Semiclassical calculations of half-widths and line shifts for transitions in the 30012←00001 and 30013←00001 bands of CO2, I: Collisions with N2

Calculations of the half-width, its temperature dependence, and the line shift are made for the rotational states J=0–120 for two of the Fermi-tetrad bands (30012←00001 and 30013←00001) of CO₂ perturbed by N₂. The calculations employ the semi-classical complex Robert–Bonamy method with no ad hoc scaling, J-dependent or otherwise, and an intermolecular potential (IP) comprised of an electrostatic part, an atom–atom part, and an isotropic London dispersion part. The averaging over the impact parameter b and relative speed v are explicitly carried out. Many interesting features about CO₂ as the radiating molecule are elucidated. Effects of the trajectory model, the order of the expansion of the atom–atom component of the potential, and the inclusion of the imaginary terms are studied. It is shown that the results are very sensitive to the intermolecular potential. The final IP parameters give results that demonstrate excellent agreement with measurement for the three line shape parameters studied in this work.     

Experimental studies by complementary terahertz techniques and semi-classical calculations of N2- broadening coefficients of CH335Cl

Room-temperature N₂-broadening coefficients of methyl chloride rotational lines are measured over a large interval of quantum numbers (6≤J≤50, 0≤K≤18) by a submillimeter frequency-multiplication chain (J≤31) and a terahertz photomixing continuous-wave spectrometer (J≥31). In order to check the accuracy of both techniques, the measurements of identical lines are compared for J=31. The pressure broadening coefficients are deduced from line fits using mainly a Voigt profile model. The excellent signal-to-noise ratio of the frequency-multiplication scheme highlights some speed dependence effect on the line shape. Theoretical values of these coefficients are calculated by a semi-classical approach with exact trajectories. An intermolecular potential including atom–atom interactions is used for the first time. It is shown that, contrary to the previous theoretical predictions, the contributions of short-range forces are important for all values of the rotational quantum numbers. Additional testing of modifications required in the semi-classical formalism for a correct application of the cumulant expansion is also performed. It is stated that the use of the cumulant average on the rotational states of the perturbing molecule leads, for high J and small K values, to slightly higher line-broadening coefficients, as expected for the relatively strong interacting CH₃Cl–N₂ system. The excellent agreement between the theoretical and the experimental results ensures the reliability of these data.     

Measurements and calculations of Ar-broadening parameters of water vapour transitions in a wide spectral region

The water vapour line-broadening (γ) and shift (δ) coefficients for 310 lines of 10 vibrational bands ν₁, ν₃, 2ν₂, ν₁+ ν₂, ν₂+ ν_3, 2ν₂ +ν₃, 2ν₁, ν₁+ ν₃, 2ν₃ and ν₁ +2ν₂ induced by argon pressure were measured with a Bruker IFS HR 125 spectrometer. The measurements were performed at room temperature, at the spectral resolution of 0.01 cm^–1 and over a wide pressure range of Ar. The calculations of the broadening coefficients γ and δ were performed in the framework of the semi-classical method. The intermolecular potential was taken as the sum of the atom–atom potential and the vibrationally and rotationally dependent isotropic induction+dispersion potential. The measured γ and δ were combined with literature data for the ν₂ and 3ν₁+ν₃, 2ν₁+2ν₂+ν₃ vibrational bands, and the optimal sets of potential parameters that gave the best agreement with the measured broadening coefficients for each vibrational band separately were found. Then, combined experimental data of 13 vibrational bands of H₂O perturbed by Ar were used to determine the analytical dependence of some potential parameters on vibrational quantum numbers.     

Vibration-rotational matrix elements for infrared transitions of diatomic molecules

Theoretical expressions for the vibro-rotational matrix elements corresponding to i.r. transitions vJ→v′J′ with v ⩽ v ′ ⩽ v + 6 are obtained in terms of quadratic polynomials in m, including contributions from the Dunham potential energy parameters a₁ to a₅ and from dipole-moment expansion coefficients M₀ to M₇. The formalism has been applied to vibrational transitions in the ground electronic state of CO and HCl. The Herman-Wallis coefficients have been derived for the bands 0-0 to 0-4 of CO and 0-0 to 0-6 of HCl and are compared with experimental data.     

