Full Close-coupling Calculations Research Articles

Collision-Induced Rotational Excitation of CO2 by N(4S) Atoms: A New Ab Initio Potential Energy Surface and Scattering Calculations.

Collisional excitations of CO2 molecules are significant to fully understand the physical and chemical processes of astrophysical and atmospheric environments. Rotational excitations of CO2 molecules induced by N(4S) atoms have been studied for the first time. First, we have computed a new highly accurate ab initio potential energy surface (PES) of a CO2-N(4S) van der Waals complex. The PES has been obtained by employing the partially spin-restricted coupled cluster with open-shell single, double, and perturbative triple excitation method with aug-cc-pVQZ basis sets. The full close-coupling calculations have been performed to compute cross sections for kinetic energies up to 800 cm-1. For all of the excitations, rotational cross sections exhibit an overall decrease with the increase of the energy gaps. Rate coefficients are calculated by averaging the cross sections over a Maxwell-Boltzmann distribution for temperatures ranging from 1 to 150 K. The trends in rate coefficients are in good agreement with those of similar collision systems. The decrease in energy gaps and the increase in temperature are the key factors to enhance the rate coefficients of CO2 excitation. Our study will be useful for accurately establishing the atmospheric model of terrestrial planets and determining the abundance of CO2 and N(4S) in space.

Ab Initio Potential Energy Surfaces of C3 Collision with Proton and Quantum Dynamics of Rotational Transition.

New ab initio potential energy surfaces have been generated for the ground state and low-lying excited states of the H+ + C3 system using the multireference configuration interaction (MRCI) method with Dunning's augmented correlation consistent polarized valence quadruple-zeta (aug-cc-pVQZ) basis sets. The ground state and low-lying excited states show avoided crossing, indicating nonadiabatic coupling. The anisotropy of the ground-state surface has been analyzed by computing the multipolar expansion coefficients with the frozen C-C equilibrium bond length. The asymptotic potential has been merged with the interaction potential by spline fit. This potential is then used in the full close coupling calculations of rotational excitation in C3 collision with the proton for rotational levels j = 0, 2, 4, 6, 8 at very low collision energy. By averaging the cross sections over a Boltzmann distribution of velocities of the incoming atom, we obtain and discuss corresponding rate coefficients of C3 collision with the proton in the interstellar medium.

Ultracold chemistry with alkali-metal–rare-earth molecules

A first principles study of the dynamics of $^6$Li($^{2}$S) + $^6$Li$^{174}$Yb($^2\Sigma^+$)$ \to ^6$Li$_2(^1\Sigma^+$) + $^{174}$Yb($^1$S) reaction is presented at cold and ultracold temperatures. The computations involve determination and analytic fitting of a three-dimensional potential energy surface for the Li$_2$Yb system and quantum dynamics calculations of varying complexities, ranging from exact quantum dynamics within the close-coupling scheme, to statistical quantum treatment, and universal models. It is demonstrated that the two simplified methods yield zero-temperature limiting reaction rate coefficients in reasonable agreement with the full close-coupling calculations. The effect of the three-body term in the interaction potential is explored by comparing quantum dynamics results from a pairwise potential that neglects the three-body term to that derived from the full interaction potential. Inclusion of the three-body term in the close-coupling calculations was found to reduce the limiting rate coefficients by a factor of two. The reaction exoergicity populates vibrational levels as high as $v=19$ of the $^6$Li$_2$ molecule in the limit of zero collision energy. Product vibrational distributions from the close-coupling calculations reveal sensitivity to inclusion of three-body forces in the interaction potential. Overall, the results indicate that a simplified model based on the long-range potential is able to yield reliable values of the total reaction rate coefficient in the ultracold limit but a more rigorous approach based on statistical quantum or quantum close-coupling methods is desirable when product rovibrational distribution is required.

Quantum defect theory for cold chemistry with product-quantum-state resolution

We present a formalism for cold and ultracold atom-diatom chemical reactions that combines a quantum close-coupling method at short-range with quantum defect theory at long-range. The method yields full state-to-state rovibrationally resolved cross sections as in standard close-coupling (CC) calculations but at a considerably less computational expense. This hybrid approach exploits the simplicity of MQDT while treating the short-range interaction explicitly using quantum CC calculations. The method, demonstrated for D+H$_2\to$ HD+H collisions with rovibrational quantum state resolution of the HD product, is shown to be accurate for a wide range of collision energies and initial conditions. The hybrid CC-MQDT formalism may provide an alternative approach to full CC calculations for cold and ultracold reactions.

