Homopolar Dipole

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Abstract
Numerical tables for the homopolar dipole or overlap moment μh.d. associated with various molecular orbitals (MO's) are presented. The present tables include values of μh.d./R for the common MO's constructed from linear combinations of atomic orbitals (the LCAO approximation), one of which is an 1s, 2s, 2pσ, 2pπ, 3s, or 3pσ orbital. The calculations employ approximate atomic orbitals of the Slater type. Formulas for x̄AB, the x coordinate of the centroid of negative charge for an electron in an MO, are given as functions of the parameters p=12R(ζA+ζB) and t=(ζA−ζB)/(ζA+ζB), where R is the internuclear distance, ζ (n—δ) is the effective nuclear charge found by the Slater rules, and (n—δ) is an effective quantum number. Values of μh.d./R are also given for some MO's in which one AO is a hybrid. The variation of μh.d. with the parameters p and t is shown graphically for certain MO's. The overlap moment μh.d. has been computed for various chemical bonds by use of the tables. Overlap integrals for the AO combinations 1s—3dσ, 2s—5s, 2s—5pσ, 2pπ—3dπ, and 3s—3s were computed since these were not available in the literature over the necessary range of the variables.

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