ChemViz

The original Hartree method expresses the total wavefunction of the system as a product of one-electron orbitals. In the Hartree-Fock method, the wavefunction is an antisymmetrized determinantal product of one-electron orbitals (the "Slater" determinant). Schrodinger's equation is transformed into a set of Hartree-Fock equations. The Hartree-Fock approximation is also known at the self-consistent field (SCF) method

begin with a set of approximate orbitals for all the electrons in the system
one electron is selected, and the potential in which it moves is calculated by freezing the distribution of all the other electrons and treating their averaged distribution as the centrosymmetric source of potential
the Schrodinger equation is solved for this potential, which gives a new orbital for it
the procedure is repeated for all the other electrons in the system, using the electrons in the frozen orbitals as the source of the potential
at the end of one cycle, there are new orbitals from the original set
the process is repeated until there is little or no change in the orbitals

defined as the wavefunction of an electron in an atom

square of the AO gives the probability density

any electron described by an orbital is said to occupy that orbital

atomic orbitals have a well-defined significance only for hydrogenic atoms

hydrogenic atoms are used in many of the computational approximations

the orbital is a mathematical expression, describing the probability of finding an electron at some point near the nucleus

the amplitude of an atomic orbital varies with distance from the nucleus in a not quite exponential fashion
generally, MOs are expressed as linear combinations of atomic orbitals (LCAO), the sum of atomic orbitals centered on each nucleus

the accuracy of the representation of the true molecular orbital as an LCAO increases with the size of the basis set

basis set is the number of atomic orbitals employed in the approximation

basic features of LCAO MOs:

MOs are formed from all the valence orbitals, but do not refer to the number of electrons that are to be accommodated
N atomic orbitals overlap to form N molecular orbitals
for a given set of contributing atomic orbitals, the greater the number of interatomic nodes, the greater the energy
the appropriate number of electrons is accommodated in accord with the rules of the building up principle.

Developed by

The Shodor Education Foundation, Inc.
in cooperation with the
National Center for Supercomputing Applications

ChemViz

Overview

Overview of Hartree-Fock (HF) Approximation

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Overview