Obtaining the Hessian from the force covariance matrix: Application to crystalline explosives PETN and RDX
Abstract
We show that for solids the effective Hessian matrix, averaged over the canonical ensemble, can be calculated from the force covariance matrix. This effective Hessian reduces to the standard Hessian as the temperature approaches zero, while at finite temperatures it implicitly includes anharmonic corrections. As a case study, we calculate the effective Hessians and the corresponding normal mode eigenvectors and frequencies for the crystalline organic explosives pentaerythritol tetranitrate and α-1,3,5-trinitro-1,3,5-triazacyclohexane. The resulting normal mode frequencies are compared to those obtained by diagonalizing the standard Hessian matrix of second derivatives in Cartesian displacements about the potential energy minimum. Effects of temperature and statistical noise on the effective Hessians and normal mode frequencies are discussed.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Apr 07, 2015
- Source ID
- 10.1063/1.4916614
Entities
People
- Andrey Pereverzev
- Tommy Sewell
Organizations
- Office of Naval Research
- University of Missouri