Integral and state-to-state cross sections for the reaction D + H2(νf) → HD(νf) + H: A quantum mechanical study within the infinite order sudden approximation

In this paper are presented quantum mechanical t-initial and t-average cross sections and rate constants for the reactions D + H₂(ν₁ = 0, 1) → HD(ν_f = 0, 1) + H. The calculations were done employing the infinite order sudden approximation. It was found that the t-average total cross sections overlap very nicely with the available classical cross sections. As for rate constants a reasonably good fit was found with available experimental results.     

On the classical mechanical reactive infinite order sudden approximation

The classical mechanical formulation of the reactive infinite order sudden approximation (RIOSA) is reconsidered. It is shown that the classical RIOSA conserves the total energy of the system not only in each arrangement channel, but also on the borderline separating the different arrangement channel configuration spaces. A unique interchannel transformation rule for the RIOSA angular momenta parameters is derived, which is valid for any masses of the interacting atoms and which explicitly incorporates the specificity of the RIOSA approach.     

离子对生成反应截面的量子散射理论研究

将Miller的S-矩阵变分法推广到离子对生成反应动力学的研究。M＋X~2→M^+＋X~2^-反应体系包括共价态(M＋X~2)和离子态(M^+＋X~2^-)两个势能面及其交叉效应,本文在此两态模型下导出了生成截面公式。在矩阵元计算中,平动波函数采用分布Gauss基作展开。作为上述公式的应用,对Cs＋O~2→Cs^+＋O~2^-反应体系作了数值计算并取得了满意结果。     

Computational tests of the factorization of cross sections in the sudden approximation

The factorization expressions for cross sections reported by Goldflam, Green and Kouri and independently by Khare are tested using accurate close coupling input for e^? + H₂, H + H₂, He + (HF, DF, HCl, DCl) and Ar + N₂. The results at the degeneracy averaged cross section level are used to illustrate accuracy criteria given for the factorization. Effects studied include variation of the projectile reduced mass, influence of initial and final rotor state, collision energy and potential anisotropy.     

A new approximation for atom-diatom rotational-relaxation cross sections

A semiclassical approximation to the S matrix of the infinite-order-sudden approximation is introduced. This is employed to yield for the energy-transfer effective cross section a purely classical approximation, analogous to the Mason-Monchick approximation [J. Chem. Phys. 36, 1622 (1962)] for traditional collision integrals. Constraints on energy and on angular momentum transfer are included. Numerical evaluation of this new approximation can readily be performed alongside that for traditional collision integrals. The new result is tested against full classical trajectory calculations for six potential energy surfaces for the collision systems H-N(2), He-N(2), He-CO, and Ar-CO(2). Differences of no more than 15% from the classical trajectory calculations have been obtained.     

On the sudden approximation of cross: computational tests and factorization of cross sections and related scattering phenomena

A sudden approximation recently derived by Cross using a semiclassical treatment of the orbital motion is recast into a form which permits factorization of differential and integral degeneracy averaged cross sections, opacities as a function of final angular momentum quantum number, the scattering amplitude, and the phenomenological cross section which describes spectral line broadening. Calculations are done using an average of initial and final orbital angular momentum quantum numbers for the partial wave parameter for ArN₂, ArTIF, H⁺H₂ and Li⁺H₂. The results indicate that the method is a good approximation for integral cross sections and opacities when the energy sudden approximation is valid and when the coupling of the orbital motion is important.     

Accurate quantum mechanical calculations of differential and integral cross sections and rate constant for the O+OH reaction using an ab initio potential energy surface

The authors report accurate quantum mechanical studies of the O+OH reaction on the improved Xu-Xie-Zhang-Lin-Guo potential energy surface. The differential cross section was obtained at several energies near the reaction threshold using a time-independent method. The dominant forward and backward peaks in the angular distribution are consistent with a complex-forming mechanism, which is also confirmed by the extensive rotational excitation in the O2 product. However, the asymmetry of these peaks suggests a significant nonstatistical component. The initial state (upsilon i=0, j i=0) specified integral cross section, which was calculated up to 1.15 eV of collision energy using the Chebyshev wave packet method, shows no energy threshold and decreases with the increasing collision energy, consistent with the barrierless nature of the reaction. The resulting rate constant exhibits a negative temperature dependence for T>100 K and decays as the temperature is lowered, in qualitative agreement with available experimental data.     

A classical reactive study within the infinite order sudden approximation: integral cross sections for the reactions F + H2vi = 0) → HF(vf = 0,1,2,3) + H

Integral reactive classical cross sections and product vibrational distributions are presented for the F+H₂ system. The calculations were made within the infinite order sudden approximation (IOSA) and the results compared with recent quantum-mechanical IOSA and exact classical results.     

