Chem6440 basis - Chemistry 6440 7440 Basis Sets for...

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Chemistry 6440 / 7440 Basis Sets for Molecular Orbital Calculations
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Resources Foresman and Frisch, Exploring Chemistry with Electronic Structure Methods, Chapter 5 Cramer, Chapter 6 Jensen, Chapter 5
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LCAO Approximation numerical solutions for the Hartree-Fock orbitals only practical for atoms and diatomics diatomic orbitals resemble linear combinations of atomic orbitals e.g. sigma bond in H 2 σ 1s A + 1s B for polyatomics, approximate the molecular orbital by a linear combination of atomic orbitals (LCAO) = μ μ μ χ φ c
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Basis Functions 2200 χ ’s are called basis functions usually centered on atoms can be more general and more flexible than atomic orbitals larger number of well chosen basis functions yields more accurate approximations to the molecular orbitals = μ μ μ χ φ c
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Slater-type Functions exact for hydrogen atom used for atomic calculations right asymptotic form correct nuclear cusp condition 3 and 4 center two electron integrals cannot be done analytically ( 29 ( 29 ( 29 ) 2 / exp( 32 / ) ( ) 2 / exp( 96 / ) ( ) exp( / ) ( 2 2 / 1 5 2 2 2 2 / 1 5 2 2 1 2 / 1 3 1 1 r x r r r r r r p p px s s s s s s ζ π ζ χ ζ π ζ χ ζ π ζ χ - = - = - =
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Gaussian-type Functions die off too quickly for large r no cusp at nucleus
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