Analytical second derivatives in the Amsterdam density functional package

Abstract

ABSTRACT:Recently, analytical second derivatives with respect to nuclear coordinates have been implemented in the Amsterdam density functional (ADF) package. This article presents the detailed formalism of that implementation. Calculations on small molecules such as methane show good agreement between the analytical and numerical frequencies. Calculations on benzene and larger molecules show that the analytical second derivatives code is 2 to 3 times faster than the numerical. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem 104: [645][646][647][648][649][650][651][652][653][654][655][656][657][658][659] 2005 Key words: analytical; derivatives; Hessian; DFT; ADF; second derivatives 1. ADF Package T he second derivatives of the molecular energy with respect to nuclear coordinates are required to calculate the vibrational frequencies of a molecule. They are also required to calculate the Hessian from which stationary points can be characterized as maxima, minima, or saddle points.Recently, analytical second derivatives have been implemented in the Amsterdam density functional package (ADF) [1][2][3]. This article presents the detailed formalism of that implementation.ADF is a package that was initially developed by Baerends and coworkers [4 -7], and further developed over the years by a great many researchers and programmers throughout the world. ADF uses density functional theory (DFT) exclusively and provides a substantial range of exchange-correlation functionals.

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Density functional theory study of the Jahn-Teller effect in cobaltocene

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