Comparison of quantum mechanical and semiclassical cross sections for rotational excitation of hydrogen

Partial and integral cross sections for rotational transitions in He  H₂ have been calculated by a semiclassical coupled states method. The agreement with corresponding quantum mechanical values is excellent.     

A study of measured neutron elastic differential neutron cross sections for 23Na

Elastic neutron scattering angular distributions from ²³Na have been measured for incident neutron energies between 1.0 and 4.0 MeV at the University of Kentucky Accelerator Laboratory using neutron time-of-flight techniques for the scattered neutrons. This is an energy region in which existing data are very sparse. Measurements are compared with the predictions of the light particle-induced reaction code TALYS. The calculations reproduce forward angle scattering but have difficulty with relative minima in the differential cross section and large-angle scattering.     

Geometric phase effects in the H+H2 reaction: quantum wave-packet calculations of integral and differential cross sections

We report quantum wave-packet calculations on the H+H(2) reaction, aimed at resolving the controversy over whether geometric phase (GP) effects can be observed in this reaction. Two sets of calculations are reported of the state-to-state reaction probabilities, and integral and differential cross sections (ICSs and DCSs). One set includes the GP using the vector potential approach of Mead and Truhlar; the other set neglects the phase. We obtain unequivocal agreement with recent results of Kendrick [J. Phys. Chem. A 107, 6739 (2003)], predicting GP effects in the state-to-state reaction probabilities, which cancel exactly on summing the partial waves to yield the ICS. Our results therefore contradict those of Kuppermann and Wu [Chem. Phys. Lett. 349 537 (2001)], which predicted pronounced GP effects in the cross sections. We also agree with Kendrick in predicting that there are no significant GP effects in the full DCS at energies below 1.8 eV, and in the partial (0相似文献   

Rotational excitation in the Ar+N2 system.: A computational study of opacity functions and differential cross sections by the P-helicity decoupling approximation

Rotational excitation in the Ar+N₂ system is investigated using the P-helicity decoupling approximation. The accuracy of this approximation is demonstrated. Opacity functions, elastic and inelastic differential cross sections are computed. The results agree reasonably well with those available from molecular beams scattering experiments. The energy dependence and oscillatory structure of the differential cross sections is discussed. It is explained by an interference mechanism very similar in nature to that of elastic scattering. The relative role of the short- and long-range anisotropies, kinematics factors and type of transition in determining the shape of the inelastic differential cross sections is analyzed in some detail.     

Experimental and theoretical differential cross sections for the N(2D) + H2 reaction

In this paper, we report a combined experimental and theoretical study on the dynamics of the N(2D) + H2 insertion reaction at a collision energy of 15.9 kJ mol(-1). Product angular and velocity distributions have been obtained in crossed beam experiments and simulated by using the results of quantum mechanical (QM) scattering calculations on the accurate ab initio potential energy surface (PES) of Pederson et al. (J. Chem. Phys. 1999, 110, 9091). Since the QM calculations indicate that there is a significant coupling between the product angular and translational energy distributions, such a coupling has been explicitly included in the simulation of the experimental results. The very good agreement between experiment and QM calculations sustains the accuracy of the NH2 ab initio ground state PES. We also take the opportunity to compare the accurate QM differential cross sections with those obtained by two approximate methods, namely, the widely used quasiclassical trajectory calculations and a rigorous statistical method based on the coupled-channel theory.     

Coriolis coupling effects in the calculation of state-to-state integral and differential cross sections for the H+D2 reaction

The quantum wavepacket parallel computational code DIFFREALWAVE is used to calculate state-to-state integral and differential cross sections for the title reaction on the BKMP2 surface in the total energy range of 0.4-1.2 eV with D2 initially in its ground vibrational-rotational state. The role of Coriolis couplings in the state-to-state quantum calculations is examined in detail. Comparison of the results from calculations including the full Coriolis coupling and those using the centrifugal sudden approximation demonstrates that both the energy dependence and the angular dependence of the calculated cross sections are extremely sensitive to the Coriolis coupling, thus emphasizing the importance of including it correctly in an accurate state-to-state calculation.     