Line shifts in the ν2, 2ν2, and ν4 bands of NH3 perturbed by O2

Pressure-induced line shift coefficients have been measured for more than 200 rovibrational lines of NH₃ perturbed by O₂ at room temperature (T = 295 K) in some branches of the ν₂, 2ν₂, and ν₄ bands. These lines with J values ranging from 1 to 13 are located in the spectral range 800-1800 cm⁻¹. Experiments were made with a high-resolution Fourier transform spectrometer. The treatment of vibration-rotation lines includes interference effects caused by the overlapping of lines. The O₂ pressure-induced shift coefficients have been derived from the non-linear least-squares multi-pressure fitting technique. The results illustrate a vibrational dependence of line shifts with vibrational quantum number. Most of the measured shifts are negative in the ν₄ band. They are positive for the ν₂ and 2ν₂ bands. The measured shift coefficients are compared with previous measurements and with those calculated from a semiclassical theory based upon the Robert-Bonamy formalism extended to the case of symmetric top molecule with inversion motion. The predictions are generally in satisfactory agreement with the experimental data. Analyses of measured and predicted results illustrate that these shifts mainly originate from the isotropic part of the intermolecular potential.     

Raman spectra of asymmetric top molecules

A detailed analysis of the Raman-active v ₁, v ₃ (both A-type) and v ₅ (B_c -type) vibration-rotation bands of ethylene is presented. In addition to structural data simulation of the spectra yields values for the polarizability ratios of the totally symmetric bands, giving information on the polarizability ellipsoid as the molecule vibrates. v ₃ is shown to be perturbed by a c-type Coriolis interaction which complicates the interpretation of the negative value of the polarizability ratio required to match the observed spectrum.

The effects of asymmetry are pronounced; one result being the formation of heads in the ^R,PR _{K p} and ^R,P P _{K p} branches of low K _p in the v ₅ band.     

On the determination of the intermolecular potential between a tetrahedral molecule and an atom or a linear or a tetrahedral molecule—application to CH4 molecule

A brief summary of the general theory of the long-range potential energy between two molecules, previously developed by Buckingham, is first presented. Then the first detailed expressions of this potential energy are given for the three following molecular pairs : tetrahedral molecule-atom, tetrahedral molecule-linear molecule and tetrahedral molecule-tetrahedral molecule. These expressions are applied to the calculation of the spectral moments of the far infra-red pressure induced absorption band, the second virial coefficient and the intermolecular mean square torque. This allows a discussion of the magnitude of the various terms contributing to this potential energy and leads to a determination, for CH₄, of the octupole and hexadecapole moments, and of the hyperpolarizability:

     

Collision-broadened linewidths of tetrahedral molecules—III. Dispersion and induction interactions

Expressions for the interruption functions S₂(b) have been derived for the dispersion interaction between a tetrahedral molecule and a linear molecule, and for the interaction between the octopole moment of a tetrahedral molecule and the octopole-induced dipole moment in a perturbing molecule.     

Franck-Condon Factors and r-Centroids of the B-X Bands of Be18O Molecule

Abstract

The Franck-Condon factors, q_v′,v″ and r-centroids, r_v′,v″, for the bands of the B¹Σ⁺ ? X¹Σ⁺ transition of Be¹⁸O molecule (420–520 nm) are determined. A comparison of calculated q_v′,v″ values with the experimental estimated intensities of the bands shows reasonable agreement.     

Semiclassical calculations of half-widths and line shifts for transitions in the 30012←00001 and 30013←00001 bands of CO2. III: Self collisions

This paper is the third in a series devoted to accurate semi-empirical calculations of pressure-broadened half-widths, pressure-induced line shifts, and the temperature dependence of the half-widths of carbon dioxide. In this work complex Robert–Bonamy (CRB) calculations were made for transitions in two of the Fermi-tetrad bands for self-collisions, i.e. the CO₂–CO₂ system. The intermolecular potential (IP) was adjusted to match measurements of the half-width, its temperature dependence, and the line shift. It is shown that small changes in the parameters describing the IP lead to noticeable changes in the line shape parameters and that it is possible to find a set of IP parameters, which, when used in the CRB formalism, yield half-widths, their temperature dependence, and line shifts in excellent agreement with measurement. This work demonstrates that this agreement can be obtained if the atom–atom potential is expanded to high order and rank (here 20 4 4), the real and imaginary (S₁ and Im(S₂)) components are retained, and the determination of the trajectories is made by solving Hamilton's equations. It was found that the temperature dependence of the half-width is sensitive to the range of temperatures used in the fit and that the vibrational dependence of the line shape parameters for these two bands is very small. Databases of the half-width, its temperature dependence, and the line shift for the atmospheres of Venus (296–700 K fit range for the temperature exponents of the half-widths) and Mars (125–296 K fit range for the temperature exponents of the half-widths) are provided. The calculations are compared with the measured data for the bands under study.     

