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Biochemistry and theory of proton-coupled electron transfer.

Migliore A, Polizzi NF, Therien MJ, Beratan DN - Chem. Rev. (2014)

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Affiliation: Department of Chemistry, ‡Department of Biochemistry, and §Department of Physics, Duke University , Durham, North Carolina 27708, United States.

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(a) Typical (free) energyprofile for ET or PCET along a reactioncoordinate x (see the main text) and (b) its magnificationnear the transition-state coordinate (origin of the abscissa), usingthe diabatic energy difference Δ12(x) as the reaction coordinate.121,216,222 Both diabatic (dashed lines) and adiabatic (solid lines) curvesare illustrated. Panel a qualitatively represents a case of electronicallyadiabatic reaction under the two-state approximation. However, thediabatic states ϕ1 and ϕ2 can stillbe used as a basis, and their connection with the electronic adiabaticstates ϕ12ad and ϕ̃12ad is summarized in the inset, where H0 is the channel Hamiltonian and V is a constant(Condon approximation) interaction component of the Hamiltonian. Thedependence of H0 on x can be formulated in terms of Δ12. ϕ12ad and ϕ̃12ad are eigenfunctionsof the electronic Hamiltonian for each Δ12.
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fig24: (a) Typical (free) energyprofile for ET or PCET along a reactioncoordinate x (see the main text) and (b) its magnificationnear the transition-state coordinate (origin of the abscissa), usingthe diabatic energy difference Δ12(x) as the reaction coordinate.121,216,222 Both diabatic (dashed lines) and adiabatic (solid lines) curvesare illustrated. Panel a qualitatively represents a case of electronicallyadiabatic reaction under the two-state approximation. However, thediabatic states ϕ1 and ϕ2 can stillbe used as a basis, and their connection with the electronic adiabaticstates ϕ12ad and ϕ̃12ad is summarized in the inset, where H0 is the channel Hamiltonian and V is a constant(Condon approximation) interaction component of the Hamiltonian. Thedependence of H0 on x can be formulated in terms of Δ12. ϕ12ad and ϕ̃12ad are eigenfunctionsof the electronic Hamiltonian for each Δ12.

Mentions: Equation 5.43 is the Schrödinger equationfor the (reactive) electron atfixed nuclear coordinates within the BO scheme. Therefore, ϕαad is theelectronic component of a BO product wave function that approximatesan eigenfunction of the total Hamiltonian at x valuesfor which the BO adiabatic approximation is valid. In fact, theseadiabatic states give Vαβ = Eαδαβ, butcorrespond to (approximate) diagonalization of the full Hamiltonian (eq 5.1) only forsmall nonadiabatic kinetic coupling terms. We now (i) analyze andquantify, for the simple model in Figure 24, features of the nonadiabatic coupling between electronic statesinduced by the nuclear motion that are important for understandingPCET (therefore, the nonadiabatic coupling terms neglected in theBO approximation will be evaluated in the analysis) and (ii) showhow mixed electron–proton states of interest in coupled ET–PTreactions are derived from the analysis of point i.


Biochemistry and theory of proton-coupled electron transfer.

Migliore A, Polizzi NF, Therien MJ, Beratan DN - Chem. Rev. (2014)

(a) Typical (free) energyprofile for ET or PCET along a reactioncoordinate x (see the main text) and (b) its magnificationnear the transition-state coordinate (origin of the abscissa), usingthe diabatic energy difference Δ12(x) as the reaction coordinate.121,216,222 Both diabatic (dashed lines) and adiabatic (solid lines) curvesare illustrated. Panel a qualitatively represents a case of electronicallyadiabatic reaction under the two-state approximation. However, thediabatic states ϕ1 and ϕ2 can stillbe used as a basis, and their connection with the electronic adiabaticstates ϕ12ad and ϕ̃12ad is summarized in the inset, where H0 is the channel Hamiltonian and V is a constant(Condon approximation) interaction component of the Hamiltonian. Thedependence of H0 on x can be formulated in terms of Δ12. ϕ12ad and ϕ̃12ad are eigenfunctionsof the electronic Hamiltonian for each Δ12.
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fig24: (a) Typical (free) energyprofile for ET or PCET along a reactioncoordinate x (see the main text) and (b) its magnificationnear the transition-state coordinate (origin of the abscissa), usingthe diabatic energy difference Δ12(x) as the reaction coordinate.121,216,222 Both diabatic (dashed lines) and adiabatic (solid lines) curvesare illustrated. Panel a qualitatively represents a case of electronicallyadiabatic reaction under the two-state approximation. However, thediabatic states ϕ1 and ϕ2 can stillbe used as a basis, and their connection with the electronic adiabaticstates ϕ12ad and ϕ̃12ad is summarized in the inset, where H0 is the channel Hamiltonian and V is a constant(Condon approximation) interaction component of the Hamiltonian. Thedependence of H0 on x can be formulated in terms of Δ12. ϕ12ad and ϕ̃12ad are eigenfunctionsof the electronic Hamiltonian for each Δ12.
Mentions: Equation 5.43 is the Schrödinger equationfor the (reactive) electron atfixed nuclear coordinates within the BO scheme. Therefore, ϕαad is theelectronic component of a BO product wave function that approximatesan eigenfunction of the total Hamiltonian at x valuesfor which the BO adiabatic approximation is valid. In fact, theseadiabatic states give Vαβ = Eαδαβ, butcorrespond to (approximate) diagonalization of the full Hamiltonian (eq 5.1) only forsmall nonadiabatic kinetic coupling terms. We now (i) analyze andquantify, for the simple model in Figure 24, features of the nonadiabatic coupling between electronic statesinduced by the nuclear motion that are important for understandingPCET (therefore, the nonadiabatic coupling terms neglected in theBO approximation will be evaluated in the analysis) and (ii) showhow mixed electron–proton states of interest in coupled ET–PTreactions are derived from the analysis of point i.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemistry, ‡Department of Biochemistry, and §Department of Physics, Duke University , Durham, North Carolina 27708, United States.

Show MeSH