A combined quantum mechanical and molecular mechanical study of the reaction mechanism and alpha-amino acidity in alanine racemase

Combined quantum mechanical/molecular mechanical simulations have been carried out to investigate the origin of the carbon acidity enhancement in the alanine racemization reaction catalyzed by alanine racemase (AlaR). The present study shows that the enhancement of carbon acidity of alpha-amino acids by the cofactor pyridoxal 5'-phosphate (PLP) with an unusual, unprotonated pyridine is mainly due to solvation effects, in contrast to the intrinsic electron-withdrawing stabilization by the pyridinium ion to form a quinonoid intermediate. Alanine racemase further lowers the alpha-proton acidity and provides an overall 14-17 kcal/mol transition-state stabilization. The second key finding of this study is that the mechanism of racemization of an alanine zwitterion in water is altered from an essentially concerted process to a stepwise reaction by formation of an external aldimine adduct with the PLP cofactor. Finally, we have used a centroid path integral method to determine the intrinsic kinetic isotope effects for the two proton abstraction reactions, which are somewhat greater than the experimental estimates.     

Sudden approximation relations between tensorial cross sections for the collision of two diatomic molecules

We demonstrate relations between tensorial cross sections for the collision between two diatomic molecules, one of which does not rotate during the collision. The demonstration relies on a factorisation of the S matrix. A numerical example is presented for the rotational excitation problem of CO by H₂ (j = 1) molecules     

Fully converged integral cross sections of collision induced dissociation, four-center, and single exchange reactions, and accuracy of the centrifugal sudden approximation in H2 + D2 reaction

The initial state selected time-dependent wave packet method was employed to calculate the integral cross sections for the H(2) + D(2) reaction with and without the centrifugal sudden (CS) approximation by including all important K (the projection of the total angular momentum on the body-fixed axis) blocks. With a full-dimensional model, the first fully converged coupled-channel (CC) cross sections for different competitive processes from the ground rotational state were obtained: collision induced dissociation (CID), four-center (4C) reaction and single exchange (SE) reaction. The effect of the total angular momentum J on the reaction dynamics of H(2) + D(2) and the accuracy of the CS approximation have also been studied. It was found that the CID and SE processes occur in a wide range of J values while the 4C process can only take place in a narrow window of J values. For this reason, the CC cross section for the 4C channel is merely comparable to the SE channel. A comparison of the integral cross sections from CC and CS calculations showed that the CS approximation works well for the CID process but not for the 4C and SE processes, and the discrepancy between the CC and CS cross sections grows larger as the translational energy and/or the vibrational energy increase(s).     

A useful approximation and simple scaling laws for predicting ion—dipole capture cross sections and rate coefficients

A useful analytical approximation for ion—dipole capture cross sections is reviewed and used to obtain capture coefficients. Numerical scaling laws for obtaining cross sections from new numerical data are outlined. The results are compared with the predictions of Su and Bowers which are in good agreement with experiment even though certain of their assumptions are in conflict with numerical trajectory results.     

Exact quantum calculations of the kinetic isotope effect: cross sections and rate constants for the F+HD reaction and role of tunneling

In this paper we present integral cross sections (in the 5-220 meV collision energy range) and rate constants (in the 100-300 K range of temperature) for the F+HD reaction leading to HF+D and DF+H. The exact quantum reactive scattering calculations were carried out using the hyperquantization algorithm on an improved potential energy surface which incorporates the effects of open shell and fine structure of the fluorine atom in the entrance channel. The results reproduce satisfactorily molecular beam scattering experiments as well as chemical kinetics data for both the HF and DF channels. In particular, the agreement of the rate coefficients and the vibrational branching ratios with experimental measurements is improved with respect to previous studies. At thermal and subthermal energies, the rates are greatly influenced by tunneling through the reaction barrier. Therefore exchange of deuterium is shown to be penalized with respect to exchange of hydrogen, and the isotopic branching exhibits a strong dependence on translational energy. Also, it is found that rotational excitation of the reactant HD molecule enhances the production of HF and decreases the reactivity at the D end, obtaining insight on the reaction stereodynamics.     

A numerical method for the determination of atom—atom scattering amplitudes from the measured differential cross sections

A numerical method is given for the determination of the scattering amplitude, hence all the phase shifts, from the differential cross section at fixed energy. To obtain the phase of the scattering amplitude, the unitarity equation of scattering theory is solved, using the (experimental) cross section as input information. A straightforward iterative approach diverges for atom—atom input data, thus an appropriately modified method of solution is introduced to overcome this difficulty. The method was applied to two test cases, in both of which calculated atom—atom cross sections were used as simulated input data. Convergence to the correct phase was obtained in both examples, starting in each case with a guess phase function that differed considerably from the true solution. Convergence cannot be obtained, however, from an extremely poor starting phase. This study shows that the scattering amplitude for atomic scattering at thermal energies can be determined systematically, without use of parametrized functions, if a sufficiently accurate experimental cross section is available. A subsequent article describes a quantum mechanical procedure whereby the interaction potential can be constructed from the determined scattering amplitude.