DIFFERENT BANDS FOR DIFFERENT SPINS. I. THE COHESIVE ENERGY OF AN ALKALI METAL. II. APPLICATION TO A LINEAR CHAIN OF HYDROGEN ATOMS. CRYSTAL INTEGRALS AND MOLECULAR INTEGRALS,
Abstract
The alternant molecular orbital (AMO) method was adapted to calculate the cohesive energy of an alkali metal. A certain amount of correlation between electrons with different spins is thereby taken into account. This is particularly important for large internuclear distances. While the ordinary Hartree-Fock energy for large distances tends to a value which is considerably higher than the ground state energy of free atoms, the AMO-energy tends to the correct limit. The main emphasis is placed on an AMO-version of the MO-LCAO-method, with the overlap between the atomic orbitals properly treated. Despite obvious similarities there are important differences in the type and amount of integral calculations required in a MO-LCAO calculation for a crystal and molecule. These differences are discussed and it is pointed out that some of the difficulties connected with 'crystal integrals' can be overcome by means of Lowdin's 'combined atomic orbitals.' A general formula is derived for the expansion of a function centered at one lattice site, around another site, when all the coordinate axes at the two sites are parallel. By means of this formula one can take maximum advantage of the crystal symmetry in the integral calculations. As illustrative examples we treat some typical Coulomb and exchange integrals occurring in calculations for crystals with cubic symmetry. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 15, 1964
- Accession Number
- AD0625411
Entities
People
- Jean-louis Calais
Organizations
- Uppsala University