General method for the reduction of the effective rotational hamiltonian of molecules. Rational approximants and Padé approximants

A general method for reducing the effective rotational Hamiltonian for moleculesH _rot to the empirically constructed form in the {J_±, J_z} representation (molecules of the asymmetric-top type), applicable to Hamiltonians having improved convergence with nonpolynomial dependence on the angular momentum J, is developed. Rational forms for the reducedHrot and reduced Padé approximants for the rotational energy operator of the molecules are proposed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 32–37, August, 1985.     

Symmetry properties of the effective hamiltonians of some nonrigid molecules

Group-theoretical methods are used to identify the nonvanishing parameters and establish relations between them in the effective Hamiltonians which describe rotation and motion with large amplitude. The cases considered are 1) bending vibration in molecules of the type XY₂ and XYZ and 2) inversion vibration in pyramidal molecules of the type XY₃. For the latter type of molecule, the symmetry properties of the parameters in the effective centrifugal Hamiltonian for quasidegenerate inversion states are investigated. The general form of this Hamiltonian and its symmetry properties are established and studied in an arbitrary order in the small parameter.Translated from Izvestiya Vysshikh Uchebnykh Zavednii, Fizika, No. 2, pp. 22–26, February, 1981.     

The operator method for perturbations in the theory of infrared molecular spectra

The application of contact transformations of Hamiltonians with a degenerate zeroth approximation to an approximate separation of variables is studied. Unitary transformations are formed that interrelate various effective Hamiltonians by the method of contact transformations of Van Vleck, Jorgensen, Pedersen, Primas, ENRST and Soliverez with an accuracy up to 0(⁵). The relation between the contact transformations and the perturbation theory of Rayleigh-Schrödinger is studied, and it is shown that the intermediate denominators in effective Hamiltonians vanish in a nondegenerate case. A generalized variant is constructed of contact transformations and of transformation yielding an even effective Hamiltonian from which the results of the above methods in particular cases follow.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, No. 7, pp. 82–90, July, 1977.The authors would like to thank V. N. Bryukhanov and P. I. Gaev for useful discussions.     

Ab initio method for calculating electron-phonon scattering times in semiconductors: application to GaAs and GaP

We propose a fully ab initio approach to calculate electron-phonon scattering times for excited electrons interacting with short-wavelength (intervalley) phonons in semiconductors. Our approach is based on density functional perturbation theory and on the direct integration of electronic scattering probabilities over all possible final states with no ad hoc assumptions. We apply it to the deexcitation of hot electrons in GaAs, and calculate the lifetime of the direct exciton in GaP, both in excellent agreement with experiments. Matrix elements of the electron-phonon coupling, and their dependence on the wave vector of the final state and on the phonon modes, are shown to be crucial ingredients of the evaluation of electron-phonon scattering times.     

Analysis of the CH3D Nonad from 2000 to 3300 cm

As part of the simultaneous analysis of line positions and intensities of the first two polyads of monodeuterated methane, the results achieved for the region 3-5 μm are reported. It involves the three highest fundamentals, (ν₁, ν₂, ν₄), overlapped by overtone (2ν₃, 2ν₅, 2ν₆) and combination (ν₃+ν₆, ν₃+ν₅, ν₅+ν₆) bands. The theoretical model was based on the global tensorial model implemented in the MIRS package. Some 10 000 line positions and 2400 line intensities have been modeled to ±0.000 88 cm⁻¹ and ±3.6% respectively, using measurements obtained at 0.0056 and 0.011 cm⁻¹ resolution with the Fourier transform spectrometer at National Solar Observatory located at Kitt Peak. The strongest band in this polyad is ν₄(E) at 3016.7 cm⁻¹ with a strength of 6.3×10⁻¹⁸ cm⁻¹/(molecule cm⁻²) at 296 K; the weakest band is 2ν₃(E) at 2597.7 cm⁻¹ with a strength of 1.9×10⁻²⁰ cm⁻¹/(molecule cm⁻²) at 296 K. The total calculated absorption arising from the CH₃D nonad is 8.95×10⁻¹⁸ cm⁻¹/(molecule cm⁻²) at 296 K.     

Extended Analysis of Line Positions and Intensities of Ozone Bands in the 2900-3400 cm Region

The 2900-3400 cm⁻¹ spectral range is revisited for an accurate determination of line positions and line intensities of the 3ν₃, ν₁+2ν₃, 2ν₁+ν₃, and 3ν₁ bands of ozone. The fit on 4520 rotational energy levels of (012), (111), (210), (130), (003), (102), (201), and (300) vibrational states determined from observed transitions of cold and hot bands in the 2400-3400 cm⁻¹ region with J_max=65 and K_{a max}=20 gives a r.m.s.=7×10⁻⁴ cm⁻¹ and provides a satisfactory agreement between calculated and observed line positions (dimensionless standard deviation is χ=1.44). The set of 2580 line intensities of 7 rovibrational bands has been measured and fitted with a r.m.s.=6.9% (χ=1.2), leading to the determination of transition moment parameters for these bands. Using these parameters we have obtained more precise estimation for the integrated band intensities S(3ν₃)=1.41×10⁻¹⁹, S(ν₁+2ν₃)=1.28×10⁻²⁰, S(2ν₁+ν₃)=7.91×10⁻²¹, S(3ν₁)=4.72×10⁻²² cm⁻¹/mol cm⁻² at 296 K, with a cutoff 2×10⁻²⁶ cm⁻¹/mol cm⁻². The interactions of the tetrad (003)/(102)/(201)/(300) with the (130) state and the tetrad (040)/(012)/(111)/(210) are studied.     

Analysis of High-Resolution Spectra of (18)O(3)

Using a Fourier transform spectrometer, we have recorded the spectra of the (18)O(3) species of ozone in the region 1300-3100 cm(-1), with a resolution of 0.003 cm(-1). The large product pathlength x pressure enable us to record 18 bands, 14 for the first time. The analysis has been performed using effective Hamiltonians for polyads of strongly interacting states for ozone, accounting for Coriolis and anharmonic resonances. The spectral parameters are derived for 16 vibrational states, including the two "dark" states (040) and (130). Various resonances are studied through the mixing coefficients of rovibrational wavefunctions. Systematic intensity measurements allow determination of transition moment parameters for 16 bands. Finally, a complete list of all transitions from 1300 to 3100 cm(-1), with cutoffs 10(-26) cm(-1)/mol cm(-2) (296 K), is calculated. Copyright 2001 Academic Press.