A One-Center Wave Function for the Methane Molecule

Abstract

Slater orbitals, centered on the carbon nucleus and having variable orbital exponents and principal quantum numbers, are used to construct electronic wave functions for the ground state of the methane molecule of the form $${\mathrm{\Psi =C}}_1{\mathrm{(s}}^2{s}^{\text{*2}}{p}^6{\mathrm{)+C}}_2{\mathrm{(s}}^2{s}^{\text{*2}}{p}^5{\mathrm{d)+C}}_3{\mathrm{(s}}^2{s}^{*}{\mathrm{fp}}^6{\mathrm{)+C}}_4{\mathrm{(s}}^2{s}^{\text{*2}}{p}^5{f}^{\prime }{\mathrm{)+C}}_5{\mathrm{(s}}^2{s}^{\text{*2}}{p}^5\mathrm{g).}$$ Values for the five linear coefficients, the seven orbital exponents, and the seven principal quantum numbers are determined by the variational method. The total molecular energy obtained from a one‐term wave function of this form is —39.50 a.u.; the five‐term result is —39.80 a.u.; the experimental nonrelativistic energy is —40.51 a.u. Comparison with a similar calculation for the neon atom indicates that most of the residual error is in correlation energy, and it favors the high value for the heat of sublimation of carbon.