Valence bond formulation of Hartree-Fock instability conditions for simple and multiple bonds

• Published in: Chemical physics Vol. 130; no. 1-3; pp. 229 - 239
• Main Authors: Lepetit, M.B., Malrieu, J.P., Trinquier, G.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.02.1989; Elsevier
• Subjects: Atomic and molecular physics; Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations); Density-functional theory; Electronic structure of atoms, molecules and their ions: theory; Exact sciences and technology; Physics; Acetylenic aliphatic compound; Potential energy curve; Hydrocarbon; Chemical bond; Ethylene; Carbon Molecules; Theoretical study; Hartree Fock theory; Spin density; Single bond; Contracted gaussian orbital; Acetylene; Inorganic compound; Double bond; Ethylenic aliphatic compound; Diatomic molecule; Valence bond method; Nitrogen Molecules; Organic compounds
• ISSN: 0301-0104
• DOI: 10.1016/0301-0104(89)87053-3

For model problems like H2 and C2, the HF instability conditions are expressed in an orthogonal valence bond (OVB) language, i.e. as functions of the ratio of the neutral/ionic coupling over the energy difference between ionic and neutral OVB determinants. The relationship between the instability conditions and the convergence radius of the perturbative CI expansion is discussed. It is analytically demonstrated and numerically illustrated on the C2 problem that some symmetry-broken HF solutions (i.e. for which the energy is stationary) are not real minima of the energy at intermediate interatomic distances. For systems with several non-equivalent bonds the successive occurrence of instability in the π bond and in the σ bond and the coupling between them is analytically analysed and numerically illustrated on the ethylene, acetylene and nitrogen molecules.