Generalized Spin in the Variance-Based Wave Function\nOptimization Method within the Doubly Occupied Configuration Interaction\nFramework

In this work, we implement a generalized\nspin formulation of the\ndoubly occupied configuration interaction methodology using the energy\nvariance of the <i>N</i>-electron Hamiltonian. We perform\nthe optimization of the <i>N</i>-electron wave functions\nand calculate their corresponding energies, using a unified variational\ntreatment for ground and excited states based on the energy variance,\nwhich allows us to describe the entire energy spectra on an equal\nfooting. We analyze the effects produced by the breakdown of the <i>Ŝ</i>​<sup>2</sup> and <i>Ŝ</i><sub><i>z</i></sub> symmetries in the spectra of model\nhydrogenic clusters in terms of energies and spin-related quantities,\narising from the restricted, unrestricted, and generalized spin methods.\nThe results are compared with other related methods as well as full\nconfiguration interaction.