Embedding parameters in ab initio theory to develop approximations based on molecular similarity

TL;DR

This paper introduces a method to embed adjustable parameters into low-cost ab initio models, leveraging molecular similarity to significantly improve their accuracy in predicting electronic properties while reducing computational costs.

Contribution

The authors develop a parametrized low-level ab initio model that uses scaling factors based on molecular features, demonstrating systematic improvements over traditional models.

Findings

Reduced RMS energy prediction errors by over 85% on training data

Achieved over 75% error reduction on test molecules

Model flexibility allows systematic improvement with additional data

Abstract

A means to take advantage of molecular similarity to lower the computational cost of electronic structure theory is explored, in which parameters are embedded into a low-cost, low-level (LL) ab initio model and adjusted to obtain agreement with results from a higher-level (HL) ab initio model. A parametrized LL (pLL) model is created by multiplying selected matrix elements of the Hamiltonian operators by scaling factors that depend on element types. Various schemes for applying the scaling factors are compared, along with the impact of making the scaling factors linear functions of variables related to bond lengths, atomic charges, and bond orders. The models are trained on ethane and ethylene, substituted with -NH2, -OH and -F, and tested on substituted propane, propylene and t-butane. Training and test datasets are created by distorting the molecular geometries and applying uniform electric fields. The fitted properties include changes in total energy arising from geometric distortions or applied fields, and frontier orbital energies. The impacts of including additional training data, such as decomposition of the energy by operator or interaction of the electron density with external charges, are also explored. The best-performing model forms reduce the root mean square (RMS) difference between the HL and LL energy predictions by over 85% on the training data and over 75% on the test data. The argument is made that this approach has the potential to provide a flexible and systematically-improvable means to take advantage of molecular similarity in quantum chemistry.