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lecture29_umn - Lecture 29 A Hartree-Fock Calculation on...

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Lecture 29 November 20, 2009 A Hartree-Fock Calculation on the Water Molecule
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Hartree Fock Molecular Orbitals Solve the HF secular determinant and find its various roots. (29-1) We know how to compute overlap integrals. Fock matrix elements are defined by (29-2) F 11 ES 11 F 12 ES 12 ! F 1 N ES 1 N F 21 ES 21 F 22 ES 22 ! F 2 N ES 2 N " " # " F N 1 ES N 1 F N 2 ES N 2 ! F NN ES NN = 0 F μ ! = μ 1 2 " 2 ! Z k k nuclei # μ 1 r k ! + P $% $% # μ ! $% ( ) 1 2 μ $ !% ( ) ( )
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Choose a basis set Choose a molecular geometry Compute Store integrals Guess initial density matrix P (0) Construct and solve HF secular equation Construct P From occupied MOs Is P (n) sufficiently similar to P (n-1)? Output data single point Replace P (n-1) with P (n) no P !" = 2 a ! i i occupied # a " i a : coefficients of the basis functions in the occupied molecular orbitals. (29-3)
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HF for the Water Molecule In cartesian coordinates (Å): O (0.000, 0.000, 0.116) H (0.000, 0.751, 0.465) H (0.000, 0.751, 0.465) Origin: molecular center of mass Atoms lie in the yz plane (all x coordinates are zero) z axis is the symmetry axis of rotation present in the water molecule that makes it belong to the symmetry point group C 2 v 0.95 Å 0.95 Å 104.5° z y
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H a O H b x y z Basis Functions 1s 2s 2p x 2p y 2p z 1s(H a ) 1 2 3 4 5 6 7 1s(H b )
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(29-4) S = 1.000 0.237 1.000 0.000 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.055 0.479 0.000 0.313 ! 0.242 1.000 0.055 0.479 0.000 ! 0.313 ! 0.242 0.256 1.000 " # $ $ $ $ $ $ % Lower packed triangular: every element m , n is the same as the element
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This note was uploaded on 12/14/2010 for the course CHEM 3502 taught by Professor Staff during the Fall '08 term at Minnesota.

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lecture29_umn - Lecture 29 A Hartree-Fock Calculation on...

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