Multichannel quantum defect theory for rovibrational transitions in ultracold molecule-molecule collisions

Multichannel quantum defect theory (MQDT) has been widely applied to resonant and nonresonant scattering in a variety of atomic collision processes. In recent years, the method has been applied to cold collisions with considerable success, and it has proven to be a computationally viable alternative to full close-coupling (CC) calculations when spin, hyperfine, and external field effects are included. In this paper, we describe a hybrid approach for molecule-molecule scattering that includes the simplicity of MQDT while treating the short-range interaction explicitly using CC calculations. This hybrid approach, demonstrated for ${\mathrm{H}}_{2}\text{\ensuremath{-}}{\mathrm{H}}_{2}$ collisions in full dimensionality, is shown to adequately reproduce cross sections for quasiresonant rotational and vibrational transitions in the ultracold $(1\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K})$ and $\ensuremath{\sim}1\ensuremath{-}10\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ regime spanning seven orders of magnitude. It is further shown that an energy-independent short-range $K$ matrix evaluated in the ultracold regime $(1 \ensuremath{\mu}\mathrm{K})$ can adequately characterize cross sections in the mK-K regime when no shape resonances are present. The hybrid CC-MQDT formalism provides an alternative approach to full CC calculations at considerably less computational expense for cold and ultracold molecular scattering.

Highly Correlated Electronic Structure Calculations of the He–C3 van der Waals Complex and Collision-Induced Rotational Transitions of C3

An accurate 2D ab initio potential energy surface of the He-C3 collisional system is calculated using the supermolecular coupled-cluster method with up to perturbative quadruple excitations, CCSDT(Q). This interaction potential is then incorporated in full close-coupling calculations of rotational excitation/de-excitation cross sections in He + C3 collisions for rotational levels j = 0, 2, ..., 10 and collision energies up to 1000 cm(-1). Corresponding rate coefficients are reported for temperature between 1 and 100 K. Results are found to be in excellent agreement with available theoretical data that were restricted to the temperature range of 5-15 K. Implications of the computed rate coefficients to astrophysical models of C3 and carbon clusters in interstellar and circumstellar environments are discussed.

Pressure broadening of water and carbon monoxide transitions by molecular hydrogen at high temperatures

Water and carbon monoxide are two major compounds in the predominantly H2 atmospheres of stars, brown dwarfs and extrasolar planets. Recent radiative transfer models suggest that there is an urgent need for data on the pressure broadening of molecular transitions by H2 at high temperatures. We present a set of theoretical H2 pressure broadening parameters for 228H2O transitions in the range of 10–20,000GHz and 30 CO transitions in the 115–3500 GHz region. These parameters are appropriate for temperatures between 200 and 3000K. The random phase approximation is employed to derive the broadening parameters from recent state-of-the-art inelastic collisional rate coefficients. This approximation is compared both to full close-coupling calculations and to available experimental data. It is shown to be valid at temperatures above 200K, as expected from theoretical considerations, with an accuracy of about 25%.

Ab initiocomputation of the broadening of water rotational lines by molecular hydrogen

Theoretical cross sections for the pressure broadening by hydrogen of rotational transitions of water are compared to the latest available measurements in the temperature range 65-220 K. A high accuracy interaction potential is employed in a full close coupling calculation. A good agreement with experiment is observed above ~80 K while the sharp drop observed experimentally at lower temperatures is not predicted by our calculations. Possible explanations for this discrepancy include the failure of the impact approximation and the possible role of ortho-to-para conversion of H2.

Imaging the Inelastic Scattering of Water with Helium. Comparison of Experiment and Theory

State-to-state differential cross sections for rotationally inelastic He-H(2)O scattering have been measured at 53.3 meV (429 cm(-1)) collision energy, using the crossed molecular beam technique. The inelastic events are detected by velocity map imaging of nascent H(2)O(+) ions, which are formed by state-selective (2 + 1) resonance enhanced multiphoton ionization (REMPI) of the scattered H(2)O molecules. Raw density images are converted to flux images and the extracted differential cross sections are compared with full close-coupling calculations of state-to-state cross sections for rotational excitation based on a previously published ab initio potential. A hard-shell ellipsoid model is also employed to yield a more physical insight useful in interpreting the results. The excellent agreement of fully quantum theory and experiment found here for water collisions with helium at a collision energy relevant to that of the interstellar media place the theoretically determined potential energy surface and the collision cross sections extracted using this surface on a firmer basis.

