Adiabatic capture calculations

Prof. Troe has presented to us the capture cross sections for two colliding particles, for example, an induced dipole with a permanent dipole interacting via the potential V(r,0) = ctq/2rA - ocos 0/r2 (see Recent Advances in Statistical Adiabatic Channel Calculations of State-Specific Dissociation Dynamics, this volume). The results have been evaluated using classical trajectories or SAC theory. But quantum mechanically, a colliding pair of an induced dipole and a permanent dipole could never be captured because ultimately they have to dissociate after forming some sort of a collision complex. I would therefore like to ask for the definition of the capture cross section. ... 

At low temperature the classical approximation fails, but a quantum generalization of the long-range-force-law collision theories has been provided by Clary (1984,1985,1990). His capture-rate approximation (called adiabatic capture centrifugal sudden approximation or ACCSA) is closely related to the statistical adiabatic channel model of Quack and Troe (1975). Both theories calculate the capture rate from vibrationally and rotationally adiabatic potentials, but these are obtained by interpolation in the earlier work (Quack and Troe 1975) and by quantum mechanical sudden approximations in the later work (Clary 1984, 1985). 

Figure 6. Temperature dependence of the reaction efficiency per collision for the reactions of OD + CH3Cl (open circles), 0D D20 + CH3Cl (filled circles and 0D (D20)2 + CH3Cl (half-filled circles). The reaction efficiency per collision is the experimental rate constant divided by the calculated collision rate constant, calculated by Clary using the adiabatic capture centrifugal sudden approximation (ACCSA) (28). For experimental reasons (29), the measurements were made with completely deuterated...

ABSTRACT. Calculation of the rate constant at several temperatures for the reaction +(2p) HCl X are presented. A quantum mechanical dynamical treatment of ion-dipole reactions which combines a rotationally adiabatic capture and centrifugal sudden approximation is used to obtain rotational state-selective cross sections and rate constants. Ah initio SCF (TZ2P) methods are employed to obtain the long- and short-range electronic potential energy surfaces. This study indicates the necessity to incorporate the multi-surface nature of open-shell systems. The spin-orbit interactions are treated within a semiquantitative model. Results fare better than previous calculations which used only classical electrostatic forces, and are in good agreement with CRESU and SIFT measurements at 27, 68, and 300 K. ... 

In Figure 3 we show cross sections for the He + HCt(J) charge transfer reaction calculated [10] using the accurate quantum theory (denoted CC) described in Section 2.3, a CSA approximation to this theory and the rotationally adiabatic capture theory (denoted AC) described in Section 2.4. It can be seen that the agreement between all the results is very good and this provides an excellent test of the AC theory for this type of reaction. 

Important further work by Troe and Nikitin and co-workers " considered the calculation of the capture rate from the perspective of the statistical adiabatic channel model (SACM). Ramillon and McCarroll demonstrated that the adiabatic capture method of Clary and the SACM method of Troe are identical in concept. However, there are still some minor differences in the approaches used to evaluate the rotational energies. Direct comparison for a number of ion-dipole capture rates found good agreement down to about 50 K, but there were increasing discrepancies at lower temperatures. These discrepancies are apparently a... 

Nikitin EE, Troe J. (1997) Quantum and classical calculations of adiabatic and non-adiabatic capture rates for anisotropic interactions. Ber. Bun-senges. Phys. Chem. 101 445-458. 

Because T -> V energy transfer does not lead to complex formation and complexes are only formed by unoriented collisions, the Cl" + CH3C1 -4 Cl"—CH3C1 association rate constant calculated from the trajectories is less than that given by an ion-molecule capture model. This is shown in Table 8, where the trajectory association rate constant is compared with the predictions of various capture models.9 The microcanonical variational transition state theory (pCVTST) rate constants calculated for PES1, with the transitional modes treated as harmonic oscillators (ho) are nearly the same as the statistical adiabatic channel model (SACM),13 pCVTST,40 and trajectory capture14 rate constants based on the ion-di-pole/ion-induced dipole potential,... 

Figures 5A and 5B present the total reactive cross section for reaction N( D) + 0 2(X E ) —> O( P) -I- NO(X n) as a function of the initial relative translational energy [115] on its two lowest adiabatic surfaces (2 A and 1 A"). The Oo reactant is in its ground vib-rotational state in both cases. The cross sections have been calculated using the real wavepaeket [98] and the capture model approaches [112]. Figure 5A shows the total reactive cross section on the 2 A surface.

The idea that the vibrational enhancement of the rate is due to the attraetive potential for excited vibrational states of the reactant is closely related to the observation made long ago based on transition state theoiy [25,26]. Poliak [25] found that for vibrationally highly excited reactants the repulsive pods (periodic orbit dividing surface) is way out in die reactant valley, and the corresponding adiabatic barrier is shallow. Based on this theory one can explain why dynamical thresholds are observed in reactions with vibrationally excited reactants. The simplicity of the theory and its success for mostly collinear reactions has a real appeal. However, to reconcile the existence of a vibrationally adiabatic barrier with the capture-type behavior - which seems to be supported by the agreement of the calculated and experimental rate coefficients [23] -needs further study. 

Qei and Qvtbrot denote electronic and rovibrational partition fimctions, respectively. In general, the contributions of the internal degrees of freedom of A and B cancel in g and gviiroXA)gv iro((B ), such that only contributions Irom the external rotations of A and B and the relative motion, summarized as "transitional modes", need to be considered. Under low temperature quantum conditions, these can be obtained by statistical adiabatic channel (SACM) calculations [9],[10] while classical trajectory (CT) calculations [11]-[14] are the method of choice for higher temperatures. CT calculations are run in the capture mode, i.e. trajectories are followed Irom large separations of A and B to such small distances that subsequent collisions of AB can stabilize the adduct. 

This result is due to Dykhne [48] and Davis and Pechukas [49] and has been extended to A-level systems [50]. The conditions of validity of the so-called Dykhne-Davis-Pechukas (DDP) formula has been established in [51,52], This formula allows us to calculate in the adiabatic asymptotic limit the probability of the nonadiabatic transitions. This formula captures, for example, the result of the Landau-Zener formula, which we study below. 

The calculations from Ref. 9 employ the adiabatic electronic assumption. This assumption provides slightly improved agreement with experiment at the lowest temperatures observed (27 K). However, the distinction between the adiabatic and statistical predictions is still quite minor at 27 K, because the inner transition state still plays an important role. It would be useful to have some experimental results in the long-range capture dominated temperature regime for some system where the adiabatic statistical and electronic predictions differ. 

Maergoiz et al. [28-30] performed classical trajectory calculations for ion-dipole, ion-quadrupole and dipole-dipole collisions, deriving results for capture rate coefficients and expressing them in terms of two reduced parameters, the reduced temperature, d, closely related to the Tr parameter in the work of Chesnavich and co-workers, and the Massey parameter, which is equal to the ratio of the coUisional timescale to the rotational period of the neutral. 3> 1 corresponds to the adiabatic limit (see below). They gave parameterized expressions for k /ki, similar to those given by Su and Chesnavich [26], but extending the range of validity. 

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