Description of the Distribution of Electrons in the Methane Molecule

A formal scheme is presented for describing the electron distribution in the methane molecule. Purely theoretical electron density contour maps for the ground state of the molecule are displayed, and various aspects of the electronic distribution are discussed. The electronic wavefunction employed is an analytical form composed of atomic orbitals of s through g type centered on the carbon nucleus. The electronic charge density ρ is expressed as a series of normalized (to 4π) tetrahedral harmonics T_l (θ,φ), which are certain symmetrical linear combinations of spherical harmonics of the given l value. Namely, $${\text{4πρ(r,θ,φ)=Σ}}_l{A}_l{\mathrm{(r)T}}_l\mathrm{(\theta ,\phi ),}$$ where the A_l(r) depend only on r, the radial distance from the carbon nucleus. The functions A_l(r) are tabulated, and contour maps of ρ are developed. The molecular octupole moment is predicted to be about 1.7×10^—24e·cm³. The distribution of electrons in a single carbon—hydrogen bond is considered from several points of view, with the purpose, among others, of elucidating the question of the sign and magnitude of the ``CH bond moment.''