Vibrational Sudden Approximation Research Articles

Mutual neutralization in collisions of Li+ with CN.

The mutual neutralization reaction in collisions of Li+ with CN- is a promising candidate for rigorous multi-dimensional ab initio studies of atom-molecule charge transfer processes. The reaction is driven by the non-adiabatic interaction between the lowest two 1A' electronic states at large Li-CN distances, resulting in a large cross section for mutual neutralization. As a first step, the relevant adiabatic potential energy surfaces and non-adiabatic interaction are computed ab initio, and the process is studied quantum mechanically using the vibrational sudden approximation, where the vibrational and rotational motions of the CN molecule are assumed to be frozen during the collision.

Static surface temperature effects on the dissociation of H2 and D2 on Cu(111)

A model for taking into account surface temperature effects in molecule-surface reactions is reported and applied to the dissociation of H(2) and D(2) on Cu(111). In contrast to many models developed before, the model constructed here takes into account the effects of static corrugation of the potential energy surface rather than energy exchange between the impinging hydrogen molecule and the surface. Such an approximation is a vibrational sudden approximation. The quality of the model is assessed by comparison to a recent density functional theory study. It is shown that the model gives a reasonable agreement with recently performed ab initio molecular dynamics calculations, in which the surface atoms were allowed to move. The observed broadening of the reaction probability curve with increasing surface temperature is attributed to the displacement of surface atoms, whereas the effect of thermal expansion is found to be primarily a shift of the curve to lower energies. It is also found that the rotational quadrupole alignment parameter is generally lowered at low energies, whereas it remains approximately constant at high energies. Finally, it is shown that the approximation of an ideal static surface works well for low surface temperatures, in particular for the molecular beams for this system (T(s) = 120 K). Nonetheless, for the state-resolved reaction probability at this surface temperature, some broadening is found.

Quantum-mechanical calculations of vibrationally resolved cross sections for non-dissociative charge transfer of O3+ with H2

Charge transfer due to collisions of ground state O3+(2s22p 2P) ions with molecular hydrogen is investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) method，and electronic and vibrational state-selective cross sections along with the corresponding differential cross sections are calculated for projectile energies of 100，500，1000 and 5000eV/u at the orientation angles of 25°，45° and 89°. The adiabatic potentials and radial coupling matrix elements utilized in the QMOCC calculations were obtained with the spin-coupled valence-bond approach. The infinite order sudden approximation (IOSA) and the vibrational sudden approximation (VSA) are utilized to deal with the rotation of H2 and the coupling between the electron and the vibration of H2. It is found that the distribution of vibrationally resolved cross sections with the vibrational quantum number v′ of H+2(v′) varies with the increment of the projectile energy; and the electronic and vibrational state-selective differential cross sections show similar behaviors: there is a highest platform within a very small scattering angle，beyond which the differential cross sections decrease as the scattering angle increases and lots of oscillating structures appear，where the scattering angle of the first structure decreases as E-1/2p with the increment of the projectile energy Ep; and the structure and amplitude of the differential cross sections are sensitive to the orientation of molecule H2，which provides a possibility to identify the orientations of molecule H2 by the vibrational state-selective differential scattering processes.

Vibrationally resolved charge transfer ofO3+with molecular hydrogen

Charge transfer due to collisions of ground state ${\mathrm{O}}^{3+}(2{s}^{2}2p{\phantom{\rule{0.2em}{0ex}}}^{2}{P}^{o})$ ions with molecular hydrogen are investigated using the quantum-mechanical molecular-orbital (QMO) coupled-channel method. The QMO calculations utilize $ab$ initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond approach for a representative range of orientation angles and diatom internuclear separations. Vibrationally resolved cross sections for nondissociative single electron capture are obtained for energies between 0.1 eV∕u and 10 keV∕u for ${\mathrm{H}}_{2}$ in its ground vibrational level using the infinite order sudden approximation (IOSA). Two further approximations are considered in which the electronic radial couplings are assumed to be independent of the diatom stretching. In the first case, vibrational motion is taken into account by multiplying the electronic radial couplings by Franck-Condon (FC) ionization factors while in the second, vibrational motion is completely neglected. We refer to these two approaches as the vibrational sudden approximation (VSA) and the electronic approximation (EA), respectively. In the latter, the resulting cross sections for electronic transitions are multiplied by FC factors to obtain relative vibrationally resolved cross sections which are independent of the collision energy (the centroid approximation). Comparison with existing experimental data for total and electronic state-selective cross sections shows best agreement with IOSA and VSA, but discrepancies for EA. The triplet-singlet electronic cross section ratio reveals a departure at low collision energies from the statistical value.

