Low-temperature behavior of capture rate constants for inverse power potentials

Dashevskaya, E. I.; Maergoiz, A. I.; Troe, J.; Litvin, I.; Nikitin, E. E.

doi:10.1063/1.1562159

Cited by 66 publications

(90 citation statements)

References 28 publications

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“…We note that approximate result (15) works relatively well in all cases for energies E 100E 6 , except for y = 1 when there is no contribution from the shape resonances. Moreover, we have verified that at large energies the rates for bosons, fermions, and distinguishable particles become equal which agrees with the approximate result of Eq.…”

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confidence: 88%

“…[8]. One class of theories based on Quantum Defect Theory (QDT) allows us to systematize and develop tools for understanding such collisions [9][10][11][12][13][14][15]. One special limiting case is that of highly reactive collisions, where simple classical trajectory capture models known as the Langevin (n = 4) [16] or Gorin (n = 6) [17] models apply when the long range potential takes on the form −C n /r n (n > 3).…”

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confidence: 99%

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Quantum Theory of Reactive Collisions for1/rnPotentials

et al. 2013

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We develop a general quantum theory for reactive collisions involving power-law potentials (−1/r n ) valid from the ultracold up to the high-temperature limit. Our quantum defect framework extends the conventional capture models to include the non-universal case when the short-range reaction probability P re < 1. We present explicit analytical formulas as well as numerical studies for the van der Waals (n = 6) and polarization (n = 4) potentials. Our model agrees well with recent merged beam experiments on Penning ionization, spanning collision energies from 10mK to 30K [Henson et al, Science 338, 234(2012)].PACS numbers: 34.50. Cx, 03.65.Nk, 34.10.+x, 34.50.Lf Much recent work involves the inelastic and reactive collisions of cold atoms or molecules with one another [1][2][3][4] or with ions in hybrid traps [5][6][7]. These could involve the ultracold regime with translational temperature on the order of µK or less or the cold regime between a few mK and a few K. Systematic theoretical principles for understanding the quantum dynamics of such collisions are needed. Much work has already been done in this area, as reviewed by Ref. [8]. One class of theories based on Quantum Defect Theory (QDT) allows us to systematize and develop tools for understanding such collisions [9][10][11][12][13][14][15]. One special limiting case is that of highly reactive collisions, where simple classical trajectory capture models known as the Langevin (n = 4) [16] or Gorin (n = 6) [17] models apply when the long range potential takes on the form −C n /r n (n > 3). These familiar models assume that every classical trajectory contributes to the collision cross section that is captured by the long range potential so the particles spiral in to short distance where they react or relax with probability P re . We use the term "universal" to describe capture models with P re = 1, since they do not depend on any details of the strong short-range chemical interactions.In the cold and ultracold regimes, it is essential to build in quantum corrections to these classical models due to quantum threshold laws [18][19][20]. This has been done using QDT for both the Langevin [21,22] and Gorin [23,24] universal models where P re = 1. Here, we will follow the formalism by Idziaszek et al. [22,23] and generalize the previous results to the nonuniversal regime with P re < 1, and to the arbitrary collision energy. In the limiting cases of low and high temperatures we give analytic formulas that are valid for power-law potentials (−1/r n ). We apply our theory to interpret the ionization rate constants measured by recent merged beam experiments in the cold regime [25]. Using a single complex QDT parameter found by fitting low energy data only, we are able to reproduce the experimental data over four orders of magnitude in energy including about twenty partial waves in the calculation.Generalized complex scattering length. We consider reactive collisions of particles interacting via power-law potential V (r) = −C n /r n (n > 3) at large distances r R 0 ...

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Quantum Theory of Reactive Collisions for1/rnPotentials

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“…Electron attachment to polarizable neutral molecules is often treated in terms of the Vogt-Wannier model for electron capture [1][2][3][4] in an interaction potential V(r) = Àe 2 a/2r 4 ( 1.1) where a is the polarizability of the neutral molecule and r is the center-of-mass distance between the molecule and the electron. Obviously, this potential is realistic only for large r. The accommodation of the incoming electron by the molecular electrons and the nuclear frame, through ''electron-phonon coupling'' or ''intramolecular vibrational redistribution (IVR)'', at small r requires a different treatment without separation of electronic and nuclear coordinates, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Finite-size effects in capture cross sections and thermal capture rate constants Making use of the transmission coefficients P l (k,r 0 ) elaborated in section 2, capture cross sections s cap and rate constants k cap are easily calculated. We again represent the results as scaled quantities 3 . The scaled energy-dependent rate coefficients.…”

Section: Introductionmentioning

confidence: 99%

Electron capture by finite-size polarizable molecules and clusters

Nikitin

Troe

2010

Phys. Chem. Chem. Phys.