Intracavity Electronic Absorption Spectra of MoO and WO Molecules in the Visible Region

Absorption electronic spectra of MoO and WO molecules have been investigated by a intracavity laser technique in the region 550–800 run. New features have been discovered.

As for MoO molecule the rotational analysis of the four bands have been carried out for the first time. Two of these bands were referred to 0–0 transitions arisen from the new (probable triplet) low-lying electronic state, two other bands were referred to transitions arisen from excited components of X⁵II ground state.

As for WO molecule the rotational analysis of 0–0 and 1–0 bands represented A-X and B-X systems have been carried out for the first time. The new band has been discovered which has been referred to new electronic transition.

Molecular constants of new states of both molecules studied have been evaluated.     

Electron impact ionisation cross sections derived from total inelastic cross section for CF3X and CF2X2 (X = H,Cl, Br and I) molecules

We report here the total ionisation cross sections for CF₃X and CF₂X₂ (X = H, Cl, Br and I) molecules by electron impact from ionisation threshold to 5 keV. The total inelastic cross section is obtained employing a quantum mechanical approach called spherical complex optical potential formalism. Then, using a semi-empirical complex scattering potential-ionisation contribution method, the ionisation cross section is derived from the inelastic cross section. The results obtained are compared with previous measurements and theoretical values, wherever available and a satisfactorily agreement is observed. The ionisation cross section values for CF₂I₂ molecule are reported for the first time.     

Extended perturbation formulae for Jahn-Teller molecules

The effect of the Jahn-Teller interaction on a symmetric top molecule with a threefold axis of symmetry in a ^2S + 1E state has been investigated by perturbation theory. Contributions up to sixth order are included. Explicit formulae for various quantities have been derived on the assumption that there is only one Jahn-Teller active mode of vibration; both linear and quadratic Jahn-Teller interactions are considered. The quantities concerned are (i) the vibronic energy levels, (ii) the orbital quenching factor d_t, (iii) the correction to the A-rotational constant, (iv) the correction to the spin-spin dipolar coupling term, and (v) the correction to the spin-rotation coupling constant ε_aa. Because the perturbation expansion converges slowly, the results are only applicable to molecules subject to a weak Jahn-Teller effect. There are several examples of this type of molecule which have been studied experimentally.     

Critical binding of diatomic molecules

The behaviour of two bodies that are just bound or nearly bound is discussed. A class of potentials is given for which Schrödinger's equation has exact solutions at critical binding (zero binding energy). This class includes the known solution for the 6–10 potential. For a general potential characterized by a coupling parameter α, it is shown that the bound state energy tends to zero as -(α - α₀)², where α₀ is the critical value of the coupling parameter. Small energy scattering of atoms which are near critical binding (e.g. helium atoms) is examined. It is shown that determination of the total cross-section up to terms of order k ² is in principle sufficient to distinguish between bound and virtual states of the diatomic molecule.     

Internal stresses in molecules

Earlier work on internal stresses in one-electron systems is now extended to many-electron systems. The expressions for local stresses and local force densities involve electrostatic fields arising from given electronic and nuclear charge distributions and, therefore, the stress at any point in 3-D space again assumes a maxwellian form. As an illustration of the stress formalism, the interaction between two many-electron systems has been considered, taking the formation of the hydrogen molecule from its constituent atoms as a simple example. Using the double-zeta gaussian wavefunctions of Snyder and Basch, the stresses and fields experienced by an observer at three points on the internuclear axis are evaluated as functions of the internuclear distance R, and their respective variations are rationalized by means of classical arguments. The most interesting observation is that, depending on the location of the point considered, the interaction stress or the total stress or both may either vanish or pass through an extremum at an R value close to R _eq. The consequences of a charge build-up in the binding region are clearly apparent. The picture of chemical binding in the H₂ molecule that emerges from these calculations is a local one in which binding occurs due to variations of electrostatic pressure from point to point in such a manner as to cause the vanishing of either the total electrostatic force density or the difference force density or both at certain points on the internuclear axis; this complements the existing viewpoints on binding in the molecule. It may not be too early to say that the stress formalism which includes the Hellmann-Feynman force viewpoint as a special case has the potential to develop into a powerful interpretive tool for understanding molecular phenomena.     

