Anharmonic Vibrational States of Double-Well Potentials in the Solid State from DFT Calculations

TL;DR

This paper presents a DFT-based method for simulating quantum vibrational states in double-well potentials, capturing anharmonic effects relevant for thermodynamic and spectroscopic properties of materials.

Contribution

The authors develop and implement a general approach to model anharmonic vibrational states in molecules and solids using DFT-calculated potentials, integrated into the CRYSTAL package.

Findings

Successfully characterized soft lattice modes in thiourea phases

Identified anharmonic spectral features in terahertz spectra

Demonstrated temperature-dependent anharmonic behavior

Abstract

We introduce a general approach for the simulation of quantum vibrational states of (symmetric and asymmetric) double-well potentials in molecules and materials for thermodynamic and spectroscopic applications. The method involves solving the nuclear Schr\"odinger equation associated with a one-mode potential of the type $V (Q) = aQ^2 + bQ^3 + cQ^4$ (with $a < 0$ and $c > 0$), and thus explicitly includes nuclear quantum effects. The potential, $V (Q)$, is obtained from density functional theory (DFT) calculations performed at displaced nuclear configurations along the selected normal mode, $Q$. The strategy has been implemented into the CRYSTAL electronic structure package and allows for i) the use of many density functional approximations, including hybrid ones, and ii) integration with a quasi-harmonic module. The method is applied to the spectroscopic characterization of soft lattice modes in two phases of the molecular crystal of thiourea: a low-temperature ferroelectric phase and a high-temperature paraelectric phase. Signature peaks associated to structural changes between the two phases are found in the terahertz region of the electromagnetic spectrum, which exhibit strong anharmonic character in their thermal evolution, as measured by temperature-dependent terahertz time-domain spectroscopy.