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

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

• Yuri Georgievskii and Stephen J. Klippenstein

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Long Range TST

• At large interfragment separations J Jorb
  and the expression for NE,J is simplified

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LR-TST Analytic Results
Ions Neutrals

• Dipole-Dipole
• Dipole-Quadrupole

• Ion-Induced Dipole
• Langevin Result
• Ion-Dipole
• Ion-Quadrupole

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O(3P) H3
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CO H3
Jarrold, Bowers, DeFrees, McLean, Herbst,
Astrophys. J, 303, 392 (1986)
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LR-TST comparison with experiment
Reaction T, K Expt D-D D-Q D-iD Disp S Ratio
OHisoprene 58 0.78 1.45 3.85 2.50 4.23 5.54 7.10
OHPropene 58 0.57 2.13 2.97 2.23 3.84 4.8 8.42
OH1-Butene 23 4.27 2.71 2.63 2.00 3.44 4.55 1.07
OHZ-2-Butene 23 3.89 1.73 2.77 2.02 3.43 4.24 1.09
OHE-2-Butene 23 4.52 0 2.76 2.03 3.44 4.18 0.92
CNC2H2 25 4.60 0 4.08 1.38 3.94 4.98 1.08
CNC2H4 25 4.35 0 2.87 1.44 4.04 4.49 1.03
CNC2H6 25 1.13 0 1.34 1.43 4.09 4.24 3.75
CNCH3CCH 15 3.8 3.26 3.43 1.34 3.76 5.04 1.33
CNCH2CCH2 15 4.4 0 2.84 1.39 3.84 4.3 0.98
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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

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Two-transition-states model

• Inner transition state
• Direct VTST or RRHO TST
• Outer transition state
• Long range TST

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

• Minimum Energy Path

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CN C2H6 2TS Results
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Alkenes O(3P)

• Ethene, Propene, 1,Z,E,Iso-butenes O

Potential energy surface structure
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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(mix2,shift0.2)/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

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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
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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

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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 calculationCASPT2/AUG-CC-PVDZ

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CNC2H6/ 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