Potential energy surfaces and bound states for the open-shell van der Waals cluster Br–HF

Semiempirical potential energy surfaces for the lowest three electronic states of the open-shell complex Br–HF are constructed, based on existing empirical potentials for Kr–HF and Kr–Ne and coupled-cluster electronic structure calculations for Br–Ne. Coupled cluster calculations are also described for He–F, Ne–F and Ar–F. Electrostatic interactions that arise from the quadrupole of the Br atom and the permanent multipoles of HF are also included in the Br–HF surfaces. The well depth of the lowest adiabatic surface is found to be 670 cm−1 at a linear equilibrium geometry. The results of helicity decoupled and full close-coupling calculations of the bound states of the complex are also described. The ground state, with total angular momentum projection quantum number |P|=3/2, is found 435 cm−1 below dissociation to Br (2P3/2)+HF (j=0). The lowest-frequency intermolecular bending and stretching vibrations are predicted around 145 and 211 cm−1, respectively. Parity splittings are found to be extremely small for bound states with projection quantum number |P|=3/2. The relevance of the results to recently recorded spectra of Br–HF is discussed.

Elastic and rotationally inelastic differential cross sections for He+H2O collisions

Elastic and rotationally inelastic cross sections have been measured for He+H2O scattering at two collision energies, 66.3 and 99.0 meV, using the crossed molecular beam technique. The inelastic events are detected by time-of-flight analysis of the scattered He atoms. The data are converted to elastic differential cross sections and inelastic angular-dependent energy loss spectra in the center-of-mass system. They are compared with averaged, full close-coupling calculations of state-to-state cross sections for rotational excitation based on a newly calculated ab initio potential using symmetry-adapted perturbation theory. The agreement with the elastic differential cross sections is excellent. The energy loss spectra are reproduced satisfactorily and among the largest differential cross sections that contributed to the measurements are excitations around all three possible axes for ΔJ=1 but a preference of the excitation around the in-plane C axis for ΔJ=2 transitions.

Dissociation dynamics ofH2+ with short intense laser pulses: a close-coupling study

A full close-coupling calculation is carried out for the dissociation of H2+ (1s g) by strong, short laser pulses. This is done in the approximation of `no rotation' and with the retention of only the two lowest electronic states. The basis set consists of the bound vibrational states and a number of groups of dissociating states that represent all the `essential' continuum states needed to achieve full numerical convergence for the dissociation probabilities. The initial states v = 4 and 7 were studied with laser wavelengths giving strong initial coupling to the continuum, pulse durations of 15 and 150 fs, and peak laser intensities up to 1 × 1013 W cm-2. The case of weak initial coupling to the continuum was also studied for 150 fs pulses and a wide range of intensities for the initial states v = 3, 4 and 5.

Theoretical studies of He(1S)+CH(X 2Π). II. Fully ab initio cross sections for the inelastic scattering and comparison with experiment

We report a series of full close-coupling calculations of integral cross sections for fine structure resolved, rotationally inelastic transitions of CH induced by collisions with He. These calculations use the necessary two CH(X 2Π)+He potential energy surfaces as determined by a variety of ab initio techniques described in the preceeding paper. The calculated N=1→N=2−7 cross sections confirm a previous prediction of preferential population of final state levels in which the electronic wave function of the CH molecule is antisymmetric with respect to reflection in the plane of rotation of the molecule. A generally good overall agreement is found between the energy-dependent cross sections determined in earlier experiments of Macdonald and Liu and appropriate averages of the calculated cross sections. However, small, systematic, qualitative discrepancies persist between theory and experiment. Diagnostic calculations were carried out to identify the cause of these discrepancies. These calculations explored the influence of restrictions in basis set, configuration interaction, and functional forms used in fitting the potential energy surfaces. They also explored the consequences of the dynamical approximations of CH as a rigid rotor and the independence of the CH spin–orbit constant on the approach of the He partner. All these diagnostic calculations generally confirm the anticipated marginal influence of these approximations.

