Resolving orbital pathways for intermolecular electron transfer

Over 60 years have passed since Taube deduced an orbital-mediated electron transfer mechanism between distinct metal complexes. This concept of an orbital pathway has been thoroughly explored for donor–acceptor pairs bridged by covalently bonded chemical residues, but an analogous pathway has not yet been conclusively demonstrated for formally outer-sphere systems that lack an intervening bridge. In our present study, we experimentally resolve at an atomic level the orbital interactions necessary for electron transfer through an explicit intermolecular bond. This finding was achieved using a homologous series of surface-immobilized ruthenium catalysts that bear different terminal substituents poised for reaction with redox active species in solution. This arrangement enabled the discovery that intermolecular chalcogen⋯iodide interactions can mediate electron transfer only when these interactions bring the donor and acceptor orbitals into direct contact. This result offers the most direct observation to date of an intermolecular orbital pathway for electron transfer.


Supplementary Figure 1 | Marcus theory.
A simplified poten0al energy surface for a generic electron transfer reac0on. In this diagram, the green and purple parabolas represent the energy of the donor-acceptor pair before and aaer electron transfer, respec0vely, and the blue region represents the devia0on of the reac0on coordinate from ideality due to electronic coupling. The variables described in this plot correspond to their values in the Marcus equa0on (equa0on 1 in the main text): G°ET represents the driving force for electron transfer, represents the reorganiza0on energy of the donor-acceptor pair, and HDA represents the electronic coupling factor.  , and Se-Me (green triangles) anchored to SnO2-TiO2 core-shell thin films as a func0on of iodide concentra0on in acetonitrile electrolyte. b, Plot of observed pseudo-first order rate constants for IET averaged from two different experiments (kavg) with S-Ar (purple inverted triangles) and Se-Ar (teal diamonds) anchored to SnO2-TiO2 core-shell thin films as a func0on of iodide concentra0on in acetonitrile electrolyte. In both plots, linear fits of the data for each compound are indicated by solid lines matching the color of the corresponding symbols. Comparison of the op0cal spectra of the reduced (colored lines) and oxidized (black lines) forms of the indicated compounds anchored to nano-ITO, from spectroelectrochemical analysis (Supplemental Figure 5a). The ver0cal lines represent the major op0cal transi0ons calculated with 0me-dependent density func0onal theory (TD-DFT). Each transi0on is visualized in Supplementary Table 1

Synthesis of compounds
All reagents were obtained from commercial sources and were used as received. All reac0ons were carried out under a dry nitrogen atmosphere using standard Schlenk techniques.

3,5-di(2-pyridyl)-selenoanisole (L-Se-Me).
A solu0on of 1,3-bis(2-pyridyl)-5-bromo-benzene (0.353, 1.13 mmol) in tetrahydrofuran (50 ml) was cooled to -78°C in a dry ice-acetone bath, and n-butyl lithium (1.6M in hexanes, 1.05 ml, 1.7 mmol) was added dropwise. To the resul0ng black mixture was added dimethyldiselenide (0.16 ml, 1.7 mmol) and the mixture allowed to warm slowly to room temperature overnight. The resul0ng pale brown mixture was quenched by the addi0on of methanol (45 ml) and solvent removed under high vacuum. The crude product was taken up in 25 ml dichloromethane and poured into 25 ml water. This mixture was separated and the aqueous phase extracted with 2x25 ml dichloromethane. The organic phase was dried with MgSO4 and concentrated under reduced pressure. The crude product was purified on a 28 cm silica column, elu0ng with 10% diethyl ether in toluene (Rf = 0. Hz, Ha). 13

