Comparative analysis of purely classical and semiclassical approaches to collision line broadening of polyatomic molecules: I. C2H2-Ar case

Semiclassical approaches to the computation of spectral line parameters stay up to nowadays one of the working tools complementary to refined but costly quantum-mechanical methods. Using of the trajectory concept together with quantum treatment of internal molecular motions imposes however the hypothesis of rotation-translation decoupling and translational motion governed by the isotropic potential. When a posteori justified for small heavy colliders, this hypothesis appears as doubtful for long polyatomic molecules. At the same time, purely classical methods, even requiring the artificial procedure of the correspondence principle with quantum mechanics, easily take into account the rototranslational energy transfer through the trajectory governed by the full anisotropic potential. The infrared line broadening of a typically classical C₂H₂-Ar system at various temperatures is analyzed here from these two different points of view. When a refined ab initio potential is chosen to represent the interaction energy, the semiclassical approach leads to a visible overestimation of the line broadening for all values of the rotational quantum number and for all temperatures studied whereas the fully classical treatment gives a quite satisfactory prediction. These fully classical computations show that even for C₂H₂-Ar the rototranslational coupling is quite important, and variations of the translational motion parameters during collisions produce detectable changes in rotation. When, for the sake of a meaningful comparison with the semiclassical approach, the isotropic trajectories are imposed within the classical method, this leads to smaller line widths; the effect strongly depends, however, on the peculiarities of potential energy surface, temperature, and rotational quantum number value.     

Comparison of quantum, semiclassical and classical methods in hydrogen broadening of nitrogen lines

We use an accurate N₂-H₂ab initio potential energy surface (PES) in order to inter-compare various methods commonly employed to calculate pressure broadening coefficients. Close-coupling (CC) calculations of the collisional linewidths of the isotropic Raman lines of N₂ perturbed by H₂ are performed for temperatures between 77 and 2000 K. The CC results compare well with available experimental values. Three less exact methods of calculation are also used: the full classical (FC) model of Gordon, the semiclassical (SC) formalism of Robert and Bonamy and the quantum dynamical coupled states (CS) method. The CS method provides good agreement with CC calculations for all studied temperatures, FC calculations can be considered as accurate above room temperature while the SC method gives overestimated values by about 20-30% in all cases. The temperature dependences of pressure broadening coefficients provided by each method are very similar at elevated (above room) temperatures.     

Comparison of classical, semiclassical and quantum methods in hydrogen broadening of acetylene lines

Quantum close coupling (CC) calculations of H₂-broadening coefficients of infrared and isotropic Raman lines of acetylene (C₂H₂) are performed for temperatures between 77 and 2000 K. They are used to test three more approximate methods, the quantum coupled states (CS) theory, the semiclassical Robert-Bonamy (RB) formalism and the full classical (FC) model of Gordon. In order to allow a clear and well founded comparison, all the dynamical calculations were performed employing the same ab initio potential energy surface free of any adjustable parameters. It is shown that below room temperature both the coupled states method and full classical method fail at reproducing the close coupling pressure broadening coefficients while above room temperature they are correct and predict comparable accurate values for temperatures greater than about 1000 K. The values provided by the RB method are clearly not satisfactory even at the highest temperature examined. However, the temperature dependence of the RB results follows the functional form used for interpolating and extrapolating CC, CS and FC pressure broadening coefficients.     

3s vacancy production in Ar+-Ar and Ar+-He collisions

The 3s vacancy production in Ar⁺-He and Ar⁺-Ar collisions has been studied at impact energies of 100 keV to 550 keV. A comparison is made for the Ar⁺-He system with theoretical calculations based on the quasi-molecular model.     

