Accurate Thermochemistry\nwith Multireference Methods:\nA Stress Test for Internally Contracted Multireference Coupled-Cluster\nTheory

The internally contracted multireference coupled-cluster\nmethod\nwith single, double and perturbative triple excitations, icMRCCSD(T),\nwas tested for its performance in the context of computational high-accuracy\nthermochemistry. The results were gauged against the standard single-reference\ncoupled-cluster hierarchy with up to 5-fold excitations. The test\nset comprised of a selection of first-row dinuclear compounds and\nthe three 3d-transition metal compounds MnH, FeH, and CoH. The results\nrevealed two problems with the current formulation of icMRCCSD(T).\nFirst, the choice of the Dyall Hamiltonian as the zeroth-order Hamiltonian,\nwhich leads to a biased description of the different orbital subspaces\nand particularly poor results for the atomic correlation energies,\nand second, the tendency to overestimate the perturbative correction\nfor triply excited clusters, in particular in the presence of open\nshells and correspondingly low orbital-energy gaps. The two problems\ncould be solved by resorting to the effective Fock operator as zeroth-order\nHamiltonian and by adopting a modified amplitude equation that includes\nterms quadratic in the pair clusters. A similar modification was recently\nproposed by Masios et al. (<i>Phys. Rev. Lett.</i> <b>2023</b>, <i>131</i>, 186401) in the context of applying\nsingle-reference coupled-cluster theory to systems with small or vanishing\nband gaps and we chose the acronym ‘(cT*) correction’\nin analogy to that work. In contrast to the work of Masios et al.,\nadditional terms including single excitation clusters were omitted,\nas these again lead to an overestimation of correlation effects in\nmore difficult cases. We also tested another alternative for the zeroth-order\nHamiltonian and additional higher-order corrections for the correlation\nenergy. These extensions did not significantly improve the results\nand were also computationally more demanding. The improved icMRCCSD(cT*)<sub>F</sub> method yields very accurate results with errors, relative\nto accurate benchmarks, better than 2 kJ/mol for total energies and\natomization energies for the entire set of examples considered in\nthis work.