1,3-di(2-pyridyl)-5-(2-thienyl)-benzene (L-S-Ar).
This compound was prepared following a modifica0on of a previously reported synthesis. 4  11.0 mmol) in 10 ml toluene was heated at reflux under nitrogen for 2 days. Aaer cooling to room temperature, 10 ml of saturated aqueous potassium fluoride was added and the mixture s0rred for 5.5 hours. The resul0ng black mixture was filtered, rinsed with dichloromethane, and the orange filtrate washed with 150 ml 50% saturated aqueous sodium bicarbonate. This mixture was separated, the aqueous phase extracted with dichloromethane (3x15 ml), and the combined organic phases back extracted into 1 M aqueous hydrochloric acid (3x25 ml). The acid layer was neutralized by addi0on of 1 M potassium hydroxide and the colorless suspension extracted with dichloromethane (3x25 ml). The combined organic layers were dried with potassium carbonate and concentrated to a colorless solid. The remaining impuri0es were removed by recrystalliza0on from ethanol (20 ml) yielding L-S-Ar as a colorless solid (0.213 g, 61% yield). 1

1,3-di(2-pyridyl)-5-(2-selenyl)-benzene (L-Se-Ar).
A mixture of P-Se-Ar (0.404 g, 1.11 mmol), 2t r i b u t y l s t a n n y l -p y r i d i n e ( 1 . 2 5 4 g a t 8 4 % p u r i t y , 2 . 8 m m o l ) , tetrakis(triphenylphosphine)palladium (0.070 g, 0.061 mmol), and lithium chloride (0.461 g, 10.9 mmol) in 10 ml toluene was heated at reflux for 4 days. Aaer cooling to room temperature, 10 ml of saturated aqueous potassium fluoride was added and the mixture s0rred for 4.5 hours. The resul0ng black mixture was filtered, rinsed with toluene, and the orangebrown filtrate washed with 150 ml 50% saturated aqueous sodium bicarbonate. This mixture was separated, the aqueous phase extracted with dichloromethane (3x50 ml), and the combined organic phases back extracted into 1 M aqueous hydrochloric acid (3x25 ml). The acid layer was neutralized by addi0on of 1 M potassium hydroxide and the colorless suspension extracted with DCM (5x25 ml). The combined organic layers were dried with potassium carbonate and concentrated to a colorless solid. The remaining impuri0es were removed by column chromatography on alumina (gradient elu0on from petroleum ether to diethyl ether/ petroleum ether 6:4, Rf = 0.50 in 1:1 diethyl ether/petroleum ether) yielding L-Se-Ar as a colorless solid (0.267 g, 67% yield). It was observed that this product turned yellow upon prolonged storage in air, however this impurity could be removed by recrystalliza0on from ethanol. 1   General procedure to prepare X-Me methyl esters. A mixture of the appropriate L-X-Me ligand (1 equivalent) and mercuric acetate (1 equivalent) in 20 ml dry ethanol were heated to reflux. Aaer 24 hours, lithium chloride (2.2 equivalents) was added as a solu0on in 20 ml methanol and the mixture returned to reflux for an addi0onal 15 minutes. Aaer cooling to room temperature, the mixture was poured into 100 ml water and filtered. The resul0ng colorless solid was rinsed immediately to a mixture of [Ru(Me3tctpy)Cl3] (1 equivalent) and silver tetrafluoroborate (4 equivalents) in methanol. This mixture was heated to reflux in the dark for 4 hours. The resul0ng black mixture was concentrated, taken up in dichloromethane, filtered, and concentrated to a black solid. Ini0al purifica0on was performed on a 15 cm silica column elu0ng as rapidly as possible with a 400:1 mixture of acetonitrile and 0.1M aqueous ammonium tetrafluoroborate. The resul0ng crude black solid was then purified twice on sephadex LH-20, elu0ng first with acetone, then with methanol. Finally, the complexes were dissolved in minimal dichloromethane and precipitated by the addi0on of diethyl ether, filtered, and washed with copious diethyl ether to afford X-MeMe in high purity as fine black powders.  13  Finally, the complexes were dissolved in minimal dichloromethane and precipitated by the addi0on of diethyl ether, filtered, and washed with copious diethyl ether to afford X-ArMe in high purity as fine black powders.    General procedure to produce saponified catalysts. An approximately 5 mM solu0on of the X-Me or X-Ar methyl esters in a mixture of dimethyl formamide, water, and triethylamine (3:1:1) was brought to reflux for 4 hours. The solu0on was then concentrated to a black solid, suspended in dichloromethane and collected by vacuum filtra0on to yield the corresponding free acid compound as a black powder. The protona0on state of the as-prepared compounds was ambiguous, though the compounds were presumed to be in their doubly protonated    from Evonik Industries and deposited in thin films following literature procedures. 12 Briefly, a small aliquot of the 30 wt % ITO dispersion was sonicated for 20 minutes in a sonica0on bath and diluted to 10 wt % by addi0on of hydroxypropyl cellulose suspension in ethanol (10 wt %). The resul0ng mixture was s0rred at room temperature overnight prior to use. This mixture was deposited on fluorine-doped 0n oxide coated glass (FTO, Har•ord Glass Co. Inc., 2.3 mm thick, 15 Ω cm -2 ) by doctor blading masked with Scotch™ tape. These films were then sintered under air at 450°C for 1 hour. Op0cally transparent TiO 2 thin films were prepared following literature procedures. 13 In short, 0.42 ml concentrated nitric acid was dissolved in 60 ml deionized water in a 125 ml erlenmeyer flask. The flask was covered with aluminum foil and 10 ml of 0tanium(IV) isopropoxide was added dropwise over the course of 20 minutes with vigorous s0rring. The flask was then heated and s0rred in a water bath at ~95°C for 6 hours, resul0ng in an opaque pale blue mixture. Excess water was allowed to boil away un0l the volume was reduced to 20 ml. The mixture was transferred to a Teflon-lined stainless steel acid diges0on bomb and heated to 200°C for 12 hours. The resul0ng viscous opaque white mixture was allowed to cool The metal-oxide thin films described above were func0onalized by immersion in saturated ethanol solu0ons of the saponified catalysts overnight in the dark. The func0onalized films were washed thoroughly with ethanol and stored in neat acetonitrile un0l use.

