Quantum scattering calculations

Ediund A and Peskin U 1998 A parallel Green s operator for multidimensional quantum scattering calculations Int. J. Quantum Chem. 69 167... 

Fig. 9. The excitation function in A2 for the reaction F + p-H2 —> H + HF versus collision energy. The solid line is the result of quantum scattering calculations done with the SW-PES and the points are the molecular beam experiments.

Fig. 39. The experimental differential cross-section (dots) for H + D2(v = 0,j = 0) — D + HD(i/ = 0,j = 2), measured at the laboratory angle of 70°, versus CM collision energy, Ec. The curve is the result of the quantum scattering calculation.

Based on this physical view of the reaction dynamics, a very broad class of models can be constructed that yield qualitatively similar oscillations of the reaction probabilities. As shown in Fig. 40(b), a model based on Eckart barriers and constant non-adiabatic coupling to mimic H + D2, yields out-of-phase oscillations in Pr(0,0 — 0,j E) analogous to those observed in the full quantum scattering calculation. Note, however, that if the recoupling in the exit-channel is omitted (as shown in Fig. 40(b) with dashed lines) then oscillations disappear and Pr exhibits simple steps at the QBS energies. As the occurrence of the oscillation is quite insensitive to the details of the model, the interference of pathways through the network of QBS seems to provide a robust mechanism for the oscillating reaction probabilities. 

Generalization and Numerical Implementation of Pseudo-Time Schroedinger Equation for Quantum Scattering Calculations. 

Describe the theory for quantum scattering calculations of cross sections for molecular collisions in external electromagnetic fields. 

Quantum Scattering ("close coupling") (1). The feasibility of a full quantum scattering calculation depends mostly upon the... 

Distorted Wave Bom Approximation. Quantum scattering calculations are sometimes made using the distorted wave Bom approximation (15). Such calculations have the advantage of almost always being feasible numerically. For simple cases, one can also obtain some results analytically (16). However, the accuracy of the results is generally poor, for most molecular collisions. A... 

We first follow the flow chart for the simple case of elastic scattering of structureless atoms. The number of internal states, Nc, is one, quantum scattering calculations are feasible and recommended, for even the smallest modem computer. The Numerov method has often been used for such calculations (41), but the recent method based on analytic approximations by Airy functions (2) obtains the same results with many fewer evaluations of the potential function. The WKB approximation also requires a relatively small number of function evaluations, but its accuracy is limited, whereas the piecewise analytic method (2) can obtain results to any preset, desired accuracy. 

For rotational excitation of HC1 by Ar at room temperature, the maximum rotational angular momentum quantum number coupled during collision is about 12. The maximum number of coupled j,m states is Nc = (jmax + 1)(jmax + 2)/2 = since HC1 is a heterodiatomic molecule, and thus all states of the same total parity are coupled. With 91 channels, the quantum scattering calculations are feasible, but rather expensive. A further complication of the... 

S.C. Althorpe, D.C. Clary, Quantum scattering calculations on chemical reactions, Annu. Rev. Phys. Chem. 54 (2003) 493. 

In this section we review three simple approximate time-independent methods which are specifically designed for calculating absorption spectra. Time-independent quantum scattering calculations, which can give exact results, will not be discussed. Such methods have been reviewed for instance by Nyman and Yu 2000 [81] and Althorpe and Clary 2004 [82]. In Section 6 we instead describe the time-dependent wavepacket approach, which can also give exact results. In the present section we review (i) a zero point energy model, (ii) the simple reflection principle model and (iii) the reflection principle model [3]. The accuracy of these models, which should only be applied to direct or near-direct reactions, will... 

Our quantum scattering calculations refer to the reduced dimensional (reaction path) model of O + H2 dci)ictcd in Figure f. As mentioned above, the four states that we include are one singlet = 0)), and three triplets ( A. Mn —... 

Mandelshtam, V.A. and Taylor, H.S. (1995) Spectral projection approach to the quantum scattering calculations, J. Chem. Phys. 102, 7390-7399. 

In quantum scattering calculations we are typically interested in the eigenstates in the low energy end of the spectrum. For this purpose tm exponential filter f Hs) = cxp[—— Hmin)] is useful as it will dilate the eigenvalues at low energies. The action of the filter on the vectors can be performed via the Chebyshev polynoinicds[63, 64],... 

The progression from accurate quantum scattering calculations of three atoms to four atoms by TI methods proved formidable.[6,7,8] It is only in recent years that we... 

Abstract A generalization of the Landau-Teller model for vibrational relaxation of diatoms in collisions with atoms at very low energies is presented. The extrapolation of the semiclassical Landau-Teller approach to the zero-energy Bethe-Wigner limit is based on the quasiclassical Landau method for calculation of transition probabilities, and the recovery of the Landau exponent from the classical collision time. The quantum suppression-enhancement probabilities are calculated for a general potential well, which supports several bound states, and for a Morse potential with arbitrary number of states. The model is applied to interpretation of quantum scattering calculations for the vibrational relaxation of H2 in collisions with He. 

J.D. Kress, R.T. Pack, and G.A. Parker, Accurate 3-dimensional quantum scattering calculations for F+H2 - HF+H with total angular-momentum J = 1. Chem. Phys. Lett., 170 306-310, 1990. 

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