Numerical Optimization of Density Functional Tight Binding Models: Application to Molecules Containing Carbon, Hydrogen, Nitrogen, and Oxygen

Abstract

New parametrizations for semiempirical density functional tight binding (DFTB) theory have been developed by the numerical optimization of adjustable parameters to minimize errors in the atomization energy and interatomic forces with respect to ab initio calculated data. Initial guesses for the radial dependences of the Slater-Koster bond integrals and overlap integrals were obtained from minimum basis density functional theory calculations. The radial dependences of the pair potentials and the bond and overlap integrals were represented by simple analytic functions. The adjustable parameters in these functions were optimized by simulated annealing and steepest descent algorithms to minimize the value of an objective function that quantifies the error between the DFTB model and ab initio calculated data. The accuracy and transferability of the resulting DFTB models for the C, H, N, and O system were assessed by comparing the predicted atomization energies and equilibrium molecular geometries of small molecules that were not included in the training data from DFTB to ab initio data. The DFTB models provide accurate predictions of the properties of hydrocarbons and more complex molecules containing C, H, N, and O.

Examining the chemical and structural properties that influence the sensitivity of energetic nitrate esters

“… 1 , 15 Since our DFTB theory is an approximate, semi-empirical method, we have tested the accuracy of its predictions against more exact ab initio calculations. 47 Our analysis of bond dissociation and isomerization energies of PETN using the DFTB- lanl1 parameter set 46 versus density functional theory calculations by Tsyshevsky et al 15 showed very good quantitative agreement, which allows us to apply DFTB theory to nitrate ester chemistry with good confidence. The reactive MD simulations presented here were performed with a new parameterization, DFTB- lanl22 , which improves the description of the relative energies of the HONO and HNO 2 isomers with respect to DFTB- lanl1 .…”

“…It has been applied extensively in simulations of organic materials, including explosives. 45 The simulations employed the DFTB parameterizations for C/H/N/O-containing molecules developed using the numerical optimization framework that was advanced recently by Krishnapriyan et al 46 …”

A Density Functional Tight Binding Layer for Deep Learning of Chemical Hamiltonians

“…A number of recent DFTB parameterizations have, in addition to fitting the repulsive potential, empirically adjusted parameters that define the electronic Hamiltonian during the fitting process. [53][54][55][56][57] Adjusted parameters include those that define the constraining potential and electron density cutoffs in the standard approach utilized to construct the DFTB electronic Hamiltonian from QC solutions for isolated atoms. 53,55,56 Empirical fits have also adjusted the atomic orbital energies, and the Hubbard parameters that specify electron-electron repulsion.…”

BOPcat software package for the construction and testing of tight-binding models and bond-order potentials

“…The objective function can also be normalized by the variance of the properties as in Ref. 25 . For construction purposes, this module provides an interface between objective function and optimizer algorithms that are either readily available in the Python modules Scipy 26 and NLopt 27 or provided by the user as external module.…”