Critical Phenomena for Electronic Structure at the Large-Dimension Limit.

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We show that the symmetry breaking of the electronic structure configurations at the large-D limit is completely analogous to the standard phase transitions and critical phenomena in statistical mechanics. Electronic structure at the large-D limit exhibits critical points with mean field critical exponents ( $\ensuremath{\beta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{2}$, $\ensuremath{\alpha}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0}_{\mathrm{dis}}$, $\ensuremath{\delta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$, and $\ensuremath{\gamma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$). The complete mapping is presented for the Hartree-Fock two-electron atom in weak electric field and the two Coulomb center problems.