CW-cavity ring down spectroscopy of the ozone molecule in the 6625-6830 cm region

The absorption spectrum of ozone, ¹⁶O₃, has been recorded by CW-cavity ring down spectroscopy in the 6625-6830 cm⁻¹ region. The typical sensitivity of these recordings (α_min ∼ 3 × 10⁻¹⁰ cm⁻¹) allows observing very weak transitions with intensity down to 2 × 10⁻²⁸ cm/molecule. 483 and 299 transitions have been assigned to the 2ν₁ + 3ν₂ + 3ν₃A-type band and to the 2ν₁ + 4ν₂ + 2ν₃B-type band, respectively, which are the highest frequency bands of ozone recorded so far under high resolution. Rovibrational transitions with J and K_a values up to 46 and 12, respectively, could be assigned. Despite well-known difficulties to correctly reproduce the energy levels not far from the dissociation limit, it was possible to determine the parameters of an effective Hamiltonian which includes six vibrational states, four of them being dark states. The line positions analysis led to an rms deviation of 8.5 × 10⁻³ cm⁻¹ while the experimental line intensities could be satisfactorily reproduced. Additional experiments in the 5970-6021 cm⁻¹ region allows detecting the (233) ← (010) hot band reaching the same upper state as the preceding cold band. From the effective parameters of the (233) state just determined and those of the (010) level available in the literature, 329 transitions could be assigned and used for a further refinement of the rovibrational parameters of the effective Hamiltonian leading to a value of 7.6 × 10⁻³ cm⁻¹ for the global rms deviation. The complete list of the experimentally determined rovibrational energy levels of the (233), (242), and (520) states is given. The determined effective Hamiltonian and transition moment operators allowed calculating a line list (intensity cut off of 10⁻²⁸ cm/molecule at 296 K), available as Supplementary material for the 6590-6860 and 5916-6021 cm⁻¹ regions. The integrated band strength values are 1.75 × 10⁻²⁴ and 4.78 × 10⁻²⁵ cm/molecule at 296 K for the 2ν₁ + 3ν₂ + 3ν₃A-type band and to the 2ν₁ + 4ν₂ + 2ν₃B-type band, respectively, while the band intensity value of the (233) ← (010) is estimated to be 1.03 × 10⁻²⁴ cm/molecule.     

Accurate ab initio determination of the adiabatic potential energy function and the Born-Oppenheimer breakdown corrections for the electronic ground state of LiH isotopologues

High level ab initio potential energy functions have been constructed for LiH in order to predict vibrational levels up to dissociation. After careful tests of the parameters of the calculation, the final adiabatic potential energy function has been composed from: (a) an ab initio nonrelativistic potential obtained at the multireference configuration interaction with singles and doubles level including a size-extensivity correction and quintuple-sextuple ζ extrapolations of the basis, (b) a mass-velocity-Darwin relativistic correction, and (c) a diagonal Born-Oppenheimer (BO) correction. Finally, nonadiabatic effects have also been considered by including a nonadiabatic correction to the kinetic energy operator of the nuclei. This correction is calculated from nonadiabatic matrix elements between the ground and excited electronic states. The calculated vibrational levels have been compared with those obtained from the experimental data [J. A. Coxon and C. S. Dickinson, J. Chem. Phys. 134, 9378 (2004)]. It was found that the calculated BO potential results in vibrational levels which have root mean square (rms) deviations of about 6-7 cm(-1) for LiH and ～3 cm(-1) for LiD. With all the above mentioned corrections accounted for, the rms deviation falls down to ～1 cm(-1). These results represent a drastic improvement over previous theoretical predictions of vibrational levels for all isotopologues of LiH.     

Isotope shift of the rotational structure of the levels of flexural states in H2Ox molecules (x=16, 17, 18)

In the paper we obtain analytic relations that determine the isotope shift of the rotational levels of the (Ov₂O) states of H₂O^x molecules (x = 16, 17, 18). We give theoretical predictions of the rotational levels of the ground state of the molecules H₂O¹⁷ and H₂O¹⁸ with high values of the quantum numbers J and k_a.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 80–84, September, 1984.     

