Benchmarks for Electronically Excited States with CASSCF Methods

Abstract

The accuracy of three different complete active space (CAS) self-consistent field (CASSCF) methods is investigated for the electronically excited-state benchmark set of Schreiber , M. ; et al. J. Chem. Phys. 2008 , 128 , 134110 . Comparison of the CASSCF linear response (LR) methods MC-RPA and MC-TDA and the state-averaged (SA) CASSCF method is made for 122 singlet excitation energies and 69 oscillator strengths. Of all CASSCF methods, when considering the complete test set, MC-RPA performs best for both excitation energies and oscillator strengths with a mean absolute error (MAE) of 0.74 eV and 51%, respectively. MC-TDA and SA-CASSCF show a similar accuracy for the excitation energies with a MAE of ∼1 eV with respect to more accurate coupled cluster (CC3) excitation energies. The opposite trend is observed for the subset of n → π* excitation energies for which SA-CASSCF exhibits the least deviations (MAE 0.65 eV). By looking at s-tetrazine in more detail, we conclude that better performance for the n → π* SA-CASSCF excitation energies can be attributed to a fortunate error compensation. For oscillator strengths, SA-CASSCF performs worst for the complete test set (MAE 100%) as well as for the subsets of n → π* (MAE 192%) and π → π* excitations (MAE 84.9%). In general, CASSCF gives the worst performance for excitation energies of all excited-state ab initio methods considered so far due to lacking the major part of dynamic electron correlation, though MC-RPA and TD-DFT (BP86) show similar performance. Among all LR-type methods, LR-CASSCF oscillator strengths are the ones with the least accuracy for the same reason. As state-specific orbital relaxation effects are accounted for in LR-CASSCF, oscillator strengths are significantly more accurate than those of MS-CASPT2. Our findings should encourage further developments of response theory-based multireference methods with higher accuracy and feasibility.

Figure 1

Normal distribution of deviation from the CC3 reference singlet excitation energies of the complete test set and subsets of n → π* and π → π* excitations.

Figure 2

Lowest singlet excitation energies of s-tetrazine with different CASSCF methods and CC3. Solid lines are n → π* excitations; dashed lines are π → π* excitations.

Figure 3

Normal distribution of deviation from the CC3 reference singlet excitation energies computed with various methods.

Figure 4

Normal distribution of deviation from the CC3 reference oscillator strengths of the complete test set and subsets of n → π* and π → π* excitations.

Figure 5

Normal distribution of deviation from the CC3 reference oscillator strengths computed with various methods.