N2- and O2-broadening coefficients of C2H2 IR lines

Pressure-broadening parameters of six lines belonging to the ν₅ band of C₂H₂ in collision with N₂ have been measured with a tunable diode-laser spectrometer in order to complete up to J = 33 our earlier measurements (D. Lambot, G. Blanquet, and J. P. Bouanich, J. Mol. Spectrosc.136, 86–92 (1989)) on the broadening of C₂H₂ by N₂ and O₂ at 297 K. These N₂- and O₂-broadening coefficients have been first calculated on the basis of the Anderson-Tsao-Curnutte theory; in this approach, we show that the short-range interactions which contribute significantly to the linewidths are not correctly treated. Next, we consider the improved semiclassical model proposed by Robert and Bonamy. The intermolecular potential consists in the addition of the atom-atom interaction model to the quadrupolar interactions. The limited radial spherical harmonics expansion of the atom-atom potential, from which expressions for the differential cross section were derived, appears to be quite insufficient at short intermolecular distances. Therefore, we use a more accurate representation of this potential, avoiding an inadequate truncation and keeping the analytic expressions obtained by Bonamy and Robert. In the calculations we take into account the contributions derived from the radial functions U₀₀₀(r), U₂₀₀(r), and U₂₂₀(r), as well as from U₄₀₀(r). A theoretical expression is obtained for the U₄₀₀ contribution to the differential cross section. The results of the calculations arising from the exact radial expansion of the atom-atom potential appear to be significantly larger for high J lines than those arising from the truncated expansion. The latter results, which do not include adjustable atom-atom parameters, are in good agreement with experimental broadening coefficients for C₂H₂---O₂ and in reasonable agreement (except at large J values) for C₂H₂---N₂. It is also shown that the contributions to the linewidths derived from U₄₀₀ are rather small for C₂H₂---N₂ and more important for C₂H₂---O₂. Finally, by calculating the collisional linewidths of C₂H₂---N₂ and C₂H₂---O₂ at 200 K, we have predicted their temperature dependences.     

Electronic-excitation transfer collisions in flames-VII. Some alkali-doublet mixing cross sections for inert gas collisions,at 1720 K

Doublet mixing cross sections for K(4²P)-Ar and He and for Rb(5²P)-He collisions have been measured, in flames at 1720 K. The ratio σ₁₂/σ₂₁ was measured separately and was found to agree within 2 per cent with predictions derived from detailed balance. The experiments are compared with available semiclassical theoretical results.     

A multispectrum analysis of the ν2 band of HCN: Part II. Theoretical calculations of self-broadening, self-induced shifts, and their temperature dependences

A semiclassical theory based upon the Robert-Bonamy formalism has been developed to explain the experimental measurements of self-broadening, self-induced pressure shift coefficients in the ν₁,ν₂, 2ν₂ bands of H¹²C¹⁴N and the 2ν₁ band of H¹³C¹⁴N, as well as the temperature dependences of these parameters with special emphasis on the ν₂ band. Our calculations include only electrostatic interactions and neglect the vibrational dependence of the isotropic part of the intermolecular potential, which probably has a weak contribution to the HCN self-shifts for the bands investigated in this study. The agreement between theory and measurements is good in the cases of self-broadening coefficients and their variation with temperature, as well as the self-shift coefficients determined at room temperature. However, the observed temperature dependence of self-shift coefficients in the ν₂ band is different from that derived theoretically.     

Carbon K-shell excitation of C2H2, C2H4, C2H6 and C6H6 by 2.5 keV electron impact

Energy loss spectra of 2.5 keV electrons in the region of the carbon K-edge in C₂H₂, C₂H₄, C₂H₆ and C₆H₆ are report     

Carbon-13 Isotopic Species of H2C3, H2C4, and H2C5: High-Resolution Rotational Spectra

The microwave rotational spectra of the carbon-13 isotopic species of H₂C₃, H₂C₄, and H₂C₅ have been observed in a pulsed supersonic molecular beam by Fourier transform microwave spectroscopy. At high resolution all of the rotational lines exhibit hyperfine structure produced by the magnetic interaction between the nuclear spin of ¹³C and the overall rotation of the molecule. The component of the nuclear spin-rotation tensor along the a-inertial axis is large for most isotopic species, especially at the carbene carbon; at this position C_aa is two to three times larger than at other substituted positions along the chain. In contrast to both H₂C₃ and H₂C₃, in H₂C₄C_aa exhibits a pronounced alternation along the carbon chain backbone. Following detection of the five carbon-13 isotopic species and D₂C₅, an experimental structure (r₀) has been determined to high accuracy for H₂C₅.     

