Rotational relaxation of homonuclear diatomic molecules by classical trajectory computation

The rotational relaxation times of molecular nitrogen and molecular chlorine have been obtained using an exact classical mechanical calculation and Wang Chang—Uhlenbeck's theory of polyatomic gases. The intermolecular potential used was an extended Lennard-Jones potential of the form V(R,_X1, _X2) = C₁₂R⁻¹² _1+b [P ₂(cos_X1)+P₂(cos_X2)]-C₆R⁻⁶ 1+ a[P₂(cos_X1) + P₂(cos_X2)]. Numerical results were obtained for a number ef values of the anisotropy parameters (a,b) for nitrogen and for a single set of values for chlorine. Comparison with experimental ultrasonic results for nitrogen gave very good agreement for (a,b) around (0.1, 0.7). Using a box-quantization procedure we have furthermore obtained detailed cross sections for inelastic collisions from which a surprisal analysis was carried out. The analysis showed that our results follow the exponential gap law of Polanyi, Ding and Woodall reasonably well although this law was suggested for atom—diatom collisions.     

Use of central-field potentials for describing H2(D2) elastic scattering by other molecules

Differential elastic scattering cross sections have been measured for the systems H₂ + O₂, SF₆, NH₃, CO and CH₄ and for D₂ + O₂, SF₆, and NH₃ using crossed molecular beams. These experiments represent a wide variation in the size, anisotropy and initial relative collision energy E of the scattering partners, and of the corresponding de Broglie wavelengths. In all cases, rapid quantum oscillations have been resolved. From these differential cross sections, central-field potentials have been obtained which were independent of the energy and the isotopic composition of the hydrogen molecule used, as required for such potentials to be physically meaningful. Therefore, anisotropy effects do not seem important in describing the differential elastic scattering of these H₂(D₂) systems.     

Substantial velocity dependence of rotationally inelastic collision cross sections in Li2—Xe

A Doppler-based velocity selection technique has been used to measure the relative velocity dependence of the cross sections σ_ji,Δ(ν_r) for rotationally inelastic collisions from level j_i to j_i + Δν₁ = 8,22,42) in ⁷Li^*₂ A ¹Σ⁺_u)—Xe. The σ_jν^±2(ν_r) are strongly attenuated at a smaller ν_r by “torque averaging” due to molecular rotation; in contrast, for large |Δ|, σ_jiΔ = ν_r⁻ⁿ (1 n 2). An empirical intermolecular potential which reproduces these types of behavior for 3-D classical trajectories is exhibited.     

Dissociative excitation of SiH4, SiD4, Si2H6 and GeH4 by 0–100 eV electron impact

We have measured emission cross sections of various electronically excited fragments produced by electron-impact dissociation of SiH₄, SiD₄, Si₂H₆ and GeH₄. At low impact energy (10–20 eV), the measured appearance potentials are correlated to specific dissociation processes. Below 22 eV superexcited states of SiH₄ play a dominant role in the formation of neutral excited fragments. In agreement with the results obtained on alkanes, the cross sections for fragment emission from Si₂H₆ are lower than those for SiH₄. On the other hand, the comparison of cross sections at 100 eV for fragment emission, dissociation and ionization on going from CH₄ to SiH₄ and GeH₄ shows an increase of the probability for production of neutral ground-state fragments at the cost of excited or ionic fragments. Both effects can be explained by a growing probability for internal conversion among the decay channels of superexcited states with increasing number of atoms or electrons in the parent molecule. For each molecule, the H Balmer-emission cross sections at 100 eV are proportional to n^−b, where n 3 is the principal quantum number of the upper state of H and 3 < b < 5 is a parameter characteristic of the parent molecule. Finally, a detailed analysis of the isotopic effect between SiH₄ and SiD₄ on both fragment emission and ionization cross sections from 0 to 100 eV gives strong evidence of the competition between dissociation and autoionization in the decay of superexcited states.     

Molecular beam maser measurements of relaxation cross sections in NH3

Direct measurements of scattering cross sections for NH₃ in well-defined quantum states are made using a molecular beam maser spectrometer. Cross sections are compared for a pure inversion state with those for a coherent superposition state for scattering gases He, Ar, N₂, N₂O, NH₃, CH₃H and CH₃CN. The cross sections are significantly larger for scattering of the pure inversion state by NH₃, CF₃H and CH₃CN than for scattering of the superposition state. The scattering is the same for both states on non-polar gases. These cross sections are related to relaxation parameters describing transitions between rotation and inversion states.     

Classical path sudden approximations for atom—rigid rotor collisions

The classical path sudden approximation has been used to calculate cross sections for rotational excitation in atom—molecule collisions. Three different decoupling approximations for the angular momentum of the molecule are used: one effective potential approach and two different coupled states approaches, all in their semiclassical versions. Numerical results are presented and discussed for the systems Ar---N₂, Ar---Li₂, Ar---LiH, He---CO and Ar---HCl assumming intermolecular potentials of P₁ symmetry, P₂ symmetry and combinations.     

