Tool for assessing the accuracy of approximate electronic wave functions

The authors propose a tool for assessing the accuracy of approximate electronic wave functions produced by diverse electronic structure calculations. The plots of f(n) = (pi(2)/nu(n))(1/4) <psi(n)((r) over right arrow)vertical bar[Phi((r) over right arrow)](1/4)vertical bar psi(n) ((r) over right arrow)>/<psi(n)((r) over right arrow)vertical bar(T) over cap vertical bar psi(n)((r) over right arrow)> vs nu(n), where psi(n) ((r) over right arrow) is the nth natural (spin) orbital, nu(n) is its occupation number, Phi((r) over right arrow) is the on-top two-electron density, and (T) over cap is the kinetic energy operator, are found to vividly reveal inaccuracies of the underlying wave functions. As such, they provide synthetic yet detailed visual information well suited for accuracy assessments especially in the cases of approaches employing unstandardized basis sets and/or energy minimizations with unascertainable global convergence characteristics.