Rotational relaxation of symmetric tops CH3D and CD3H in some inert liquids

Infra-red spectra of CH₃D and CD₃H dissolved in liquid Ar, Kr, Xe, N₂, O₂ and CH₄ or CF₄ have been recorded. From the band shapes, rotational correlation functions, band moments and intermolecular mean square torques have been calculated. To describe the tumbling motion, involved in the parallel band profiles, we have computed the theoretical correlation functions in the m or j diffusion limits. The validity of these Gordon models is discussed. In an attempt to obtain some information on the rotational diffusion tensor, experimental correlation times have been estimated from A₁ and E bands of CD₃H.     

The v 3 and 2v 3 I.R. bandshapes and dipole correlation functions of compressed gaseous N2O; intensity measurements of the 2v 3 band

The I.R. spectrum of the ν₃ band (4·5 µm) of N₂O has been studied for temperatures varying from 219 to 298 K and densities up to 85 kg m^-3. The 2v ₃ band (2·3 µm) has been analysed at room temperature for densities up to 182 kg m^-3; measurements of the integrated intensities as a function of density show no evidence of pressure induced absorption. This band has also been observed in the vicinity of the critical region.

The dipole moment autocorrelation function is used to assess a collisional model derived from the impact approximation and the Gordon M- and J-diffusion models developed classically as well as the semi-classical M-diffusion model. The M- and J-diffusion models reproduce well the experimental correlation function for the ₃ band; the semi-classical M-diffusion model is better than the classical ones for the overtone 2v ₃ and gives a satisfactory account of the correlation functions. For the collisional model considered which implies uncorrelated rotational levels, a discrepancy between theoretical and experimental correlation functions and bandshapes becomes noticeable from about 40 kg m^-3 and increases with density.     

Etude des mouvements moléculaires en milieu liquide à partir du profil des bandes de vibration dans l'infrarouge et des fonctions de corrélation

We have studied the fundamental bands of chloroform and bromoform, both pure and in solution in various solvents; also the first harmonics of v ₁, and a few other harmonics and combination bands. The correlation functions of v ₁ and v ₂ and band moments of v ₁ have been calculated. The comparison of our results with those obtained in microwave and far IR and Raman spectra offers an opportunity to discern, in widths and correlation functions, what can be attributed to vibration and what originates in rotational diffusion. Our results are interpreted with the assumption that rotational diffusion is produced by small angles jumps and that the vibrational effect is very important. The v ₁ band shows an additional widening not accounted for in existing theories.     

Raman study of CF4 in liquid Ar

The rotational behaviour of CF₄ dissolved in liquid argon is derived from the band contour analysis of Raman spectra recorded over the concentration range from 10^-2 mole fraction to 1 mole fraction at 85 K. The angular momentum correlation times have been determined with the help of the J-diffusion model and used to apply the rough hard sphere model. A study of the transition dipole-transition dipole (TD-TD) interaction is made using the v ₃ mode at 85 K for different concentrations.     

Computer simulation of a diatomic molecule dissolved in a monatomic fluid—Correlation functions,band shapes,and relaxation times

Four N₂-Ar ‘solute-solvent’ systems representing different temperatures and densities were simulated on a computer by the molecular dynamics technique. From the data for each system, the dipole, angular velocity, force-on-the-bond, and P ₂ correlation functions were calculated. These functions were used to determine rovibrational infra-red and Raman band-shapes, and N.M.R. relaxation times for quadrupolar, magnetic dipole-dipole and spin-rotation relaxation mechanisms. The P ₂ and dipole correlation functions were compared with those calculated by Gordon from experimental data. The lack of agreement was examined to determine restrictions on the application of Gordon's method for obtaining these correlation functions. Also, the band shapes were compared with the experimental data to help determine these restrictions. The N.M.R. relaxation times were examined for temperature dependence and for dominant contributions to the total relaxation time. The force-on-the-bond correlation function was found to require an extra term that takes into account the average force field to which the N₂ molecule is subjected. A three-parameter model for rotational diffusion of a diatomic molecule is tested and compared with existing models.     

