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Title: Efficient Procedure for the Numerical Calculation of Harmonic Vibrational Frequencies Based on Internal Coordinates

We propose a general procedure for the numerical calculation of the harmonic vibrational frequencies that is based on internal coordinates and Wilson’s GF methodology via double differentiation of the energy. The internal coordinates are defined as the geometrical parameters of a Z-matrix structure, thus avoiding issues related to their redundancy. Linear arrangements of atoms are described using a dummy atom of infinite mass. The procedure has been automated in FORTRAN90 and its main advantage lies in the nontrivial reduction of the number of single-point energy calculations needed for the construction of the Hessian matrix when compared to the corresponding number using double differentiation in Cartesian coordinates. For molecules of C1 symmetry the computational savings in the energy calculations amount to 36N – 30, where N is the number of atoms, with additional savings when symmetry is present. Typical applications for small and medium size molecules in their minimum and transition state geometries as well as hydrogen bonded clusters (water dimer and trimer) are presented. Finally, in all cases the frequencies based on internal coordinates differ on average by <1 cm–1 from those obtained from Cartesian coordinates.
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 1089-5639; KC0301020
DOE Contract Number:
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory; Journal Volume: 117; Journal Issue: 32
American Chemical Society
Research Org:
Pacific Northwest National Laboratory (PNNL), Richland, WA (US)
Sponsoring Org:
Country of Publication:
United States