New Scaled Atoms-in-Molecules Theory for Predicting Diatomic Potential-Energy Curves III. Refined Applications to the X 1Σg+ and E 1Σg+ States of H2

Abstract

Scaled atoms‐in‐molecules theory is applied to the ground $X^1{\Sigma }_g^{+}$ and first excited $E^1{\Sigma }_g^{+}$ states of H₂. Five basis functions are included, corresponding to $\text{1s}\mathrm{H}\text{\hspace{0.17em}+\hspace{0.17em}1s}\mathrm{H}$ , ${}^{1}S{\mathrm{H}}^{-}{\mathrm{\hspace{0.17em}+\hspace{0.17em}H}}^{+}$ , $\text{1s}\mathrm{H}\text{\hspace{0.17em}+\hspace{0.17em}2s}\mathrm{H}$ , $\text{1s}\mathrm{H}{\text{\hspace{0.17em}+\hspace{0.17em}2p}}_0\mathrm{H}$ , and ${\text{2p}}_{+}\mathrm{H}{\text{\hspace{0.17em}+\hspace{0.17em}2p}}_{-}\mathrm{H}$ . Variational scaling parameters are introduced into the A‐ and B‐atom eigenfunctions comprising each basis function; the ground and first excited state energy roots of the secular determinant are independently minimized with respect to these scaling parameters. For computing interatomic contributions to the energy and overlap matrix elements, three different approximations to the ¹S H⁻ ground‐state eigenfunction are used. Scaled atoms‐in‐molecules theory in this approximation yields an H₂ ground‐state energy which is 6.5 kcal/mole above the exact result. An $E^1{\Sigma }_g^{+}$ excited‐state curve is obtained with the proper double minimum; the predicted energy at the outer minimum is almost exact, and at the inner minimum it is about 7.5 kcal/mole too high.