Observation of the fast component in the fluorescence of gaseous SO2 excited to the A1A2 state in the presence of a magnetic field

Effects of an external magnetic field (B) on the SO₂ fluorescence have been examined under excitation of the ‘C’ band and the single rotational levels of the ‘B’ and ‘E’ bands of the A(¹A₂) ← X¹A₁ transition. For the ‘C’ band, the total SO₂ fluorescence was studied, while for excitation of the single rotational levels, fluorescence of the single rotational lines of (^rR₅(5) (31711 cm^-1), ^pP₇(7) (31662 cm^-1)) (‘E’ band) and of (^rR₈(8) (31000 cm^-1), ^pP₁₀(10) (30927 cm^-1)) (‘B’ band) was studied. Decay of the SO² fluorescence was studied with nanosecond time resolution in the 1?5–50 mTorr region. In the presence of a magnetic field, decay of the total SO₂ fluorescence and of the fluorescence belonging to the single rotational lines were fitted by the bi-exponential functions. In the case of the total SO₂ fluorescence, this function also includes the time independent term, which, however, is dependent on a magnetic field. The time independent term belongs to the long-living component, which can be approximated by a constant in the time-scale studied. Radiationless processes induced by an external field were directly observed. The magnetic field and pressure dependences of the processes induced by a field were studied under excitation of the SO₂ fluorescence by light of a different wavelength. The data obtained were explained by the direct mechanism.     

Infrared absorptions and band widths of dilute solutions of CF3H in liquid Ar,N2, and Xe

The spectra of fluoroform (CF₃H) in the solvents Ar, N₂, and Xe have been obtained in the fundamental region (400–4000cm^?1) using a low temperature cryostat and a Fourier transform infrared spectrophotometer. Ab initio calculations at the HF/6-31G? level have been performed to obtain the calculated vibrational frequencies of the isolated CF₃H molecule and CF₃H in the presence of the solvents (Ar, N₂, and Xe). Comparison of the frequency shifts of CF₂H in solution with respect to the gas phase frequencies is made for the experimental and theoretical results. Lorentzian functions were used to fit the bands and obtain the wavenumber at the peak absorbance and the vibrational band widths. An analysis of the dynamics of relaxation has been made based on the infrared time correlation functions for three of the fundamental modes (ν₁, ν₃, and ν₄). Bandwidths, band moments, and relaxation times were obtained by appropriate fitting of the experimental correlation functions to theoretical models. In liquid argon, the temperature dependence of the second moment (M ₂) indicates that rotational relaxation explains the bandwidth of the ν₃ mode. For the ν₄ mode, the temperature dependence of M ₂ can be attributed to rotational relaxation if it is corrected with a Coriolis coupling term. The bandwidths of the ν₁ mode do not follow the rotational relaxation model, and probably vibrational relaxation is the dominant mechanism.     

Hubbard relations for linear molecules

The Hubbard relations for linear molecules in the cases of the extended diffusion model (EDM) and Ivanov's theory are derived. The M-diffusion variant of the EDM leads to an unphysical result as the dielectric and Raman correlation times approach infinity and it is suggested that M-diffusion is not a realistic model. The J-diffusion is almost the same as for spherical molecules. When the reduced angular momentum correlation time, τ _J *, is very much less than unity both EDM and Ivanov theory give a relation similar to the friction model [2], i.e. the original Hubbard relations [14] with the coefficient 6^-1, instead of 2^-1 as obtained by O'Reilly [3]. For τ _J * > 1 the various versions of Hubbard's relations are different enough to be distinguished experimentally.     

Raman band shapes and the dynamics of liquid N2O4

The Raman spectra of the totally symmetric A _g modes, v ₁, v ₂ and v ₃, of the N₂O₄ molecule have been measured in the liquid state at 262, 279 and 297 K. The vibrational and the rotational correlation functions are calculated. The long-time exponential decay of the rotational correlation functions of all the A _g modes reflects an asymptotic diffusional behaviour of molecular reorientation. The rotational relaxation rate is found to increase with increasing temperature. A marked point of inflection from the short time inertial correlation to the long time exponential decay appears at about 0·35 ps for the v ₂ mode. This is an indication of orientational rebound arising from the librational motion in a temporary solvent cage. The isotropic bandwidth increases in the order v ₁ < v ₂ < v ₃, which is also the order of decreasing vibrational frequency. The temperature dependence of the peak frequency and of the bandwidth are also found to increase in the same order. These observations are analysed qualitatively in terms of two models of vibrational dephasing which take into account the effect of vibrational anharmonicity.     

