Knowledge Bank

Approximate molecular orbitals for the ground state of $CH4$ have been obtained as linear combinations of Gaussian functions (of the form exp $-ar2,r2exp-br2$, and $x,y,zexp-cr2$) 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 $\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}P$ carbon and $CH4$. The binding energy obtained for $CH4$ 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 $CH4$ molecular orbitals has its charge centroid at a point $1.344ao$ from the carbon atom. The CH bond length was taken to be $2.0665ao$. Most of the numerical work was programmed for the EDSAC digital computer at Cambridge University.