Bond charge parameters from integrated infrared intensities

A procedure is outlined to analyze the infrared absorption intensities of fundamental vibration bands in terms of “bond charge parameters”. The method is illustrated for some small C_2v- and C_3v-type molecules: SO₂, NF₃, and PF₃. The values obtained for the “bond charge reorganizations” and “effective bond charges” for SO, NF, and PF bonds are discussed. The method offers the possibility of calculating rotational contributions without the use of a reference molecule.     

Effective Hamiltonian for degenerate vibrational states in symmetric top molecules

A mixed matrix-operator form of the effective rotational Hamiltonian has been discussed for the degenerate vibrational states of symmetric top molecules. In this scheme, a rotational contact transformation can be applied to the effective Hamiltonian such that the operators of the “2, +2,” “2, −2,” and “2, −1” l-type interactions as well as the operators of the Δk = ±3 and ±4 interactions are eliminated from the first-order terms of the expansion of the rotational Hamiltonian in terms of the small parameter λ. The results have been used to discuss the correlation between various interaction parameters in the effective rotational Hamiltonian for the doubly degenerate fundamental vibrational levels of semirigid symmetric top molecules. For example, for C_3v or D₃ molecules, the parameter of the “2, −1” interaction is correlated with other parameters and cannot be determined separately by fitting the experimental data (unless there are certain accidental resonances between vibrational-rotational levels).     

Collapse of vortex lines in hydrodynamics

A new mechanism is proposed for collapse in hydrodynamics associated with the “breaking” of vortex lines. The collapse results in the formation of point singularities of the vorticity field, i.e., a generalized momentum curl. At the point of collapse the vorticity |Ω| increases as ((t ₀ ? t)^?1 and its spatial distribution for t → t ₀ approaches quasi-two-dimensional: in the “soft” direction contraction obeys the law l ₁ → (t ₀ ? t)^3/2 whereas in the other two “hard” directions it obeys l ₂ → (t ₀ ? t)^1/2. It has been shown that this collapse scenario takes place in the general case for three-dimensional integrable hydrodynamics with the Hamiltonian ? = ∫|Ω| d r.     

ESR- and magnetic susceptibility measurements on the potassium molybdenum bronzes

Magnetic and transport properties of the transition metal bronzes are determined by the extent of delocalization of the transition metal 4d-electrons. We report on ESR investigations of single crystals of the “red” potassium molybdenum bronze K_0.33MoO₃ and of the “blue” potassium molybdenum bronze K_0.30MoO₃. ESR spectra due to unpairedd-electrons are observed at both compounds. Analyzing the hyperfine structure we find that thed ¹-electrons are delocalized over six molybdenum lattice sites in semiconducting K_0.33MoO₃. The same K_0.33MoO₃ crystals show another spectrum which is caused by pairs of exchange coupledd-electrons. Our results are compared with those from magnetic susceptibility measurements and are discussed in connection with the crystal structure of K_0.33MoO₃ and K_0.30MoO₃.     

Study of microwave pressure lineshifts: Dynamic and isotopic dependences

The study of pressure lineshifts and line broadenings initiated earlier (J. Mol. Spectrosc.94, 264–282 (1982)) is extended to some other perturbing gases and to isotopic species. New dependences of the lineshifts on the molecular parameters are found. One of them is the dependence, as well as the proportionality of the lineshift to the line frequency found before is explained in terms of a “dynamic Stark effect” model. The dependence of the lineshifts on the isotopic composition of the absorbing molecule is also reported. One of the main results of the study is the demonstration of higher sensitivity of lineshifts to the characteristics of molecular interactions as compared to the corresponding line broadening.     

Fourier transform and CARS spectroscopy of the ν1 and ν3 fundamental bands of 14NH3

The ν₁ and ν₃ fundamental bands of ¹⁴NH₃ have been measured using the techniques of Fourier transform and coherent anti-Stokes Raman spectroscopy. The effective values of the band origins, rotational and centrifugal distortion constants, and parameters of the vibrational-rotational interactions have been obtained by analyzing these bands as essentially regular parallel and perpendicular bands, with the “off-diagonal” local resonance interactions excluded from the fit. The “diagonal” l-type resonance effects have been included into the analysis of the ν₃ band for the +l, K = 1 and ?l, K = 2 levels.     

