The ν2, 2ν2, 3ν2, ν4, and ν2 + ν4 bands of 15NH3

The ir absorption of gaseous ¹⁵NH₃ between 510 and 3040 cm^?1 was recorded with a resolution of 0.06 cm^?1. The ν₂, 2ν₂, 3ν₂, ν₄, and ν₂ + ν₄ bands were measured and analyzed on the basis of the vibration-rotation Hamiltonian developed by V. ?pirko, J. M. R. Stone, and D. Papou?ek (J. Mol. Spectrosc.60, 159–178 (1976)). A set of effective molecular parameters for the ν₂ = 1, 2, 3 states was derived, which reproduced the transition frequencies within the accuracy of the experimental measurements. For ν₄ and ν₂ + ν₄ bands the standard deviation of the calculated spectrum is about four times larger than the measurements accuracy: a similar result was found for ν₄ in ¹⁴NH₃ by ?. Urban et al. (J. Mol. Spectrosc.79, 455–495 (1980)). This result suggests that the present treatment takes into account only the most significant part of the rovibration interaction in the doubly degenerate vibrational states of ammonia.     

Molecular constants for the interacting upper states of the ν1, ν3, 2ν2, ν2 + ν4, and 2ν4 bands in 12CH4

In a previous paper (J.-E. Lolck and A. G. Robiette, J. Mol. Spectrosc.88, 14 (1981)) a theoretical model for the interacting upper states of the ν₁, ν₃, 2ν₂, ν₂ + ν₄, and 2ν₄ bands in methane was described. The present paper summarizes the results obtained, using this model, in a comprehensive analysis of the five bands of ¹²CH₄ through J′ = 12. Values of 80 molecular constants, of which 17 correspond to vibrationally off-diagonal operators, are reported. In addition the computed energy levels of the v₃ = 1 state are compared to the experimental ones and to the result of the previous isolated band approach.     

A theoretical model for the interacting upper states of the ν1, ν3, 2ν2, ν2 + ν4, and 2ν4 bands in methane

The effective vibration-rotation Hamiltonians complete to fourth order in the Amat-Nielsen scheme for the upper states of the ν₁, ν₃, 2ν₂, ν₂ + ν₄, and 2ν₄ bands in methane are reviewed, and the major vibration-rotation interactions (H₃₀, $\text{H}\text{?}{}_{40}$, $\text{H}\text{?}{}_{21}$, $\text{H}{}_{31}$, $\text{H}\text{?}{}_{22}$) connecting the different vibrational states are discussed. Explicit matrix elements in a basis of harmonic oscillator-symmetric rotor basis functions are given for the purely vibrational terms and for the vibration-rotation interactions. Expressions for spectral intensities of infrared and Raman spectra are presented, and the selection rules and transition moment matrix elements are stated. A computer program is described which, incorporating all these features, can be used for prediction of infrared and Raman spectra and for determination of molecular constants from observed spectra by a least-squares routine. As an example the program is applied to the 2ν₄ isotropic Raman spectrum of ¹²CH₄, leading to a very good agreement between the experimental and calculated spectra.     

The ν2 + ν4 and 2ν2 isotropic Raman bands of 12CH4

The purely isotropic Raman spectrum of the ν₁ band, the ν₂ + ν₄ band (enhanced through interaction with ν₁), and the 2ν₂ band of ¹²CH₄ was obtained with a spectral resolution of 0.30–0.35 cm^?1 from exposures with different orientations of the linearly polarized exciting light. The ν₂ + ν₄ and 2ν₂ bands show partially resolved rotational structure. The spectra are interpreted in terms of a model which takes explicitly into account vibrational and rovibrational interactions with other vibrational states, using molecular constants determined primarily from infrared spectra. The computed contours are in excellent agreement with the experimental ones and the observed and calculated peak wavenumbers agree within one tenth of the spectral resolution limit, except for a small region near the ν₁ band. The good overall agreement represents an independent check on the overall correctness of the previously reported molecular constants. A detailed discussion is given of the contributions to the intensities of individual transitions from the three transition moment matrix elements, which in an isolated-band model are the intensity parameters of the ν₁, 2ν₄, and 2ν₂ isotropic bands, respectively.     

