Erratum to: Monatsh Chem (2011) 142:861–873 DOI 10.1007/s00706-011-0540-4

On page 864, four equations contained errors:

The equation \( \hat{H} = - {\kern 1pt} \left( {\frac{i\hbar }{2m}} \right){\kern 1pt} \sum {\nabla^{2} - \hat{U}} \) should read:

$$ \hat{H} = {\kern 1pt} - {\frac{{\hbar^{2} }}{2m}} \nabla^{2} + \hat{U} $$

Equation (2) should read:

$$ K(\Upomega ) - G(\Upomega ) = - \left( {\frac{{\hbar^{2} }}{4m}} \right)\int\limits_{\Upomega } {\nabla^{2} } \rho\,{\text{d}}\tau = - \left( {\frac{{\hbar^{2} }}{4m}} \right)\oint {{\text{d}}S} (\Upomega )\nabla \rho \cdot n $$

Equation (4) should be substituted by:

$$ 2G(\Upomega ) + U(\Upomega ) = \left( {\frac{{\hbar^{2} }}{4m}} \right)\nabla^{2} \rho $$

On line 63, the equation ∇2 ρ(r) = λi + λ1 + λ2 + λ3 should read:

$$ \nabla^{2} \rho (r) \equiv \lambda_{i} = \, \lambda_{1} + \, \lambda_{2} + \, \lambda_{3} $$