lecture29_umn

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

This preview shows pages 1–7. Sign up to view the full content.

Lecture 29 November 20, 2009 A Hartree-Fock Calculation on the Water Molecule

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 \$ !% ( ) ( )
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)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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 )

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
(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
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 12/14/2010 for the course CHEM 3502 taught by Professor Staff during the Fall '08 term at Minnesota.

### Page1 / 17

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

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online