《分子电子结构》研究生课程教学资源（Electronic Structure of Molecules）5-BOA-LCAO-Semi-ROHF

B-OapproximationsummaryFreeze the nuclear positions (nuclear kinetic energy is zero inthe electronic Hamiltonian);Calculate the electronic wavefunction and energy E;E depends on the nuclear positions throughthe nuclear-electron attraction and nuclear-nuclear repulsion terms;E = O corresponds to all particles at infinite separation;Born-Oppenheimerapproximationisprettyrobust12

B-O approximation summary • Freeze the nuclear positions (nuclear kinetic energy is zero in the electronic Hamiltonian); • Calculate the electronic wavefunction and energy E; • E depends on the nuclear positions through the nuclear￾electron attraction and nuclear-nuclear repulsion terms; • E = 0 corresponds to all particles at infinite separation; • Born-Oppenheimer approximation is pretty robust 12

Hartree-FockorbitalsForatoms,theHartree-FockorbitalscanbecomputednumericallyThe Φ's resemble the shapes of the hydrogen orbitalss, p, d orbitalsRadial part somewhat different, because of interaction withthe other electrons (e.g. electrostatic repulsion andexchangeinteractionwithotherelectrons)13

Hartree-Fock orbitals • For atoms, the Hartree-Fock orbitals can be computed numerically • The  ‘s resemble the shapes of the hydrogen orbitals • s, p, d orbitals • Radial part somewhat different, because of interaction with the other electrons (e.g. electrostatic repulsion and exchange interaction with other electrons) 13