The authors propose a tool for assessing the accuracy of approximate electronic wave functions produced by diverse electronic structure calculations. The plots of $f_n=(\frac{{\pi }^2}{{\nu }_n}{)}^{1/4}\frac{\langle {\psi }_n\left(\vec{r}\right)\left|{\left[\mathrm{\Phi }\left(\vec{r}\right)\right]}^{1/4}\right|{\psi }_n\left(\vec{r}\right)\rangle }{\langle {\psi }_n\left(\vec{r}\right)\left|\widehat{T}\right|{\psi }_n\left(\vec{r}\right)\rangle }$ vs ${\nu }_n$, where ${\psi }_n\left(\vec{r}\right)$ is the $n\mathrm{th}$ natural (spin) orbital, ${\nu }_n$ is its occupation number, $\mathrm{\Phi }\left(\vec{r}\right)$ is the on-top two-electron density, and $\widehat{T}$ 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.

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• Electronic structure
• First-principles calculations