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Theoretical Chemistry Accounts

, Volume 121, Issue 5–6, pp 257–266 | Cite as

Rotational symmetry of the molecular potential energy in the Cartesian coordinates

  • Paweł GrochowskiEmail author
Regular Article

Abstract

We consider the molecular Born-Oppenheimer potential energy as a function of atomic Cartesian coordinates and discuss the non-stationary Hessian properties arising due to rotational symmetry. A connection with the extended Hessian theory is included. New applications of Cartesian representation for examining and correcting raw numerical Hessian data and a simple formulation of harmonic vibrational analysis of partially optimized systems are proposed. Exemplary calculations for the porphyrin molecule with an internal proton transfer are reported. We also develop the normal transformation method to incorporate the rotational symmetry into the approximate analytical potentials, which are parametrized in the Cartesian coordinates. The transformation converts the coordinates from the space fixed frame to the frame which translates and rotates with the molecule and is determined by the Eckart conditions. New simple analytical formulas for the first and second derivatives of the transformed potential are derived. This fast method can be used to calculate the potential and its derivatives in the simulations of chemical reaction dynamics in the space fixed Cartesian frame without the need to constrain the molecular rotation or to define the local non-redundant internal coordinates.

Keywords

Potential energy surface Hessian Rotations Cartesian coordinates 

Notes

Acknowledgments

The author would like to thank Grzegorz Bakalarski for his expert help in using Gaussian program, and Joanna Trylska for critical reading of the manuscript. The author acknowledges support from University of Warsaw (115/30/E-343/S/2007/ICM BST 1255) and Polish Ministry of Science and Higher Education (3 T11F 005 30, 2006–2008).

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Interdisciplinary Centre for Mathematical and Computational ModellingUniversity of WarsawWarsawPoland

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