By D. B. Cook

ISBN-10: 0408705515

ISBN-13: 9780408705516

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**Sample text**

2 is the most common. Molecules have different shapes and symmetries and so any basis functions used to expand the molecular orbitals can not be so general. It is easy to guess 1 a limiting form for the MO s in the region of each atom: the molecular orbitals must pass over into atomic orbitals close to each nucleus. What better form for the approximate MO ! s, on both mathematical and chemical grounds, than a Linear Combination of Atomic Orbitals (LCAO) - a linear combination of the orbitals of the constituent atoms of the molecule?

R)$(s) is written φ.. A bar over a spatial orbital signifies that the occupying electron has 3 spin and no bar means a spin. Unless they are required for emphasis, the appearances of the explicit variables of the electrons - r. and x. - are also suppressed. There is little danger of confusion over the two possible meanings of φ. - a spatial orbital and an a spin spin-orbital - since, in practice, the spin-orbital form usually only appears in a determinant. 1) becomes f = deti+j Φ\ Φ 2 Φ 2 ... 5)).

K ... 10) have been collected into the matrix GJ the "total electron interaction matrix1' of Roothaan: Gk = m I r,s=l {[2(k£,rs)-(kr,*s)] = m I r,s=l {2(k*,rs)-(kr,*s)} n/2 ... 13) ( C C )rs The integrals involving the basis functions χ. and the electron repulsion operator g(1,2) have been abbreviated to (ki,,rs) where (U,rs) = fdr 1 fdr 2 x k (r 1 ) Xjl (r 1 )è(l,2)x r (r 2 )x s (r 2 ) The matrix H i s u s u a l l y r e f e r r e d t o as t h e Hamiltonian matrix one-electron and t h e b a s i s f u n c t i o n i n t e g r a l s as the electron repulsion two-electron integrals.

### Ab Initio Valence Calculations in Chemistry by D. B. Cook

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