Diode-laser measurements and calculations of H2-broadening coefficients in the ν3 band of CH3D

Using a tunable diode-laser spectrometer, we have measured at room temperature the H₂-broadening coefficients of for 36 lines belonging to QP and QR branches in the ν₃ parallel band. The recorded lines with J values ranging from 1 to 15 and K from 0 to 9 (K?J) are located between 1196 and 1412 cm⁻¹. The H₂-broadening coefficients were determined by fitting each spectral line with Voigt, Rautian, and Galatry profiles. They were also calculated on the basis of a semiclassical model of interacting linear molecules performed by considering in addition to the weak electrostatic contributions the atom-atom Lennard-Jones potential. The theoretical results are in reasonable agreement with the experimental data, except for high J transitions where they are overestimated and for K approaching or equal to J with J?3 where they are underestimated. The latter discrepancy may be caused by the assumption to consider only ΔK=0 collision-induced transitions, associated with |ΔJ| transitions up to 4.     

Microwave l-type resonance transitions of the v4 = 1 state in PF3: Detailed interactions and molecular structure

Observation of the direct l-type resonance transitions in the microwave spectrum of the v₄ = 1 state of PF₃ has been extended to J = 36. The w-type interaction, (Δl = 0, ΔK = 6), has been found from measurements on the “forbidden” Stark trasitions in the $\text{K}\text{= 3}$ series. Also in this series a close accidental degeneracy was found between J = 30, $\text{K}\text{= 3}$ and 0, leading to new zero-field “forbidden” transitions through the r-type interaction (Δl = 2, ΔK = ?1) and to the determination of the C rotational constant. Nine spectroscopic parameters were determined using 140 observed frequencies including two “forbidden” trasitions. After suitable correction the B and C constants were used to determine the r₀, r_z, and r_e structures for PF₃. The equilibrium structure is estimated to be P-F = 1.561 ± 0.001 Å and ∠FPF = 97.7 ± 0.2°.     

Pressure broadening spectroscopy of formaldehyde,ammonia, isocyanic acid,trimethylene sulfide,and methyl chloride using far-infrared lasers

Pressure-broadened rotational spectra were observed for H₂CO, NH₃, HNCO, CH₃Cl, and CD₃Cl in the far-infrared region using the H₂O, D₂O, and HCN lasers. Absorption due to a ring-puckering transition was also observed for (CH₂)₃S. In cases where the absorption lines are well isolated from other lines, we could determine two parameters from the pressure dependence of the absorption coefficient at the laser frequency, that is, the peak absorption coefficient α₀ and the separation between the transition and laser frequency divided by the pressure broadening parameter γ = |ν - ν_L|/Δν_p. Molecular constants obtained from other sources are used to estimate |ν - ν_L| and Δν_p separately. The dependence of the pressure broadening parameter on the rotational quantum numbers J and K is discussed for ammonia and methyl chloride.     

Spin forbidden transitions in the Ka = 0 subband of NO2 in the λ = 592.5 nm region

In a high resolution laser excitation spectrum of NO₂, lines were recorded which do not follow the selection rule ΔN = ΔJ = ΔF of “spin allowed” transitions. Line positions and intensities of these “spin forbidden” lines were investigated for all rotational lines up to N″ = 12 of the K_a = 0 subband around λ = 592.5 nm. While the observed line intensities of “spin allowed” transitions can be well described by the J-coupling scheme, neither the J- nor the G-coupling scheme sufficiently describes the “spin forbidden” transitions. The observations can be fitted satisfactorily by perturbation theory, in which the Fermi interaction in ²A₁ is treated as the perturber. This looks similar to a superposition of J and G scheme in the ²A₁ ground state.     

