Estimation of isomer energies by sparse modeling with local explanatory variables

Abstract

If the molecular energy obtained from the quantum chemical calculation can be modeled with local explanatory variables such as atomic charges, it is possible to drastically reduce the computational cost. We attempted to model the total energies of C₃H₆O₂ isomers by using Mulliken, Lowdin, natural, and ESP charges as the explanatory variables. By applying the MC+ regression, we could obtain a model showing good agreement with the calculated energy with a couple of explanatory variables. Applying this modeling scheme to the isomers of C₈H₁₀O₂, C₉H₁₀O₂, C₉H₁₀O₃, and C₁₀H₁₂O₂, however, resulted in failing to obtain good models. By adding the numbers of 3 to 8 membered rings as the explanatory variable, we could obtain good sparse models. In addition, it was found that all these sparse models contain the largest natural charge and the number of 6-membered rings as the explanatory variable.