Ab-initio perspective on the Mollwo-Ivey relation for F-centers in alkali halides

We revisit the well-known Mollwo-Ivey relation that describes the universal dependence of the absorption energies of F-type color centers on the lattice constant $a$ of the alkali-halide crystals, $E_{mbox{abs}}propto a^{-n}.$ We perform both state-of-the-art ab-initio Quantum Chemistry and post-DFT calculations of F-center absorption spectra. By tuning independently the lattice constant and the atomic species we show that the scaling of the lattice constant alone (keeping the elements fixed) would yield $n=2$ in agreement with the particle-in-the-box model. Keeping the lattice constant fixed and changing the atomic species enables us to quantify the ion-size effects which are shown to be responsible for the exponent $n approx 1.8$.