Dynamics of proton transfer reactions in polar solvent in the non-adiabatic two-state approximation: test calculations for carbon-carbon reaction centre

doi:10.1016/0301-0104(96)00058-4

Chemical Physics

Volume 208, Issue 2, 1 August 1996, Pages 267-282

https://doi.org/10.1016/0301-0104(96)00058-4 Get rights and content

Abstract

The quantum dynamics of a proton (PT) reaction in a polar solvent, treated as continuum, is considered taking as an example the PT process Flu⁻ + HFlu → HFlu + Flu⁻ in ether, where FluH means fluorene. Using the model three-dimensional free-energy surface (FES) derived from quantum-chemical SCRF calculations, the dynamical description is reduced to a two-level stochastic Liouville equation in the two-dimensional subspace spanned by the solute vibrational mode (representing a relative motion of heavy atoms constituting the PT reaction centre) and a solvent collective coordinate. The two quantum states involved in a reactive event are a pair of lowest proton levels obtained by means of quantum-mechanical averaging the basic three-dimensional FES. The new methodology of a direct evaluation of the coupling matrix element is elaborated. The rate calculation involves a treatment of extremely small (∼ 10⁻⁵ -10⁻¹⁰) transmission factors for which two different approximate non-adiabatic approaches are tested. The whole variety of experimental data on reaction (a) involving both the absolute values of the rate constant (K^H) and the $H D$ isotope effect cannot be consistently described within the present two-level scheme.

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Cited by (17)

Semiempirical modeling free energy surfaces for proton transfer in polar aprotic solvents
2000, Chemical Physics
Citation Excerpt :
The cross-sections of LEPS-3 surface along R and Z represent single-well potentials. Quantum-mechanical averaging LEPS-3 was performed by solving one-dimensional s-dependent Schrödinger equation [45] for given pairs of heavy-particle coordinates R and Z. Most interesting characteristics of the ground-state electron–proton FES-2 are given in Table 4. Averaging over the proton coordinate reduces the barrier from 7.0 to 1.2 kcal/mol and shifts the TS along the R-direction.
A method of calculation of a free-energy surface (FES) of the proton transfer (PT) reaction in a polar aprotic solvent is developed. This is based on the two-state (valence bond) VB description of the solute combined with recent continuum medium models. Its essential new feature is an explicit quantum-chemical treatment of VB wave functions, including internal electronic structure of a chemical subsystem. The FES includes a pair of intrasolute coordinates, R, the distance between hydrogen-bonded atoms and s, the proton coordinate, together with the collective medium polarization mode. Two hydrogen-bonded systems immersed in a polar solvent (Freon) were considered. The first one is the H₅O₂⁺ ion, a model system which was used as a benchmark testifying the validity of our semiempirical calculations. The second system is the neutral (CN)(CH₃)N–H⋯N(CH₃)₃ complex in Freon. PT for this system has been studied experimentally. The dependencies of basic parameters controlling FES properties (the overlap integral, the coupling matrix element and the reorganization energy E_r) on intrasolute coordinates R and s are evaluated and discussed. In particular, for the neutral complex, E_r depends on s linearly, and its dependence on R is weak. The FES, for the neutral system, has two potential wells separated by the energy barrier of ∼7 kcal/mol. Quantum-mechanical averaging over the proton coordinate, s, reduces the barrier from 7.0 to 1.2 kcal/mol. The value of the nonadiabatic parameter on the averaged FES is equal to 0.13. This implies that the PT in the second system corresponds to an intermediate dynamic regime and that proton tunneling effects are hardly significant for this reaction.
Non-equilibrium interlevel transitions in condensed phase far away from the avoided crossing region
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The quantum-classical dynamics of interlevel transitions in condensed phase is considered in a special case when the transitions are localized far away from the avoided crossing region on the ground state free energy surface. A resonance case of a transition is studied when the two energy levels have the same shapes and equilibrium positions and are only shifted on the energy axis. For this simplified model the analytical expression for the non-equilibrium rate constant was derived starting from the multichannel Smoluchowski equations in the high-temperature limit. A deficiency of the existing multichannel diffusion theory is revealed and discussed. The illustrative calculations were performed for the model of proton transfer (PT) reaction in condensed phase. The results support the conclusion that the earlier proposed two-state model exaggerates the role of tunneling in PT processes.
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A collective medium coordinate (CMC) represents a highly correlated motion of a large ensemble of medium particles, which, as a single variable, undergoes a significant change during a chemical process proceeding in this medium. CMCs naturally arise when charge transfer reactions in polar solvents are considered. In this context, the most important problems addressed by the CMC theory are:
- 1.
  (1) quantum chemical computations of free energy surfaces explicitly treating a CMC as an essential coordinate, including location of minimum (reactants and products) and saddle (transition states) points on these surfaces;
- 2.
  (2) derivation of stochastic dynamical equations for CMCs and evaluation of their parameters, such as masses, friction coefficients, etc.;
- 3.
  (3) deduction of the rate expression for stochastic dynamical systems including CMCs.
These problems are discussed using as examples electron and proton transfer and S_N2 reactions. Qualitative criterion formulated for when an explicit consideration of a CMC is absolutely necessary and when it can be discarded.
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¹: Present address: Theoretische Chemie, Universität Hannover, Am Kleinen Felde 30, D-30167 Hannover, Germany.

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Dynamics of proton transfer reactions in polar solvent in the non-adiabatic two-state approximation: test calculations for carbon-carbon reaction centre

Abstract

Chem. Phys.

Chem. Phys.

J. Chem. Phys.

J. Mol. Liquids

Chem. Phys.

Chem. Phys.

Chem. Phys.

Chem. Phys.

Chem. Phys.

Chem. Phys.

Chem. Phys. Letters

J. Chem. Phys.

J. Chem. Phys.

J. Chem. Phys.

Charge transfer in condensed media

Electrochim. Acta

J. Chem. Soc. Faraday Trans. II

J. Chem. Phys.

J. Phys. Chem.

J. Chem. Phys.

J. Chem. Phys.

J. Am. Chem. Soc.

J. Am. Chem. Sec.

J. Chem. Phys.