The stochastic self-consistent harmonic approximation: calculating vibrational properties of materials with full quantum and anharmonic effects

Abstract

The efficient and accurate calculation of how ionic quantum and thermal fluctuations impact the free energy of a crystal, its atomic structure, and phonon spectrum is one of the main challenges of solid state physics, especially when strong anharmonicy invalidates any perturbative approach. To tackle this problem, we present the implementation on a modular Python code of the stochastic self-consistent harmonic approximation (SSCHA) method. This technique rigorously describes the full thermodynamics of crystals accounting for nuclear quantum and thermal anharmonic fluctuations. The approach requires the evaluation of the Born-Oppenheimer energy, as well as its derivatives with respect to ionic positions (forces) and cell parameters (stress tensor) in supercells, which can be provided, for instance, by first principles density-functional-theory codes. The method performs crystal geometry relaxation on the quantum free energy landscape, optimizing the free energy with respect to all degrees of freedom of the crystal structure. It can be used to determine the phase diagram of any crystal at finite temperature. It enables the calculation of phase boundaries for both first-order and * Authors to whom any correspondence should be addressed.Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Quantum anharmonic enhancement of superconductivity in P63/mmc ScH6 at high pressures: A first-principles study

“…The effect of quantum ionic fluctuations and anharmonicity is estimated using the stochastic self-consistent harmonic approximation (SSCHA) code [40], whose theoretical basis was developed in Refs. [29,30,41,42].…”

“…We used PAW pseudopotentials [51,52], including 11 electrons in the valence for Sc. The SSCHA [40] minimization requires the calculation of energies, forces, and stress tensors in supercells. These were calculated as well within DFT at the PBE level with Quantum ESPRESSO, making use of the same pseudopotentials.…”

TOLOMEO, a Novel Machine Learning Algorithm to Measure Information and Order in Correlated Networks and Predict Their State

“…If the inequality ( 11) is not satisfied, a new Monte Carlo-Metropolis algorithm is performed with the last h, J values and the ensemble is updated. The use of Equation (11) to evaluate the importance sampling proved to be very efficient in similar algorithms [27,28].…”

The microscopic origin of the anomalous isotopic properties of ice relies on the strong quantum anharmonic regime of atomic vibration

“…The coexistence of strong intra-molecular and weak intermolecular bonds in ice produces a vast vibrational spectrum. To compare with experimental results, we computed the real phonons from the dynamical interacting Green function within the timedependent SSCHA 60,62,82 (TD-SSCHA) to account for dynamical quantum anharmonic effects (see Appendices A and F for further details). We employed the static approximation of the selfenergy for the low-energy modes, as described in Appendix A and Refs.…”

“…[52][53][54][55][56][57][58] An accurate description of atomic vibrations is of paramount importance to reproduce thermodynamic and dynamical properties. In this work, we overcome the intrinsic limitations of other methodologies by using the selfconsistent harmonic approximation (SSCHA), [59][60][61][62]82 which exploits a full-quantum variational principle on the free energy to account for the effect of anharmonicity arising from thermal and quantum fluctuations.…”