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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 5.04 Principles of Inorganic Chemistry II Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . 5.04, Principles of Inorganic Chemistry II Prof. Daniel G. Nocera Lecture 6: LCAO and Hckel Theory 1 (Eigenfunctions) A common approximation employed in the construction of molecular orbitals (MOs) is the linear combination of atomic orbitals (LCAOs). In the LCAO method, the k th molecular orbital, k , is expanded in an atomic orbital basis, k = c a a + c b b + c i i where the i s are normalized atomic wavefunctions and i i d = 1. Solving Schrdingers equation and substituting for k yields, k = E k E = k E c a a + c b b + ... + c i i = 0 Left-multiplying by each i yields a set of i linear homogeneous equations, c a E + c b E + K + c i E = a a a b a i c a E + c b E + K + c i E = b a b b b i c a E + c b E + K + c i E = i a i b i i Solving the secular determinant, aa aa ES H ab ab ES H L L ai ai ES H ba ba ES H bb bb ES H L L bi bi ES H M O M = 0 M O M ia ia ES H ib ib ES H L L ii ii ES H where H ii = i i d ; S ii = i i d = 1; H ij = i j d ; S ij = i j d 5.04, Principles of Inorganic Chemistry II Lecture 6 Prof. Daniel G. Nocera Page 1 of 6 In the Hckel approximation, H ii = H ij = 0 for i not adjacent to j H ij = for i not adjacent to j S ii = 1 S ij = 0 The foregoing approximation is the simplest. Different computational methods treat these integrals differently. Extended Hckel Theory (EHT) includes all valence orbitals in the basis (as opposed to the highest energy atomic orbitals), all S ij s are calculated, the H ii s are estimated from spectroscopic data (as opposed to a constant, ) and H ij s are estimated from a simple function of S ii , H ii and H ij (zero differential overlap approximation)....
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Lecture_6 - MIT OpenCourseWare http://ocw.mit.edu 5.04...

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