The removal of a fluorine atom from its central position in a cubiclike Li14F13+ cluster creates an F-center vacancy that may or may not be occupied by the remaining odd electron. The topology exhibited by the electron density in Li14F12+, the F-center cluster, enables one to make a clear distinction between the two possible forms that the odd electron can assume. If it possesses a separate identity, then a local maximum in the electron density will be found within the vacancy and the F-center will behave quantum mechanically as an open system, bounded by a surface of local zero flux in the gradient vector field of the electron density. If, however, the density of the odd electron is primarily delocalized onto the neighboring ions, then a cage critical point, a local minimum in the density, will be found at the center of the vacancy. Without an associated local maximum, the vacancy has no boundary and is undefined. Self-consistent field (SCF) calculations with geometry optimization of the Li14F13+ cluster and of the doublet state of Li14F12+ show that the creation of the central vacancy has only a minor effect upon the geometry of the cluster, the result of a local maximum in the electron density being formed within the vacancy. Thus the F-center is the physical manifestation of a non-nuclear attractor in the electron density. It is consequently a proper open system with a definable set of properties, the most characteristic being its low kinetic energy per electron. In addition to determining the properties of the F-center, the effect of its formation on the energies, volumes, populations, both electron and spin, and electron localizations of the ions in the cluster are determined. (C) 1997 American Institute of Physics. [S0021-9606(97)51344-4].