Absorption of 12CH3D at 6–10 μm: Triad ν3, ν5, ν6

The absorption of ¹²CH₃D at 6–10 μm was recorded under vacuum with a resolution of 0.0054 cm⁻¹. For the first time the ν₅ band was assigned extensively, allowing the analysis of ν₃, ν₅, and ν₆ together within a “triad model,” including a rigorous treatment of all the Coriolis couplings involved. The assignments in the spectral range were anlarged from the original 1000 to the present 3500. The newly assigned lines essentially concerned the ν₅ band and a great number of perturbation-allowed transitions (about 30% of all observations). Ground state energy parameters were refined from 2641 combination differences involving J up to 19 and |ΔK| up to 6; the standard deviation of the fit was 0.0003 cm⁻¹. A set of 35 triad upper state energy parameters was derived, reproducing all observations with a standard deviation of 0.0076 cm⁻¹. The three dipole moment derivatives involved in the intensity calculations were estimated theoretically, by taking advantage of the recent accurate determination of the band strengths S₃ and S₄ of ¹²CH₄. Finally, about 6000 triad transitions predicted with linestrengths at least equal to 4 × 10⁻²⁵ cm·molecule⁻¹ were tabulated with assignments, wavenumbers, linestrengths, and lower and upper energy levels.     

Clusters and Ising droplets in the antiferromagnetic lattice gas

A definition of clusters of particles and holes with antiferromagnetic order is given for a lattice gas with coupling constant K < 0. In two dimensions it is shown that the Ising antiferromagnetic critical line is also a percolation line if P_b = 1 - exp(-|K|/2). Along this line these clusters called “droplets” diverge with Ising exponents.     

High-resolution infrared atmospheric spectra of ozone in the 10-μm region: Analysis of ν1 and ν3 bands-assignment of the (ν1 + ν2) − ν2 band

1988 lines of ozone have been observed in the atmospheric spectrum in the region 1060 to 1220 cm^?1, 1394 of them have been assigned to the ν₁ band, and 480 to the ν₃, particularly corresponding to ΔK_?1 = 2. The analysis has been performed using the Watson Hamiltonian, taking account of the strong Coriolis coupling between the 001 and 100 levels. The constants for the latter two states, the spectra and a listing of the observed and calculated wave-numbers, with their assignment, are given. In addition, 114 lines of the “hot” band (ν₁ + ν₂) ? ν₂ have been observed and assigned and are reported.     

Submillimeter spectrum and spectroscopic constants of the arsine molecule in the ground vibrational state

The submillimeter spectrum of the arsine molecule, AsH₃, of both the allowed R-branch transitions (J + 1 ← J, J = 0, 1, 2, 3) and forbidden transitions of the Q branches, |K| = 4 ← 7, 5 ← 8, 6 ← 9, is investigated in the frequency range from 220 to 900 GHz. Weak absorption lines were observed by using the spectrometer RAD with sensitivity increased by a nontunable cavity cell. On the basis of the results obtained and microwave data available in the literature the rotational spectrum of the arsine molecule in the ground state is analyzed.     

High-resolution infrared spectrum of the ν3 and ν2 + ν3 − ν2 bands of 14N16O2

The infrared absorption spectrum of the ν₃ band of ¹⁴NO₂ has been recorded with a resolution and a frequency accuracy much improved over the previous investigations. The K- and N-line assignments have been greatly extended and a more accurate set of spectroscopic constants derived. Several lines in the subbands with K_a ≥ 3 have been observed to be doubled by spin-rotation interaction and spin-rotation interaction constants have been obtained. Several weak series of lines in the spectrum (K_a = 0, 1, 2, and 3) have been unambiguously assigned to the “hot band” ν₂ + ν₃ ? ν₂. Lines of the K_a = 3, 4, 5, and 6 sub-bands of ν₃ have been found to be perturbed by a Coriolis interaction with the K_a = 4, 5, 6, and 7 levels of 2ν₂.     

