ESCAPE: A novel approach for a fast estimation of dynamic correlation energies: Application to large organic...

Advanced wave function-based quantum chemical ab initio methods, such as CCSD(T), are able to calculate the energies of small- to medium-sized molecules with chemical accuracy. Unfortunately, these methods scale quite unfavorably with the size of the system and are getting too time consuming-and too expensive-for larger molecules. In order to be able to treat larger organic molecules, we propose a novel scheme for a quick and reliable estimate of molecular correlation energies, which we call ESCAPE (EStimation of CorrelAtion energies by Pair Energies). It is based on the pair correlation energies for localized molecular orbitals that have been generated by CCSD[T] and fitted to suitable functional forms. All fit parameters are stored in a large parameter file. Aiming at chemical accuracy (±1 kcal/mol), we have first limited our approach to aliphatic hydrocarbons. The total molecular CCSD[T] correlation energies of a training set of 41 aliphatic hydrocarbons could be reproduced with a mean absolute error (MAE) of 0.56 kcal/mol or 0.11%. A similar accuracy could be obtained for a test set of 11 additional hydrocarbons with up to eight carbon atoms (MAE of 0.65 kcal/mol or 0.09%). In a more critical test, we checked the small energy differences for a set of 13 isomerization reactions. The comparison with experimental data showed that we could reach chemical accuracy as well. Our estimate (MAE of 0.55 kcal/mol) is slightly inferior to the CCSD[T] result (MAE of 0.17 kcal/mol), but superior to SCF, DFT/B3LYP, and DFT/B3LYP + D3. Moreover, in all cases, we obtained the correct sign, that is, the correct equilibrium structure. A similar accuracy could be reached in an application to the three lowest isomers of the C₆₀ molecule. Using the example of a set of eight alcohols, we were able to proof the method's ability for molecules including heteroatoms. Three fast steps are necessary for the application to any aliphatic hydrocarbon or alcohol: (1) An SCF calculation at the selected molecular geometry; it can be fast since a medium size basis set is generally sufficient. (2) The localization of the occupied molecular orbitals and determination of their properties (center of charge and spatial extent). (3) Estimate of the correlation energy using the existing parameter file. © 2019 Wiley Periodicals, Inc.