Higher Roots in MCSCF and CI Calculations

In the process of determining the expansion coefficients that define an MCSCF wave function along lines similar to Eq. (7.10), CI calculations are carried out in die space of the orbitals that are active in the MCSCF. Excited states that can be generated by electronic excitations within that active space then have a corresponding root in diat limited CI window and, if one chooses, one can variationally optimize the orbitals for a root other than the one of lowest energy, i.e., other than the ground state. 

In some instances, the root in question is dominated by a single CSF, allowing one to describe the state conveniently by reference to the ground state. In other instances, however, that will not be the case, and simple relationships between the excited state and the ground state cannot be easily formulated. This is, of course, purely a conceptual problem - the wave functions themselves are perfectly well defined and useful. 

MCSCF results for phenylnitrene using a complete active space formed from the six phenyl tt orbitals and the two nitrogen p orbitals and the eight electrons contained therein are presented in Table 14.1. Note that, because of symmetry and spin restrictions, only the 2 Al state must be determined as the second root of the MCSCF. The CAS results are quite 

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