Solving the Scaled Schrödinger Equation with SAC–CI and Electrostatic Force Formalism. Ground, Excited, and Ionized States of the Benzene Molecule

An exact theory for solving the scaled Schrödinger equation (SSE) has been extended to molecular ground, excited, and ionized states that satisfy the Hellmann-Feynman electrostatic force (ESF) theorem, a necessary condition for the exact wave function. This is realized by applying the free complete-element (FC) or SSE theory to the symmetry-adapted-cluster (SAC) configuration-interaction (CI) wave functions that are designed to satisfy the ESF theorem. The resultant theory, called the FC or SSE(SAC-CI, ESF) theory, is not only highly accurate but also predictive, using both energetic and force theoretic concepts. Here, this theory is applied to a benzene molecule, a 42-electron molecule, the largest system yet treated by our exact theory. Notably, the theory resolved complex features of higher singlet and triplet excited states of a benzene molecule, which had previously eluded conventional methods.