Broadening of dielectric response and sum rule conservation

Different types of broadening of the dielectric response are studied with respect to the preservation of the Thomas-Reiche-Kuhn sum rule. It is found that only the broadening of the dielectric function and transition strength function conserve this sum rule, whereas the broadening of the transition probability function (joint density of states) increases or decreases the sum. The effect of different kinds of broadening is demonstrated for interband and intraband direct electronic transitions using simplified rectangular models. It is shown that the broadening of the dielectric function is more suitable for interband transitions while broadening of the transition strength function is more suitable for intraband transitions.