A simple method to calculate specific heat at constant pressure from first principles

Calculating specific heat at constant pressure (Cp) entirely from first-principles has historically proven difficult, and what few methods which do exist are complex and require significant effort to implement. In this work, we describe a different method for calculating Cp which is entirely based on first-principles, density functional theory. It is conceptually simple, computationally efficient and easy to implement because it avoids the need for finite temperature density functional theory. In order to demonstrate the accuracy, precision and validity of our method, we present and discuss data and results for well-studied, benchmark semiconducting materials Si and Ge, where our results agree well with the prevailing literature. We also go further and calculate Cp for wurtzite GaN, a material for which there is no prevailing consensus. We use our calculated values and a review of the literature to determine a set of recommended values for GaN.