Systematic Convergence of the Numerical Taylor Series to the Best Standard and Its Potential Implication for the...

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.