Infrared crystal spectra of C2H4, C2D4, and as-C2H2D2 and the general harmonic force field of ethylene

Carbon-13 frequency shifts for C₂H₄, C₂D₄, and as-C₂H₂D₂ have been measured in isotopic solid solutions in crystalline films at 60 K. All but two of the shifts (for as-C₂H₂D₂) are compatible with recently determined ζ data for C₂H₄, with ¹³C frequency shifts for C₂H₄ and C₂D₄ in the gas phase and with conventional frequency data. Together, these data completely determine with precision all 18 parameters of the GHFF for ethylene, the previous ambiguity in choice between two sets of A_g species force constants being removed. The force field reproduces closely the observed centrifugal distortion constants for C₂H₄, a ζ constant observed for trans-C₂H₂D₂, and the inertia defects for C₂H₄, C₂D₄, and as-C₂H₂D₂. Vibration and rotation constants for all isotopically deuterated ethylenes are calculated.Possible explanations for the two anomalous crystal shifts in as-C₂H₂D₂ involve the effects of the crystal field, and failure of the use of Dennison's rule for making anharmonic corrections to the shifts. The former explanation is preferred as a result of thorough analysis of the anharmonicity constants for as-C₂H₂D₂ determined from many overtone and combination bands in the gas and crystal spectra.     

Triply hydrogen bonded van der Waals complexes: CH2F2?CF2CH2 and CH2F2?CF2CHF

The results of molecular beam Fourier transform microwave (FTMW) investigations of the van der Waals complexes of difluoromethane with 1,1-difluoroethene (DFE) and trifluoroethene (TFE) are reported. The rotational parameters of the complexes have been interpreted in terms of a C_s geometry with the two H or F atoms of CH₂F₂ lying out of the σ_v symmetry plane of the complexes. The complexes are bound by three hydrogen bonds, of which one is the stronger C-F?H-C type, and two are the weaker C-H?F?H-C or C-F?H?F-C types for DFM-DFE or DFM-TFE, respectively. The most notable difference in the two complexes is that the out of plane atoms are two hydrogens for DFM-DFE, but are two fluorines for DFM-TFE. Additional information on the structure and hydrogen bonding has been obtained from ab initio calculations.     

Calculated line broadening coefficients in the ν2 band of CH3D perturbed by helium

Line broadening coefficients have been calculated, at room temperature, for lines in the P and R branches of the ν₂ band of monodeuterated methane. A properly symmetrized semiclassical model with parabolic relative trajectories has been used. Two interaction potential models have been considered. The first is a Lennard-Jones type atom-atom potential, while the second one was derived from ab initio calculations. The calculated line widths were compared to the available experimental data and a satisfactory agreement was found, although the model contains no other adjustable parameters than the four atomic Lennard-Jones ones. Nonetheless, failures of calculations have also been evidenced for the highest rotational quantum numbers.     

Helium and argon line broadening in the ν2 band of CH4

The spectra of the gaseous mixtures CH₄-He and CH₄-Ar were obtained in the spectral region 1400-1750 cm⁻¹ with a resolution up to 0.003 cm⁻¹. Helium and argon pressure broadenings for the vibration-rotation lines of the ν₂ band of CH₄ have been estimated at room temperature for some lines in the P, Q, and R branches. These values were also calculated using the theoretical approach developed by Robert and Bonamy, extended to the case of tetrahedral molecules. The helium data have been found to be in a satisfactory agreement whereas a divergence of calculated and measured broadening coefficients has been evidenced in the case of argon. Simulations of the ν₂ band shapes of methane perturbed by helium have also been performed.     