FTIR Study of the ν1/ν4 Bands of D3SiCl near 1600 cm

The ν₁ (A₁, 1583.22 cm⁻¹) and ν₄ (E, 1615.33 cm⁻¹) Si-D stretching bands of monoisotopic D₃Si³⁵Cl have been studied by FTIR spectroscopy with a resolution of 3.3×10⁻³ cm⁻¹. We have assigned 2341 rovibrational lines for ν₁ (J_max=70, K_max=19) and 6207 for ν₄ (J_max=75, K_max=27). Both (ΔK=±1, Δ?=±1) and (ΔK=±2, Δ?=?1) interactions connect the v₁=1 and v₄=1 levels, the latter exerting moreover a weak ?(2, 2) interaction. These interactions were taken into account in a nonlinear least-squares fit, refining 29 free parameters with a standard deviation of 0.257×10⁻³ cm⁻¹ over 6722 nonzero-weighted data. Blended lines and about 250 of the 330 lines belonging to the K=11 subband of ν₁ and the KΔK=−6 subband of ν₄ were zero-weighted because they are locally perturbed respectively by the neighboring upper states of the 2ν₃+ν₆ (E, 1561.95 cm⁻¹) and 3ν₃ (A₁, 1604.81 cm⁻¹) bands. Equivalent fits were obtained for altogether three different models obeying constraints according to the theory of unitary equivalent reductions of the rovibrational Hamiltonian. By means of a band contour simulation both the transition moment ratio |M₁:M₄|=0.67 and a positive sign of the Coriolis intensity perturbation were determined.     

Microwave spectrum of tertiary-butylphosphine

The microwave spectra of tertiarybutylphosphine (CH₃)₃CPH₂, (CH₃)₃CPHD, and (CH₃)₃CPD₂ have been recorded in the region 26.5–40.3 GHz. Both a- and c-type transitions were observed and assigned for the “light” and “heavy” molecules and a-type transitions were observed and assigned for the d₁ species. The rigid rotor rotational constants were determined to be A = 4397.63 ± 0.04, B = 2878.88 ± 0.02, and C = 2870.86 ± 0.02 MHz for (CH₃)₃CPH₂ and A= 4261.98 ± 0.04, B = 2769.82 ± 0.02, and C = 2752.71 ± 0.02 MHz for (CH₃)₃CPD₂ and A = 4330 ± 2, B = 2831.45 ± 0.02, and C = 2801.50 ± 0.02 MHz for (CH₃)₃CPHD. Dipole moment components of |μ_a| = 1.06 ± 0.02, |μ_c| = 0.49 ± 0.02 and |μ_t| = 1.17 ± 0.02D were determined from the Stark effect. By assuming reasonable structural parameters for the tertiarybutyl and phosphine groups, a least-squares fit of the rotational constants gave $\text{λ}{}_{\mathrm{<mtext>P-C</mtext>}}\text{= 1.896}\text{A}\text{?}$ and $\text{?CPH = 95.7°}$. No splitting was observed of the first excited state of the phosphine torsional mode.     

Effect of the topology of a graphene/SiC nanotip emitter on the formation of rings in high electric fields

The representation of the tunneling conductance G(T) of the “dirty” (with low concentrations of the same nonmagnetic impurities in the I layer) N–I–N junction (where N is a normal metal and I is an insulator) in the form of a sum of conductances of random quantum jumpers penetrating the disordered I layer is obtained in the low-temperature region. It is shown that the axis of the parameter δ = |ε₀ ? ε_F| giving the deviation of the energy of ε₀ the quasi-local electron state on the impurity in the I layer from the Fermi energy of εF the dirty N–I–N junction contains a series of bifurcation points, at the transition through each of which (in the direction of the increase in δ) the number of maxima on the temperature dependence G(T) increases by unity; i.e., a new maximum is “born” on the curve G(T). Numerical estimates are given for the characteristic parameters of dirty N–I–N junctions indicating the possibility of the experimental observation of at least the first of these maxima.     

“Forbidden” millimeter-wave transitions in arsine

A millimeter-wave spectrometer having a sensitivity of 4 × 10^?10 cm^?1 in the 2-mm region has been used for observation of the “forbidden” transitions J → J, K = ±4 → ±1 and J → J, K = ±5 → ±2 in AsH₃. A comprehensive computer analysis was made of the frequencies measured in this work together with available microwave frequencies of other transitions. This analysis provides accurate values of the rotational constants, nuclear quadrupole couplings, and effective structural parameters of the molecule. The spectral constants B₀ and C₀ (in MHz) are 112 470.597 and 104 884.665, respectively.