Localized impurity states in the Hartree‐Fock, LCAO approximation II. The F Center in KCI

Abstract

AbstractWe apply the techniques of a previous paper (I) to the F center in KCl. Our purpose is to place the application of Hartree‐Fock methods to the F center on a firm theoretical basis by calculating in a consistent manner the magnitude and effect of approximations commonly made in less complete treatments. It is shown that the familiar point‐ion approximations and crystal‐field approximations with partial consideration of exchange effects are special cases of our results. We compute wave functions and energies step by step for each of the various levels of approximation possible with our model. It is found that the functions resulting from the point‐ion model are not good approximations to the final wave functions. Our results show that exchange effects with at least the first two shells of nearest neighbors should be considered since they are of the same order of magnitude as terms in the point‐ion model. Overlaps of the F‐center function with ion functions out to sixth neighbors are considered. The absorption energy for the F center is calculated to be 0.1619 Ry as compared with the experimentally observed energy of 0.170 Ry. The magnetic hyperfine structure contact terms are calculated for the first two shells of nearest neighbor ions, using approximate orthogonalized functions, and found to be 29.7 Mc/h for the nearest neighbor K+ ions and 10.9 Mc/h for the next nearest neighbor Cl− ions. The experimentally observed values are 21.6 and 7.0, respectively. Given these differences and the excessively low values of the one‐electron energies, it is concluded that electronic and ionic polarization effects in the ionized crystal states must be considered to calculate accurate F‐center wave functions and absolute energy levels.