Diagrammatic multiplet-sum method (MSM) density-functional theory (DFT): Completion of the two-orbital two-electron model (TOTEM) with an application to the avoided crossing in lithium hydride (LiH)

Abstract

The Ziegler–Rauk–Baerends multiplet sum method (MSM) assumes that density functional theory (DFT) provides a good description of states dominated by a single determinant. It then uses symmetry to add static correlation to DFT. In our previous article (Article I) [J. Chem. Phys.159, 244306 (2023)], we introduced diagrammatic MSM-DFT as a tool to aid in extending MSM-DFT to include the nondynamic correlation needed for making and breaking bonds even in the absence of symmetry. An attractive feature of this approach is that no functional-dependent parameters need to be introduced, although choices are needed in making correspondences between wave function theory and MSM-DFT diagrams. The preliminary examples in Article I used the two-orbital two-electron model (TOTEM) less completely than could have been the case as we wanted to limit calculations to diagonalizing 2 × 2 matrices, which can be done by solving a simple quadratic equation. Diagrammatic MSM-DFT is extended here to treat the full TOTEM, and it is shown that the unsymmetric lithium hydride molecule dissociates into neutral atoms when diagrammatic MSM-DFT techniques are used to introduce a proper description of the avoided crossing between ionic bonding and covalent bonding states. This involves diagonalizing a 3 × 3 matrix, which requires going beyond solving a quadratic equation but is still trivial these days. The method is tested for Hartree–Fock and for three functionals (LDA, PW91, and B3LYP). All the functionals yield similar results as should be expected for a properly formulated parameter-free theory. Agreement with available estimates show that the magnitude of the coupling element introduced here is excellent. However, more work will be needed to obtain quantitative agreement between our diagrammatic MSM-DFT ground-state potential energy curve and that found from high-quality ab initio calculations.