New functional form for representing vibrational eigenenergies of diatomic molecules. II. Application to H/sub 2/ ground state
An expression previously proposed for representing vibrational eigenenergies E/sub v/ as a function of quantum number v is applied to the H/sub 2/ ground electronic state. The expression is E/sub v/=D-(v/sub D/-v)/sup m/(L/N), where D is the dissociation limit energy, v/sub D/ and m are parameters, and (L/N) is a rational fraction in (v/sub D/-v). We integrate the vibrational Schroedinger equation to obtain 15 Born--Oppenheimer (BO) E/sub v/ with reduced mass ..mu../sub 0/=918.048 electron masses, and 77 BO E/sub v/ with 25 ..mu../sub 0/; error in E/sub v/ attributable to the potential is estimated to be 0.02 cm/sup -1/. The proposed functional form with a variety of (L/N) is fitted to the 14 BO ..mu../sub 0/ first differences ..delta..E (v+1/2); with the exception of (4/0) all L+N=4 fits have an rms error in calculated ..delta..E of 0.02 cm/sup -1/. The proposed formula is then fitted to 15 BO differences including D-E/sub 14/. The error in calculated D-E/sub 14/ can be made negligible while the rms error in calculated energy differences remains 0.02 cm/sup -1/. Mass 25 ..mu../sub 0/ is used to check applicability of the proposed functional form to a large number of levels; several fits yield all 76 ..delta..E with an rms error of only 0.04 cm/sup -1/. Finally, the proposed expression is applied to experimental vibrational energies. For these, better fits have an rms error of approx.0.07 cm/sup -1/, presumably due primarily to experimental errors.
- Research Organization:
- Department of Physics and Astronomy, The University of New Mexico, Albuquerque, New Mexico 87131
- OSTI ID:
- 5757756
- Journal Information:
- J. Chem. Phys.; (United States), Vol. 71:11
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
HYDROGEN
VIBRATIONAL STATES
EIGENVALUES
GROUND STATES
SCHROEDINGER EQUATION
CRYOGENIC FLUIDS
DIFFERENTIAL EQUATIONS
ELEMENTS
ENERGY LEVELS
EQUATIONS
EXCITED STATES
FLUIDS
NONMETALS
WAVE EQUATIONS
640302* - Atomic
Molecular & Chemical Physics- Atomic & Molecular Properties & Theory