Data Availability
The data suppor0ng these findings are available from the corresponding authors upon request.

Supplementary Discussion
Stepwise equilibrium constant (KA) In principal, the observed second-order electron transfer rate, kIET, is related to the firstorder electron transfer rate, kMarcus, by an equilibrium constant, KA: 58 As men0oned in the main text, the iodide oxida0on reac0on under inves0ga0on is formally a trimolecular reac0on, however it is believed to follow a two-step mechanism of sequen0al bimolecular reac0on. [59][60][61][62] The overall observed iodide oxida0on process can therefore be separated into individual physicochemical reac0on steps represented by the scheme: Where k1f and k1r are the rate constants of associa0on/dissocia0on of the cat + ···I -adduct, k2f and k2r are the rate constants of associa0on/dissocia0on of the cat + ···I -···I -encounter complex, kMarcus is the rate of electron transfer from diiodide to cat + in the encounter complex, and kdiss is the rate of dissocia0on of the products aaer electron transfer. In this analysis, it is assumed that the product cat···I2 •-complex is unstable and will dissociate on the 0me scale of vibra0onal mo0on, kdiss ~10 13 s -1 . 63 Since, in this condi0on, kdiss is likely much larger than kMarcus, and we can therefore consider the final electron transfer step to be irreversible.
In our transient absorp0on experiments, our observed signal comes from the spectroscopic signatures of the oxidized catalyst molecules on the TiO2 surface. During the course of iodide oxida0on, these oxidized catalysts form mul0ple different complexes with iodide such that the total surface concentra0on of oxidized catalysts, in all forms, can be expressed as: Where cat+, cat·I, and cat·I·I are the surface frac0ons of free oxidized catalyst, the cat + ···Iadduct, and the cat + ···I -···I -encounter complex, respec0vely. The rate of disappearance of the oxidized catalysts is given by: (1) Because the electron transfer step in the reac0on scheme represented by Supplementary Equa0on 2 is the only irreversible step before product dissocia0on, Supplementary Equa0on 4 can be rewriBen as: Assuming the law of mass ac0on, the surface frac0ons of all oxidized catalyst species as a func0on of 0me are given as: In order to simplify this series of compe0ng rates, we can make several reasonable assump0ons regarding the rela0ve rates of these processes. First, given that cat + ···I -and cat + ···I -···I -are effec0vely electrosta0c interac0ons and no major chemical transforma0ons occur in their forma0on, we can assume that the associa0on/dissocia0on reac0ons represented by k1f/k1r and k2f/k2r are effec0vely barrier-less beyond their inherent free energy. Next, we can assume that the forma0on of the cat + ···I -···I -encounter complex is unfavorable compared to the cat + ···Iadduct because electrosta0c forces encourage the forma0on of the laBer, but impede the forma0on of the former. This no0on implies in turn that the cat + ···I -adduct will reach equilibrium with free ions quickly on the 0me-scale of cat + ···I -···I -encounter complex forma0on. Finally, because the cat + ···I -···I -encounter complex is inherently unstable, it will dissociate back to cat + ···I -and free Ion the 0me scale of molecular vibra0ons (k2r ~10 13 s -1 ) 63 such that k2r >> kMarcus, implying that the any cat + ···I -···I -encounter complexes that form are far more likely to dissociate rather than undergo electron transfer. Taking these three assump0ons together, we can consider cat+, cat·I, and cat·I·I to rapidly achieve equilibrium with each other on the 0mescale of electron transfer: (6) rate obs = k obs χ cat+,tot = k Marcus χ cat·I·I The first equilibrium constant, K1, represents the forma0on of a catalyst-iodide adduct.
