ARTICLE pubs.acs.org/JPCA
Density Functional Reactivity Theory Characterizes Charge Separation Propensity in Proton-Coupled Electron Transfer Reactions Shubin Liu,*,† Daniel H. Ess,‡,§ and Cynthia K. Schauer§ †
Research Computing Center, University of North Carolina, Chapel Hill, North Carolina 27599-3420, United States Department of Chemistry and Biochemistry, Brigham Young University, Provo, Utah 84602, United States § Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, United States ‡
ABSTRACT: Proton-coupled electron transfer (PCET) reactions occur in many biological and artificial solar energy conversion processes. In these reactions the electron is often transferred to a site distant to the proton acceptor site. In this work, we employ the dual descriptor and the electrophilic Fukui function from density functional reactivity theory (DFRT) to characterize the propensity for an electron to be transferred to a site other than the proton acceptor site. The electrophilic regions of hydrogen bond or van der Waal reactant complexes were examined using these DFRT descriptors to determine the region of space to which the electron is most likely to be transferred. This analysis shows that in PCET reactions the electrophilic region of the reactant complex does not include the proton acceptor site.
I. INTRODUCTION In the proton-coupled electron transfer (PCET) mechanism14 a proton and electron can be synchronously or asynchronously transferred to different orbitals or sites of a molecular system (Scheme 1). This is in contrast with the hydrogen atom transfer (HAT) mechanism5,6 where the proton and electron are transferred to the same final location in a radical pathway. PCET is significant in many biological and solar energy conversion processes, including photosynthesis in the oxygen evolving complex of photosystem II7,8 and cytochrome P450.2,911 PCET was popularized after its discovery as the mechanism involved in the redox chemistry of ruthenium bipyridine complexes2 and has since been the focus of intense experimental and theoretical investigation.1,12 A key feature of these biological and organometallic PCET mechanisms is that an electron is often transferred to a site distant from the proton acceptor site (Scheme 1).1,2,1214 In this contribution, as an alternative to the common orbital and kinetics based descriptions of PCET reaction mechanisms, we present a density-based, thermodynamic-like description that may be used to show the propensity for an electron to be transferred to a site other than the proton acceptor site. To this end, we have examined hydrogen bond and van der Waal reactant complexes of well-known electronproton transfer reactions using reactivity descriptors from density functional reactivity theory (DFRT).1517 Also called chemical density functional theory (chemical DFT) or conceptual DFT, DFRT uses concepts and formalisms from DFT to obtain qualitative and quantitative insights into chemical reactivity. DFRT has rapidly matured since the 1980s1517 with the renaissance of the chemical potential function, equivalent to electronegativity, and has developed into useful reactivity indexes such as hardness, r 2011 American Chemical Society
softness, the Fukui function, and electrophilicity.1517 Recent developments include the dual descriptor,18,19 molecular acidity,20,21 and steric effect.2224 In this work, we have employed the dual descriptor and electrophilic Fukui function to characterize the PCET mechanism for organic reactions involving phenol and oxygen centered radicals,12,33 inorganic reactions involving ruthenium bipyridine self-exchange reaction,34,35 ruthenium terpyridylbenzoate reaction with hydroxylamine TEMPOH, and reaction of Cp(CO)2Os with 1,4-cyclohexadiene,36 and biological reactions involving model heme9,11 and photosystem II systems.38
II. METHODOLOGY AND COMPUTATIONAL DETAILS Density-based reactivity descriptors are a part of DFRT. They characterize changes in the electron density and other density related quantities when electrons are added to or removed from a molecular system. The central quantity of this work is the dual descriptor in DFRT, defined as25,26 Df ðrÞ ð2Þ f ðrÞ ¼ ð1Þ DN ν where N is the total number of electrons in the system, ν is the external potential from the atomic nuclei, and f(r) is the Fukui function.16 The Fukui function (f) relates the change in electron density, F(r), with change in electron number, N, at a constant external potential, ν(r), from atomic nuclei, f(r) = (δF(r)/δN)ν. The Fukui function is normalized to one, is discontinuous, and it Received: December 28, 2010 Revised: February 14, 2011 Published: April 20, 2011 4738
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Scheme 1
has two distinct expressions. To feature the electrophilic capability of a system, one uses f þ ðrÞ ¼ FN þ 1 ðrÞ FN ðrÞ FLUMO ðrÞ
ð2Þ
and to measure its nucleophilic power, one employs f ðrÞ ¼ FN ðrÞ FN 1 ðrÞ FHOMO ðrÞ
ð3Þ
where FNþ1(r), FN(r), and FN1(r) denote the electron density for the N þ 1, N, and N 1 systems, respectively, with the molecular structure held fixed and FLUMO(r) and FHOMO(r) are the LUMO and HOMO densities, respectively. The first equality in eqs 2 and 3 is from the finite difference approximation and the second approximate equality uses the frozen orbital approximation. The fþ(r)/f(r) function measures the response of the electron density change following an addition/removal of an electron and thus it is a reactivity descriptor to quantify electrophilicity/nucleophilicity. Under the above two approximations, dual descriptor becomes f ð2Þ ðrÞ ¼ f þ ðrÞ f ðrÞ FLUMO ðrÞ FHOMO ðrÞ
