Centrifugal Sudden Approximation Research Articles

A semiclassical study of vibrational and rotational transition in He+H 2 at suprathermal energies

Vibrational and rotational transition in suprathermal (> a few eV) He+H 2 collisions is studied by using a semiclassical method in which one degree of freedom (i.e., relative radial motion) is described by classical mechanics and the others by quantum mechanics. The present study solves the semiclassical equation in a numerically accurate manner. That is, the vibration and orbital/molecular rotation are treated without employing any decoupled approximations. Also carried out are the semiclassical calculations using a centrifugal sudden (CS) and infinite order sudden (IOS) approximations. The comparison with the accurate semiclassical calculation shows that the CS approximation is always satisfactory, but the IOS approximation is not so good as one expected.

Crossed-beam study of the Al(2P1/2,3/2)+O2(X3Σ−g)→AlO(X2Σ+)+O(3PJ) reaction at low and very low kinetic energies

The title reaction is revisited at kinetic energies between 255 and 6 meV with a new crossed-beam apparatus. The AlO dissociation energy is evaluated to be D0(AlO)=5.27±0.01 eV. Al(2P1/2) and Al(2P3/2) spin–orbit reactivities are shown to be different. The relative cross-section of Al(2P1/2)+O2 is found to increase monotonically when decreasing kinetic energy. The variation of the calculated thermal rate constant is in agreement with kinetic measurements performed between 1083 and 23 K. Good agreement is also found with theoretical treatment based on the adiabatic capture centrifugal sudden approximation.

A semiclassical study of collision-induced dissociation in He+H2: The effect of molecular rotation

Dissociation processes in three-dimensional He+H2 collisions are studied by using a semiclassical approach which treats the relative radial motion in classical mechanics and the other motions (vibration/dissociation and rotation) in quantum mechanics. Centrifugal sudden approximation is assumed to solve the semiclassical equation. The results are compared with previous full quantum mechanical calculations in which infinite order sudden approximation has been applied. The present study shows that the molecular rotation must be accurately taken into account in the dissociation process even at very high collision energies where the energy sudden assumption is usually expected to be satisfied for low molecular rotational states.

Accurate quantum chemical calculation of cross sections for the system D+H 2 → DH+H

Accurate reactive scattering calculations of reactive probabilities and integral cross sections for the system D+H2 → DH+H were carried out by using the quantum mechanical time-dependent wave packet methods. In order to simplify the calculation, we introduced the centrifugal sudden approximation to reduce the effective degrees of freedom, and show results of new calculations. In particular, the present calculations were extended to all angular momentum and obtained reaction cross sections for a range of energies. The results were also compared with those of other theoretical calculations and the differences were discussed.

Fully converged integral cross sections of diatom-diatom reactions and the accuracy of the centrifugal sudden approximation in the H2+OH reaction

The initial state selected time-dependent wave packet method has been extended to calculate integral cross sections for diatom-diatom chemical reactions without the CS (centrifugal sudden) approximation by including all important K (the projection of the total angular momentum on the body-fixed axis) blocks in the body-fixed frame. We report the first fully converged cross section for the ground rovibrational state of the title reaction and present a detail study of the accuracy of the CS approximation to the reaction. We find that for the ground rovibrational state the CS approximation works very well, but its accuracy deteriorates with increasing reagent rotational excitation. As expected, and as found in atom-diatom reactions, the CS approximation works much better in high energy region than in low energy region. In low energy region, the coupled channel cross sections are larger than the CS ones for all the rotationally excited states investigated here, in particular for the highly excited states. It is found the CS approximation gives rise to about 10% error in H2 or OH rotationally averaged rate constant. If simultaneous OH and H2 rotational excitation does not have a correlated effect on dynamics, the CS approximation introduces about 19% error in thermal rate constant for the reaction for low temperatures which is considerably larger than what is expected of a few percent.

Semiclassical dissociation dynamics in coplanar atom–diatom collisions

Dissociation processes in planar atom–diatom collisions are studied with a semiclassical method which treats the relative radial motion in classical mechanics and the other motions, i.e. vibration/dissociation and (orbital and molecular) rotation, in quantum mechanics. The semiclassical equation is solved in a numerically accurate manner. Comparison is made between the accurate numerical results and those obtained by using centrifugal sudden and infinite order sudden approximations.

Accurate variational calculations and analysis of the HOCl vibrational energy spectrum

Large scale variational calculations for the vibrational states of HOCl are performed using a recently developed, accurate ab initio potential energy surface. Three different approaches for obtaining vibrational states are employed and contrasted; a truncation/recoupling scheme with direct diagonalization, the Lanczos method, and Chebyshev iteration with filter diagonalization. The complete spectrum of bound states for nonrotating HOCl is computed and analyzed within a random matrix theory framework. This analysis indicates almost entirely regular dynamics with only a small degree of chaos. The nearly regular spectral structure allows us to make assignments for the most significant part of the spectrum, based on analysis of coordinate expectation values and eigenfunctions. Ground state dipole moments and dipole transition probabilities are also calculated using accurate ab initio data. Computed values are in good agreement with available experimental data. Some exact rovibrational calculations for J=1, including Coriolis coupling, are performed. The exact results are nearly identical with those obtained from the adiabatic rotation approximation and very close to those from the centrifugal sudden approximation, thus indicating a very small degree of asymmetry and Coriolis coupling for the HOCl molecule.

