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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.