Partial combination of composite strategy and the B3LYP functional for the calculation of enthalpies of formation

  • Mariana Toretti Caldeira
  • Rogério CustodioEmail author
Original Paper


The B3LYP functional was re-optimized using partially composite methods for the calculation of standard enthalpies of formation. Two initial methods (B3LYP-MCM1 and B3LYP-MCM2) differing in the type and number of optimized parameters were analyzed using B3LYP/6–31 + G(2df,p) as the reference energy. For the first method (B3LYP-MCM1), the exchange-correlation and higher-level correction parameters (HLC) were optimized and for the second method (B3LYP-MCM2), in addition to the previous parameters, scaling of the basis functions responsible for large errors in the enthalpy of formation were also optimized. The best parameters were also used as adapted functionals generating two other methods referred to as: B3LYP-MF1 and B3LYP-MF2. The best-performing results (B3LYP-MCM2 and B3LYP-MF2) presented mean absolute errors near 2.3 kcal mol−1 for the G3/05 test set. This is a significant improvement when compared with the respective results from B3LYP/6–31 + G(2df,p), which yielded a mean absolute error of 5.3 kcal mol−1. The errors were larger for B3LYP-MCM1 (4.17 kcal mol−1) and B3LYP-MF1 (3.98 kcal mol−1). The scaling of the experimental atomization energies used for the calculation of enthalpy of formation was also tested for all four methods. This empirical adjustment reduced the errors to 2 kcal mol−1. The uncertainty of the best results with 95% confidence tended to be ± 5.5 kcal mol−1. Substantial improvements were associated with the basis set adjustments.


Composite methods Density functional theory B3LYP Standard enthalpy of formation Empirical corrections 



The authors wish to thank Dr. Cleuton de Sousa Silva and Guilherme Luiz Chinini for helpful discussion and suggestions. We acknowledge financial support from FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo - Center for Computational Engineering and Sciences, Grant 2013/08293-7, and Grant 2017/11485-6), and FAEPEX-UNICAMP (Fundo de Apoio ao Ensino, à Pesquisa e à Extensão da UNICAMP). This study was also financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. The National Center of High-Performance Computing in São Paulo (CENAPAD-SP) is acknowledged for access to their computational facilities. MTC wishes to thank CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) for a scholarship.

Supplementary material

894_2019_3952_MOESM1_ESM.docx (82 kb)
ESM 1. The supplemental file contains: Table S.1 (the mean absolute error of B3LYP with different basis functions for enthalpies of formation for a selected set of molecules), Table S.2 (compilation of the scaled basis set in a format compatible with the Gaussian input file), Table S.3 (experimental and theoretical enthalpies of formation (kcal mol−1) for the G3/05 test set using B3LYP, B3LYP-MCM1, B3LYP-MCM2, B3LYP-MF1 and B3LYP-MF1), and Table S.4 (experimental and theoretical enthalpies of formation (kcal mol−1) for the G3/05 test set using B3LYP-MCM1-At, B3LYP-MCM2-At, B3LYP-MF1-At and B3LYP-MF1-At). (DOCX 82 kb)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Instituto de QuímicaUniversidade Estadual de CampinasSão PauloBrazil

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