# DFT Calculations of Temperature-Dependent NQR Parameters in {\alpha}-paradichlorobenzene and {\beta}-HMX

## TL;DR

This paper presents a first-principles DFT-based method to predict temperature-dependent NQR spectra in molecular crystals without relying on empirical potentials or detailed internal motion models, applicable to any periodic solid with known structure.

## Contribution

The method combines DFT, molecular dynamics, and dynamic corrections to accurately predict T-dependent NQR parameters ab initio, independent of specific intermolecular potential assumptions.

## Key findings

- Successfully predicts temperature-dependent NQR frequencies for 35Cl and 14N in two crystals.
- Requires no prior knowledge of intermolecular potentials or internal motions.
- Applicable to any periodic solid with known structural data.

## Abstract

A method for first principles predictions of observed temperature-dependent NQR spectra is presented using density functional theory (DFT) and the isobaric T-dependent NQR frequencies of 35Cl and 14N nuclei are computed for the two molecular crystals (1) alpha-paradichlorobenzene, and (2) the nitroamine high explosive beta-HMX (beta-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) over a range of 200 K and up to room temperature. Notably, the method requires no supposition of a form for the intermolecular potentials or wave functions, requires no particular insight as to the nature of the internal motions or of the chemical bonds present, and does not depend on the crystal structure, making the method amenable to any periodic solid for which experimentally determined structural data are available. For each substance, unit cells of various volume are prepared using experimentally determined atomic positions and cell parameters. In each of the prepared volume-corrected cells, a molecular dynamics (MD) simulation generates a set of perturbed atomic positions, the collection of which is intended to represent the system at a given T,V. For each configuration of atoms generated along the MD trajectory, the electric field gradient (EFG) tensors are computed at the site of each quadrupolar nucleus. The rotational displacements of the moving EFG principal axes from their equilibrium directions are used to apply a dynamic correction to the DFT-computed static-lattice NQR frequencies, resulting in first-principles DFT predictions of T-dependent NQR spectra at constant pressure. Because the V-dependence from thermal expansion and the T-dependence due to internal motions are simultaneously considered, the NQR's notoriously model-dependent temperature coefficients are computed entirely ab-initio.