Construction of effective operators for the time-dependent Schrödinger equation

The contact transformation method is used to solve the time-dependent Schrödinger equation describing the behavior of a multilevel system in a resonance electromagnetic field. A solution not containing secular terms is obtained for the evolution operator in the interaction representation U₀. The derivation of the equation for the probability of the simultaneous absorption of two photons with the dipole interaction is presented as an example of the effectiveness of the obtained solution.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 78–81, August, 1982.     

Calculation of the dependence of the centrifugal constants of the molecule H2O on the quantum number v2 on the basis of the Morse oscillator

An explanation is given in this paper for the anomalous dependence of the centrifugal distortion in flexible molecules of the type H₂O on the bending quantum number v₂ on the basis of the Morse oscillator. A computation of the dependence of the rapidly varying rotational, quartic, sextic constants of the molecule H₂O on v₂ describes the experimental behavior of these constants well.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 93–96, August, 1982.     

CW-Cavity Ring Down Spectroscopy of O3. Part 3: Analysis of the 6490–6900 cm region and overview comparison with the O3 main isotopologue

This paper is devoted to the third part of the analysis of the very weak absorption spectrum of the ¹⁸O₃ isotopologue of ozone recorded by CW-Cavity Ring Down Spectroscopy between 5930 and 6900 cm⁻¹. In the two first parts [A. Campargue, A. Liu, S. Kassi, D. Romanini, M.-R. De Backer-Barilly, A. Barbe, E. Starikova, S.A. Tashkun, Vl.G. Tyuterev, J. Mol. Spectrosc. (2009), doi: 10.1016/j.jms.2009.02.012 and E. Starikova, M.-R. De Backer-Barilly, A. Barbe, Vl.G. Tyuterev, A. Campargue, A.W.Liu, S. Kassi, J. Mol. Spectrosc. (2009) doi: 10.1016/j.jms.2009.03.013], the effective operators approach was used to model the spectrum in the 6200–6400 and 5930–6080 cm⁻¹ regions, respectively. The analysis of the whole investigated region is completed by the present investigation of the 6490–6900 cm⁻¹ upper range. Three sets of interacting states have been treated separately. The first one falls in the 6490–6700 cm⁻¹ region, where 1555 rovibrational transitions were assigned to three A-type bands: 3ν₂ + 5ν₃, 5ν₁ + ν₂ + ν₃ and 2ν₁ + 3ν₂ + 3ν₃ and one B-type band: ν₁ + 3ν₂ + 4ν₃. The corresponding line positions were reproduced with an rms deviation of 18.4 × 10⁻³ cm⁻¹ by using an effective Hamiltonian (EH) model involving eight vibrational states coupled by resonance interactions. In the highest spectral region – 6700–6900 cm⁻¹ – 389 and 183 transitions have been assigned to the ν₁ + 2ν₂ + 5ν₃ and 4ν₁ + 3ν₂ + ν₃ A-type bands, respectively. These very weak bands correspond to the most excited upper vibrational states observed so far in ozone. The line positions of the ν₁ + 2ν₂ + 5ν₃ band were reproduced with an rms deviation of 7.3 × 10⁻³ cm⁻¹ by using an EH involving the {(054), (026), (125)} interacting states. The coupling of the (431) upper state with the (502) dark state was needed to account for the observed line positions of the 4ν₁ + 3ν₂ + ν₃ band (rms = 5.7 × 10⁻³ cm⁻¹).The dipole transition moment parameters were determined for the different observed bands. The obtained set of parameters and the experimentally determined energy levels were used to generate a complete line list provided as Supplementary Materials.The results of the analyses of the whole 5930–6900 cm⁻¹ spectral region were gathered and used for a comparison of the band centres to their calculated values. The agreement achieved for both ¹⁸O₃ and ¹⁶O₃ (average difference on the order of 1 cm⁻¹) indicates that the used potential energy surface provides accurate predictions up to a vibrational excitation approaching 80% of the dissociation energy. The comparison of the ¹⁸O₃ and ¹⁶O₃ band intensities is also discussed, opening a field of questions concerning the variation of the dipole moments and resonance intensity borrowing by isotopic substitution.     

