Variational H2+, the LCAO method, and Hartree-Fock SCF#
The one-electron H2+ molecular ion in a small Gaussian basis: LCAO
bonding and antibonding orbitals, bonding density, the Born-Oppenheimer
potential curve, Gaussian-type orbital integrals, the Roothaan-Hall
secular equation HC=SCE, and the shared electron pair; then
closed-shell restricted Hartree-Fock SCF for HeH+ and H2, and the
STO-3G contracted-Gaussian basis.
Hund-Mulliken LCAO molecular orbitals of H2+: bonding and antibonding
Heitler-London’s insight: bonding vs. antibonding electron density
Born-Oppenheimer clamped-nuclei potential curve of H2+
Boys’s Gaussian-type orbitals and the Gaussian product theorem
Roothaan-Hall equations: solving HC = SCE in a finite basis
Lewis’s shared electron pair: two opposite-spin electrons in one bonding orbital
Roothaan-Hall self-consistent field: RHF for HeH+ and H2
Hehre, Stewart and Pople’s STO-3G basis: three Gaussians for one Slater orbital