Tag Archives: Akshay Krishna Ammothum Kandy

Curvature Constrained Splines for DFTB Repulsive Potential Parametrization

Authors: Akshay Krishna Ammothum Kandy, Eddie Wadbro, Balint Aradi, Peter Broqvist, and Jolla Kullgren 

The Curvature Constrained Splines (CCS) methodology has been used for fitting repulsive potentials to be used in SCC-DFTB calculations. The benefit of using CCS is that the actual fitting of the repulsive potential is performed through quadratic programming on a convex objective function. This guarantees a unique (for strictly convex) and optimum two-body repulsive potential in a single shot, thereby making the parametrization process robust, and with minimal human effort. Furthermore, the constraints in CCS give the user control to tune the shape of the repulsive potential based on prior knowledge about the system in question. Herein, we developed the method further with new constraints and the capability to handle sparse data. We used the method to generate accurate repulsive potentials for bulk Si polymorphs and demonstrate that for a given Slater-Koster table, which reproduces the experimental band structure for bulk Si in its ground state, we are unable to find one single two-body repulsive potential that can accurately describe the various bulk polymorphs of silicon in our training set. We further demonstrate that to increase transferability, the repulsive potential needs to be adjusted to account for changes in the chemical environment, here expressed in the form of a coordination number. By training a near-sighted Atomistic Neural Network potential, which includes many-body effects but still essentially within the first-neighbor shell, we can obtain full transferability for SCC-DFTB in terms of describing the energetics of different Si polymorphs.

J. Chem. Theory Comput. 2021, 17, 3, 1771–1781

CCS: A software framework to generate two-body potentials using Curvature Constrained Splines

Authors: Akshay Krishna A. K., Eddie Wadbro, Christof Köhler, Pavlin Mitev, Peter Broqvist, and Jolla Kullgren

We have developed an automated and efficient scheme for the fitting of data using Curvature Constrained Splines (CCS), to construct accurate two-body potentials. The approach enabled the construction of an oscillation-free, yet flexible, potential. We show that the optimization problem is convex and that it can be reduced to a standard Quadratic Programming (QP) problem. The improvements are demonstrated by the development of a two-body potential for Ne from ab initio data. We also outline possible extensions to the method.

Program summary
Program Title: CCS

CPC Library link to program files: http://dx.doi.org/10.17632/7dt5nzxgbs.1

Developer’s repository link: http://github.com/aksam432/CCS

Licensing provisions: GPLv3

Programming language: Python

External routines/libraries: NumPy, matplotlib, ASE, CVXOPT

Nature of problem: Ab initio quantum chemistry methods are often computationally very expensive. To alleviate this problem, the development of efficient empirical and semi-empirical methods is necessary. Two-body potentials are ubiquitous in empirical and semi-empirical methods.

Solution method: The CCS package provides a new strategy to obtain accurate two body potentials. The potentials are described as cubic splines with curvature constraints.

Computer Physics Communications, 258, 107602, (2021);