Lattice dynamics,thermodynamic and elastic properties of CdGeAs2

Summary An extended Keating’s model with two-bond-stretching and one-angle-bending force constants within the rigid-ion approximation is applied to the investigation of the lattice dynamics of CdGeAs₂. Five model parameters of the theory are determined by a least-square fitting to the infrared reflectivity measurements. The phonon spectrum along two high-symmetry directions and the one-phonon density of states are calculated. The theoretical values of the elastic constants, the constant-volume specific heat and the Debye temperature show a reasonable agreement with the experimental data reported by other authors.     

Account of the nonbinary nature of the ion interaction in lattice dynamics

The real multiparticle Hamiltonian for a solid with a Coulomb interaction between electrons and nuclei is used in the approximation of dynamic independence of the electrons from the ionic and valence shells to obtain an expression for the crystal energy in terms of the ion-ion interaction and the pseudopotential for the interaction of a valence electron with an ion. A correction to the dynamic matrix due to the existence of a three-particle interaction among ions is found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 88–94, September, 1970.     

Line Positions and Intensities of the ν1+ ν2+ 3ν3, ν2+ 4ν3, and 3ν1+ 2ν2Bands of Ozone

Using a Fourier transform spectrometer, we have recorded the spectra of ozone in the region of 4600 cm⁻¹, with a resolution of 0.008 cm⁻¹. The strongest absorption in this region is due to the ν₁+ ν₂+ 3ν₃band which is in Coriolis interaction with the ν₂+ 4ν₃band. We have been able to assign more than 1700 transitions for these two bands. To correctly reproduce the calculation of energy levels, it has been necessary to introduce the (320) state which strongly perturbs the (113) and (014) states through Coriolis- and Fermi-type resonances. Seventy transitions of the 3ν₁+ 2ν₂band have also been observed. The final fit on 926 energy levels withJ_max= 50 andK_max= 16 gives rms = 3.1 × 10⁻³cm⁻¹and provides a satisfactory agreement of calculated and observed upper levels for most of the transitions. The following values for band centers are derived: ν₀(ν₁+ ν₂+ 3ν₃) = 4658.950 cm⁻¹, ν₀(3ν₁+ 2ν₂) = 4643.821 cm⁻¹, and ν₀(ν₂+ 4ν₃) = 4632.888 cm⁻¹. Line intensities have been measured and fitted, leading to the determination of transition moment parameters for the two bands ν₁+ ν₂+ 3ν₃and ν₂+ 4ν₃. Using these parameters we have obtained the following estimations for the integrated band intensities,S_V(ν₁+ ν₂+ 3ν₃) = 8.84 × 10⁻²²,S_V(ν₂+ 4ν₃) = 1.70 × 10⁻²², andS_V(3ν₁+ 2ν₂) = 0.49 × 10⁻²²cm⁻¹/molecule cm⁻²at 296 K, which correspond to a cutoff of 10⁻²⁶cm⁻¹/molecule cm⁻².     

On the lattice dynamics of AgGaS2

Summary The vibrational spectrum and one-phonon density of states of a chalcopyrite crystal AgGaS₂ are calculated in an extended Keating’s model with two-bond-stretching and one-bond-bending force constants. Three charges of ions and three force constants are determined by a least-square fitting to experimental frequencies of long-wave phonons taken from Raman-scattering experiments. The calculated constant-volume specific heat, Debye temperature and elastic constants, of AgGaS₂ are in agreement with the experimental data of other authors.