Theoretical analysis of the vibrational structure of the electronic transitions involving a state with double minimum: E, F 1 Σg+ of H2

Abstract

It is shown that the convergence problem encountered in the numerical integration of the vibrational Schrödinger equation for an electronic state with a double‐minimum potential does not exist in the analytical expansion method. For the ${\mathrm{B\hspace{0.17em}}}^1{\Sigma }_u^{+}$ , C ¹π_u, and E, ${\mathrm{F\hspace{0.17em}}}^1{\Sigma }_g^{+}$ states of H₂, the expansion method gives consistently and progressively better energy eigenvalues than the numerical integration. method. Franck‐Condon factors for the transitions $B^1{\Sigma }_u^{+}{\mathrm{-\; E,F}}^1{\Sigma }_g^{+}$ and $C^1{\Pi }_u{\mathrm{-\; E,F}}^1{\Sigma }_g^{+}$ were computed, and the vibrational structure of the case $B^1{\Sigma }_u^{+}{\mathrm{-\; E,F}}^1{\Sigma }_g^{+}$ is discussed in some detail.