCISD+EN2) or a posteriori Davidson corrections (ΔCISD+Q). These models were gauged against a vast and diverse set of 294 reference excitation energies. We have found that ΔCI is significantly more accurate than standard ground-state-based CI, whereas close performances were found between ΔCISD and EOM-CC2 and between ΔCISD+EN2 and EOM-CCSD. For larger systems, ΔCISD+Q delivers more accurate results than EOM-CC2 and EOM-CCSD. The ΔCI route can handle challenging multireference problems, singly and doubly excited states, from closed- and open-shell species, with overall comparable accuracy and thus represents a promising alternative to more established methodologies. In its current form, however, it is reliable only for relatively low-lying excited states.

Figure 1

Types of configuration state functions (CSFs) employed as a reference for different classes of excited states in our ΔCSF and ΔCISD approaches.

Figure 2

Distribution of errors in excitation energies with respect to reference theoretical values and the corresponding mean signed error (MSE) and mean absolute error (MAE) for various excited-state methodologies.

Figure 3

Distribution of errors in excitation energies with respect to reference theoretical values and corresponding mean signed error (MSE) and mean absolute error (MAE), for various forms of the Davidson-corrected ΔCISD+Q models. The different types of Davidson corrections can be found in ref (23).