Pressure and stress tensor of complex anharmonic crystals within the stochastic self-consistent harmonic approximation

Abstract

The self-consisted harmonic approximation (SCHA) allows the computation of free energy of anharmonic crystals considering both quantum and thermal fluctuations. Recently, a stochastic implementation of the SCHA has been developed, tailored for applications that use total energy and forces computed from first principles. In this work, we extend the applicability of the stochastic SCHA to complex crystals with many degrees of freedom, with the optimisation of both the lattice vectors and the atomic positions. To this goal, we provide an expression for the evaluation of the pressure and stress tensor within the stochastic SCHA formalism. Moreover, we develop a more robust free energy minimisation algorithm, which allows us to perform the SCHA variational minimisation very efficiently in systems having a broad spectrum of phonon frequencies and many degrees of freedom. We test and illustrate the new approach with an application to the phase XI of water ice using density-functional theory. We find that the SCHA reproduces extremely well the experimental thermal expansion of ice in the whole temperature range between 0 K and 270 K, in contrast with the results obtained within the quasi-harmonic approximation, that underestimates the effect by about 25%. arXiv:1804.06793v1 [cond-mat.mtrl-sci]

Quantum crystal structure in the 250-kelvin superconducting lanthanum hydride

“…Harmonic phonon frequencies were calculated within density functional perturbation theory (DFPT) [31] making use of the Quantum ESPRESSO code [32,33]. The SSCHA [26][27][28]34] 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.…”

“…This picture completely changes when including the energy of quantum atomic fluctuations, the zero-point energy (ZPE). We calculate the ZPE within the stochastic self-consistent harmonic approximation (SSCHA) [26][27][28]. The SSCHA is a variational method that calculates the E(R) energy of the system including atomic quantum fluctuations as a function of the centroid positions R, which determine the center of the ionic wave functions.…”

“…We perform a minimization of E(R) and determine the centroid positions at its minimum. By calculating the stress tensor from E(R) [28], we relax the lattice parameters seeking for structures with isotropic stress conditions considering quantum effects. We start the quantum relaxation for both R-3m and C2 phases with the lattice that yields a classical isotropic pressure of 150 GPa and vanishing classical forces, i.e., calculated from V (R).…”

Quantum Enhancement of Charge Density Wave in NbS2 in the Two-Dimensional Limit

“…In this letter we investigate, from first-principles, the vibrational properties of bulk 2H-NbS 2 (at zero and finite pressure) and suspended 1H-NbS 2 , taking into account quantum anharmonic effects at non-perturbative level in the framework of the stochastic self-consistent harmonic approximation (SSCHA) [24][25][26][27] . For bulk 2H-NbS 2 , we show that quantum anharmonic effects remove the instability found at harmonic level, and give temperature dependent phonon energies in quantitative agreement with experiment.…”

Quantum effects in muon spin spectroscopy within the stochastic self-consistent harmonic approximation

“…In this paper, we describe a stochastic self-consistent harmonic approximation (SSCHA) that allows us to include the effects of anharmonicity in the muon vibrations [23][24][25][26]. The SSCHA is a quantum variational method that efficiently calculates anharmonic free energies and phonon frequencies in a non-perturbative way.…”