Measurements and quasi-quantum modeling of the steric asymmetry and parity propensities in state-to-state rotationally inelastic scattering of NO (2Pi1/2) with D2

Relative integrated cross sections are measured for spin-orbit-conserving, rotationally inelastic scattering of NO (2Pi1/2), hexapole-selected in the upper Lambda-doublet level of the ground rotational state (j = 0.5), in collisions with D2 at a nominal energy of 551 cm-1. The final state of the NO molecule is detected by laser-induced fluorescence (LIF). The state-selected NO molecule is oriented with either the N end or the O end toward the incoming D2 molecule by application of a static electric field E in the scattering region. This field is directed parallel or antiparallel to the relative velocity vector v. Comparison of signals taken for the different applied field directions gives the experimental steric asymmetry SA, defined by SA = (sigma v upward arrow downward arrow E - sigma v upward arrow upward arrow E)/(sigma v upward arrow downward arrow E + sigma v upward arrow upward arrow E), which is equal to within a factor of -1 to the molecular steric effect, Si-->f identical with (sigmaD2-->NO - sigmaD2-->ON)/(sigmaD2-->NO + sigmaD2-->ON). The dependence of the integral inelastic cross section on the incoming Lambda-doublet component is also measured as a function of the final rotational (jfinal) and Lambda-doublet (epsilonfinal) state. The measured steric asymmetries are similar to those previously observed for NO-He scattering. Spin-orbit manifold-conserving collisions exhibit a larger propensity for parity conservation than their NO-He counterparts. The results are interpreted in the context of the recently developed quasi-quantum treatment (QQT) of rotationally inelastic scattering [Gijsbertsen, A.; Linnartz, H.; Taatjes, C. A.; Stolte, S. J. Am. Chem. Soc. 2006, 128, 8777]. The QQT predictions can be inverted to obtain a fitted hard-shell potential that reproduces the experimental steric asymmetry; this fitted potential gives an empirical estimate of the anisotropy of the repulsive interaction between NO and D2. QQT computation of the differential cross section using this simple model potential shows reasonable agreement with the measured differential cross sections.     

Inelastic collisions between 4He and H2: Study of dynamical approximations

We report a detailed study of the convergence and accuracy of HeH₂ rotationally and ro-vibrationally inelastic cross sections, determined within both the coupled states (CS) and effective potential (EP) formalisms. Two different potential surfaces were used. CS total cross sections appear insensitive to the specific choice of centrifugal barrier. Although the CS results are more accurate, the EP method reproduces the important qualitative features of the various inelastic processes. In addition, with the counting-of-states correction, the EP cross sections for ro-vibrationally inelastic transitions out of low-lying rotational levels agree with the CS values to within a factor of two, with only few exceptions.     

Absolute dipole differential oscillator strengths for inner shell spectra from high resolution electron energy loss studies of the freon molecules CF4, CF3Cl, CF2Cl2, CFCl3 and CCl4

Absolute differential photoabsorption oscillator strengths (cross sections) for the F 1s, C 1s, and Cl 2p, 2s inner shells of the freon molecules CF₃Cl, CF₂Cl₂ and CFCl₃ have been derived from high resolution electron energy loss spectra obtained under dipole dominated conditions of high impact energy (3 keV) and zero degree mean scattering angle. Differential oscillator strengths have also been obtained from earlier reported electron energy loss spectra for CF₄ and CCl₄. The spectra are analyzed using the MO picture and the potential barrier model.     

Photoionization cross sections involving an explicitly correlated initial state: Combination of multiconfigurational linear response and the stieltjes—tchebycheff moment theory

We have performed outer valence photoionization cross section calculations for N₂ and O₂. To do this we have combined several linear response techniques, in particular time-dependent Hartree—Fock (TDHF), multiconfigurational time-dependent Hartree—Fock (MC TDHF), and a modification of MC TDHF (MMC TDHF) with Stieltjes—Tchebycheff moment theory (STMT). To our knowledge, these MC TDHF and MMC TDHF calculations are the first which combine explicitly correlated Green function approaches with STMT. Since, in addition, these calculations are fully coupled, we expect the MC TDHF and in particular the MMC TDHF—STMT results to be highly reliable. For both N₂ and O₂ our MC TDHF—STMT and MMC TDHF—STMT results are in overall agreement with previous static exchange STMT results; however, there are a few significant differences and differences in detail in the partial and total photoionization cross sections. In particular, for example, for N₂ we note that the MMC TDHF—STMT does not give a “hump” resonance in the cross section for the (1π_u⁻¹)A²Π_u ionic state. In O₂ we note that the (3σ_g⁻¹) cross section obtained using MMC TDHF—STMT is substantially lower than the static exchange results.     

