A simple natural orbital mechanism of "pure" van der Waals interaction in the lowest excited triplet state of the hydrogen molecule.

Abstract

This theoretical study examined van der Waals (vdW) interaction in the 3Σu+ state of the hydrogen molecule using density-matrix functional theory. Analysis of the configuration-interaction wave function and the exact natural orbital (NO) expansion revealed that a quantitative description of vdW bonding requires only eight NOs beyond the standard Hartree-Fock determinant. The potential-energy curve near the vdW minimum computed with this compact functional showed excellent agreement with full CI results and the Kolos-Wolniewicz benchmark. Specific products of NOs in the two-electron density were found to generate exchange-correlation holes consistent with the classical picture of dispersion as an instantaneous dipole-induced dipole (and higher multipole) effect, with higher multipoles contributing nearly 50% of the total vdW bond energy. These findings provide a foundation for density-matrix and orbital-dependent functionals applicable to vdW bonding.

Mechanism

Exchange-correlation holes generated by eight natural orbitals in the CI expansion reproduce the instantaneous dipole-induced dipole dispersion picture; higher multipole contributions account for approximately 50% of the total van der Waals bond energy in the H2 triplet state.