Time-Dependent Self Consistent Harmonic Approximation: Anharmonic nuclear quantum dynamics and time correlation functions

Abstract

Most material properties of great physical interest are directly related to nuclear dynamics, e.g. the ionic thermal conductivity, Raman/IR vibrational spectra, inelastic X-ray, and Neutron scattering. A theory able to compute from first principles these properties, accounting for the anharmonicity and quantum fluctuations in the nuclear energy landscape that can be implemented in systems with hundreds of atoms is missing. Here, we derive an approximate theory for the quantum time evolution of lattice vibrations at finite temperature. This theory introduces the time dynamics in the Self-Consistent Harmonic Approximation (SCHA) and shares with the static case the same computational cost. It is nonempirical, as pure states evolve according to the Dirac least action principle and the dynamics of the thermal ensemble conserves both energy and entropy. The static SCHA is recovered as a stationary solution of the dynamical equations. We apply perturbation theory around the static SCHA solution and derive an algorithm to compute efficiently quantum dynamical response functions. Thanks to this new algorithm, we have access to the response function of any general external time-dependent perturbation, enabling the simulation of phonon spectra without following any perturbative expansion of the nuclear potential or empirical methods. We benchmark the algorithm on the IR and Raman spectroscopy of high-pressure hydrogen phase III, with a simulation cell of 96 atoms. Our work also explores the nonlinear regime of the dynamical nuclear motion, providing a paradigm to simulate the interaction with intense or multiple probes, as in pump-probe spectroscopy, or chemical reactions involving light atoms, as the proton transfer in biomolecules

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• Quantum anharmonic enhancement of superconductivity in $P{6}_3/mmc$ ScH${}_6$ at high pressures: a first-principles study
• Automated all-functionals infrared and Raman spectra
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• Beyond Gaussian fluctuations of quantum anharmonic nuclei
• The effect of dressing on thermalization of interacting waves
• Beyond Gaussian fluctuations of quantum anharmonic nuclei. The case of rotational degrees of freedom
• Predicting electronic screening for fast Koopmans spectral functional calculations
• Optical control of the crystal structure in the bilayer nickelate superconductor La3Ni2O7 via nonlinear phononics
• The thermodynamics of CaSiO3 in Earth's lower mantle
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