a-TDEP: Temperature Dependent Effective Potential for Abinit – Lattice dynamic properties including anharmonicity

• DOI: 10.1016/j.cpc.2020.107301
• Publication Date: 2020-03-30T23:42:40Z
• Authors: François Bottin; Jordan Bieder; Johann Bouchet
• Keywords: [PHYS]Physics [physics]; 0103 physical sciences; 7. Clean energy; 01 natural sciences

Abstract In this paper, we present the a-TDEP post-process code implemented in the Abinit package. This one is able to capture the explicit thermal effects in solid state physics and to produce a large number of temperature dependent thermodynamic quantities, including the so-called anharmonic effects. Its use is straightforward and require only a single ab initio molecular dynamic (AIMD) trajectory. A Graphical User Interface (GUI) is also available, making the use even easier. We detail our home made implementation of the original “Temperature Dependent Effective Potential” method proposed by Hellman et al. (2011). In particular, we present the various algorithms and schemes used in a-TDEP which enable to obtain the effective Interatomic Force Constants (IFC). The 2nd and 3rd order effective IFC are produced self-consistently using a least-square method, fitting the AIMD forces on a model Hamiltonian function of the displacements. In addition, we stress that we face to a constrained least-square problem since all the effective IFC have to fulfill the several symmetry rules imposed by the space group, by the translation or rotation invariances of the system and by others. Numerous thermodynamic quantities can be computed starting from the 2nd order effective IFC. The first one is the phonon spectrum, from which a large number of other quantities flow : internal energy, entropy, free energy, specific heat... The elastic constants and other usual elastic moduli (the bulk, shear and Young moduli) can also be produced at this level. Using the 3rd order effective IFC, we show how to extract the thermodynamic Gruneisen parameter, the thermal expansion, the sound velocities... and in particular, how to take into account the anisotropy of the system within. As representative applications of a-TDEP capabilities, we show the thermal evolution of the soft phonon mode of α -U, the thermal stabilization of the bcc phase of Zr and the thermal expansion of diamond Si. All these features highlight the strong anharmonicity included in these systems.