Tools for analysing configuration interaction wavefunctions

The configuration interaction (CI) approach to quantum chemical calculations is a well-established means of calculating accurately the solution to the Schrödinger equation for many-electron systems. It represents the many-body electron wavefunction as a sum of spin-projected Slater determinants of orthogonal one-body spin-orbitals. The CI wavefunction becomes the exact solution of the Schrödinger equation as the length of the expansion becomes infinite, however, it is a difficult quantity to visualise and analyse for many-electron problems. We describe a method for efficiently calculating the spin-averaged one- and two-body reduced density matrices ρΨ(r̄;r̄′) and ΓΨ(r̄1,r̄2;r̄′1,r̄′2) of an arbitrary CI wavefunction Ψ. These low-dimensional functions are helpful tools for analysing many-body wavefunctions; we illustrate this for the case of the electron–electron cusp. From ρ and Γ one can calculate the matrix elements of any one- or two-body spin-free operator O. For example, if O is an applied electric field, this field can be included into the CI Hamiltonian and polarisation or gating effects may be studied for finite electron systems.