ð4Þ
Within a molecule, the electrophilic region has a positive f(2)(r) function, marked by red on its contour surface in this work, as fþ(r) or FLUMO(r) is dominant; the nucleophilic region has a negative f(2)(r) function, marked by green on its contour surface here, as f(r) or FHOMO(r) is prevailing.2630 The dual descriptor f(2)(r) provides a framework to identify electrophilic and nucleophilic molecular regions in a donoracceptor complex. If these electrophilic and nucleophilic regions are sufficiently separated (not overlapped) in space, there will be a propensity for charge separation. When f(2)(r) is plotted over a supramolecular complex consisting of the reactants, an electrophilic region is indicated by a positive f(2)(r) function value (red region) and a nucleophilic region is indicated by a negative f(2)(r) function value (green region). The complex is aligned with an assumption of the direction of proton transfer. The location of the electron transfer might be determined by the electrophilic region from the dual descriptor or electrophilic Fukui function quantities. If the electrophilic region does not include the proton acceptor site, then spatial separation between the proton and electron transfer may occur in a PCET mechanism. We note that the transition state for electronproton transfer may be more appropriate, but test calculations show similar results. In addition, our current approach is thermodynamic in nature not kinetic. It cannot predict whether concerted or stepwise electronproton transfer will occur. All calculations were performed at the DFT B3LYP level of theory.31,32 The Pople 6-311þG(d) basis set was employed except for Ru and Os for which we used the effective core LANL2DZ basis set with tight SCF convergence and ultrafine integration grids. For transition metal systems, only the lowest
Figure 1. Plot of dual descriptor contour surfaces (value of 0.0004 au) for reactant complexes of (a) ArOH þ ArO• and (b) ArOH þ CH3OO• reactions. Surfaces in red are the electrophilic regions and those in green are nucleophilic regions. A proton/charge transfer separation is seen in (a) but not in (b).
energy ground spin state was analyzed. For the heme model, this was a quintet state. For the Ru and Os systems the singlet state was found to be the ground state. For open-shell systems,39 the highest-occupied β orbital was used to calculate the LUMO density in eqs 3 and 4 because it has lower energy than the R counterpart. For the photosystem II model system, the crystal structure of photosystem II from Thermosynechococcus elongatus (PDB ID 2axt) was used.38 An ONIOM model was built with TYR161, HIS190, and P680 as the higher layer and residues within 5 Å of the high layer as the lower layer. Hydrogen atoms were added, and then their coordinates were optimized at the ONIOM(B3LYP/6-31G*:AM1) level of theory, with all nonhydrogen atoms held fixed. The final 188-atom model was used to calculate its dual descriptor at the DFT B3LYP/6-31G(d) level of theory. In this work, we employed the frozen orbital approximation for the Fukui functions, fþ(r) and f(r), and then for the dual descriptor, f(2)þ(r), where fþ(r) ≈ FLUMO(r), f(r) ≈ FHOMO(r), and f(2)(r) ≈ FLUMO(r) FHOMO(r). Our tests have shown that no qualitative differences existed between the finite difference and frozen orbital difference results for these quantities. The cubman Gaussian utility was used to generate cube files for the HOMO and LUMO orbitals and densities.
III. RESULTS AND DISCUSSION Experimental and theoretical evidence suggests that the electron and proton transfer reaction between phenol and ArO• radical proceeds through a PCET mechanism.12,33 Figure 1a shows the duel descriptor plot for the reactant complex of phenol with ArO• radical. The electron-donating (nucleophilic) region (green) is located on the phenol π-system and the electronaccepting (electrophilic) region (red) is on the π-system of the ArO• radical. Most important from this analysis is that there is no red surface located on the oxygen atom of ArO•, showing that this site is not the most electrophilic site of the complex. This suggests that an electron may be transferred to the aryl π-system rather than the oxygen atom center, leading to charge separation in a PCET mechanism. The electron and proton transfer reaction between phenol and the methyl peroxide radical ROO• (ROO•, R = CH3) is thought to occur through a HAT mechanism. Figure 1b shows the dual descriptor plot for the reactant complex of phenol with the ROO• radical. In contrast to the above reaction, the proton is transferred to an oxygen atom that has significant electrophilic character (covered by red surfaces), suggesting that charge separation is less likely for this reaction.33 A well-known biological PCET reaction involves the transfer of an electron and proton from water to an oxygen bound heme 4739
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Figure 2. (a) Model heme structure and (b) the dual descriptor contour surface of the heme model at the value of 0.0004 au. With discernible proton/ charge transfer separation, the reaction proceeds through the PCET mechanism.
Figure 3. Dual descriptor contour surface at the value of 0.0004 au for the cis-[(byp)2(py)RuIV(O)]2þ and cis-[(byp)2(py)RuII(OH2)]2þ reactant complex. With discernible proton/charge transfer separation, the reactions proceeds through the PCET mechanism.