High temperature phase transition in NH4H2PO4

NH₄H₂PO₄ (ADP) has been investigated by infrared spectroscopy, differential scanning calorimetry, thermogravimetric analysis and d.c. conductivity in the temperature range of 25–180° C. Sharp reversible changes were observed in the region from 400 to 500 cm^?1 of the infrared spectra in the temperature range of 138–174° C. Similar and supportive data were obtained with DSC, TGA and DC conductivity measurements. The results clearly suggest a high temperature phase transition for ADP before its melting point.     

Electrostatic lattice energies of some ABX3 polytypes with close-packed AX3 layers

Electrostatic lattice energies (Madelung and polarization energies) for five ideal ABX₃, structure types with close-packed AX₃ layers (X = F, Cl, Br, I, O, S) are calculated. Stability regions for the ideal structure types are indicated as function of the anion radius and the anion polarizability. The effect on the electrostatic lattice energy due to trigonal deformations of the AX₃ layers in the 2L and 3L stacked structures is discussed for the anions F and Cl.     

The pentad rotation-vibrational states of 12CD4: Wavenumber analysis of infrared and Raman spectra of the ν1, ν3, 2ν2, ν2 + ν4, and 2ν4 bands

The so-called pentad of ¹²CD₄ consists of the vibrational states v₁ = 1(symmetry A₁), v₃ = 1(F₂), v₂ = 2(A₁ + E), v₂ = v₄ = 1(F₁ + F₂), and v₄ = 2(A₁ + E + F₂). All states are located in the 1950 to 2250-cm^?1 region and all are strongly interacting. In the present work we have assigned more than 5000 infrared rotation-vibrational transitions and 163 isotropic Raman transitions from the vibrational ground state to the pentad. We have used infrared and Raman spectra of a resolution better than 0.01 cm^?1. From the experimental wavenumbers 2567 pentad rotation-vibrational energy levels with J ≦ 20 have been determined. These levels are reported in the paper. The levels have been used for refinements of the spectroscopic constants of two physically different effective Hamiltonians for the pentad states. For all levels with J ≦ 12 an unweighted standard deviation of 0.004 cm^?1 is obtained for both Hamiltonians, whereas the standard deviation increases more or less rapidly with J above 12 due to the imperfections of the Hamiltonians. The values of the spectroscopic constants of both Hamiltonians (85 and 106, respectively) are reported and the effects of the approximations are discussed.     

Analysis of the ν2 and ν4 infrared bands of CD4

The infrared spectrum of totally deuterated methane CD₄ has been recorded between 930 cm^?1 and 1180 cm^?1 under high resolution (0.003 cm^?1). The ν₂ and ν₄ bands of ¹²CD₄ have been reanalyzed on the basis of a complete third-order Hamiltonian including all the coupling terms linking the upper states of the two bands. A set of only 16 self-consistent parameters have been adjusted to fit more than 1650 assigned transitions reaching a maximum upper state J value of 20. The obtained standard deviation is 0.0041 cm^?1. In addition, 171 lines of the ν₄ band of ¹³CD₄ have been assigned. They have been analyzed, in the same dyad scheme, by adjusting 7 parameters of the ν₄ band together with the main ζ₂₄ Coriolis parameter. The obtained standard deviation is only 0.0012 cm^?1.     

The ν2 and ν4 bands of AsH3

The infrared absorption of arsine, AsH₃, between 750 and 1200 cm^?1 has been recorded at a resolution of 0.006 cm^?1. Altogether 2419 transitions, including nearly 700 “perturbation allowed” transitions with Δ∥k ? l∥ = ±3, ±6, and ±9, have been assigned to the ν₂(A₁) and ν₄(E) bands. Splitting of the transitions for K″ = 3, 6, and 9 was also observed. To fit the rotational pattern of the v₂ = 1 and v₄ = 1 vibrational states up to J = 21, all the experimental data were analyzed simultaneously on the basis of a rovibrational Hamiltonian which took into account the Coriolis interaction between ν₂ and ν₄ and also included several essential resonances within them. The derived set of 38 significant spectroscopic parameters reproduced the 2328 transition wavenumbers retained in the final fit within the accuracy of the experimental measurements.     

