An EOM-CCSD-PCM Benchmark for Electronic Excitation Energies of Solvated Molecules

Abstract

In this work, we benchmark the equation of motion coupled cluster with single and double excitations (EOM-CCSD) method combined with the polarizable continuum model (PCM) for the calculation of electronic excitation energies of solvated molecules. EOM-CCSD is one of the most accurate methods for computing one-electron excitation energies, and accounting for the solvent effect on this property is a key challenge. PCM is one of the most widely employed solvation models due to its adaptability to virtually any solute and its efficient implementation with density functional theory methods (DFT). Our goal in this work is to evaluate the reliability of EOM-CCSD-PCM, especially compared to time-dependent DFT-PCM (TDDFT-PCM). Comparisons between calculated and experimental excitation energies show that EOM-CCSD-PCM consistently overestimates experimental results by 0.4-0.5 eV, which is larger than the expected EOM-CCSD error in vacuo. We attribute this decrease in accuracy to the approximated solvation model. Thus, we investigate a particularly important source of error: the lack of H-bonding interactions in PCM. We show that this issue can be addressed by computing an energy shift, Δ, from bare-PCM to microsolvation + PCM at DFT level. Our results show that such a shift is independent of the functional used, contrary to the absolute value of the excitation energy. Hence, we suggest an efficient protocol where the EOM-CCSD-PCM transition energy is corrected by Δ(DFT), which consistently improves the agreement with the experimental measurements.

Coupled cluster theory with the polarizable continuum model of solvation

“…In fact, we showed that significant and consistent corrections to the CCSD-PCM results can be readily obtained (at DFT level) by adding a few explicit solvent molecules hydrogen-bonded to the solute, and surrounding the whole cluster in the continuum solvent. [21] With this mixed implicit/explicit model, the transition energy shifts to lower values compared to a PCM-only calculation, as shown in Figure 6. In our experience, it is important to saturate the H-bond sites with explicit solvent molecules, and the external PCM cavity should include added spheres to avoid unphysical solvent pockets in the crevices of the cavity.…”

“…The figure reports data for both nonequilibrium and equilibrium solvation regimes; the errors are considerably larger in the equilibrium solvation regime because the full dielectric constant ε 0 is used to evaluate the excited state solvent response. The cLR approach is able to reproduce the PTED results very well, and it can be used for initial studies of excited state ordering before searching for excited The main comparison with experimental transition energies is based on a benchmark study we conducted recently, [21] where we selected 16 small to medium size molecules where measurements were available in polar solvents, shown in Figure 4. [67][68][69][70][71] The measured transition energies were used as reference for CCSD, three global hybrid functionals: B3LYP, [72] PBE0, [73,74] and M06, [75] and two range-separated hybrid functionals: CAM-B3LYP [76] and LC-ωPBE.…”

“…This includes 16 molecules divided in four groups: Nitroso, NQ, AB, and U, and the solvents in which measurements were performed Reproduced with permission from Ref. [21]. Copyright 2017 American Chemical Society FIGURE 5 Stacked average errors of the excitation energies (eV) calculated with all methods and basis sets.…”

“…The molecule enumeration follows the order in Figure 4 Reproduced with permission from Ref. [21]. Copyright 2017 American Chemical Society is largely independent of the choice of the functional, which is a major departure from the well-know functional-dependence issue of approximate DFT.…”

“…The original approach for combining CC methods and continuum models was proposed by Christiansen and Mikkelsen in the late 1990s, [8,9] and it was later extended to PCM by Cammi, [10][11][12] and the present author. [6,[13][14][15][16][17][18][19][20][21][22] This scheme is historically called perturbation theory for energy and density (PTED) because it descends from perturbation theory and it evaluates the solvent response based on the full density of the solute. [23,24] In CC methods, the PTED scheme couples the equations for the various sets of amplitudes that define the ground and excited state wave functions, and their response to external fields.…”