Semiclassical quantization of the low lying electronic states of H/sub 2//sup +/
The classical dynamics of an electron moving in the presence of two equally charged, fixed nuclei is presented. The manner in which the values of the three constants of the motion determine the qualitative features of the electronic trajectory is discussed. Primitive semiclassical wavefunctions and quantization conditions for the Born--Oppenheimer electronic quantum states of H/sub 2//sup +/ are derived using the canonically invariant quantization methods of Einstein, Keller, and Maslov. Because of the presence of energetic and dynamical barriers, a uniform quantization method is needed to give quantitative results for all internuclear separations. We employ a well-established uniformization which models the effective potential barrier as a parabola. Finally, the eigenparameters computed using the primitive and uniform quantization methods are compared with exact Born--Oppenheimer quantum mechanical results for the six lowest ..sigma.. states, the two lowest Pi states, and the two lowest ..delta.. states for a wide range of internuclear separations. The electronic energies computed using the uniform quantization conditions typically agree with the exact quantum results to within a fraction of a percent.
- Research Organization:
- Department of Chemistry, University of Colorado and Joint Institute for Laboratory Astrophysics, University of Colorado and National Bureau of Standards, Boulder, Colorado 80309
- OSTI ID:
- 6309925
- Journal Information:
- J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 70:8; ISSN JCPSA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory
74 ATOMIC AND MOLECULAR PHYSICS
BORN-OPPENHEIMER APPROXIMATION
CATIONS
CHARGED PARTICLES
ENERGY LEVELS
FUNCTIONS
HYDROGEN IONS
HYDROGEN IONS 2 PLUS
IONS
MECHANICS
MOLECULAR IONS
NUCLEI
WAVE FUNCTIONS
WKB APPROXIMATION