Molecular dynamics of liquids modelled by ‘2-Lennard-Jones centres’ pair potentials

The molecular dynamics study based on two-Lennard-Jones (12-6) centres pair potentials, with reduced bond lengths in the range 0·5 ?l/σ?0[sbreve]d8, and with ε, σ-parameters simulating liquid F₂, Cl₂, Br₂ and CO₂ (14) is extended to time correlation functions. The calculated properties include: translational velocity and force self correlation functions; orientational self-correlation functions <P _1,2(Î . Î(t))>, a cross correlation function for P ₂, angular momentum (J), and torque self-correlation functions. Diffusion constants (D) and rotational relaxation times (τ₁, τ₂, τ _J ) have been evaluated and where possible compared with experimental data (D and τ _J for F₂, τ₂ for Cl₂). Calculations with 108 or 256 molecules are reported for several densities and temperatures for four model liquids. The nature of the one-particle motion is analysed qualitatively in terms of quasi-oscillations and -librations. It is difficult to fit the observed features into the framework of physical models proposed in the literature. The parametrization in terms of memory functions will be reported in a subsequent paper.     

Molecular motions in liquid NOF3

The rotational behaviour of NOF₃ is derived from the band contour analysis of the Raman spectra recorded over the liquid phase. The angular momentum correlation times derived from the J diffusion model show us that this C _3v molecule rotates almost isotropically. The band profiles are interpreted in terms of the rough hard sphere model.     

Thermodynamic and structural properties of liquids modelled by ‘2-Lennard-Jones centres’ pair potentials

Molecular dynamics calculations have been carried out for model liquid systems of N (=108 or 256) molecules interacting through two Lennard-Jones (12–6) centres coinciding with the positions of the atomic masses (the ‘atom-atom’ pair potential). The objectives were (a) to study the dependence of the properties on the molecular anisotropy defined by the reduced distance l*=l/σ between the centres in the range 0·5–0·8; and (b) to compare the computed quantities with those of real liquids (F₂, Cl₂, Br₂, CO₂). This paper deals with thermodynamic and structural features. Time-dependent correlations will be treated in a future communication.

In the liquid region not too far from the triple point the energy and pressure isochores are well represented by straight lines, the slopes of which increase with density and anisotropy. Thermodynamically consistent expressions for the energy and pressure as functions of density and temperature have been obtained for each system.

With Lennard-Jones parameters adjusted so as to secure the best overall fit, the agreement between experimental and computed thermodynamic properties is very satisfactory for F₂ (l*=0·505), quite good for Cl₂ and Br₂ (l*=0·608–0·63), but rather poor for CO₂ (l*=0·793). The ‘interatomic distances’ are close to the experimental values.

The static structural correlations are discussed in terms of the pair-correlation functions (pcf) g _A(r*) for the separation between ‘atoms’, the first few functions g_ll'm (R*) which arise from the expansion of the g(R*, θ₁, θ₂, φ₁₂) in spherical harmonics, and the pcf's for certain special near-neighbour configurations. The computed atom-atom structure factor is compared with the experimental data for liquid Br₂.

Mean square forces and torques have been evaluated and are related to some experimental results.     

Theoretical investigations of rotational phenomena and dielectric properties in a nematic liquid crystal

The molecular dynamics (MD) simulation, based on a realistic atom-atom interaction potential, was performed on 4-n-pentyl-4'-cyanobiphenyl (5CB) in the nematic phase. The rotational viscosity coefficients (RVCs) γ _i, (i = 1, 2) and the ratio of the RVCs λ = - γ ₂/γ ₁ were investigated. Furthermore, static and frequency-dependent dielectric constants and ε were calculated using parameters obtained from the MD simulation. Time correlation functions were computed and used to determine the rotational diffusion coefficient, D _⊥. The RVCs and λ were evaluated using the existing statistical-mechanical approach (SMA), based on a rotational diffusion model. The SMA rests on a model in which it is assumed that the reorientation of an individual molecule is a stochastic Brownian motion in a certain potential of mean torque. According to the SMA, γ _i are dependent on the orientational order and rotational diffusion coefficients. The former was characterized using: i) orientational distribution function (ODF), and ii) a set of order parameters, both derived from analyses of the MD trajectory. A reasonable agreement between the calculated and experimental values of γ _i and λ was obtained. Received 22 March 2000 and Received in final form 8 October 2000     

The infrared spectrum of isothiazole in the range 600–1500 cm−1, including a high-resolution study of the v 11(A′) band at 818 cm−1 and the v 16(A″) band at 727 cm−1, together with ab initio studies of the full spectrum

Abstract

The gas-phase high-resolution infrared spectrum of isothiazole in the range 600–1500 cm^?1 has been recorded, and revised band centres obtained for a number of vibrations. An analysis of the v ₁₁(A′) band at 818 cm^?1 and the v ₁₆(A″) band at 727 cm^?1 has been performed, using the Watson Hamiltonian, A-reduction, III^r representation. These were combined with previous microwave spectral data to provide combined analyses for rotational constants and quartic centrifugal distortion constants Δ _J , Δ _JK , Δ _K , δ _j and δ _K . These extend the knowledge derived from previous microwave and IR spectral studies. The equilibrium structures and the derived harmonic frequencies were calculated by ab initio methods, using a variety of basis sets with MP2, MP4 and CCSD(T) methods, and a comparison of these with experimental data is discussed. At a pragmatic level, the closest correlation of the rotational constants with experiment is not obtained with the most sophisticated methodology. Similarly, the vibration frequencies and intensities also vary strongly with the procedure. In particular, we found that the cc-pVTZ+MP2 results probably provide the best numerical comparison with experimental IR data for this molecule.     

