Chris W. Patterson

Rotational energy surfaces and high‐J eigenvalue structure of polyatomic molecules

A rotational analog of the vibrational potential energy surface is introduced for describing the rotational fine structure of polyatomic molecules. Classical trajectories on rotational energy (RE) surfaces are related to quantum rotational eigenvalue structure. Interpretation of RE surfaces shows how very different types of molecules may undergo dynamical symmetry breaking and a corresponding clustering of rotational energy sublevels for high angular momentum (J>10). Cluster splitting and spacing are calculated using semiclassical quantization methods. Some consequences of dynamical symmetry breaking such as mixing of nuclear spin species are discussed qualitatively.

Cw stimulated Raman gain spectroscopy of the ν1 fundamental of methane

Abstract We report near-Doppler-limited Raman spectra of the ν 1 fundamental in methane using direct cw stimulated Raman gain spectroscopy enhanced by a multipass optical cell. 25 MHz resolution makes possible a correct analysis of the fine structure of the ν 1 band of methane. We present line assignments to J = 10 and spectroscopic constants for this band which differ significantly from previous analyses.

Orbital level splitting in octahedral symmetry and SF6 rotational spectra. II. Quantitative treatment of high J levels

We give a quantitative analysis for the clusters of octahedral terms which appear in the high resolution rotational spectra of SF6 for large angular momentum. We derive approximate expressions for the cluster energies and the splittings within each cluster which obviate the diagonalization of the octahedral deformation potential.

Measurement and analysis of the infrared‐active stretching fundamental (ν3) of UF6

High‐resolution spectra of the infrared‐active stretching fundamental ν3 of 238UF6 have been obtained between 620.6 and 633.5 cm−1 using tunable semiconductor diode lasers. Interference from hot bands was suppressed by cooling the UF6 in a supersonic expansion, and useful monomer concentrations were produced with effective temperatures of <100 K. Portions of the band from P(77) to R(66) are illustrated. All transitions from the vibrational ground state have been assigned, and the Q branch has been fully analyzed. A total of 43 line frequencies and 110 frequency differences extending in J to P(77), Q(91), and R(67) has been used to fit seven spectroscopic constants. The ground‐ and excited‐state values of the rotational constant B could be individually determined, and the U–F bond length in the ground vibrational state is r0=1.9962±0.0007 A. The Q branch of 235UF6 has also been analyzed and the 235UF6–238UF6 ν3 isotope shift measured to be 0.603 79±0.000 17 cm−1. The isotope shift and the Coriolis constant...

Quantum and semiclassical description of a triply degenerate anharmonic oscillator

Quantum and semiclassical energies are compared as a function of anharmonicity using the Hecht Hamiltonian for the triply degenerate anharmonic oscillator for octahedral and tetrahedral molecules. Semiclassical energies are found by turning on the potential adiabatically and the corresponding classical trajectories are described in terms of an adiabatic vibrational energy (VE) surface. Accurate semiclassical energies are obtained for chaotic trajectories near the separatrix of the VE surface. The quantum wave functions corresponding to the semiclassical trajectories after the onset of chaos are used to disprove a recently proposed quantum analog to classical quasiperiodic motion.

Resonance capture and the evolution of the planets

Abstract The present nearly resonant orbital periods of the planets are explained in terms of past two-body resonance capture of planetesimals in the solar nebula. Planetary formation then occurs sequentially starting with Jupiter for the outer planets and Venus for the inner planets and propagates outward due to two-body orbital resonances. It might now be possible to reconstruct the evolutionary history of the planets from their nearly commensurable orbital periods and, hence, provide an explanation for the Titius-Bode law.

Infrared double resonance of SF6 with a tunable diode laser. III. Observations of 2ν3←ν3 transitions and collisional relaxation in v3=1

The detailed spectroscopy and transition dipole moments of the 2ν3←ν3 transition in SF6 have been investigated by high‐resolution infrared double‐resonance spectroscopy. The calculated transition frequencies are found to be reliable to within ±0.003 cm−1; in addition, we find that both the l=0←1 and ν3=l=2←1 components of the 2ν3←ν3 transition carry comparable oscillator strength, and that mixing of R states becomes appreciable in 2ν3. The net relaxation rates into depleted levels of the ground vibrational state, and out of laser‐populated levels of ν3, are approximately equal to each other (pτ≃35 ns Torr for both). There appear to be no restrictions on relaxation among fine‐structure levels in the ground vibrational state; however, initial relaxation out of specified J levels in ν3 appears to involve a limited set of final states which may possibly belong to a vibrational level other than ν3.

Infrared spectrum and potential constants of silicon tetrafluoride

Doppler‐limited tunable diode laser spectra of ν4 of 28SiF4 have been analyzed and the spectroscopic constants determined. In contrast to most earlier low‐resolution studies, the Coriolis constant ζ4, when combined with ζ3 as obtained from previous laser spectroscopy, yields a zeta sum that is within 5% of the expected harmonic value of 1/2. The band origins of 12 overtones and combinations have been obtained from Fourier‐transform spectra (0.04 cm−1 resolution), resulting in estimates of the anharmonicity constants and harmonic frequencies. From the Coriolis constants and the isotope shifts in ν3 we have redetermined the general quadratic force field of SiF4.

Quasi‐cw inverse Raman spectroscopy of the ν1 fundamental of 13CH4

A Doppler‐limited Raman spectrum of the symmetric stretching fundamental (ν1) of 13CH4 has been recorded using high‐sensitivity ’’quasi‐cw’’ inverse Raman spectroscopy. The band is very different in appearance from ν1 of 12CH4, due mainly to a much smaller value of ΔB for the heavier species, which causes many of the transitions to overlap near the band origin. Line assignments have been made for J?11. The spectroscopic constants have been determined from the frequencies of 25 resolved transitions and a computer synthesis of the largely unresolved central region. The observed 12C–13C isotope shift, 1.04±0.02 cm−2, does not agree completely with predictions based on any available set of anharmonicity constants, but it does indicate that a simplified calculation based on a Dennison‐type approximation for the anharmonicity constants of isotopic species is not valid. The large difference in ΔB between the two species is attributed to the effect of Coriolis interaction with the nearby combination level ν2+ν4.

The ν2 + ν4 band of 12CF4☆

Abstract From a high-resolution diode laser spectrum of cooled 12CF4, line assignments in ν2 + ν4 at 1066.4 cm−1 have been made for tetrahedral subspecies to J = 20, and in many cases to higher J. Spectroscopic constants have been obtained from a least-squares fit of the Hamiltonian, and the relative intensities of the assigned lines have been calculated. The ground- and excited-state rotational constants, Coriolis constant, and splitting of the F1 and F2 vibrational substates have the values a.The CF bond length in the ground vibrational state is thus r 0 = 1.31752 ± 0.00007 A . The analysis of a combination band such as this provides a method of obtaining ground-state spectroscopic constants of spherical-top molecules directly from the infrared spectrum, without the necessity of measuring weak “forbidden” transitions. The assignments allow accurate predictions of the frequencies emitted by the CO2-pumped CF4 laser.