A semiempirical Hartree-Fock approach to solid-state calculations for inelastic neutron scattering

Abstract

The scattering function, S(Q,ω), representing the interaction between the incident neutron and the pseudopotential, representing an ensemble of atoms, may be determined in a variety of ways: Via classical force-field approaches, through electronic structure calculations, through analytical approaches and through a combination of one or both of the first two approaches and applying molecular dynamics to study systems under non-equilibrium conditions. Electronic structure calculations quickly become computationally intensive and opaque once more than several hundred atoms are involved in a cluster or unit cell that represents the system under investigation.

In the case of neutron spectroscopy many systems investigated are dominated by hydrogen vibrations as the total scattering coefficient, total~82 Barn is approximately an order of magnitude larger than most total scattering coefficients from other elements. Scatter from hydrogen is mainly incoherent and therefore may be considered localised allowing potentially simple molecular models to be employed in the study of hydrogenous materials. Here, a well known Hartree-Fock semi-empirical calculation scheme is presented that is lightning fast for small molecules and adequate for large molecules, clusters, and dynamical studies.

Force constants are obtained by diagonalisation of the mass-weighted Hessian matrix to obtain the vibrational frequency for each mode assuming that each atomic-pair vibrates in a simpleharmonic fashion. The scattering function, S(Q, ω), is then calculated firstly assuming a oneatom oscillator, then secondly more thoroughly for each atom-pair vibration within the molecule/cluster, and finally as a weighted phonon density of states. A number of benchmark molecules are reported on. Interestingly, these rapid calculations give a very good estimation of the scattering function that can be used for initial peak identification and further analysis of the detailed electronic and vibrational structure.