X 1Σg+—A 3Σu+ Excitation Energy in N2

Abstract

The valence-bond method is employed to calculate the energy separations of the potential surfaces for the X 1Σg+ and A 3Σu+ states of the nitrogen molecule for internuclear distances between the respective equilibrium positions (i.e., 1.094 to 1.29 Å). The radiative π—π* transition between these states gives rise to the well-known Vegard—Kaplan bands. The N2 molecule is treated as a 10-electron problem. Separation into σ and π groups of electrons is made and excitation assumed to affect only the latter. The self-energy of the σ core is not explicitly evaluated. The σ—π interactions are nearly insensitive to variations in the σ-core bonds, a result which justifies the variational calculation of the π energy plus σ—π interactions as a valid determination of the π-electron wavefunctions. The resulting energy separation has an almost constant error, 1.1 to 1.3 eV lower than experiment; the energies themselves are more sensitive to the wavefunction than is the separation. The invariance of the error, both as obtained by several widely different calculations and as a function of internuclear separation, suggests strongly that it arises from correlation energy of two possible types, discussed below. Such an error may be ``typical'' of the error involved in a σ—π separation treatment for π—π* intersystem transitions. Within the error involved, the results justify the ``chemical'' description of these states of the nitrogen molecule.