Thermodynamic properties from static-lattice calculations with soft modes

While phase transition pressures and zero temperature thermodynamic properties can be accurately determined from electronic structure calculation, transition temperatures are more problematic because of the need to sample phase space and quantise vibrations. The quasiharmonic method has proved extremely accurate for calculating thermodynamic properties up to 90% of the melting point without explicit phase space sampling for most materials, but has low temperature divergences for soft mode materials such as perovskites. Here we present a modified quasiharmonic method which avoids these difficulties. Using a simple model system, we demonstrate trends of behaviour in both the classical and quantum limits showing the importance of phonon quantisation in soft-mode behavior.