Calculating the logarithmic mean excitation energy from the Shannon information entropy of the electronic charge density

It is shown that within the local plasma approximation, the experimental logarithmic mean excitation energy that occurs in the expression for the stopping power is directly related to the Shannon entropy of the electronic charge density. This energy is calculated from the Shannon entropy of ab initio wave functions for several atoms and molecules. The results are consistent with experimental and theoretical values calculated by independent methods. The dependence of the mean excitation energy on the quality of the wave functions is examined. Furthermore, it is shown that the maximum entropy principle can be used as a guide in evaluating the local plasma model.