Accurate Excited-State Geometries: A CASPT2 and Coupled-Cluster Reference Database for Small Molecules

Abstract

We present an investigation of the excited-state structural parameters determined for a large set of small compounds with the dual goals of defining reference values for further works and assessing the quality of the geometries obtained with relatively cheap computational approaches. In the first stage, we compare the excited-state geometries obtained with ADC(2), CC2, CCSD, CCSDR(3), CC3, and CASPT2 and large atomic basis sets. It is found that CASPT2 and CC3 results are generally in very good agreement with one another (typical differences of ca. 3 × 10–3 Å) when all electrons are correlated and when the aug-cc-pVTZ atomic basis set is employed with both methods. In a second stage, a statistical analysis reveals that, on the one hand, the excited-state (ES) bond lengths are much more sensitive to the selected level of theory than their ground-state (GS) counterparts and, on the other hand, that CCSDR(3) is probably the most cost-effective method delivering accurate structures. Indeed, CCSD tends to provide too compact multiple bond lengths on an almost systematic basis, whereas both CC2 and ADC(2) tend to exaggerate these bond distances, with more erratic error patterns, especially for the latter method. The deviations are particularly marked for the polarized CO and CN bonds, as well as for the puckering angle in formaldehyde homologues. In the last part of this contribution, we provide a series of CCSDR(3) GS and ES geometries of medium-sized molecules to be used as references in further investigations.

How accurate are TD‐DFT excited‐state geometries compared to DFT ground‐state geometries?

“…In this context, it may also be mentioned that this basis set has been used in several of the previous benchmarks on the topic of excited‐state geometries that have included the CC2 method. [ 51,66,71 ]…”

“…For this reason, when later turning to the RMSD values for different types of bonds (see Section 3.3), the analysis will exclude the C2O7, C8O9, C8O10, and O7H15 bonds in salicylic acid. It appears likely that this discrepancy between TD‐DFT and CC2, which has also been documented in studies of excited‐state intramolecular proton transfer reactions in other compounds similar to salicylic acid, [ 96 ] relates to the aforementioned tendencies of TD‐DFT to underestimate and CC2 to overestimate the lengths of formal CO double bonds in excited states, [ 51,61,65,66 ] although these tendencies have mostly been manifested in studies of nπ* states of small molecules where CO is the main chromophoric moiety.…”

“…Given that TD‐DFT has been found to underestimate [ 51,61,65 ] and CC2 to overestimate [ 51,66 ] the lengths of formal CO double bonds in nπ* excited states of small molecules like acetone where CO is the dominant chromophoric moiety, using CC2 geometries of such molecules/states as reference for TD‐DFT geometries warrants caution. Herein, out of the 20 CO bonds included in the benchmark set, 17 are formal single bonds and three are formal double bonds, occurring in salicylic acid (C8O10, see Figure S2), 5‐methoxysalicylic acid (C9O12) and 3P‐propionic acid (C9O10).…”

“…More recently, Brémond et al [ 65 ] reported the first extensive assessment of the accuracy of TD‐DFT for geometries of small organic molecules in valence excited states. Testing a panel of 48 different functionals and using geometries previously calculated [ 66 ] with CASPT2 or a high‐order coupled cluster (CC) method (CC3 [ 67 ] or CCSDR(3) [ 68 ] ) as reference, these authors concluded that excited‐state bonds lengths obtained with TD‐DFT are on average of somewhat lesser quality than the corresponding DFT ground‐state bond lengths. [ 65 ] Consistent with the above‐described findings, [ 51,61 ] this effect was manifested especially through an underestimation of CO excited‐state bond lengths.…”

Multireference Electron Correlation Methods: Journeys along Potential Energy Surfaces

“…104 The numerical gradient implementations of CASPT2 and XMCQDPT2 remain in widespread use for optimizing molecular structures. Notable examples include locating equilibrium geometries and conical intersections with MS-CASPT2 in 2011, 46 locating equilibrium geometries and conical intersection in acetophenone with XMCQDPT2 in 2013, 52 locating equilibrium geometries, conical intersections, transition state geometries, and reaction pathways of thymine with MS-CASPT2 in 2016, 60 locating equilibrium geometries of various RPSB models in 2017, 65 generating a benchmark set of excited-state geometries of organic molecules with MS-CASPT2 in 2017, 67 and optimizing equilibrium structures and crossing points in 2-selenouracil in 2019. 72…”