CHEM6670Notes4 - Post HartreeFock methods Topics CHEM 6670...

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Post Hartree Fock methods 1 CHEM 6670 omputational Chemistry & Biophysics Computational Chemistry & Biophysics Post Hartree Fock methods January 24, 2008 Course instructor: Dr. Jana Khandogin Jana.Khandogin@ou.edu Course web site: http://ccb.ou.edu/teaching.aspx Topics Review: Hartree Fock theory lectron correlation methods (post Hartree ck methods): Electron correlation methods (post Hartree Fock methods): Configuration interaction method Møller Plesset perturbation method Coupled cluster method Comparison of electron correlation methods emi mpirical methods Se epc a et ods 2 Hartree Fock theory = ˆ N e wavefunction; amiltonian Unknown “Known” e e e e E H ψ N i F i i i i ,..., 1 ˆ = = φ ε total electronic energy 1 e spin orbitals; orbital energies Hamiltonian Fock operator Slater determinant Variational principle 3 C S C F = expansion coefficients in AO’s Fock matrix Basis functions electronic structure Electronic structure methods e e e e E H = ˆ Hartree Fock method I MP coupled uster Trial wave function: Single determinant Variational principle Approximations of integrals Adding more determinants Systematic convergence to exact solution 4 Semi empirical methods CI, MP, coupled cluster Density functional methods (implicitly model electron exchange and correlation by a functional of electron density)
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Post Hartree Fock methods 2 How to add correlation Improve trial wave function: add more determinants What determinants to add? Suppose, RHF calculation with M basis functions and N electrons: Total: M molecular orbitals, occupied: N/2, virtual: M N/2 Note: Only the occupied MO’s are used in the Slater determinant h t d d ith th it l MO’ ? Φ + Φ = Ψ i i i HF a a 0 What do we do with the virtual MO’s? Put electrons into virtual MO’s and replace the empty MO with the virtual MO that is now occupied and construct a new SD. 5 Slater determinant in RHF For a system of N electrons β φ α ) ( ) ( ... ) ( ) ( ... ... ... ... ) ( ) ( ... ) ( ) ( ) ( ) ( ... ) ( ) ( ! 1 2 / 2 / 1 1 2 2 / 2 2 / 2 1 2 1 1 2 / 1 2 / 1 1 1 1 N N N N N N N N N N r r r r r r r r r r r r N r r r r r r r r r r r r The row: same electron (or spatial coordinate) but can occupy N/2 MO’s or N spin orbitals The column: same MO but can be occupied but N electrons 6 An example: H 2 molecule Suppose we use 2 basis functions and RHF to calculate the lectronic structure of H olecule. N=2, M=2 electronic structure of H 2 molecule.N2 ,M2 Energy HF Single Double excitations Virtual orbitals occupied orbitals φ 1 φ 2 7 RHF ) ( ) ( ) ( ) ( 2 1 2 1 1 1 1 1 r r r r r r r r ) ( ) ( ) ( ) ( 2 1 2 1 1 2 1 2 r r r r r r r r Reference SD single type SD Different types of excited SD 8 RHF S type D type T type Q type Reference excited states
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Post Hartree Fock methods 3 Configuration interaction
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CHEM6670Notes4 - Post HartreeFock methods Topics CHEM 6670...

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