Heats of Formation of Medium-Size Organic Compounds from Contemporary Electronic Structure Methods

Computational electronic structure calculations are routinely undertaken to predict thermodynamic properties of the various species. However, the application of highly accurate wave function theory methods, such as the “gold standard” coupled cluster approach including single, double and partly triple excitations in perturbative fashion, CCSD(T), to large molecules is limited due to high computational cost. In this work, the promising domain based local pair natural orbital coupled cluster approach, DLPNO-CCSD(T), has been tested to reproduce 113 accurate formation enthalpies of medium-size molecules (few dozens heavy atoms) important for bio- and combustion chemistry via the reaction based Feller-Peterson-Dixon approach. As for comparison, 8 density functional theory (B3LYP, B3LYP-D3, PBE0, PBE0-D3, M06, M06-2X, ωB97X-D3, and ωB97M-V) and MP2-based (B2PLYP-D3, PWPB95-D3, B2T-PLYP, B2T-PLYP-D, B2GP-PLYP, DSD-PBEP86-D3, SCS-MP2, and OO-SCS-MP2) methods have been tested. The worst performance has been obtained for the standard hybrid DFT functionals, PBE0 (Mean unsigned error (MUE)/ Mean Signed Error (MSE)=9.1/6.0 kcal/mol) and B3LYP (MUE/MSE=13.5/-13.3 kcal/mol). An influence of an empirical dispersion correction term on these functionals performance is not homogenous: B3LYP performance is improved (B3LYP-D3 (MUE/MSE=6.0/0.8 kcal/mol)) meanwhile PBE0 performance is worse (PBE0-D3 (MUE/MSE=14.1/13.6 kcal/mol)). The Minnesota functionals, M06 (MUE/MSE=3.8/-2.0 kcal/mol) and M06-2X (MUE/MSE=3.5/3.0 kcal/mol), and recently developed ωB97X-D3 (MUE/MSE=3.2/0.2 kcal/mol) and ωB97M-V (MUE/MSE=2.2/1.3 kcal/mol) methods provided significantly better formation enthalpies. Enthalpies of similar quality can also be obtained from some double hybrid methods (B2PLYP-D3 (MUE/MSE=4.7/2.0 kcal/mol), PWPB95-D3 (MUE/MSE=4.3/3.2 kcal/mol), B2T-PLYP (MUE/MSE=4.1/-3.0 kcal/mol) and B2T-PLYP-D (MUE/MSE=3.3/1.7 kcal/mol)). The two spin component scaled (SCS) MP2 methods resulted in even smaller errors (SCS-MP2 (MUE/MSE = 1.9/1.2 kcal/mol) and OO-SCS-MP2 (MUE/MSE = 1.6/0.1 kcal/mol)). The best performance was found for the frozen core (FC) DLPNO-CCSD(T) method with MUE/MSE of 1.6/-1.2 kcal/mol. The performance of the DLPNO-CCSD(T) method can be further improved by running the post-SCF calculations on the B3LYP orbitals: the MUE/MSE for DLPNO-CCSD(T, B3LYP) approximation are 1.2/-0.4 kcal/mol. We recommend the DLPNO-CCSD(T, B3LYP) method for the black box applications in thermodynamics of the medium-size organic molecules when the canonical CCSD(T) calculations with the basis sets of the reasonable quality are prohibitively expensive.