The Behaviour of the First-Order Density Matrix at the Coulomb Singularities of the Schrödinger Equation

1963/12/01 by Werner A. Bingel, W. A. Bingel · 3 citations
Chemistry · Engineering · Physics and Astronomy · #Advanced Chemical Physics Studies #Advanced Physical and Chemical Molecular Interactions #Molecular Junctions and Nanostructures

paper · pdf · doi:10.1515/zna-1963-1203

openalex publication_date 1963/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

The cusp conditions of KATO for a spinless n-electron wave function at the COULOMB Singularities of the SCHRÖDINGER Equation are used to derive corresponding conditions for the first-order density matrix. These results are applied to the united-atom expansion of the electronic energy of polyatomic molecules resulting in an exact relation between the coefficients of the quadratic and cubic terms in this expansion. Finally it is shown how the cusp condition for the first-order density matrix is modified if the wave function includes electron spin in a proper way.

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• On-top pair-correlation function in the homogeneous electron liquid
• Integral coalescence conditions in D⩾2, dimension space
• Bounds for the second and third derivatives of the electron density at the nucleus

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