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Considering the emblematic Hartree-Fock (HF) energy expression with singleSlater determinant and the ortho-normal molecular orbits (MO) in it, expressedas a linear combination (LC) of atomic orbits (LCAO) basis set functions, theHF energy expression is in fact a 4th order polynomial of the LCAOcoefficients, which is relatively easy to handle. The energy optimization viathe Variation Principle can be made with a Lagrange multiplier method to keepthe ortho-normal property and the Newton-Raphson (NR) method to find thefunction minimum. It is an alternative to the widely applied HF self consistentfield (HF-SCF) method which is based on unitary transformations and eigensolverduring the SCF, and seems to have more convenient convergence property. Thismethod is demonstrated for closed shell (even number of electrons and all MOare occupied with both, alpha and beta spin electrons) and restricted (all MOshave single individual spatial orbital), but the extension of the method toopen shell and/or unrestricted cases is straightforward.

aip conference proceedings

Optimizing single Slater determinant for Electronic Hamiltonian with  Lagrange multipliers and Newton-Raphson methods as an alternative to ground  state calculations via Hartree-Fock self consistent field