Multireference Correlated Oscillator Strengths from Adiabatic Connection Approaches Based on Extended Random Phase Approximation

Abstract

We show that accurate oscillator strengths can be obtained from adiabatic connection (AC) approaches based on the extended random phase approximation (ERPA) combined with multireference (complete active space, CAS) wave functions. The oscillator strengths calculated using the perturbation-corrected ERPA transition density matrices, proposed in this work, and the excitation energies calculated with recently introduced AC correlation energy methods, AC0 and AC0D, compete with accuracy in the perturbational CASPT2 approach and require less computational effort. AC0 and AC0D methods scale more favorably with the number of active orbitals than multiconfigurational perturbation approaches like CASPT2 and NEVPT2 thanks to their dependence on reduced density matrices up to the order of 2. Importantly, the newly developed approach for computing correlated transition dipole moments does not entail any additional costs, as all intermediate quantities become available when AC0 energies are being computed. We also test the performance of the recently proposed AC method corrected for the negative-transition contributions to the correlation energy, AC0D, for triplet excitation energies. Similarly, as for the singlet excitations, the correction improves the performance of the AC0 method, particularly for the low-lying excited states.

Figure 1

Terms included in the exact AC, see eq 7, the AC0 and AC0D approximations, cf. eq 20.

Figure 2

Triplet excitation energies in relation to the CC3 results. All values in eV.

Figure 3

MUE of oscillator strengths in reference to CC3 values.

Figure 4

TDMs d_ν⁽⁰⁾, d_ν⁽¹⁾, and d_ν^CAS for single excitations of molecules vs TDMs computed with CC3 method. Inset: mean unsigned errors of TDMs w.r.t. CC3 values.