These adducts have been modeled by DFT and the op0mized structures are visualized in Supplementary Figure 13. The electron stabiliza0on energy (ΔEint) from the forma0on of these adducts was obtained from: Where Ecat·I is the electronic energy of the adduct, and Ecat+ and EIare the electronic energies of the free oxidized catalysts and the free iodide ion, respec0vely. Using our computa0onal methods, EIwas found to be -295.906658157 Hartrees, and the values for Ecat+ and Ecat·I can be found in the Supplementary Data 1 file associated with this manuscript along with their corresponding molecular coordinates. The values of ΔEint for each catalyst compound are presented in Supplementary Table 3. If we assume the free energy of adduct forma0on (ΔGint) to be approximately equal to the electronic stabiliza0on energy, then we can calculate K1 at T = 298 K from the free energy expression: The values of K1 obtained by this method are presented in Supplementary Table 3. The second equilibrium constant, K2, represents the approach of a second iodide to a contact distance with the iodide in the cat + ···I -adduct, forming an encounter complex. To obtain this value, we have employed the model of N. Su0n for the associa0on constant of free ions in solu0on (Kion) with center-to-center distances in the range of r to r+δr: 64 Where S is a steric correc0on factor accoun0ng for restricted access to one of the ions, NA is Avogadro's number, w(r) is a func0on defining the thermodynamic work (vide infra), and the remaining terms have their standard defini0ons. For the purposes of this analysis, it was assumed that electron transfer occurs when the iodide ions are at a contact distance defined twice their ionic radii (r = 4.24 Å), and δr was set at r/3, a value which has been shown to give reasonable values for ion associa0on. 65 Because the cat + ···I -adduct is anchored to a surface, it was assumed that the second iodide equivalent could only approach from half of the spherical volume surrounding the adduct, and therefore S = ½ was used. In Supplementary Equa0on 17, w(r) represents the thermodynamic work of bringing two ions in solu0on from an infinite distance to a center-to-center distance of r, and is given by: 64,66 Where z1 and z2 are the charges of the two ions, σ1 and σ2 are the radii of two ions (2.12 Å for iodide), is the elementary charge, DS is the sta0c absolute permitvity of the solvent (DS = 5.06x10 -39 C 2 eV -1 Å -1 for acetonitrile), µ is the ionic strength of the solvent (0.5 M in the current study), and the remaining terms have their standard defini0ons. Using Supplementary  Equa0ons 17 and 18, and assuming that the work term is en0rely due to two iodides coming into contact, we obtain a value of K2 = 3.64x10 -5 M -1 . Both terms can be evaluated simultaneously using DFT methods. 67,68 By taking the differences in electronic energies of the reactant pair before electron transfer at their op0mized geometries, with an equilibrium PCM-modeled solvent shell, and at their non-equilibrium geometry (defined as the op0mized geometries of the product pair aaer electron transfer), with the iner0al charges of the solvent set to values corresponding to the non-equilibrium geometry, we can obtain a reasonable es0ma0on of the overall value. In order to simplify these calcula0ons, can instead be divided into individual terms trea0ng the electron donor and acceptor separately: Where cat+ is the reorganiza0on energy of the catalysts and 2I-is the reorganiza0on energy of the iodide ions. Using the DFT models developed for the X-Me and X-Ar series, cat+ was determined to be between 0.78 and 0.83 eV for all compounds. The value for 2I-was taken from literature as 0.522 eV. 68 Combining these values, we obtain the total for iodide oxida0on (Supplementary Table 3).

