V2-dependence of centrifugal constants of H2O molecules in the Morse oscillator model

It is shown in this paper that the centrifugal constantsC ^l (t) calculated in the Morse, oscillator model for the sequence from the operator H _red ^(t) , which is used in processing the rotational levels of the H₂O molecule, are linked by recurrence relations, which enables H _z ^(t) –H _z ^(O) to be given in closed form.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 56–58, October, 1982.     

Analysis of the CRDS spectrum of 18O3 between 6950 and 7125 cm−1

The absorption spectrum of the ¹⁸O₃ isotopologue of ozone was recorded by CW-Cavity Ring Down Spectroscopy in the 6950–7125 cm^?1 region. The typical noise equivalent absorption of the recordings is α_min ≈1×10^?10 cm^?1. The spectrum is dominated by three very weak bands: 3ν₁+5ν₃ near 7009 cm^?1 and the ν₂+7ν₃ and 4ν₂+5ν₃ interacting bands near 7100 cm^?1. In total 260, 206 and 133 transitions were assigned for the 3ν₁+5ν₃, ν₂+7ν₃ and 4ν₂+5ν₃ bands, respectively. The line positions of the 3ν₁+5ν₃ band were modelled using an effective Hamiltonian (EH) model involving two dark states – (6 0 1) and (2 5 2) – in interaction with the (3 0 5) bright state. The EH model developed for the ν₂+7ν₃ and 4ν₂+5ν₃ bands involves only the (0 1 7) and (0 4 5) interacting bright states. Line positions could be reproduced with rms deviations on the order of 0.01 cm^?1 and the dipole transition moment parameters were determined for the three observed bands. The obtained set of parameters and the experimentally determined energy levels were used to generate a list of 984 transitions of the three bands which is provided as Supplementary Material.     

Measurements of line intensities and determination of transition moment parameters from experimental data for the ν1 and ν3 bands of D2S

First measurements of line intensities for ν₁ and ν₃ bands of D₂³²S are reported. About 300 intensities of D₂³²S vibration–rotation lines were obtained from experimental high-resolution spectra recorded in the 1810–2051 cm⁻¹ region with the Fourier Transform Spectrometer built in Reims. Empirical values of transition moment parameters for ν₁ and ν₃ bands of D₂³²S were determined for the first time using a least-square fit to the observed intensities. Experimental D₂³²S intensities were compared with recent global variational predictions [Vl.G. Tyuterev, L. Régalia-Jarlot, D.W. Schwenke, S.A. Tashkun, Y.G. Borkov, C. R. Phys. 5 (2004) 189–199] computed from isotopically invariant potential and dipole moment functions of the hydrogen sulphide molecule. Average discrepancy between these calculations and our observed data was 0.03 cm⁻¹ for line positions of this spectral range. The discrepancy between these calculations and our measurements for the sum of line intensities was 5.5% and 3.5% for the ν₁ and ν₃ bands, correspondingly.     

Ab initio ro-vibrational Hamiltonian in irreducible tensor formalism: a method for computing energy levels from potential energy surfaces for symmetric-top molecules

A theoretical approach to study ro-vibrational molecular states from a full nuclear Hamiltonian expressed in terms of normal-mode irreducible tensor operators is presented for the first time. Each term of the Hamiltonian expansion can thus be cast in the tensor form in a systematic way using the formalism of ladder operators. Pyramidal XY₃ molecules appear to be good candidates to validate this approach which allows taking advantage of the symmetry properties when doubly degenerate vibrational modes are considered. Examples of applications will be given for PH₃ where variational calculations have been carried out from our recent potential energy surface [Nikitin et al., J. Chem. Phys. 130, 244312 (2009)].     

First assignment of the 5ν4 and ν2+4ν4 band systems of CH4 in the 6287-6550 cm region

This paper reports the first assignment of rovibrational transitions of the 5ν₄ and ν₂+4ν₄ band systems of ¹²CH₄ in the 6287-6550 cm⁻¹ region, which is usually referred to as part of the 1.58 μm methane transparency window. The analysis was based on two line lists previously obtained in Grenoble by cavity ring down spectroscopy at T=297 and 79 K completed by three long-path Fourier transform spectra recorded in Reims (at 290 K, L=1603 m, P=1-34 mbar). In order to determine the dipole transition moment parameters and quantify the intensity borrowing due to the resonance interactions, we had to include in the fit of the effective Hamiltonian model some lines of the stronger ν₁+3ν₄ and ν₂+4ν₄ bands. For this purpose, intensities of 179 additional lines were retrieved from FTS spectra above 6550 cm⁻¹ though the analysis of these higher bands is not complete. About 1955 experimental line positions and 1462 line intensities were fitted with RMS standard deviations of 0.003 cm⁻¹ and 13.1%, respectively. A line list of 8029 calculated and observed transitions which are considered as dominant was constructed for ¹²CH₄ in the 6287-6550 cm⁻¹ region. This is the first high-resolution analysis and modelling of 5-quanta band systems of ¹²CH₄.     

Critical behaviour and associated conformal algebra of the Z3 Potts model

The conformal algebra for operators of the Z₃ model in the phase transition point is built. Critical exponents are found in this approach as solutions of simple algebraic equations, which are the consistency conditions of the algebra.Multipoint correlation functions obey linear differential equations. Some solutions are given for the four-point correlation functions of the Z₃ model at the phase transition point.     

The use of a generalized model based on the relaxation spectrum for calculation of the first normal stress difference from a flow curve

In this work a derivation has been made of a model based on the relaxation spetrum. This model can be used for the calculation of the first normal stress difference from a flow curve. The model has been generalized in order to describe better shear rate dependence of the first normal stress difference. Predictions of the generalized model are compared with experimental data. The comparison has been made for materials with dependencies taken from the literature, and also for materials investigated by the authors of this work.