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Long-Range TST for predicting rate constants of barrier-less reactions at low temperatures

Long-Range TST for predicting rate constants of barrier-less reactions at low temperatures. Yuri Georgievskii and Stephen J. Klippenstein. LR interaction potential can be represented by a sum of a few 1/R n terms When a single term in the potential dominates

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Long-Range TST for predicting rate constants of barrier-less reactions at low temperatures

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  1. Long-Range TST for predicting rate constants of barrier-less reactions at low temperatures Yuri Georgievskii and Stephen J. Klippenstein

  2. LR interaction potential can be represented by a sum of a few 1/Rn terms • When a single term in the potential dominates • an analytical expression for the capture rate constant is obtained • Where C1 is a unique constant corresponding to a given angular form f0 Long Range TST • At large interfragment separations J ~= Jorb and the expression for NE,J is simplified

  3. LR-TST: Analytic Results IonsNeutrals • Dipole-Dipole • Dipole-Quadrupole • Ion-Induced Dipole • Langevin Result • Ion-Dipole • Ion-Quadrupole

  4. O(3P) + H3+

  5. CO + H3+ Jarrold, Bowers, DeFrees, McLean, Herbst, Astrophys. J, 303, 392 (1986)

  6. LR-TST: comparison with experiment

  7. Long range TST: conclusions • LR-TST agrees with Classical Trajectories to within 10% • A single term in the potential expansion is generally not sufficient • At higher temperatures chemical bonding region important • In all cases LR-TST provides an upper bound for the reaction constant • Situation in which LR-TST rate constant estimate is too high even at low temperatures usually indicates the presence of an inner TS state which effects the rate constant. • Alternatively, this effect may be related to the presence of multiple electronic surfaces • Difference between LR-TST and experiment usually increases with temperature in accordance with the growing role of the inner TS region

  8. V Outer TS Inner TS R 0 “Two-transition-states” model • Inner transition state: • Direct VTST or RRHO TST • Outer transition state: • Long range TST

  9. Inner Transition State CN + C2H6 Minimum energy path Minimum Energy Path Minimum Energy Path + Zero Point Energy

  10. CN + C2H62TS Results

  11. J=0 M=1 A J=1 M=2 J=2 X M=3 Alkenes + O(3P) Ethene, Propene, 1,Z,E,Iso-butenes + O Potential energy surface structure:

  12. Methods • Inner transition state: • Parabolic barrier with tunneling, quantum harmonic normal modes, classical rotations • Optimization & frequencies calculation: CAS(6e5o2s)PT2/ADZ • Energies: CAS(6e5o2s)PT2(mix=2,shift=0.2)/ATZ • Outer transition state: • Long range TST • Center-of-mass-to-center-of-mass reaction coordinate • Effective isotropic interaction chosen to fit the ab initio minimized LR reactive flux • Energies: CAS(4e3o3s)PT2

  13. O(3P) + Alkenes: Rate Constants Barrier Heights (1/cm) Cis-Butene -312 Trans-Butene -386 Iso-Butene -337 1-Butene -168 Propene -51 Ethylene 324

  14. Conclusions • The “two transition state” feature seems to be common for many barrierless reactions at low temperatures • There is a broad range of temperatures from tens to several hundreds K in which it is important to take into account both effects from short range and long range interactions for correct prediction of the rate constant • Because of the conservation of energy and angular momentum in the TS region the resultant 2TS rate constant is essential reduced in comparison with its value for either of the TS separately. It is crucially important to use the E,J-resolved level of the theory for rate constant calculations • LR-TST in conjunction with the 2TS model provides a way for a quantitative prediction of the rate constant

  15. Electronic structure methods • Direct configurational space sampling: • Conserved modes relaxation: UMP2/6-31G* • SP energy calculation: CASPT2/CC-PVDZ • Minimum energy path: • Constrained optimization: CASPT2/6-311G** • SP energy calculation: RQCISD(T)/CC-PVDZ,CC-PVTZ, CC-PVQZ, AUG-CC-AVDZ, AUG-CC-AVTZ • Zero-point energy: • Constrained optimization: CASPT2/CC-PVTZ • Frequency calculation:CASPT2/AUG-CC-PVDZ

  16. CN+C2H6/ C2D6 kinetic isotope effect • ZPE correction to the potential explains the KIE for CN + ethane reaction • orientation-dependent ZPE correction is needed to provide quantitatively accurate agreement with experiment • KIE increases as the temperature decreases. At low temperatures the outer TS starts to play bigger role and KIA should become smaller. It would be interesting to check this prediction

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