Methods of Molecular Quantum Mechanics || Self-Consistent-Field Calculations and Model Hamiltonians

✍ Scribed by Magnasco, Valerio

• Publisher: John Wiley & Sons, Ltd
• Year: 2009
• Weight: 559 KB
• Category: Article
• ISBN: 0470684429
• DOI: 10.1002/9780470684559.ch7

✦ Synopsis

Self-consistent-field Calculations and Model Hamiltonians

Hartree-Fock (HF) theory was developed in the early 1930s by the theoretical physicists Hartree (1928a, 1928b) and Fock (1930) to deal with the quantum mechanical problem of many-particle atomic and molecular systems. Initially developed by Hartree for complex atoms in a numerical form using as Y the simple product of N spin-orbitals, the theory was put on a more sound basis by Fock, who first solved the variational problem of optimizing the orbitals in a determinantal Y obeying Pauli's antisymmetry principle. HF theory amounts essentially to finding the best form for the orbitals inside the so-called independent particle model (IPM), where an electron in the molecule is assumed to move in the average field provided by all nuclei and the sea of all other electrons. Besides the Coulomb potential J due to all electrons, the antisymmetry requirement imposed by Fock upon the wavefunction Y originates a nonlocal exchange potential K.

Since no correlation between the electrons is provided by this model, the HF energy is used to define exactly the correlation energy of the system as Correlation energy ¼ Exact energy of the nonrelativistic Hamiltonian À HF energy ð7:1Þ