A precise study of the rotational spectrum of formaldehyde H212C16O,H213C16O,H212C18O,H213C18O

The rotational spectra of formaldehyde, H₂¹²C¹⁶O and its isotopic species H₂¹³C¹⁶O, H₂¹²C¹⁸O, and H₂¹³C¹⁸O have been investigated in the ground vibrational state in the frequency region between 8 and 460 GHz. For most cases in which measurements of the a-type R- and Q-branch transitions already existed the accuracy of the line position has been improved to about 10 kHz. For H₂¹²C¹⁶O and H₂¹³C¹⁶O a large number of ΔK_a = ±2 transitions were measured with similar accuracy. These new data when combined with all other available data and appropriate weightings lead to a set of ground state parameters which for the first time are compatible with infrared and ultraviolet data. The rotational constants (and 3σ standard deviations) obtained using Watson's A-reduced Hamiltonian are:

     

15.

The influence of structural defects on the adsorption of simple molecules (H₂, C₂H₂, C₂H₄, C₂H₆, CO,NO) on rhenium single crystals     

R. Ducros  M. Housley  G. Piquard  M. Alnot 《Surface science》1981,108(2):235-252

Using Thermal Programmed Desorption (TPD), Low Energy Electron Diffraction (LEED) and Auger Electron Spectroscopy (AES) we have studied the adsorption of hydrogen-containing molecules (H₂, C₂H₂, C₂H₄, C₂H₆) and oxygen-containing molecules (CO and NO) on two vicinal planes of the Re(0001) surface. The two surfaces are designated thus: ReS ¦14(0001)(101̄1)¦, ReS |6(0001)(167̄1) | . The structural defects have little effect on the adsorption of hydrogen and the hydrocarbons. They are more influential in the case of the oxygen-containing molecules. This is particularly true for CO; on the kink sites the CO molecules can completely dissociate whereas only a partial dissociation is possible on the steps. These results should be viewed in relation to the strong bond energy between carbon and oxygen in a CO molecule of 256 kcal/mole and the great affinity of oxygen for rhenium; E_Re?O = 127 kcal/mole.     

16.

The microwave spectrum of cyanophosphine, H₂PCN     

Lu Kang 《Journal of Molecular Spectroscopy》2004,225(1):66-72

The rotational spectra of cyanophosphine, H₂PCN, have been measured between 10 and 42.5 GHz by Fourier transform microwave spectroscopy. The rotational constants, centrifugal distortion constants, the ¹⁴N quadrupole coupling constant, and the nuclear spin-rotation coupling constants of ³¹P have been determined. Density functional ab initio calculations were performed, and the calculated values of the molecular constants are in excellent agreement with our experimentally determined results. The spectra of three isotopomers were measured, H₂P¹²C¹⁴N, H₂P¹³C¹⁴N, and H₂P¹²C¹⁵N. The derived r₀ structure is quite comparable to the ab initio predicted H₂PCN equilibrium geometry.     

17.

Pressure broadening and collisional shift of the Rb D2 absorption line by CH₄, C₂H₆, C₃H₈, n-C₄H₁₀, and He     

Nathan D. Zameroski  Gordon D. Hager  Christopher J. Erickson 《Journal of Quantitative Spectroscopy & Radiative Transfer》2011,112(1):59-67

The pressure broadening and shift rates of the rubidium D2 absorption line 5²S_1/2→5²P_3/2 (780.24 nm) with CH₄, C₂H₆, C₃H₈, n-C₄H₁₀, and He were measured for pressures ≤80 Torr using high-resolution laser spectroscopy. The broadening rates γ_B for CH₄, C₂H₆, C₃H₈, n-C₄H₁₀, and He are 28.0, 28.1, 30.5, 31.3, and 20.3 (MHz/Torr), respectively. The corresponding shift rates γ_S are −8.4, −8.8, −9.7, −10.0, and 0.39 (MHz/Torr), respectively. The measured rates of Rb for the hydrocarbon buffer gas series of this study are also compared to the theoretically calculated rates of a purely attractive van der Waals difference potential. Good agreement is found to exist between measured and theoretical rates.     

