| Abstract: | A one‐dimensional probability density function, analogous to the atomic radial density for the hydrogen atom, r2Rnl(r), is defined for an arbitrary three‐dimensional density. It is obtained numerically by taking the derivative of a cumulative probability distribution with respect to the cubic root of the volume enclosed by each in a series of isosurfaces. Each point in the function is associated with a unique isosurface, and the isosurface associated with the maximum of the defined function represents the most probable isosurface with respect to the putative radius. This function therefore provides an objective selection criterion for a single isosurface to represent a three‐dimensional density. This technique is applied to set of canonical molecular orbitals. The selected threshold value varies from orbital to orbital, but the enclosed probability falls in the range of 20% to 55% for the reported orbitals. In all cases, the enclosed probability is much smaller than the common choices found in the literature. The concomitant smaller volume often makes possible a more localized interpretation and helps to clarify the conventional delocalized interpretation of molecular orbitals. For example, the isosurface plots selected by this method distinguish the formally bonding orbital in He2 from the true bonding orbital in H2. Examples from N2, F2, HF, H2O, C2H6, and Ni(CO)4 are also presented. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 310–321, 2000 |
