Atomic Orbitals (AO) and Molecular Orbitals (MO)

Abstract

The solution of the Schrödinger equation for the hydrogen atom can rarely be used directly in more complex chemical problems. This solution nevertheless forms a basis for the study of more complicated atoms and even for molecules. The possible modes of graphical representation of the radial and angular parts of hydrogen-type functions — the atomic orbitals — have already been described. Thus only a few remarks will be given here in this connection:

• (i) The application of computers permits information on the graphical representation of complete AO’s to be obtained¹.

• (ii) Frequently, the graphical representation of the angular part is particularly useful. It should be noted that the contours in Fig. 3–10b indicate the regions in space in which the electron can be found (with the given probability). This figure is not to be understood as describing a “smearing out” of the electron charge in space.

• (iii) The sign of the wave function (+ or −) in the individual AO parts must be specified. This is important when analyzing the symmetry of the studied formations and in the calculation of some integrals. The sign of the wave function is, however, of no physical importance (in the sense of comparison with a physical quantity).