Consider a molecule consisting of N quantized electrons at positions xi, and M nuclei of charges Z = (Z1,..., ZM) fixed at positions y = (yl,..., yM). The Schrödinger Hamiltonian of such a system is given by ]]</EquationSource><EquationSource Format="TEX"><![CDATA[$${H_{Z,H}} = \sum\limits_{i = 1}^N {\left( { - {\Delta _{{x_i}}} + {V_{Coulomb}}\left( {{x_i}} \right)} \right)} + \frac{1}{2}\sum\limits_{i \ne j} {\frac{1}{{\left| {{x_i} - {x_j}} \right|}}} $$ ]]</EquationSource><EquationSource Format="TEX"><![CDATA[$${V_{Coulomb}}\left( x \right) = - \sum\limits_{j = 1}^M {\frac{{{Z_j}}}{{\left| {x - {y_j}} \right|}}} $$ acting on ]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$H = \Lambda _{i = 1}^N{L^2}\left( {{R^3} \times {Z_q}} \right)$$ ; in this exposition, in order to simplify notation, we neglect spin by putting q = 1. Define the ground state of such a system by ]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$\begin{array}{*{20}{c}} {E\left( {Z,y} \right) = \mathop {\inf }\limits_N E\left( {Z,y;N} \right)}&{E\left( {Z,y;N} \right) = \mathop {\inf }\limits_{\begin{array}{*{20}{c}} {\left\| \psi \right\| = 1} \\ {\psi \in H} \end{array}} \left\langle {{H_{Z,N}}\psi ,\psi } \right\rangle } \end{array}$$ When M = 1, this system is an atom. In this case we can assume y = 0 and we denote its energy simply by Eatom(Z).