Extrapolation formulas based on power and exponential formulas, as well as alternatives from a Taylor series, were tested and used with density functional theory (DFT) for the calculation of enthalpies of formation. The following four functionals were analyzed: B3LYP, BMK, M06‐2X, and B2PLYP. Preliminary tests pointed to B2PLYP and B3LYP as the best and worst functionals, respectively. Taylor series expressions were as accurate as the power formulas and presented better performance than the exponential equation. The power formula (Equation (2)) and one of the simplest Taylor expressions (Equation (13)) were selected for the calculations with B3LYP and B2PLYP, with further empirical adjustments based on the higher level correction (HLC) and scaling of the experimental atomization energies used to calculate enthalpies of formation. HLC improved the B3LYP mean absolute error (MAE) from approximately 4.3 to 3.5 kcal mol−1 using both extrapolation alternatives. For B2PLY, the MAEs were improved from 2.7 to 2.6 kcal mol−1. Regarding the G3/05 test set, a significant improvement in the MAEs around 2.5 and 1.5 kcal mol−1 were achieved using B3LYP and B2PLYP, respectively. The accuracy obtained from these empirical corrections was equivalent to other composite methods. The MAEs from B3LYP and B2PLYP may be suggested as ranges for the possible accuracy to be achieved by some DFT methods. The empirical corrections suggested in this work are improvements that may be considered to provide acceptable accuracy for enthalpies of formation and possibly other properties.

Ata da defesa assinada pelos membros da Comissão Examinadora, consta no SIGA/Sistema de Fluxo de Dissertação/Tese e na Secretaria do Programa da Unidade. Este exemplar corresponde à redação final da Tese de Doutorado defendida pelo aluno Guilherme Luiz Chinini, aprovada pela Comissão Julgadora em 19 de junho de 2020. A minha esposa Bruna Agradecimentos A minha esposa Bruna, pelo apoio incondicional, companheirismo, amizade e carinho durante todo esse tempo. Aos meus pais, Maria Goreti e Antonio Carlos e o meu irmão Gabriel pelos valores, apoio e força.Ao Prof. Dr. Rogério Custodio por sua mente inquieta, pela confiança, por todo aprendizado e ajuda, sem a qual a concepção desse trabalho não seria possível.

The numerical Taylor series is used as an alternative to systematically converge to a high-level calculation showing that it has the potential to be used in the development of composite methods. Five methods are tested, with two of them differing in the truncation of the series expansion and basis sets, namely, Taylor–Dunning and Taylor–Pople, and three of the interpretations of the G4, ccCA-TZ, and CBS-QB3, which are referred to as G4-Taylor, ccCA-TZ-Taylor, and CBS-QB3-Taylor, respectively. The Taylor–Dunning and Taylor–Pople methods restricted to second-order expansion show mean absolute errors of 1.16 and 1.11 kcal mol–1, respectively, for a training set involving enthalpies of formation, ionization energies, and electronic affinities. The G4-Taylor, ccCA-TZ-Taylor, and CBS-QB3-Taylor methods achieve the lowest mean absolute errors of 0.96, 1.54, and 0.58 kcal mol–1, respectively. The CBS-QB3-Taylor method is submitted to a validation step. The method using either forward or backward derivatives achieves a mean absolute error of 0.82 kcal mol–1. These results show that the numerical Taylor series and possibly other series expansions can be applied systematically for the development of accurate alternatives for composite methods.

Objective: To evaluate neuropathic pain (NP), its intensity, and complications in people with type 2 diabetes mellitus (T2DM) in a city of eastern São Paulo. Method: Cross-sectional study conducted with 96 individuals with T2DM served by primary health units in São João da Boa Vista-SP. The following instruments were used to screen NP: Michigan Neuropathy Screening Instrument, Leeds Assessment of Neuropathic Symptoms and Signs, Douleur Neuropathique 4, and Brief Pain Inventory. The data were analyzed using descriptive and inferential statistics, with a 5 % significance level. Results: Of the 96 people with T2DM for longer than five years, 22.9 % had pain. NP was related to high levels of fasting blood glucose (mean = 214 ± 65.58 mg/dl; p = 0.0002), glycated hemoglobin (mean = 8.8 ± 0.11 %; p < 0.001), absence of a balanced diet (p = 0.0066), obesity (p = 0.023), and high blood pressure (p < 0.001). Conclusion: Higher values ​​of glycated hemoglobin rates increased three times the chance of NP. The screening and management of painful diabetic neuropathy is a challenge but adopting a screening protocol supports the secondary prevention of this manifestation.