Quantum stereodynamics of the Li+HF(v,j) reactive collision for different initial states of the reagent

The effect of the reagent initial state excitation on the reactive cross section in the Li+HF(v,j) collision is analyzed for v=0, 1 and j=0, 1, 2 and 3. A wave packet treatment is used within the centrifugal sudden approximation on a global potential energy surface recently proposed [Aguado et al., J. Chem. Phys. 107, 10085 (1997)]. The reaction cross-section for v=0 is in good agreement with the available experimental data, and for low j shows oscillations as a function of the translational energy which are due to the structure of the transition state. For v=1 the reaction cross-section increases by a factor of 10–50 with respect to that of v=0. The influence of the alignment of the initial angular momentum on the reaction cross section is studied.

Effects of reagent rotation on the dynamics of the H2+OH reaction: A full dimension quantum study

We have extended the time-dependent wave packet method to calculate cross sections and rate constants for rotationally excited initial states by using the centrifugal sudden (CS) approximation. A detailed study of the effects of rotational excitation of reagents on the title reaction on the WDSE PES has been carried out. It is found that (a) OH rotational excitation very mildly enhances the total cross section, (b) H2 rotational excitation quite substantially reduce the cross section, and (c) simultaneous OH and H2 rotational excitation has a largely uncorrelated effect. As a result, we found that the thermal rate constant can be obtained fairly accurately by only taking into account the effect of H2 rotation. A model calculation by changing the mass of an O atom reveals that the weak dependence of the cross section on OH rotation is not because the O atom is left relatively stationary by OH rotation. We speculate that it may be a general feature for the diatom-diatom reaction that the nonreactive diatom acts as a spectator not only vibrationally but also rotationally. It was also found that the “J-shifting” approximation works quite well for the reaction. On the other hand, the effect of K on the dynamics is found to be much stronger and more complicated than the J effect, making the “K-shifting” approximation not good for the reaction.

Quantum rate constants for the H2+OH reaction with the centrifugal sudden approximation

The cumulative reaction probability (CRP) has been calculated for the H2+OH↔H2O+H in its full dimensionality by using the centrifugal sudden (CS) approximation for J>0. The Boltzmann average of the CRP provides the most accurate thermal rate constant to date for the title reaction on the Walch, Dunning, Schatz, Elgersma (WDSE) potential energy surface (PES). It is found that the theoretical rate is larger than the experimental value in the low temperature region (a factor of ∼1.8 at 300 K), and smaller than the experimental value for temperatures higher than 500 K, indicating that a more accurate PES is needed to provide a quantitative description of the title reaction. We also demonstrate that the “J-shifting” approximation in which we calculate N(J>K,K) from N(J=K,K) by an energy shift works very well for this reaction. However, the “J- and K-shifting” approximation [calculating N(J,K) from N(J=0,K=0)] overestimates the rate for this reaction by about 60% for all the temperatures investigated. It is also found that the CS rate constant is substantially lower than the rate constant for the ground rovibrational state of the reagents calculated on the same PES, indicating that initial rotational excitation is important to the thermal rate constant for this reaction (it causes a decrease).

Rate constant calculations for atom–diatom reaction involving an open-shell atom and a molecule in a Σ electronic state Application to the reaction Al(2P1/2,3/2)+O2(X3Σg-)→AlO(X2Σ+) +O(3P2,1,0)

We present a short study of the influence of the open-shell nature of the reactants on the kinetics of the title reaction. We use the adiabatic capture centrifugal sudden approximation (ACCSA) method and a long-range potential comprising the sum of the quadrupole–quadrupole, spin–orbit and dispersion contributions. Matrix elements of this potential are evaluated in the spin–orbit basis set of each reactant for the Al(2P1/2,3/2)+O2(X3Σg-) reaction and used within the ACCSA method to calculate the temperature dependence of the rate constant in the range 15–300 K. In the limit of zero temperature, the reactivities of the two spin–orbit states of the aluminium atom, Al(2P1/2) and Al(2P3/2), towards the O2 molecule are demonstrated to be different and analytical formulae for the rate constants are obtained as a function of temperature.

Calculations of rate constants for reactions of first and second row cations

Calculations of rate constants for 35 reactions of first and second row monocations with different neutrals are presented. A combined rotationally adiabatic capture and centrifugal sudden approximation is used. The majority of predicted rate constants are in good agreement with the experimental measurements. An exploration of energetics of the potential energy surface for some of those cases in which prediction fails has been done using ab initio G2 theory. These cases usually correspond to situations in which the reaction is not as exothermic as the application of capture approximation requires or secondary barriers exist in the reaction path. Second row cations present these kind of problems due to their smaller electronegativity with respect to cations of the first row.