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The effects of finite molecular target size are investigated for partial-wave selected capture of electrons by isotropically polarizable molecules and clusters within a generalized Vogt-Wannier model. It is shown how expressions for partial-wave selected capture probabilities of zero-size targets from Dashevskaya et al. (Phys. Chem. Chem. Phys., 2009, 11, 9364) can be modified to account for finite target sizes of the molecules and clusters. The transition from quantum to classical, from single-to multiple-and all-wave, behaviour of capture probabilities, cross sections, and rate constants is illustrated.

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“…Nonadiabatic dynamics and quantum effects were also investigated. It was shown [9] that the SACM/CT concept works down to temperatures in the milli-and even micro-Kelvin range, particularly if Coriolis coupling effects are properly accounted for [10]. The presence of open electronic shells also becomes relevant at low temperatures and needs to be taken into account, see e.g.…”

Section: Introductionmentioning

confidence: 99%

Classical Trajectory and Statistical Adiabatic Channel Study of the Dynamics of Capture and Unimolecular Bond Fission. VII. Thermal Capture and Specific Rate Constants k(E,J) for the Dissociation of Molecular Ions

Troe¹,

Ushakov²,

Viggiano³

2005

Zeitschrift Für Physikalische Chemie

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Reaction Kinetics / Unimolecular Reactions /Ion FragmentationsSpecific rate constants, k(E, J), and thermal capture rate constants, k 01 p(T), are determined by statistical adiabatic channel model/classical trajectory (SACM/CT) calculations for unimolecular dissociation and the reverse association reactions of representative polyatomic molecular ions. Simple short-range valence/long-range ion-induced dipole model potentials without reverse barriers have been employed, using the reactions C 8 H 1 o+ -# C 7 H 7 + + CH 3 and C 9 HI 2 + ,#. C 7 H 7 + + C 2 H 5 as illustrative examples. Simplified representations of k (E) and kc, 5 (T) from rigid activated complex Rice-Ramsperger-Kassel-Marcus (RRKM) theory are compared with the SACM/CT treatment and with experimental results. The Massey parameters of the transitional mode dynamics, for the systems considered, are smaller than unity such that their dynamics is nonadiabatic while the dynamics of the conserved modes is adiabatic. Because of the long-range/short-range switching character of the potential, simple rigid activated complex RRKM theory cannot be used without modifications. The effects of a shifting of the effective bottle-neck of the dynamics with increasing energy towards smaller interfragment distances in the present cases are amplified by a shift into a range of increasing anisotropy of the potential. As a consequence, the thermal capture rate constants markedly decrease with increasing temperature. REPORT DOCUMENTATION PAGE OMB No. 0704-01-0188The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S)AFRL/VSBXT SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution unlimited. SUPPLEMENTARY NOTESReprinted from Z. Phys. Chem. V. 219 (2005), pp. 715-74 1. © Oldenbourg Vissenschaftverlag, Munich, Germany. *University of Goettingen, Goettingern, Germany. **Inst. for Problems of Chem. Phys., Russian Acad. of Sciences, 142432 Chernogolovka, Russia 14. ABSTRACT Specific rate constants k(E, J) and thermal capture rate constants, kLap(T), are determined by statistical adiabatic channel model/classical trajectory (SACM/CT) calculations for unimolecular dissociation and the reverse association reactions of representative polyatomic molecular ions. Simple short-range valence/long-range ion-induced dipole model potentials without reverse barriers have been employed, using the reactions C 8 H1 10 ' C 7 H 7 + + CH 3 and C 9 H,2+. <* C 7 H 7 ++ C 2 H 5 as illustrative examples. Simplified representations of k(E) and kLap(7) from rigid activated complex Rice-Ramsperger-Kassel-Marcus (RRKM) theory are compared with the SACM/CT treatment and with experimental results. The Massey parameters of the tran...

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Low-temperature behavior of capture rate constants for inverse power potentials

Cited by 66 publications

References 28 publications

Quantum Theory of Reactive Collisions for1/rnPotentials

Quantum Theory of Reactive Collisions for1/rnPotentials

Electron capture by finite-size polarizable molecules and clusters

Classical Trajectory and Statistical Adiabatic Channel Study of the Dynamics of Capture and Unimolecular Bond Fission. VII. Thermal Capture and Specific Rate Constants k(E,J) for the Dissociation of Molecular Ions

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