Observations on the electronic spectrum of gaseous FeO

About 400 lines are assigned to FeO emission bands in the region 5580 to 6265 Å. The lower state of all the bands analyzed is identified as the ground state of the molecule, for the value of the lower-state vibration frequency (ω_e = 880.61 ± 0.02 cm^?1) is in excellent agreement with that observed in low-temperature matrix isolation, itself confirmed by isotopic substitution. This state is also observed as the lower state in laser-induced fluorescence. However, 880 cm^?1 is significantly smaller than the value found in laser photodetachment studies of FeO^? (970 ± 60 cm^?1). The rotational analysis is consistent with a parallel transition, ΔΛ = 0, but the value of Λ is not determined. According to theoretical calculations, the orange bands most probably arise from a ⁵Σ-⁵Σ transition. There is at least one nearby excited state, for all analyzed upper levels are perturbed.     

Equation of state for systems of soft diatomic molecules

A new potential that is a modification of the BBL (Bratko, D.,Blum, L., and Luzar, A.,1985, J. chem. Phys., 83, 6367; Blum, L., Vericat, F., and Bratko, D., 1995, J. chem. Phys., 102, 1461) potential and of the one recently solved analytically by Blum and Vericat (BV) (1995, Molec. Phys., 86, 809; 1996, J. phys. Chem., 100, 1197) is studied by Monte Carlo simulation. The main feature of this potential is that it can be solved using only a small number of parameters (3 in the case treated by BV), and therefore produces a substantial simplification of earlier work. The new potential has an orientational octupole–octupole interaction term which is found necessary to reproduce the broad peak of the oxygen–oxygen structure function due to the tetrahedral position of the second nearest neighbour water molecule. This important feature was absent in the original BBL potential. This model agrees also with the experimental pair correlation functions for oxygen–hydrogen and hydrogen–hydrogen, and yields 42·6 kJ mol^-1 for the internal energy of water, also in agreement with experiment. The hard core central repulsion causes the sharpness of the first peaks in all three correlation functions. This is not necessary but convenient for an analytical solution.     

The near ultra-violet absorption spectrum of tropolone vapour

A vibrational analysis of the 370 nm system of tropolone (-OH) and (-OD) has shown that pairs of bands, resembling the O₀ ⁰ and H₁ ¹ bands (where v _H is the internal hydrogen-bonding vibration), dominate the spectrum. Pairs built on O₀ ⁰ and H₁ ¹ and due to the excitation of totally symmetric vibrations in the ground or excited electronic state are well-behaved in the sense that their separations and rotational contours are very similar to those of O₀ ⁰ and H₁ ¹. About seven sequence intervals, in vibrations other than v _H, have also been identified and it is observed that rotational contours of Z₁ ¹H₁ ¹ bands in five sequence-forming vibrations Z are quite strongly perturbed (four of them in a very similar way) while the corresponding Z₁ ¹ bands are unperturbed.

It is concluded that the unusual nature of v _H is in some way responsible for the rotational perturbations and also for the very unusual behaviour of some quite intense vibronic bands in the region 290–540 cm^-1 to high wavenumber of the O₀ ⁰ band: however, the evidence is only circumstantial.     

Collision-induced rovibrational energy transfer in small polyatomic molecules: the role of intramolecular perturbations

ABSTRACT

Various forms of time-resolved optical double-resonance spectroscopy facilitate rotationally resolved measurements of collision-induced intramolecular vibration-to-vibration (V–V) energy-transfer processes, which take a gas-phase polyatomic molecule from one distinct rovibrational energy level to another. Of longstanding mechanistic interest are questions concerning the extent to which such V–V energy transfer (ET) may be influenced by intramolecular perturbations – notably Fermi resonance (and other anharmonic mixing effects) and Coriolis coupling – within polyatomic molecular rovibrational manifolds of interest. It is evident that quantum-mechanical interference effects can arise, either inhibiting or enhancing the probability of collision-induced ET in perturbed rovibrational manifolds of certain small gas-phase polyatomic molecules, notably CO₂, D₂CO and C₂H₂. This article focuses on a blend of high-resolution rovibrational spectroscopy (characterising initial and final molecular levels and their intramolecular perturbations) and collision dynamics (with colliding molecules defined in terms of isolated-molecule spectroscopic basis states). It aims to offer fresh insights and to consider some apparent mechanistic anomalies (e.g. collision-induced quasi-continuous background effects in the 4ν_CH rovibrational manifold of C₂H₂). Various reported experiments and related theoretical treatments are critically re-examined, in order to pose and address mechanistic questions some of which still challenge detailed understanding.