A Mountaineering Strategy to Excited States: Highly Accurate Reference Energies and Benchmarks

Abstract

Striving to define very accurate vertical transition energies, we perform both high-level coupled cluster (CC) calculations (up to CCSDTQP) and selected configuration interaction (sCI) calculations (up to several millions of determinants) for 18 small compounds (water, hydrogen sulfide, ammonia, hydrogen chloride, dinitrogen, carbon monoxide, acetylene, ethylene, formaldehyde, methanimine, thioformaldehyde, acetaldehyde, cyclopropene, diazomethane, formamide, ketene, nitrosomethane, and the smallest streptocyanine). By systematically increasing the order of the CC expansion, the number of determinants in the CI expansion as well as the size of the one-electron basis set, we have been able to reach near full CI (FCI) quality transition energies. These calculations are carried out on CC3/ aug-cc-pVTZ geometries, using a series of increasingly large atomic basis sets systematically including diffuse functions. In this way, we define a list of 110 transition energies for states of various characters (valence, Rydberg, n → π, π → π*, singlet, triplet, etc.) to be used as references for further calculations. Benchmark transition energies are provided at the aug-cc-pVTZ level as well as with additional basis set corrections, in order to obtain results close to the complete basis set limit. These reference data are used to benchmark a series of 12 excited-state wave function methods accounting for double and triple contributions, namely ADC(2), ADC(3), CIS(D), CIS(D), CC2, STEOM-CCSD, CCSD, CCSDR(3), CCSDT-3, CC3, CCSDT., and CCSDTQ. It turns out that CCSDTQ yields a negligible difference with the extrapolated CI values with a mean absolute error as small as 0.01 eV, whereas the coupled cluster approaches including iterative triples are also very accurate (mean absolute error of 0.03 eV). Consequently, CCSDT-3 and CC3 can be used to define reliable benchmarks. This observation does not hold for ADC(3) that delivers quite large errors for this set of small compounds, with a clear tendency to overcorrect its second-order version, ADC(2). Finally, we discuss the possibility to use basis set extrapolation approaches so as to tackle more easily larger compounds.

CCSD‐PCM Excited State Energy Gradients with the Linear Response Singles Approximation to Study the Photochemistry of Molecules in Solution

“…In terms of absorption energies, the calculations overestimate experiment by about 0.5 eV with 6-31 + G(d,p), and 0.3-0.4 eV with aug-cc-pVDZ, see Table 1, which is typical for this level of theory/basis set combination. [9] The emission energy for the LE state is overestimated by 0.4 eV with the small basis set, and 0.3 eV for the larger one, see Table 2. The comparison with an extrapolated value of the experimental CT emission energy shows that the calculations underestimate this quantity by 0.4-0.46 eV; this underestimation is discussed in more detail later, when we present the data in acetonitrile.…”

“…Although implicit models represent a drastic approximation in the description of the environment, it is still important to treat the solute with a high level of theory, because the accurate description of the solute electron density is ultimately responsible for the reliability of the simulation. [9] In previous work, we presented the theory and implementation of excited state energy and energy gradients with the equation of motion single and double excitations method (EOM-CCSD), [10] combined with PCM within the state specific (SS) solvation formalism. [11,12] This approach describes the solvent polarization response to the excited state solute electron density, thus the solute-solvent interaction in the excited state is treated more completely.…”

A Mountaineering Strategy to Excited States: Highly Accurate Energies and Benchmarks for Medium Sized Molecules

“…For the vertical singlet excitation, there is also a recent 4.06 eV CCSD//CAM-B3LYP estimate, 116 which slightly overshoots ours, consistent with the expected error sign of CCSD. 20,70,117 Silylidene. One notes an excellent agreement between CCSDT, CCSDTQ, and FCI for this derivative.…”

“…Our computational protocol closely follows the one of Ref. 20. Consequently, we only report key elements below.…”

Noniterative Doubles Corrections to the Random Phase and Higher Random Phase Approximations: Singlet and Triplet Excitation Energies

“…[31] Although CC2 performed best for singlet excitation energies, [26,31] CCSD performed slightly better for triplet excitation energies. [31] In a recent study by Loos et al [34] on 106 different singlet and triplet excited states, the CCSD method was found to perform slightly better than CC2 and again the CC3 method was found to perform very well-giving results almost identical to the CCSDT and coupled cluster singles, doubles, triples and quadruples (CCSDTQ) methods. In this study, we have chosen to use the CC3 results as reference values.…”