18.

Vibronic structure of the 3s Rydberg state of the 2-methylallyl radical     

Michael Gasser 《Journal of Molecular Spectroscopy》2010,263(1):93-100

Resonance-enhanced multiphoton ionization combined with electronic ground state depletion spectroscopy of jet-cooled 2-methylallyl (C₄H₇) radicals provides vibronic spectra of the 3s and 3p Rydberg states. Analysis of the vibronic structure following one-photon and two-photon excitation of rovibronically cold 2-methylallyl radicals and its isotopologues C₄H₄D₃ and C₄D₇ reveals transitions to more than 30 vibrational levels in the 3s Rydberg state that are identified and reassigned on the basis of predictions from ab initio calculations and results from pulsed-field-ionization zero-kinetic-energy photoelectron spectra obtained with resonant multiphoton excitation via selected intermediate states. Depletion spectroscopy reveals transitions to short-lived 3p Rydberg states that have a large oscillator strength.     

19.

Auger spectra of CO,C₂H₄, C₂N₂ and C₆H₆ adsorbed on Pt(111)     

F.P. Netzer  J.A.D. Matthew 《Journal of Electron Spectroscopy and Related Phenomena》1979,16(3):359-370

Electron excited carbon KVV Auger spectra of CO, C₂H₄, C₂N₂ and C₆H₆ adsorbed on Pt(111) are compared. By estimating the effective Coulomb interaction between the final-state holes it is possible to associate some features with transitions observed in free molecule spectra, but others must involve at least one electron with energy within the conduction band of the metal. Such “cross-transitions” are associated with strong 2π* character of filled states in the presence of a core hole in molecules such as CO.     

20.

Spectroscopic absorption model for CN(X²Σ→B²Σ): Comparison of experiments and theory     

M.B. Colket 《Journal of Quantitative Spectroscopy & Radiative Transfer》1984,31(1):7-13

A spectroscopic model for absorption by the CN radical at 388.3 nm [B²Σ⁺(0)→X²Σ⁺(0) transition] is described. Predictions from this model have been compared with equilibrium levels of absorption by CN in shock-heated C₂N₂-Ar mixtures. A best fit of experimental and predicted absorption levels is obtained for ΔH°_f (CN)=99.2±1.5 kcal/mole at 0°K, f_el=0.036±0.003, and d (opticalcollisiondiameter)=0.4±0.1 nm. These results are compared with literature values.     

	H212C16O	H213C16O	H212C18O	H213C18O
A/MHz	281 970.572 (24)	281 993.258(135)	281 961.94 (39)	281 985.00 (93)
B/MHz	38 836.0456(13)	37 811.0887(25)	36 904.1693(66)	35 859.256(10)
C/MHz	34 002.2034(12)	33 213.9790(25)	32 511.5311(63)	31 697.868(10)

The influence of structural defects on the adsorption of simple molecules (H2, C2H2, C2H4, C2H6, CO,NO) on rhenium single crystals

Using Thermal Programmed Desorption (TPD), Low Energy Electron Diffraction (LEED) and Auger Electron Spectroscopy (AES) we have studied the adsorption of hydrogen-containing molecules (H₂, C₂H₂, C₂H₄, C₂H₆) and oxygen-containing molecules (CO and NO) on two vicinal planes of the Re(0001) surface. The two surfaces are designated thus: ReS ¦14(0001)(101̄1)¦, ReS |6(0001)(167̄1) | . The structural defects have little effect on the adsorption of hydrogen and the hydrocarbons. They are more influential in the case of the oxygen-containing molecules. This is particularly true for CO; on the kink sites the CO molecules can completely dissociate whereas only a partial dissociation is possible on the steps. These results should be viewed in relation to the strong bond energy between carbon and oxygen in a CO molecule of 256 kcal/mole and the great affinity of oxygen for rhenium; E_Re?O = 127 kcal/mole.     