Differential measurements on Ne*(2p3sP0.2)-Ne collisions in the hyperthermal energy range

Differential cross sections for collisions of metastable neon atoms with ground state neon atoms have been measured in the energy range 0.247–0.551 eV in a crossed nozzle beam experiment using heating and seeding techniques. At large angle, the cross sections exhibit a rainbow feature due to a hump in the 0_u⁻ and 1_u potentials. The present data are in good agreement with calculations based on potential energy curves deduced from previous experiments at thermal energy.     

Total cross sections of electron collisions with S atoms; H2S,OCS and SO2 molecules (Ei ≥ 50 eV)

Collisions of intermediate to high energy electrons are considered with S-atoms as well as H₂S, OCS and SO₂ molecules as targets. We employ e^- atom total cross sections calculated in the complex optical potential, to calculate e^--molecule total cross sections in a simple and a modified Additivity Rule. Our total (elastic + inelastic) cross sections above 50 eV, fare reasonably well as compared to various experimental and theoretical data. The calculated inelastic cross sections serve as the upper limit of total ionization cross sections. Results are presented graphically from about 10 to 5000 eV.     

Detection of collision-induced rotational alignment in counterpropagating beam scattering

Collision-induced rotational alignment of NH₃ scattered from He is detected in a counterpropagating pulsed molecular beam scattering experiment. Starting from an isotope distribution of the initial rotational angular momentum, the generation of a highly aligned product ensemble due to inelastic scattering is observed. For all probed state-resolved differential cross sections the alignment changes from negative values for backward scattering to positive values at small deflection angles which is in qualitative agreement with predictions from a geometric apse model. The degree of alignment strongly depends on the final rotational state, indicating a correlation with the involved energy transfer.     

Absolute absorption cross section measurements of CO2 in the wavelength region 163–200 nm and the temperature dependence

Laboratory measurements of the absorption cross section of CO₂ at the temperatures 195 and 295 K have been made throughout the wavelength region 163–200 nm by using a high resolution grating spectrometer. Cross sections at 195 K are smaller than those at 295 K, and the band structures are more emphasized as expected. In combining with our previous measurements [J. Quant. Spectrosc. Radiat. Transfer, 55 (1996) 53], the absorption cross sections of CO₂ are available in the wavelength region 117.8–200.0 nm at 295 K and 117.8–192.5 nm at 195 K.     

Collisional transfer of rovibrational energy from quantum calculations. II. The case of LiH with He

The collisional exchange of energy between He atoms and a strongly polar diatomic, the LiH target, has been studied theoretically over a range of relative energies that had been previously sampled by experiments with molecular beams. The relative importance of the rotational and/or vibrational channels is examined by studying in detail the effect of the interaction via a model potential coupling parameter. The different behavior exhibited by differential cross sections (total and partial inelastic) is also analyzed in terms of the strength and shape of the interaction anisotropy.     

Photodissociation of homonuclear diatomics: Fine structure cross sections for Na2(XΣg) → Na(S1/2) + Na(P1/2,3/2

Exact quantum calculations are presented for fine structure cross sections in photodissociation of Na₂. Resonance peaks in the Na(²P_3/2) cr     

Intermolecular potentials obtained from high-energy alkali scattering

Intermolecular potentials have been obtained from high-energy total cross sections for several alkali metal systems: CS + He, Ne, Ar, CH₃NO₂; K + CH₄, C(CH₃)₄, C₆H₆, c-C₆H₁₂, CH₃I, CCl₄, SF₆, N₂. For the CS-rare gas cases and K + N₂ only the repulsive part was determined. For the rest both attractive and repulsive parts were seen.     

Theoretical investigation on the two-photon absorption of C60

We present a theoretical study on the two-photon absorption (TPA) properties of C₆₀. On the basis of the equilibrium geometry optimized by B3LYP/6-31G method, we employ the ZINDO method combined SOS formula to investigate the second hyperpolarizability and TPA cross section of C₆₀. The calculated result of the real part of the second hyperpolarizability of C₆₀ is in good agreement with the previous calculation and the experimental observation. In the 400–1000 nm range of TPA wavelength, we calculated TPA cross sections corresponding to all two photon allowed states. As a result, we find that there is only a TPA cross section maximum—995.7×10⁻⁵⁰ cm⁴ s/photon at 518 nm. Another interesting phenomenon is that C₆₀ possesses the distinct TPA process in contrast to other conjugated molecules in terms of three-state approximation. This paper provides a theoretical basis of further studying TPA properties of C₆₀.     

List of subjects

Elastic and inelastic cross sections for well specified m_j-states have been investigated in exact quantum mechanical calculations for H₂—inert gas systems using realistic potentials. The influence of different approximations like the neglect of closed channels and the distorted wave approximation is investigated, especially also in the orbiting resonances of H₂Ar. Compensations of effects of the repulsive and attractive part of the intermolecular potential are found in many cross sections. The diffraction pattern in the inelastic differential cross sections is shown to depend only on k′_j, the wave number of the final state.