lecture36_umn

lecture36_umn - Lecture 36 Electron Correlation...

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Lecture 36 December 11, 2009 Electron Correlation Multiconfiguration Self-Consistent Field Theory Configuration Interaction with a Single Determinant Reference
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Hartree-Fock Theory again Approximation : each electron moves in the static electric field created by all of the other electrons . Optimization of the orbitals in a self-consistent fashion subject to a variational constraint . Expectation value: lowest possible energy for a single- determinantal wave function formed from the chosen basis set . How can we improve the HF wave function? Variational principle: a more accurate wave function. We cannot do better than the HF wave function with a single determinant .
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How to do better Construct a wave function as a linear combination of multiple determinants (36-1) coefficients c reflect the weight of each determinant in the expansion and also ensure normalization. First determinant: HF determinant. For the majority of the chemical species , the chief error in the HF approximation derives from ignoring the correlated motion of each electron with every other . " = c 0 " HF + c 1 " 1 + c 2 " 2 + !
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Definition : difference between the exact eigenvalue of the non- relativistic Hamiltonian and the restricted HF energy. This kind of electron correlation is called dynamical correlation . It refers to the dynamical character of the electron-electron interactions. Empirically, it is observed that for most systems the HF wave function dominates in the linear combination expressed by eq. 36-1; even though the correlation energy may be large, it tends to be made up from a large sum of small contributions from other determinants. Definition works well for closed-shell systems! More problems when degeneracies or near degeneracies occur between different electronic configurations. Ex: RHF energy for H 2 at large internuclear distance has an error of 7 eV. " = c
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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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lecture36_umn - Lecture 36 Electron Correlation...

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