Calculated energy levels and intensities for the ν1 and 2ν2 bands of HDO

A Hamiltonian taking explicitly into account both Fermi and Coriolis interactions has been set up for triatomic molecules of symmetry C_s and used to reproduce, very satisfactorily, the available rotational energy levels of the {(100), (020)} interacting states of HDO, providing us with realistic wavefunctions as well as precise rotational constants and vibrational energies. Then, to calculate line intensities, these wavefunctions were used together with suitably chosen transition moment operators expanded up to degree 2 in $\text{J}$ and having the correct symmetry in the C_s group, leading to hybrid bands of both A and B type., Using this formalism, it has been possible to determine, from the fit of the existing experimental intensities, the coefficients appearing in the expansions of the transition moment operators of the 2ν₂ and ν₁ bands of HDO. In this way, we have improved upon the F-factor formalism which needs much more parameters to reproduce the line intensities with the same precision. Finally, using the transition moments as well as the wavefunctions and energy levels deduced from the diagonalization of the Hamiltonian matrix, we have calculated the whole spectrum of the ν₁ and 2ν₂ bands of HDO.     

The assignment of ν2 and ν4 of SO3

Three experiments have been performed to resolve an uncertainty in the assignment of ν₂ and ν₄ for SO₃: (i) the gas phase Raman spectrum has been measured; (ii) the infrared active combination band ν₃ + ν₄ has been measured; (iii) a band contour calculation has been performed taking account of the ?-type resonance in ν₄ and a strong Coriolis resonance between ν₂ and ν₄. These experiments establish beyond any doubt that ν₂ lies at about 497.5 cm^?1 and ν₄ lies at about 530.2 cm^?1. The contour calculation also shows that the Coriolis resonance gives rise to a positive intensity perturbation.     

Simultaneous analysis of the ν1, ν4, 2ν2, ν2 + ν5, and 2ν5 infrared bands of 12CH3F

The Fourier-transform spectrum of CH₃F from 2800 to 3100 cm^?1, obtained by Guelachvili in Orsay at a resolution of about 0.003 cm^?1, was analyzed. The effective Hamiltonian used contained all symmetry allowed interactions up to second order in the Amat-Nielsen classification, together with selected third-order terms, amongst the set of nine vibrational basis functions represented by the states ν₁(A₁), ν₄(E), 2ν₂(A₁), ν₂ + ν₅(E), 2ν₅⁰(A₁), and 2ν₅^±2(E). A number of strong Fermi and Coriolis resonances are involved. The vibrational Hamiltonian matrix was not factorized beyond the requirements of symmetry. A total of 59 molecular parameters were refined in a simultaneous least-squares analysis to over 1500 upper-state energy levels for J ≤ 20 with a standard deviation of 0.013 cm^?1. Although the standard deviation remains an order of magnitude greater than the precision of the measurements, this work breaks new ground in the simultaneous analysis of interacting symmetric top vibrational levels, in terms of the number of interacting vibrational states and the number of parameters in the Hamiltonian.     

The ν4 and ν2 Raman bands of CHD3

The CHD₃ Raman spectrum from 1925 to 2455 cm^?1 has been photographed with a resolution of about 0.2 cm^?1, showing the overlapping ν₂ and ν₄ bands. Ground state combination differences yield C₀ = 2.6297 ± 0.0003 cm^?1. The ν₄ state is weakly perturbed, but reasonably accurate values could be obtained for ν₄ = 2250.88 ± 0.10 cm^?1, (Cζ)₄ = 0.656 ± 0.010 cm^?1, C₄ - C₀ and B₄ - B₀. Some of these constants differ significantly from values previously estimated by infrared workers. For the ν₂ state the constants determined are in good agreement with recent infrared results.     

