Semiclassical determination of eigenvalues in nonbending ozone

Journal Article · Thu May 21 04:00:00 EDT 1987 · J. Phys. Chem.; (United States)

DOI:https://doi.org/10.1021/j100295a024· OSTI ID:6368047

Knudson, S K; Noid, D W; Koszykowski, M L

The authors have determined all the vibrational eigenvalues below 16,000 cm/sup -1/ for a two-mode ozone potential, using the surface of section semiclassical method combined with interpolation to integer quantum numbers; with this approach more than 80 eigenvalues were determined from only 21 arbitrary classical trajectories. The ozone potential surface is represented by a 20 x 20 grid of points obtained at the 6-31G* level with electron correlation included via a fourth-order Moeller-Plesset perturbation calculation. The forces needed to integrate the classical equations of motion are found by using a two-dimensional spline fit to the potential points. Classical trajectories are then generated; each gives tow surfaces of section from which classical actions and noninteger quantum numbers are extracted. A two-dimensional interpolation of the energy surface expressed as a function of these quantum numbers then rapidly locates the eigenvalues. These semiclassical eigenvalues generally agree with variationally determined quantum eigenvalues to within a few wavenumbers, for the first five states of each parity; this agreement holds even for states with eigenvalues corresponding to trajectories located in a classical resonance region.

• Research Organization: College of William and Mary, Williamsburg, VA
• DOE Contract Number: AC05-84OR21400
• OSTI ID: 6368047
• Journal Information: J. Phys. Chem.; (United States), Journal Name: J. Phys. Chem.; (United States) Vol. 91:11; ISSN JPCHA
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400201* -- Chemical & Physicochemical Properties
DATA
DIFFERENTIAL EQUATIONS
EIGENVALUES
ENERGY LEVELS
EQUATIONS
EQUATIONS OF MOTION
EXCITED STATES
INFORMATION
MECHANICS
NUMERICAL DATA
OZONE
PARTIAL DIFFERENTIAL EQUATIONS
POTENTIALS
QUANTUM MECHANICS
SEMICLASSICAL APPROXIMATION
THEORETICAL DATA
VIBRATIONAL STATES