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# QUESTDB: A database of highly accurate excitation energies for the electronic structure community

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Abstract We describe our efforts of the past few years to create a large set of more than 500 highly accurate vertical excitation energies of various natures (π → π*, n → π*, double excitation, Rydberg, singlet, doublet, triplet, etc.) in small‐ and medium‐sized molecules. These values have been obtained using an incremental strategy which consists in combining high‐order coupled cluster and selected configuration interaction calculations using increasingly large diffuse basis sets in order to reach high accuracy. One of the key aspects of the so‐called QUEST database of vertical excitations is that it does not rely on any experimental values, avoiding potential biases inherently linked to experiments and facilitating theoretical cross comparisons. Following this composite protocol, we have been able to produce theoretical best estimates (TBEs) with the aug‐cc‐pVTZ basis set for each of these transitions, as well as basis set corrected TBEs (i.e., near the complete basis set limit) for some of them. The TBEs/aug‐cc‐pVTZ have been employed to benchmark a large number of (lower‐order) wave function methods such as CIS(D), ADC(2), CC2, STEOM‐CCSD, CCSD, CCSDR(3), CCSDT‐3, ADC(3), CC3, NEVPT2, and so on (including spin‐scaled variants). In order to gather the huge amount of data produced during the QUEST project, we have created a website (https://lcpq.github.io/QUESTDB_website) where one can easily test and compare the accuracy of a given method with respect to various variables such as the molecule size or its family, the nature of the excited states, the type of basis set, and so on. We hope that the present review will provide a useful summary of our effort so far and foster new developments around excited‐state methods. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods
Composition of each of the five subsets making up the present QUEST dataset of highly accurate vertical excitation energies
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Distribution of the error (in eV) in excitation energies (with respect to the TBE/aug‐cc‐pVTZ values) for various methods for the entire QUEST database considering only closed‐shell compounds. Only the “safe” TBEs are considered (see Table 2). See Table 4 for the values of the corresponding statistical quantities. QC and TM indicate that Q‐CHEM and TURBOMOLE scaling factors are considered, respectively. The SOS‐CC2 and SCS‐CC2 approaches are obtained with the latter code
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Molecules from each of the five subsets making up the present QUEST dataset of highly accurate vertical excitation energies: QUEST#1 (red), QUEST#2 (magenta and/or underlined), QUEST#3 (black), QUEST#4 (green), and QUEST#5 (blue)
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Deviation from the CCSDT excitation energies for the lowest singlet and triplet excitation energies (in eV) of five‐ and six‐membered rings obtained at the CIPSI/6‐31+G(d) level of theory. Red dots: excitation energies and error bars estimated via the present method (see Section 2.3.3). Blue dots: excitation energies obtained via a three‐point linear fit using the three largest CIPSI wave functions, and error bars estimated via the extrapolation distance, that is, the difference in excitation energies obtained with the three‐point linear extrapolation and the largest CIPSI wave function
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Histogram of the random variable X(m) (see Equation (4) in the main text for its definition). About 200 values of singlet and triplet excitation energies taken at various iteration number n for the 13 five‐ and six‐membered ring molecules have been considered to build the present histogram. The number M of iterations kept at each calculation is chosen according to the statistical test presented in the text
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