Vector algebra and molecular symmetry: a tribute to Professor Josiah Willard Gibbs

Abstract

Vector algebra, as developed by Josiah Willard Gibbs, is much simpler than matrix or tensor algebra, therefore, it is more suitable to introduce the students of chemistry into the wonderful world of molecular symmetry. A program based on elementary vector algebra has been written to determine all symmetry elements and symmetry operations of rigid molecular structures. The program also contains data for 57 point groups common in chemistry. Therefore, it automatically supplies the particular point group to which the structure belongs. Since the locations of the nuclei related to the symmetry elements are also revealed by the program, even the detailed notation of the framework group of the molecular structure can be deduced. The program can be a great help in determining the symmetries of the normal modes of vibration, too.

Normal-Mode Vibrational Analysis of Weakly Bound Oligomers at Constrained Stationary Points of Arbitrary Order

“…Upon termination of the constrained geometry optimization, the point-group symmetry of the cSP is identified with the SYVA (SYmmetry analyzer using Vector Algebra) code in an automated way (the distortion tolerance parameter , is set to 2 mÅ). After recognition of the highest point group, the analyzed geometry is symmetrized by SYVA and replaces that obtained by .…”

“…Comparison of Selected Quantum-Chemical Quantities Characterizing the Global Minimum, WW 1 , of the Water Dimer, Obtained via Different Approaches ab SYmmetry analyzer using Vector Algebra 63 )62 code in an automated way (the distortion tolerance parameter62,63 is set to 2 mÅ). After recognition of the highest point group, the analyzed geometry is symmetrized by SYVA and replaces that obtained by oligoCGO.…”