Magnetic ordering in rare earth iron silicides and germanides of the RFe2X2 type

Rare earth iron silicides and germanides of the RFe₂Si₂ or RFe₂Ge₂ type with R = La, Ce, Pr, Nd, Sm, Gd and Dy were measured for their magnetic susceptibility. The silicides and germanides of Nd and Gd are antiferromagnetically ordered below a Neel point of, respectively, 11 and 7°K for the silicides and 13 and 11 for the germanides. The Nd sublattice under-goes a spin-flop transition which at 4.2°K is at 11 KOe. Although the Fe sublattice is diamagnetic, all the samples showed a weak ferromagnetic ordering below a temperature of about 700°K. The ratio between the dia- and ferromagnetic phases is 94:6 per cent in the silicides and 80:20 in the germanides, as determined by Mössbauer spectroscopy and supported by magnetization measurements.     

The stretching fundamental bands ν1, ν2 and ν4 of HSiD3

The ν₁(A₁), Si-H stretching, ν₂(A₁) and ν₄(E), Si-D stretchings, fundamental bands of HSiD₃ have been recorded at an effective resolution of ca. 0.003 cm⁻¹ between 2080 and 2280 cm⁻¹ and between 1480 and 1720 cm⁻¹, respectively. Ro-vibrational transitions of the H²⁸SiD₃ isotopologue have been assigned in the two spectral ranges, about 700 belonging to ν₁, with J′ up to 25 and K up to 21, and about 1600 to the ν₂/ν₄ dyad, with J′ up to 24 and K′ up to 19. The spectra of all the bands evidence the existence of several perturbations. The transitions of ν₁ have been analyzed either neglecting or including in the model A₁/E Coriolis-type interactions with nearby dark states. The υ₂ = 1 and υ₄ = 1 states have been fitted simultaneously taking into account several ro-vibrational interactions between them and, in addition, with the υ₅ = 2, l = 0 component, and with few other close dark states. The standard deviation of the fit for both ν₁ and the ν₂/ν₄ dyad is, however, more than one order of magnitude larger than the estimated experimental precision and is independent on the adopted model.     

Correlation between energy levels of linear and bent X2Y2 molecules

The permutation-inversion group developed by Longuet-Higgins is extended to a classification of the vibronic, torsional, and rotational wavefunctions of a nonrigid X₂Y₂ molecule by introducing a symmetry operation $\text{T}\text{?}$, which rotates the top half of the molecule by 2π and, accordingly, the molecule-fixed x axis by π. Since the energy levels of linear (D_∞h) and bent (C_2h, C_2h, and C₂) forms of X₂Y₂ are classified according to a set of common symmetry operations of this extended permutation-inversion group, their energy levels can be correlated, including those of nonrigid forms such as a quasilinear system or a free internal rotor. Nuclear spin weights and selection rules are derived.     

The 2ν1 + ν4 band of carbon tetrafluoride

The 2ν₁ + ν₄ band of ¹²CF₄ at 2445 cm^?1 has been remeasured with a 0.005-cm^?1 resolution by means of a Fourier interferometer. The spectral region investigated here lies between P(70) and R(52). More than 500 line clusters have been assigned. From these a least-squares fit with an overall standard deviation of 0.001 cm^?1 has led to seven significant constants.     

Analysis of FTIR spectra of CH2BrCl; the ν4 and ν5 fundamentals and their hot-bands ν4+ν6−ν6 and ν5+ν6−ν6

The infrared spectrum of isotopically pure CH₂⁷⁹BrCl has been recorded at a resolution of 0.0023 cm⁻¹ (FWHM) in the range 550-800 cm⁻¹ with a Bruker IFS 120 HR Fourier transform spectrometer in Wuppertal. Here we report the full rotational analysis of the ν₄ and ν₅ fundamentals and of the hot-bands ν₄+ν₆−ν₆ and ν₅+ν₆−ν₆. Ground state combination differences were constructed for all bands, yielding improved ground state constants, up to quartic terms, as well as reliable rotational constants for the ν₄, ν₅, and ν₆ states.