Benchmarks for Electronically Excited States with CASSCF Methods.

Benjamin Helmich-Paris

doi:10.1021/acs.jctc.9b00325

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 SchreiberM.; et al. J. Chem. Phys.2008, 128, 13411018397056. 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.

Highlights

In 2008, Schreiber et al established a benchmark set of 28 closed-shell organic molecules that are intended to represent the most important classes of chromophors,[1] which is commonly referred to as Thiel’s test set
We examine the accuracy of three different CASSCF methods for excited states
Singlet excitation energies were computed with multiconfigurational random phase approximation (MC-RPA), MC-TDA, and SA-CASSCF for a subset of the original benchmark set of ref 1, which in the present study comprises 122 π → π*, n → π*, and σ → π* excitations for the TZVP basis set altogether

Summary

Introduction

In 2008, Schreiber et al established a benchmark set of 28 closed-shell organic molecules that are intended to represent the most important classes of chromophors,[1] which is commonly referred to as Thiel’s test set. On the basis of their results[1,10,11] and on previously published literature data, best estimates for each excited state in the test set were proposed that served as reference values in later studies. The same benchmark set has been employed in subsequent studies by many groups to assess the accuracy of a plethora of excited-state electronic structure methods that were not covered in Thiel’s test set[1] originally. Silva-Junior et al.[12] reported time-dependent density functional theory (TDDFT)[13,14] calculations with standard density functionals (BP86,15,16 B3LYP,[15,17,18] and BHLYP17,19) as well as calculations with the semiempirical DFT-based multireference configuration interaction (DFT/MRCI) method.[20,21] The

Methods

Results

Conclusion