Quantum Monte Carlo study of the ground state and low-lying excited states of the scandium dimer

Abstract

A large set of electronic states of scandium dimer has been calculated using high-level theoretical methods such as quantum diffusion Monte Carlo ͑DMC͒, complete active space perturbation theory as implemented in GAMESS-US, coupled-cluster singles, doubles, and triples, and density functional theory ͑DFT͒. The 3 ⌺ u and 5 ⌺ u states are calculated to be close in energy in all cases, but whereas DFT predicts the 5 ⌺ u state to be the ground state by 0.08 eV, DMC and CASPT2 calculations predict the 3 ⌺ u to be more stable by 0.17 and 0.16 eV, respectively. The experimental data available are in agreement with the calculated frequencies and dissociation energies of both states, and therefore we conclude that the correct ground state of scandium dimer is the 3 ⌺ u state, which breaks with the assumption of a 5 ⌺ u ground state for scandium dimer, believed throughout the past decades.

The Sc2 dimer revisited

“…26 As expected, DFT results vary wildly depending on the functional used. We believe that even qualitative results are questionable, at least for the time being, for this kind of molecular systems at the DFT level; see also Finally the most recent work on Sc 2 published in 2008 is that of Matxain et al 29 These workers examined ten states singlets, triplets, quintets, and septets 7 ⌬ u ͒, reporting r e and e values at the DFT͑B3LYP͒ / TZVP+ G͑3df, 2p͒ level; for some reason parities of the ⌺ states are not given. At the DFT equilibrium distances diffusion Monte Carlo ͑DMC͒ single point calculations were performed using the relativistic Stuttgart pseudopotentials and basis sets ͑ECP10MDF͒, thus obtaining T e values for the above states.…”

“…According to DMC the ground state is of 3 ⌺ u symmetry with the 5 ⌺ u lying at 0.17 eV ͑=3.9 kcal/ mol͒ higher. 29 In addition, DMC D e values are given for the X 3 ⌺ u ͑1.10 eV͒ and 5 ⌺ u ͑0.93 eV͒ states, but without clarification as to the asymptotic channels. This particular ordering of the 3 ⌺ u and 5 ⌺ u states has been corroborated by CASPT2 / TZVP+ G͑3df, 2p͒ calculations.…”

“…No dissociation energies of the 5 ⌺ u and 3 ⌺ u states are given at the CASPT2 level. 29 The question arises now as to what we really know for the Sc 2 molecule since 1964 when the first experimental work was published. 2 According to the previous exposition the theoretical results are conflicting, nevertheless it appears to favor a 5 ⌺ u − symmetry for the ground state, disputed, however, by the recent theoretical work of Matxain et al 29 Recall, however, that the 5 ⌺ u − state which correlates to Sc͑ 2 D g ͒ +Sc͑a 4 F g ͒ is one of 80 possible ͉ 2S+1 ⌳ g,u Ϯ ͘ states sprouting out from this channel ͑vide supra͒.…”

Erratum: “Quantum Monte Carlo study of the ground state and low-lying excited states of the scandium dimer” [J. Chem. Phys. 128, 194315 (2008)]

“…The Multi Reference Perturbation Theory ͑MRPT͒ calculations presented in the manuscript were revised and we consider that the following points ought to be clarified. The TZVP+ G͑3df, 2p͒ basis set, described in the manuscript, 1 was used for the B3LYP, Unrestricted Hartree-Fock ͑UHF͒, and CCSD͑T͒ calculations, but it was substituted by the smaller 6-311+ G͑2df, p͒ ͑Refs. 2-4͒ basis set for MRPT calculations, due to lack of enough computational resources.…”

Unitary perturbation theory applied to multiconfigurational reference functions

“…We adopt the basis set denoted TZVP+G(3df,2p), specified in detail in the Method section of the report of Matxain et al65 Matxain et al in fact applied a smaller basis set in their MRPT calculations 66. Based on the studies of Miranda and Kaplan,64 relativistic corrections were not considered in our model.…”