Differential and integral cross sections for the inelastic scattering of NO (X 2Π) by Ar based on a new ab initio potential energy surface

New ab initio potential energy surfaces for the Ar–NO (X 2Π) system are reported based on correlated electron pair approximation (CEPA) calculations. The fitted, rigid-rotor surface was then used in full close-coupling calculations of differential and integral cross sections for excitation of NO at a center-of-mass energy of 442 cm−1 (0.0548 eV), as well as differential cross sections at lower energies of 119 and 149 cm−1 (0.0145 and 0.0185 eV). The calculated cross sections are compared with those determined using earlier electron-gas potential energy surfaces and with the results of available experimental measurements. In general, the new CEPA potential energy surfaces yield very good agreement with available experimental integral and differential cross sections. Both theory and experiment reveal a significant tendency for population of final rotational states of Π(A″) reflection symmetry.

Hybrid approach to electron scattering from polar molecules.

Electron scattering from polar molecules is studied in a hybrid approach that uses the recently introduced algebraic-eikonal approach to describe the forward-angle scattering and the results of, for example, a close-coupling calculation for larger angles. The two calculations are matched by making a partial-wave expansion and combining the high partial waves of the algebraic-eikonal approach with the low partial waves obtained in a full close-coupling calculation. The method is illustrated by applying it to electron scattering from a rigid-rotor molecule with a large dipole moment.

The intramultiplet mixing of Zn(4 3P J) by collisions withrare gas atoms

The intramultiplet mixing processes of Zn(4 3P J ) by collisions with rare gas atoms were studied by employing a pulsed laser technique. The efficiency for the intramultiplet mixing by He was found to be much larger than those by Ne, Ar, Kr and Xe. This variation in mixing efficiencies was discussed on the basis of the results of a full close-coupling calculation. It is shown that the variation can partly be attributed to the difference in relative collisional velocities. The rates for the electronic quenching by rare gas atoms were found to be small in any case. The radiative lifetime of Zn(4 3P 1) was determined to be 20.4±1.6 μs.

Calculating vibrational-excitation cross sections off the energy shell: A first-order adiabatic theory.

We report the implementation of a first-order nondegenerate adiabatic theory for vibrational excitation of ${\mathrm{H}}_{2}$ by electrons with energies from threshold to 10 eV. Solution of the scattering equations in this method is far simpler than in a full close-coupling calculation because the method is based on an adiabatic factorization of the electron-molecule scattering ket. The method, however, yields low-energy cross sections that are far more accurate than those of traditional adiabatic-nuclei approximations because its transition matrix is calculated off the energy-momentum shell.

Close coupling calculations of magnetic transitions for He + H 2 in an uncoupled space frame

Full close coupling calculations of magnetic transitions in He + H 2 collisions are reported. The results are analyzed using the uncoupled space frame approach of Kouri and Shimoni. This enables one to study the magnetic transition T-matrices as a function of orbital angular momentum quantum number l. The results for transitions which are elastic in rotor state j are found to be dominated by j z -conserving transitions. Those which are inelastic in j are dominated by j z -conserving transitions for very low l but at higher l values, the non- j z -conserving transitions dominate. The results for He + H 2 are consistent with the recent studies of Shimoni and Kouri of the coupled states approximation.

Rotationally inelastic scattering of two HF molecules

For rotationally inelastic HF–HF collisions we have determined fully quantum partial opacities and integral cross sections for the j1=0, j2=0→11, 02, and 22 transitions at total energies of 500, 1000, and 8000 cm−1 and the 11→02 transition at 1000 cm−1. The potential was obtained from a recent fit of an ab initio surface and consisted of a spherically symmetric component and an anisotropic term with dipole–dipole symmetry. The collision dynamics were treated using the recently developed decoupled l-dominant (DLD) and coupled-states (CS) methods as well as within the Born approximation (BA). Comparison with selected full close-coupling calculations indicates that the CS method is very accurate for processes where collisions at small impact parameter play a large role, while the DLD method is to be preferred when large parameter collisions make the major contribution. The BA is, unfortunately, consistently unreliable, overestimating cross sections by more than an order of magnitude except at high energy. Additionally, the BA does not predict correctly the relative ratio of the 11→02 to 11→00 cross sections.