(Figure 2a).2,911 In our heme model system, the oxygen binds to the iron center with a quintet spin state. Figure 2b plots the contour surface of the dual descriptor and shows that the electrophilic regions are located on the porphyrin ring that is distant from the proton acceptor site, the terminal oxygen atom at the FeO2 motif. This indicates that when the proton is transferred from H2O to O2, the electron may be transferred in a different direction toward the porphyrin ring. Next, we have analyzed the protonelectron transfer reaction between cis-[(byp)2(py)RuIV(O)]2þ and cis-[(byp)2(py)RuII(OH2)]2þ. Experimentally, a PCET mechanism has been proposed in this self-exchange reaction:1,13,34,35 cis-½ðbypÞ2 ðpyÞRuIV ðOÞ2þ þcis-½ðbypÞ2ðpyÞRuIIðOH2 Þ2þ f 2 cis-½ðbypÞ2ðpyÞRuIIIðOHÞ2þ Figure 3 shows the reactant complex of [(byp)2(py)RuIV(O)]2þ and [(byp)2(py)RuII(OH2)]2þ and the plotted dual descriptor surface. The nucleophilic region (green) is located on the [(byp)2(py)RuII(OH2)]2þ complex while the electrophilic region (red) is located on one of the bipyridine ligands of the [(byp)2(py)RuIV(O)]2þ complex. No electrophilic surface is observed on the Ru(IV)O bond of [(byp)2(py)RuIV(O)]2þ, which is the site of proton transfer. This indicates that when the water proton is transferred to the oxygen atom of the Ru(IV) oxo, an electron from the [(byp)2(py)RuII(OH2)]2þ complex is
Figure 4. Electrophilic Fukui function contour surface (red) at 0.0004 au for (a) ruthenium terpyridylbenzoate þ hydroxylamine TEMPOH and (b) Cp(CO)2Os and 1,4-cyclohexadiene systems. A proton/charge transfer separation is seen in (a) but not in (b).
transferred to the bipyridine ligand of [(byp)2(py)RuIV(O)]2þ.1,13,34,35 The electrophilic Fukui function,16 eq 2, can also be used as an alternative to the dual descriptor function. Figure 4a shows the electrophilic Fukui function contour surface for the ruthenium terpyridylbenzoate complex with hydroxylamine TEMPOH.36 This is another example where experiment has suggested a PCET pathway.36 The electrophilic Fukui function plotted in Figure 4a is located only on the terpyridine part of the terpyridylbenzoate ligand. This is 10 bonds and 11.2 Å in space between the metal (Ru) and carboxylate group, which is the site of proton transfer. Shown in Figure 4b is the electrophilic Fukui function plot for an osmium centered radical, Cp(CO)2Os•, weakly coordinated to 1,4-cyclohexadiene. In this reaction, Cp(CO)2Os• abstracts a hydrogen atom through the HAT mechanism to give Cp(CO)2OsH.37 The electrophilic Fukui function plotted in 4740
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Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001011. We acknowledge the use of the computational resources provided by the Research Computing Center at University of North Carolina at Chapel Hill. D. H.E. thanks BYU for financial support.
’ REFERENCES
Figure 5. Dual descriptor contour surfaces (0.0004 au) for the photosynthesis II protein model (PDB ID 2axt).
Figure 4b shows that the proton acceptor site at the osmium metal center has significant electrophilic character (red) and suggests it is likely that the proton and electron will transfer to the same place. Lastly, Figure 5 shows a QM/MM model system of the photosystem II reaction center (PDB ID 2axt) and the plotted dual descriptor function.38 This is also a well-studied system and the mechanism is widely accepted to be PCET.14 The proton is transferred from tyrosine 161 (Tyr161) to histidine 190 (His190), and a long-range (ca. 10 Å) electron transfer occurs from Tyr161 to P680.14 The plotted dual descriptor contour surface shows that the electron that originates from the nucleophilic tyrosine π system will likely be transferred to the electrophilic region that is concentrated on P680, consistent with the proposed PCET mechanism.14
IV. CONCLUSIONS In biological and organometallic PCET reactions an electron is often transferred to a different site than the proton. Here we showed that reactivity descriptors such as the dual descriptor and the electrophilic Fukui function from density functional reactivity theory (DFRT) can characterize the propensity for an electron and proton to transfer to separate locations. This was done by examining the electrophilic regions of reactant complexes. This analysis revealed that in PCET reactions the electrophilic region of the reactant complex did not include the proton acceptor site. In contrast, for HAT reactions the electrophilic region of the complex includes the proton acceptor site. Again, we note that this approach is thermodynamic in nature and does not provide kinetics or dynamics related information. However, this density-based description provides an alternative to typical orbital analyses. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT Helpful discussion with Robert G. Parr, Thomas J. Meyer, and Lee G. Pedersen of University of North Carolina at Chapel Hill is gratefully acknowledged. This work was supported in part by UNC EFRC: Solar Fuels and Next Generation Photovoltaics, an
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