Vibrational relaxation in NO +He: accurate quantum mechanical study

A quantum mechanical study of the vibrational relaxation in the collisions of NO + with He is reported. An ab initio potential energy surface has been computed using the coupled cluster singles-doubles approximation. Vibration relaxation cross-sections have been calculated on this surface by using the centrifugal sudden approximation. The corresponding vibration relaxation rate coefficients are obtained for the temperature range 100–1000 K. A comparison of the theoretical and experimental results is discussed.

Fast reactions between a linear molecule and a polar symmetric top

We present rate constant calculations for fast neutral reactions between a linear molecule and a polar symmetric top. The adiabatic capture, partial centrifugal sudden approximation (ACPCSA) is adapted in order to account for the degeneracy of the rotational states of the symmetric top molecule. We use a long range potential made from the sum of the dipole-dipole, induction and dispersion contributions. The three reactions CN + NH 3, CH + NH 3 and OH + PBr 3 are studied. ACPCSA calculations of rate constants are compared with experimental results at 300 K and analytical formulae are derived in the limit of zero temperature.

Rate constant calculations for atom-diatom reactions involving an open shell atom and a molecule in a Π electronic state: Application to the reaction

We present a study of the influence of the open shell nature of the reactants on the kinetics of the title reaction. We use the adiabatic capture centrifugal sudden approximation (ACCSA) method and a long-range potential made of the sum of the dipole-quadrupole, quadrupole-quadrupole, spin-orbit and dispersion contributions. This potential is calculated using the spin-orbit basis set of each reactant for the C + NO reaction and used within the ACCSA method to propose a value of the rate constant at 300 K. We compare our results with experiment and with those obtained by using the ACIOSA method. We also discuss the role played by the dispersion forces in the kinetics of this reaction.

Distorted wave correction of centrifugal sudden wave packet approximation

A distorted wave procedure is employed to correct the centrifugal sudden wave packet approximation, and the accurate results compared with the standard close coupling method for m-dependent integral cross sections for short- and long- range Ar+N2 potentials at E = 0.0258 eV are obtained only by using the second-order corrections to the CSWP wave function.

Adiabatic capture models for fast chemical reactions

It is shown that the adiabatic capture centrifugal sudden approximation and the statistical adiabatic channel model for the determination of state selected reactive rate constants in atom-molecule collisions are identical.

Counterpropagating pulsed molecular beam scattering of NH3–Ar. I. State resolved integral cross sections

A new approach to molecular beam scattering is described. The method uses counterpropagating molecular beam pulses to define a scattering geometry of cylindrical symmetry while resonance enhanced multiphoton ionization is applied for the state specific product detection. The simple correlation of laboratory and center-of-mass quantities allows a straightforward determination of differential cross sections from measured ion time-of-flight distributions. In addition, the short duration of the pulses causes a delay dependence of the scattering signal which is used as an additional control parameter to define the size of the scattering volume. The method is applied to the rotational excitation of NH3 in collisions with Ar at a collision energy of 158 meV. Delay and depletion studies yield an effective mean free path of 60 cm, confirming single collision condition. While parity averaged integral cross sections are determined for the para modification of NH3, fully state resolved integral cross sections are determined for o-NH3. The general behavior of the integral cross sections for both modifications is well described by an exponential energy gap law. Deviations of individual cross sections from the scaling law confirm the propensity for inelastic collisions with Δk=3. Transitions to parity levels, which are forbidden in the centrifugal sudden approximation, show significantly less intensity.

Counterpropagating pulsed molecular beam scattering of NH3–Ar. II. State resolved differential cross sections

State resolved differential cross sections (DCSs) for the rotational excitation of NH3 in collisions with Ar for various final states at a collision energy of 158 meV have been determined in a counterpropagating pulsed molecular beam scattering experiment. Simultaneous state and velocity specific detection of scattered products is achieved through resonance enhanced multiphoton ionization with subsequent ion time-of-flight analysis. The supersonic expansion ensures the preparation of well-defined initial states in both nuclear spin modifications. While measured DCSs for para-NH3 are parity averaged, state resolved cross sections could be determined for ortho-NH3. All DCSs are dominated by small or intermediate angle scattering, indicating the importance of the anisotropy in the long range part of the potential surface. The maxima in the DCSs are shifted towards larger scattering angles with increasing energy transfer, a behavior characteristic of a rotational rainbow. Excitation probabilities to states which are forbidden in the centrifugal sudden approximation are characterized by a significant decrease in intensity in the backward direction as well as a steeper exponential fall off at small angles.

Classical centrifugal-sudden calculations of transport and relaxation cross-sections for Ar−N2

Classical limits of the quantal centrifugal-sudden approximation to generalized cross-sections have been derived and compared with the exact classical results. Detailed comparisons between the classical centrifugal-sudden approximation (cCSA) values, the exact classical trajectory results, and the corresponding quantal calculations are then carried out for the Ar−N2 system, and contrasted with similar comparisons for He−N2. Above 150 K the cCSA is found to be accurate to within 1% for the temperature dependent viscosity and diffusion cross-sections and 5% for the viscomagnetic and depolarized Rayleigh light-scattering cross-sections.