A general pseudopotential model for molecules with many valence electrons

Criteria are discussed for the practical application of ‘valence-electron only’ calculations aimed at simulating ab initio all-electron calculations on molecules containing heavy atoms with many core electrons. A theoretical model is outlined based on the use of pseudopotentials derived from atomic SCF calculations. The model has been used in calculations for NaH, Na₂, H₂S, S₂, H₂S₂, HCl, Cl₂ and NaCl, and has been tested by comparison with reference all-electron calculations. Most of these tests employ double-zeta basis sets and SCF wavefunctions, although polarization functions and complete valence-electron CI wavefunctions have been used in some cases. The model is generally successful for ground-state equilibrium structures, charge distributions and orbital energies.     

The ν2 fundamental vibration-rotation band of T2O

The ν₂ fundamental vibration-rotation band of T₂O vapor has been measured at grating resolution, and the rotational structure has been analyzed. The band center and the values of the rotational constants A, B, and C for the ground state and excited state have been determined. These values are consistent with the data for J through 6, and with extrapolation from H₂O and D₂O.     

The rovibrational levels of ammonia

In this paper we report variational rovibrational studies on ammonia and its isotopomers. We use six internal coordinates (one of which describes the umbrella motion). The expansion functions are products of one-dimensional functions of these internal coordinates, multiplied by appropriate functions of the Euler angles to describe the rotational motion. We use a previously published high accuracy six-dimensional potential energy surface [LEONARD, C., HANDY, N. C., CARTER, S., and BOWMAN, J. M., 2002, Spectrachim. Acta, 58, 825]. We derive the full kinetic energy operator for the rovibrational motion in these coordinates. This operator has been completely checked to give a hermitian secular matrix. All matrix elements are evaluated numerically by quadrature. The symmetry of the expansion functions is fully described in D_3h, C_2v and C_s. It is not possible to perform the calculations in D_3h, but complete degeneracy in the appropriate levels is obtained with the C_2v program. The algebraic complexity of this program has been far greater than for any other variational study we have undertaken for a tetra-atomic molecule.

We present J = 0, 1, 2 energy levels for the experimentally observed band origins of NH₃, and J = 0, 1 energy levels for the ground state and fundamentals of NH₂D, ND₂H and ND₃. For the asymmetric isotopomers, identical results are obtained for both C_2v and C_s, thus confirming the validity of the method. The levels we obtain are completely converged. Agreement with observation is of the order of 0.5% (of course being dependent upon the accuracy of the potential energy surface); therefore the ordering of the rotational levels and their splitting is completely predicted and understood.     

Solid state reactions and transport properties in the quasibinary system AgI/RbI

The reactions between AgI and Rb₂AgI₃, RbI and RbAg₄I₅ and AgI and RbI have been investigated by measurements of reaction layer thickness and by experiments with inert markers. A theoretical derivation of the growth kinetics for reactions with double layers is given. The Rb⁺-diffusion coefficients, which are needed to apply these relations to the reaction between AgI and RbI, have been obtained from an investigation of the other two reactions which form only a single product layer. The diffusion coefficient of Ag⁺in Rb₂AgI₃ was also determined from conductivity measurements on Rb₂AgI₃.     

Doppler-limited spectroscopy of the 3ν3 band of SF6

The strongest portion of the 3ν₃ band of SF₆ has been recorded at T = 160 and 295 K with Doppler-limited resolution using a tunable laser difference-frequency spectrometer. The structure in this band has been identified with the P, Q, and R branches of one F_1u sublevel (with essentially l = 1 character) within the 3ν₃ vibrational manifold. Preliminary effective rotational constants have been obtained for this band from which the anharmonic parameters X₃₃, G₃₃, and T₃₃ can be estimated. The role of hot bands and of the other anharmonic sublevels is discussed in relation to prior interpretations of low resolution spectra and of the initial isotope selective stages of CO₂ laser photo-dissociation of SF₆.