The microwave spectrum of cyanophosphine, H2PCN

The rotational spectra of cyanophosphine, H₂PCN, have been measured between 10 and 42.5 GHz by Fourier transform microwave spectroscopy. The rotational constants, centrifugal distortion constants, the ¹⁴N quadrupole coupling constant, and the nuclear spin-rotation coupling constants of ³¹P have been determined. Density functional ab initio calculations were performed, and the calculated values of the molecular constants are in excellent agreement with our experimentally determined results. The spectra of three isotopomers were measured, H₂P¹²C¹⁴N, H₂P¹³C¹⁴N, and H₂P¹²C¹⁵N. The derived r₀ structure is quite comparable to the ab initio predicted H₂PCN equilibrium geometry.     

Pressure broadening and collisional shift of the Rb D2 absorption line by CH4, C2H6, C3H8, n-C4H10, and He

The pressure broadening and shift rates of the rubidium D2 absorption line 5²S_1/2→5²P_3/2 (780.24 nm) with CH₄, C₂H₆, C₃H₈, n-C₄H₁₀, and He were measured for pressures ≤80 Torr using high-resolution laser spectroscopy. The broadening rates γ_B for CH₄, C₂H₆, C₃H₈, n-C₄H₁₀, and He are 28.0, 28.1, 30.5, 31.3, and 20.3 (MHz/Torr), respectively. The corresponding shift rates γ_S are −8.4, −8.8, −9.7, −10.0, and 0.39 (MHz/Torr), respectively. The measured rates of Rb for the hydrocarbon buffer gas series of this study are also compared to the theoretically calculated rates of a purely attractive van der Waals difference potential. Good agreement is found to exist between measured and theoretical rates.     

Vibronic structure of the 3s Rydberg state of the 2-methylallyl radical

Resonance-enhanced multiphoton ionization combined with electronic ground state depletion spectroscopy of jet-cooled 2-methylallyl (C₄H₇) radicals provides vibronic spectra of the 3s and 3p Rydberg states. Analysis of the vibronic structure following one-photon and two-photon excitation of rovibronically cold 2-methylallyl radicals and its isotopologues C₄H₄D₃ and C₄D₇ reveals transitions to more than 30 vibrational levels in the 3s Rydberg state that are identified and reassigned on the basis of predictions from ab initio calculations and results from pulsed-field-ionization zero-kinetic-energy photoelectron spectra obtained with resonant multiphoton excitation via selected intermediate states. Depletion spectroscopy reveals transitions to short-lived 3p Rydberg states that have a large oscillator strength.     

Auger spectra of CO,C2H4, C2N2 and C6H6 adsorbed on Pt(111)

Electron excited carbon KVV Auger spectra of CO, C₂H₄, C₂N₂ and C₆H₆ adsorbed on Pt(111) are compared. By estimating the effective Coulomb interaction between the final-state holes it is possible to associate some features with transitions observed in free molecule spectra, but others must involve at least one electron with energy within the conduction band of the metal. Such “cross-transitions” are associated with strong 2π* character of filled states in the presence of a core hole in molecules such as CO.     

Spectroscopic absorption model for CN(X2Σ→B2Σ): Comparison of experiments and theory

A spectroscopic model for absorption by the CN radical at 388.3 nm [B²Σ⁺(0)→X²Σ⁺(0) transition] is described. Predictions from this model have been compared with equilibrium levels of absorption by CN in shock-heated C₂N₂-Ar mixtures. A best fit of experimental and predicted absorption levels is obtained for ΔH°_f (CN)=99.2±1.5 kcal/mole at 0°K, f_el=0.036±0.003, and d (opticalcollisiondiameter)=0.4±0.1 nm. These results are compared with literature values.