Calculations of n →π* Transition Energies: Comparisons Between TD-DFT, ADC, CC, CASPT2, and BSE/ GW Descriptions
Résumé
Using a large panel of theoretical approaches, namely, CC2, CCSD, CCSDR(3), CC3, ADC(2), ADC(3), CASPT2, time-dependent density functional theory (TD-DFT), and BSE/evGW, the two latter combined with different exchange-correlation functionals, we investigate the lowest singlet transition in 23 n→π* compounds based on the nitroso, thiocarbonyl, carbonyl, and diazo chromophores. First, for 16 small derivatives we compare the transition energies provided by the different wave function approaches to define theoretical best estimates. For this set, it surprisingly turned out that ADC(2) offers a better match with CC3 than ADC(3). Next, we use 10 functionals belonging to the "LYP" and "M06" families and compare the TD-DFT and the BSE/evGW descriptions. The BSE/evGW results are less sensitive than their TD-DFT counterparts to the selected functional, especially in the M06 series. Nevertheless, BSE/evGW delivers larger errors than TD-CAM-B3LYP, which provides extremely accurate results in the present case, especially when the Tamm−Dancoff approximation is applied. In addition, we show that, among the different starting points for BSE/evGW calculations, M06-2X eigenstates stand as the most appropriate. Finally, we confirm that the trends observed on the small compounds pertain in larger molecules. ■ INTRODUCTION Like their ground-state (GS) counterparts, the theoretical methods that can be applied to model electronically excited-states (ES) can be roughly divided into two categories: single-reference and multireference approaches. 1 If the latter methods can accurately account for static correlation effects, the former theories have the indisputable advantage of allowing more black-box applications. Indeed, in multireference schemes, such as in the Complete Active Space with Second-order Perturbation Theory (CASPT2), 2 the selection of a chemically suitable active space and the follow-up of the calculations remain very consuming in terms of workforce. While single-determinant theories are obviously unsuited for intrinsically multireference cases, for example, conical intersections, they are more straightforward and are still used in the vast majority of ES applications devoted to the modeling of absorption, fluorescence, and phosphorescence spectra. Up to now, theoretical chemists had the choice between two families of single-reference approaches to treat ES. On the one hand, one finds Time-Dependent Density Functional Theory (TD-DFT), 3 an extension of DFT to ES that enjoys several advantages, among which, computational efficiency thanks to both a formal N () 4 scaling with system size and the implementations of analytical first (gradient) and second (Hessian) derivatives. 4,5 However, one of the most important limitations of TD-DFT is the dependency of the ES energies on the chosen exchange-correlation functional (XCF), a dependency that is generally much stronger than for GS properties, though it depends on the nature of the ES considered, 6 at least when the popular adiabatic formulation of TD-DFT is used. 7 In