THE ELECTRONIC WAVE FUNCTION OF $CH_{4}^{*}$
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Date
1955
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Ohio State University
Abstract
Approximate molecular orbitals for the ground state of $CH_{4}$ have been obtained as linear combinations of Gaussian functions (of the form exp $-ar^{2}, r^{2} exp -br^{2}$, and $x,y,z exp -cr^{2}$) by Roothaan’s method. An extensive configuration interation calculation was carried out, based upon perturbation methods. Five independent functions of s symmetry and two of p symmetry centered on the carbon nucleus were combined with a single function on each of the hydrogen nuclei. Values of the seven nonlinear parameters which specify the basic Gaussian functions on carbon were determined by iterating a modified Roothaan procedure for the atomic wave function. All configurations contributing more than 0.0005 atomic units to the calculated total energy were included in the configuration interaction calculations for both $^{3}P$ carbon and $CH_{4}$. The binding energy obtained for $CH_{4}$ was approximately half of the experimental value. If configuration interaction had been neglected, the calculated binding energy would have been decreased by about one-eight, or approximately seven percent of the experimental value. The CH bond ``equivalent orbital” obtained from $CH_{4}$ molecular orbitals has its charge centroid at a point $1.344 a_{o}$ from the carbon atom. The CH bond length was taken to be $2.0665 a_{o}$. Most of the numerical work was programmed for the EDSAC digital computer at Cambridge University.
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Author Institution: Massachusetts Institute of Technology