Hydrogen Abstractions by Hydroxyl through H-bonded Complexes: Pressure Dependence Jozef Peeters,* Luc Vereecken Department of Chemistry, University of Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium * INTRODUCTION Many atmospheric OH-initiated H-abstraction reactions with oxygenated compounds (OVOC) occur through H-bonded pre-reactive complexes: Examples include acetone, acetic acid, acetaldehyde,… But: Pressure dependence has not been studied extensively We investigate here theoretically the pressure dependence of reactions occurring through a pre-reactive complex. Two cases can be distinguished: Case A: E b > E a : TS of subsequent reaction is higher than reactants  k b (E) << k -a (E) for all E Case B: E b < E a : TS of subsequent reaction is lower than reactants  k b (E) non-negligible versus k -a (E) We will compare low- and high-pressure limits for each case. High-Pressure Limit : P =  Case A : E b > E a (k eff : small) -Overall equilibrium : k a [OH][OVOC] = k -a [PRC] (k b [PRC] negligible) thermal reactants OH+OVOC prereactive complex PRC - PRC population n(E)dE is collisionally thermalized  full thermodynamic equilibrium population n eq (E) of PRC (Maxwell-Boltzmann distribution) For all E with (RRKM with tunneling  ) Low-Pressure Limit : P = 0 Note: - for all E  E b :  (E)  1 - for E between -E well and E b : reaction only by tunneling, but  (E) << 1 When neglecting tunneling, and using  (E) = dG(E)/dE it can be shown that: When centrifugal effects on k b (E,J) are included, the derivation is similar but more complex. k eff can therefore also be written as the conventional TST expression: - No full thermodynamic equilibrium (Maxwell-Boltzmann) population of PRC - But: microcanonical equilibrium for all E  E a (detailed balance, k b (E) negligible) thermal reactants [OH+OVOC](E) prereactive complex PRC(E)  Maxwell-Boltzmann population of PRC for E  E a (rigorous proof can be provided)  k eff,0 expression  k eff, , but with a lower limit for the energy integral of E a : i.e. only tunneling is slightly reduced with respect to high-pressure limit (-E well to E a ) Tunneling is only important near top of barrier (i.e. upper kcal/mol) so effect is negligible Conclusion: if E b > E a, no pressure dependence of k eff is expected High-Pressure Limit : P =  Case B : E b < E a (k eff : large) Low-Pressure Limit : P = 0 Instead of equilibrium between thermal reactants and PRC, one has a steady state population, with for population-averaged : Collisions move the nascent population downward to below E a, where only step b can still occur, directly or by tunneling.  Higher pressures must result in a substantial increase of k eff over k eff,0 Analytically: The high-pressure population of the PRC shows an M-B shape due to fast collisional thermalisation, but the absolute magnitude of the steady-state n  (E) with respect to full thermodynamic equilibrium n eq (E) is reduced by a factor k -a /(k -a +k b ) on account of the fast subsequent step b: Such that: where the integral evaluates the thermal rate coefficient k b   at high pressure the integral includes the (large) contribution to step b of: - the population between E a and E b - the smaller tunneling contribution of the population below E b Note: k eff,  equation reduces to One has a steady state population determined by the microcanonical equilibrium at each energy level E  E a : The effective rate coefficient k eff,0 then follows directly from that steady state population Conclusion: if E b k eff,0 Conclusions Pressure dependence expected only for E b < E a, i.e. for larger k eff. This is in agreement with experimental data (except for HNO 3 +OH) Effects of tunneling and overall rotation: similar to a (small) shift of E b. Variational effects on TS a : influences value of absolute rate coefficient Graph: numerical verification by RRKM-Master Equation analyses using synthetic input data. E b = E a +1.5 kcal mol -1 Graph: numerical verification by RRKM-Master Equation analyses using synthetic input data. E b = E a -1.5 kcal mol -1 With the population-averaged k i (E): References: I.W.M. Smith, A.R. Ravishankara, J. Phys. Chem. A 106 (2002) F. De Smedt, X. V. Bui, T. L. Nguyen, J. Peeters, L. Vereecken, J. Phys. Chem. A 109 (2005) 2401 T.J. Dillon, A. Horowitz, D. Hölscher, J.N. Crowley, L. Vereecken, J. Peeters, PCCP 8 (2006) 236 W. Forst, Theory of Unimolecular Reactions, Academic Press: New York (1973) S.S. Brown, R.K. Talukdar, A.R. Ravishankara, J. Phys. Chem. A 103 (1999) 3031 S.S. Brown, J.B. Burkholder, R.K. Talukdar, A.R. Ravishankara, J. Phys. Chem. A 105 (2001) 1605