Algebraic methods in molecular science

Author(s)

Esmerindo de Sousa Bernardes

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Física de São Carlos (IFSC/BT)
• Defense date: 1997-01-16

Examining board members

José Eduardo Martinho Hornos; Francisco Castilho Alcaraz; Frank Michael Forger; Yoshiyuki Hase; Roberto Nicolau Onody

• Advisor: Jose Eduardo Martinho Hornos

Abstract

The vibrational spectrum of monofluoroacetylene (HCCF) and of monochloroacetylene (HCCCl) are calculated by means of algebraic techniques under the hypothesis that they result from a U(4) symmetry through the chain U(4) symmetry through the chain U(4) ⊃ O(4) ⊃ O(3). The results are compared with the 170 experimentally available vibrational lines for the HCCF and with the 23 experimentally available vibrational lines for the HCCCl. The mean square deviation is founded to be 7 cm-1 and 4 cm-1, respectivelly, establishing these spectra as the best examples of a dynamical symmetry reported in Molecular Physics so far. In another application of algebraic techniques, having in mind applications in which the algebraic handling of several different irreducible representations are necessary, we provide closed formulas for the matrix elements of the symplectic sp(4,C) Lie algebra on an arbitrary irreducible representation on the chain sp(4,C) ⊃ sp(2,C) ⊕ sp(2,C), which is being used in the study of the genetic code by Lie algebras. The used basis is orthogonal and analogous to the Gel\'fand- Tsetlin basis of unitary algebras. (AU)