Formal overlap integral (S°DA)
In order to evaluate our orbital pathway hypothesis, it was necessary to es0mate the overlap integral between isolated iodide and chalcogen atoms. During the electron transfer reac0on, the geometry of the transient pre-electron transfer [Ox···I -···I -] encounter complex is unknown, however there are only two relevant interac0ons: either the iodide interacts with the chalcogen in the plane of the beta-LUMO, whereupon the chalcogen-iodide orbital overlap relevant to electron transfer is a pi-type overlap between the valence p-orbitals of both atoms, or the iodide interacts orthogonal to the beta-LUMO, whereupon the relevant overlap will be sigma-type. If we assume that both interac0ons are possible, collision theory states that both will occur and therefore the larger overlap will dominate the electron transfer mechanism. At a fixed inter-nuclear distance, this will necessarily be the sigma-type interac0on, and therefore, for the purpose of calcula0ng S°DA, the relevant overlap is assumed to be sigma-type at the van der Waals distance between the chalcogen and iodide. Using these assump0ons, the integral can be calculated as the overlap between Slater-type orbitals of two atoms a and b at a distance R using equa0ons developed by Mulliken. 69 To simplify the equa0ons, these integrals are defined in terms of spheroidal coordinates ξ=(ra+rb)/R and η=(ra-rb)/R, where ra and rb are the distances from a point in space to atoms a and b, respec0vely, and R is the separa0on between a and b. For a sigma-type interac0on between p-orbitals with principal quantum number n, the equa0on for the overlap integral takes the form: where and the variables mj, Nj, and µj are defined for a given atom j by: Visualiza0ons of each of the TD-DFT calculated op0cal transi0ons indicated in Supplementary  Figure 12 as electron density difference maps (EDDMs). The purple regions represent a nega0ve change in electron density, while the green regions represent a posi0ve change in electron density. All EDDMs were ploBed at an isodensity of 0.0025. The inset numbers indicate the absolute transi0on number which are detailed in the Supplementary Data 2 file associated with this manuscript. calculated molecular orbitals (MOs), ploBed at an iso value of 0.05. The reduced ruthenium complexes were modeled using a restricted func0onal, and therefore the MOs represent 2electron orbitals. The oxidized complexes were modeled using an unrestricted func0onal, and therefore the MOs represent one-electron orbitals, split between alpha and beta spins, as indicated.