Detection and analysis of new bands of O3 by CRDS between 6500 and 7300 cm

The absorption spectrum of the ¹⁶O₃ isotopologue of ozone has been recorded in the 7000-7920 cm⁻¹ region by high sensitivity CW-Cavity Ring Down Spectroscopy. This report is devoted to the analyses of the 7065-7300 cm⁻¹ region dominated by the ν₁ + 2ν₂ + 5ν₃ and ν₁ + 5ν₂ + 3ν₃ A-type bands at 7130.8 and 7286.8 cm⁻¹ respectively. 289 transitions were assigned to the ν₁ + 2ν₂ + 5ν₃ band. The corresponding line positions were modeled with an effective Hamiltonian involving Coriolis resonance interactions between the (1 2 5) upper state and the (4 4 0), (0 2 6) and (6 1 0) dark states, and an anharmonic resonance interaction with the (2 0 5) state. The very strong interaction (up to 50% mixing of the wavefunctions) between the (1 2 5) and (6 1 0) states leads to the observation of two extra lines of the 6ν₁ + ν₂ band due to a resonance intensity transfer. 213 transitions of the ν₁ + 5ν₂ + 3ν₃ band were assigned and modeled taking into account a Coriolis resonance interaction with the (3 6 0) state.We take the opportunity of the present work to report the analysis of the very weak 4ν₂ + 4ν₃ B-type band at 6506.1 cm⁻¹ which was assigned from previously recorded CRDS spectra. 286 transitions were modeled using the effective Hamiltonian approach.The dipole transition moment parameters of the three analyzed bands were determined by a least-squares fit to the measured line intensities. For the three studied band systems, the effective Hamiltonian and transition moment operator parameters were used to generate line lists provided as Supplementary Materials.     

Extension of the MIRS computer package for the modeling of molecular spectra: From effective to full ab initio ro-vibrational Hamiltonians in irreducible tensor form

The MIRS software for the modeling of ro-vibrational spectra of polyatomic molecules was considerably extended and improved. The original version [Nikitin AV, Champion JP, Tyuterev VlG. The MIRS computer package for modeling the rovibrational spectra of polyatomic molecules. J Quant Spectrosc Radiat Transf 2003;82:239–49.] was especially designed for separate or simultaneous treatments of complex band systems of polyatomic molecules. It was set up in the frame of effective polyad models by using algorithms based on advanced group theory algebra to take full account of symmetry properties. It has been successfully used for predictions and data fitting (positions and intensities) of numerous spectra of symmetric and spherical top molecules within the vibration extrapolation scheme. The new version offers more advanced possibilities for spectra calculations and modeling by getting rid of several previous limitations particularly for the size of polyads and the number of tensors involved. It allows dealing with overlapping polyads and includes more efficient and faster algorithms for the calculation of coefficients related to molecular symmetry properties (6C, 9C and 12C symbols for C_3v, T_d, and O_h point groups) and for better convergence of least-square-fit iterations as well. The new version is not limited to polyad effective models. It also allows direct predictions using full ab initio ro-vibrational normal mode Hamiltonians converted into the irreducible tensor form. Illustrative examples on CH₃D, CH₄, CH₃Cl, CH₃F and PH₃ are reported reflecting the present status of data available. It is written in C++ for standard PC computer operating under Windows. The full package including on-line documentation and recent data are freely available at http://www.iao.ru/mirs/mirs.htm or http://xeon.univ-reims.fr/Mirs/ or http://icb.u-bourgogne.fr/OMR/SMA/SHTDS/MIRS.html and as supplementary data from the online version of the article.     

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.     

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.     

Symmetry properties of the polarizability matrix of an inhomogeneous electron gas

The properties of the polarizability matrix of an inhomogeneous electron gas in nonconducting crystals, are subjected to group-theoretical analysis. The analytical properties of the eigenvalues and eigenvectors of the polarization operator (intrinsic polarizabilities and intrinsic densities) are discussed. It is shown that intrinsic densities transformed with respect to the vector representation of the point symmetry group of the crystal are excited in an external homogeneous electrical field. The acoustic sum rule for a dielectric matrix is obtained as a consequence of invariance relative to an infinitely small shift of space.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 84–89, June, 1989.