? D. A. McQuarrie, J.D. Simon, Physical Chemistry: A Molecular Approach, Univers

Question

? D. A. McQuarrie, J.D. Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997.

? P. W. Atkins, J. de Paula, Physical Chemistry, 10th Ed., W. H. Freeman and Co., New York, 2010.

? T. Engel, P. Reid, Physical Chemistry, 3rd Ed., Pearson Education, INC San Francisco 2010

Hartree-Fock Equation The starting point of the Hartree-Fock procedure for helium is to write the two-electron wavefunction as a product of orbitals . The probability distribution of electron 2 can be interpreted classically a s a charge density and thus, the potential energy that electron 1 experiences at the point r, due to electron 2 is In atomic units 12 Where the superscript "eff" emphasizes an effective, or average, potential .The effective one-electron Hamiltonian operator is .The effective one-electron Hamiltonian operator is This is known as h"(r)(r)-6(t) Hartree-Fock Equation There is a similar equation for d(r2), but because (r) and d(r) have the same functional form, we need to consider only one equation .

Explanation / Answer

The Hartree-Fock method seeks to approximately solve the Schrodinger equation, and it assumes that the wavefunction can be approximated by a Slater determinant (orbital) made up of one spin orbital per electron. The Hartree-Fock method determines the set of spin orbitals which minimize the energy and give us this best determinant. The Hartree-Fock equations can be solved numerically (exact Hartree-Fock), or they can be solved in the space spanned by a set of basis functions. In either case, the solutions depend on the orbitals (determinats) . Hence, we need to guess some initial orbitals and then refine our guesses iteratively. For this reason, Hartree-Fock is called a self-consistent field (SCF) approach.

The correlation energy or exchange is used because the electron is exchanged between the two orbitals you are approximating. This overlap contribution to the charge density and potential energy is a quantum mechanical effect.

The reference is

Molecular Modelling: Principles and Applications (2nd Ed) Andrews Leach, Prentice Hall 2001

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