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Tools for analysing configuration interaction wavefunctions

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****P. Delaney**^{a}, J. C. Greer^{}^{, }
^{}^{, }^{a}

^{a}NMRC, Prospect Row, Cork, Ireland.

## Abstract

The configuration interaction (CI) approach to quantum chemical calculations is a
well-established means of calculating accurately the solution to the
Schr"odinger 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
rho_Psi ( r; r' ) and Gamma_Psi ( r_1, r_2 ; r'_1, r'_2 )$
of an arbitrary CI wavefunction Psi. These low-dimensional functions are helpful tools for
analysing many-body wavefunctions; we illustrate this for the case of the electron-electron cusp.
From rho and Gamma 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.

**Author Keywords: **