Directed Valence as a Property of Determinant Wave Functions

Making use of Slater's extension of the Heitler-London method, it is shown that the directional properties of carbon valences are a logical consequence of the combination of the hydrogen-like individual electron orbitals of carbon into a determinant wave function. It is possible to separate the radial and angular parts of such a function by factoring. Partial differentiation of the factored function with respect to the angular variables leads to proof of the directional properties, while partial differentiation with respect to the radial variable shows that, as long as all valence electrons are at equal distances from the nucleus, the electron density is maximum at points located on a sphere whose radius is calculated.