Translation-to-rotational energy transfer in scattering of H 2 molecules from Cu(111) surfaces

This work investigates rotational transitions of H 2 scattering from Cu(111). A notable feature of this study is the application of simple classical dynamics to reveal mechanisms of rotational transitions. This methodology is justified for the H 2/Cu system by remarkable agreement between quantum wavepacket calculations and classical trajectory simulations for both dissociation and ro-vibrational transitions. A vibrational sudden approximation is proposed which interprets rotational transitions in terms of an effective gas-surface potential energy surface for a molecule having a distended bond. The validity of the approximation is verified by the close correlation between molecular trajectories and this effective potential. The vibrational sudden analysis comprehensively explains the mechanism of strong translation-to-rotational energy transfer for H 2 scattering from Cu(111), observed experimentally.

Assessing the accuracy of the vibrational sudden approximation in collinear atom + triatomic molecule collisions

Exact and vibrational sudden approximation (VSA) transition probabilities for He + HI 2 BeI 2, BeBr 2 and CO 2 at 0.5 to 3.0 eV are calculated and compared. The agreement between the VSA and the exact results for the excitation of the symmetric stretch is excellent for HI 2 (even for large charges in the vibrational quantum number), degrades slightly on going to BeI 2, and again to BeBr 2 and becomes unacceptable for the CO 2 case. These trends are in accord with previous validity criteria. The agreement for the excitation of the asymmetric stretch is only qualitatively correct.

Collinear diatomic molecule-diatomic molecule collisions treated in the sudden approximation

Collinear collisions of H{sub 2} + Cl{sub 2} and O{sub 2} + Cl{sub 2} at 0.5, 1.0, 1.5, and 2.0 eV have been studied in the vibrational sudden approximation (VSA). The VSA applied only to molecule 2, the Cl{sub 2}, gives good transition probabilities for H{sub 2} + Cl{sub 2} but not for O{sub 2} + Cl{sub 2}. When the probabilities are in the range 0.1-1.0, the VSA performs excellently; with smaller probabilities, the VSA is still in qualitative agreement with exact results. The choices for n{sub 2}, the arbitrary parameter introduced in the VSA, which give the most accurate results are n{sub 2} = n{sub 2}{prime} (the final value of n{sub 2}) or n{sub 2} = (n{sub 2} + n{sub 2}{prime})/2 (the average of the initial and final values of n{sub 2}); either choice is acceptable although n{sub 2a} is more appropriate for larger {Delta}n{sub 2}. The VSA reduces the computer execution time by at least an order to magnitude compared to the exact method. The VSA applied to both colliding molecules is found to be unsatisfactory.

Improved calculation of the cross section for excitation of the asymmetric stretch of CO2 by electron impact

Our previous calculations for excitation of the 001 state of CO2 by electron impact at 10 eV are corrected for breakdown of the vibrational sudden approximation. This reduces the calculated differential cross sections at scattering angles of 1° and 3° by 41% and 6%, respectively, and the calculated integral cross section by 14%.

Electron impact cross sections for ν=0→1 vibrational excitation of N2at electron energies from 3 to 30 eV

Normalised, absolute electron impact differential cross sections (DCS) for the (0 to 1) vibrational excitation of N2, for incident electron energies from 3 to 30 eV, have been measured with the help of a crossed beam apparatus over the angular range of 20 to 130 degrees . The l=3 (f wave) contribution was found to dominate the vibrational excitation at incident energies in the range 18 to 25 eV. From the DCS, the integral and momentum transfer cross sections were calculated. It could also be verified that the enhanced vibrational excitation due to the sigma u shape resonance has a peak value at about 21 eV with a full width at half maximum of about 7 eV. The DCS and the integral cross sections are compared with recent theoretical calculations of the converged rotational close coupling and the vibrational sudden approximation, as well as with the continuum multiple-scattering method.

State-to-state cross sections for electron impact on N2. Close coupling and polarized Born calculations for rotational and vibrational excitation and pure elastic scattering at nonresonant energies

Calculations of cross sections for elastic scattering, rotational excitation, and vibrational excitation of ground state N2 by electrons with impact energies of 10 and 50 eV have been performed using realistic static-exchange-plus-polarization interaction potentials, rotational close coupling, and the vibrational sudden approximation. The effect of vibrational averaging on the elastic scattering is found to be small. The calculated integral cross sections for pure elastic scattering and for pure rotational (summed over j′≠0), pure vibrational (j′=0,v’=1 and 2), and mixed rotational–vibrational (summed over j′≠0 for v′=1 and 2) excitation are 34.4, 18.6, 2.70×10−2, and 4.13×10−2 a02, respectively, at 10 eV and 19.4, 11.7, 1.28×10−2, and 6.92×10−2 a02, respectively, at 50 eV. The sum of the differential cross sections for pure vibrational and mixed rotational–vibrational excitation for v=0→v′=1 can be compared to experiment and agreement is good at both energies except for scattering angles ϑ?30°. The pure rotational excitation differential cross section has not been resolved experimentally but we predict that it is dominated by j′=2 at 10 eV and for ϑ?130° at 50 eV and j′=4 for larger ϑ at 50 eV. The calculated state-to-state cross sections are also compared to results calculated by the polarized Born approximation with simplified model potentials based on the long-range forces.