Formulae are derived for the average value and for the dispersion of the spectrum of an electronic Hamiltonian in a finite-dimensional, antisymmetric and spin-adapted space. Both the moments are expressed in terms of the corresponding two-electron quantities. The derivation is based on the theory of spin-adapted reduced Hamiltonians.
An N-electron Hamiltonian projected onto a K-orbital, antisymmetric and spin-adapted model space (in quantum chemistry known as the full configuration interaction space) may be expressed as a linear combination of products of generators of the unitary group . Consequently, spectral density distribution moments and other quantities which characterize global properties of the Hamiltonian spectra in are defined by the averages over the model space of products of the generators. This paper presents a set of new recurrent formulae for the averages and describes a simple graphical method of their evaluation.