Correction

CHEMISTRYCorrection for “Calculation of thermodynamic hydricities andthe design of hydride donors for CO2 reduction,” by James T.Muckerman, Patrick Achord, Carol Creutz, Dmitry E. Polyansky,and Etsuko Fujita which appeared in issue 39, September 25,2012, of Proc Natl Acad Sci USA (109:15657–15662; first pub-lished July 23, 2012; 10.1073/pnas.1201026109).The authors note that on page 15659, left column, first paragraph,

line 9, “−393.3 kcal/mol” should instead appear as “−391.4 kcal/mol.”Additionally, on page 15659, left column, fourth full paragraph,

line 4, “(266.5 kcal/mol)” should instead appear as “(−266.5 kcal/mol).”Both the online article and print article have been corrected.

www.pnas.org/cgi/doi/10.1073/pnas.1214762109

www.pnas.org PNAS | September 25, 2012 | vol. 109 | no. 39 | 15965

CORR

ECTION

Dow

nloa

ded

by g

uest

on

Feb

ruar

y 1,

202

1 D

ownl

oade

d by

gue

st o

n F

ebru

ary

1, 2

021

Dow

nloa

ded

by g

uest

on

Feb

ruar

y 1,

202

1 D

ownl

oade

d by

gue

st o

n F

ebru

ary

1, 2

021

Dow

nloa

ded

by g

uest

on

Feb

ruar

y 1,

202

1 D

ownl

oade

d by

gue

st o

n F

ebru

ary

1, 2

021

Dow

nloa

ded

by g

uest

on

Feb

ruar

y 1,

202

1 D

ownl

oade

d by

gue

st o

n F

ebru

ary

1, 2

021

Calculation of thermodynamic hydricities and thedesign of hydride donors for CO2 reductionJames T. Muckerman1, Patrick Achord, Carol Creutz, Dmitry E. Polyansky, and Etsuko Fujita

Chemistry Department, Brookhaven National Laboratory, Upton, NY 11973

Edited by Thomas J. Meyer, University of North Carolina at Chapel Hill, Chapel Hill, NC, and approved June 26, 2012 (received for review January 18, 2012)

We have developed a correlation between experimental and den-sity functional theory-derived results of the hydride-donatingpower, or “hydricity”, of various ruthenium, rhenium, and organichydride donors. This approach utilizes the correlation betweenexperimental hydricity values and their corresponding calculatedfree-energy differences between the hydride donors and their con-jugate acceptors in acetonitrile, and leads to an extrapolated valueof the absolute free energy of the hydride ion without the neces-sity to calculate it directly. We then use this correlation to predict,from density functional theory-calculated data, hydricity values ofruthenium and rhenium complexes that incorporate the pbnHHligand—pbnHH ¼ 1,5-dihydro-2-(2-pyridyl)-benzo[b]-1,5-naphthyr-idine—to model the function of NADPH. These visible light-gener-ated, photocatalytic complexes produced by disproportionation ofa protonated-photoreduced dimer of a metal-pbn complex may bevaluable for use in reducing CO2 to fuels such as methanol. The ex-cited-state lifetime of photoexcited ½RuðbpyÞ2ðpbnHHÞ�2þ is foundto be about 70 ns, and this excited state can be reductivelyquenched by triethylamine or 1,4-diazabicyclo[2.2.2]octane to pro-duce the one-electron-reduced ½RuðbpyÞ2ðpbnHHÞ�þ species withhalf-life exceeding 50 μs, thus opening the door to new opportu-nities for hydride-transfer reactions leading to CO2 reduction byproducing a species with much increased hydricity.

Natural photosystems in plants convert CO2 to carbohydratesusing absorbed photons for energy and water as a reducing

agent. The light energy is converted to chemical energy in theform of ATP and reduced NADH in a complex sequence in whicha reduced hydrogen equivalent (i.e., hydride) is stored by thereduction of NADþ. The ATP and NADH are used to reduceCO2 in light-independent processes through net hydride iontransfer reactions. In artificial photochemical CO2 reduction, COand formate have been successfully produced (1); however, it isvery difficult to produce methanol and methane because of theinvolvement of more than two electrons and two protons. We pre-viously obtained clear evidence of photochemical and radio-lytic formation of the reduced form of a transition-metal complexhaving a NADH-like ligand (2), and this reduced form has beenshown separately to catalyze the reduction of acetone to 2-pro-panol under acidic conditions (3) and to transfer a hydride ion tothe trityl cation (4). These results opened a new door for photo-catalytic hydride (or proton-coupled electron) transfer reactionsoriginating from metal-to-ligand charge-transfer (MLCT) excitedstates of metal complexes. It has been shown that M─CO2

2−

can be converted to M─CO by acid-base reaction, and thatNaBH4 can reduceM─CO toM─CHO−,M─CH2OH− (precur-sor of methanol), and M─CH3

− (a precursor of methane), whenM ¼ RuðbpyÞ2ðCOÞ2þ (5, 6). NaBH4 can also reduce M─CO toM─CHO−, M─CH2OH−, and M─CH3

−, when M ¼ ReðCpÞðNOÞðCOÞþ (7). Can we use photogenerated hydride donors asa replacement for NaBH4? How strong is ½RuðbpyÞ2ðpbnHHÞ�2þas a hydride donor?

In the present work we report the results of photoexcitationof and reductive quenching of this reduced form of the modelcomplex and investigate the thermodynamic hydricities of the re-duced 2-(2-pyridyl)-benzo[b]-1,5-naphthyridine (pbn) complexesthrough density functional theory (DFT)-based computations.

Koizumi and Tanaka (3) reported the electrocatalytic abilityof ½RuðbpyÞ2ðpbnÞ�2þ (bpy ¼ 2,2′-bipyridine; see Fig. 1) for thereduction of acetone to isopropanol, presumably with ½RuðbpyÞ2ðpbnHHÞ�2þ—pbnHH ¼ 1,5-dihydro-2-(2-pyridyl)-benzo[b]-1,5-naphthyridine—as the key intermediate. It has been proposedthat this complex can act as a catalyst because it contains bulkybpy ligands that protect against the formation of the Ru dimer viacoupling of the C-centered radicals. In collaboration with Tanakaand coworkers, we recently investigated the excited-state pro-perties of ½RuðbpyÞ2ðpbnÞ�2þ and photochemical productionof ½RuðbpyÞ2ðpbnHHÞ�2þ (2, 8). Flash photolysis experimentsshowed that the 532-nm excitation of the ½RuðbpyÞ2ðpbnÞ�2þcomplex yields its metal-to-ligand charge-transfer (MLCT) ex-cited state (d → πpbn�) with a lifetime of 140 ns in acetonitrileand 30 ns in water (pH above 5). The excited state can be readilyquenched by amines, and the one-electron-reduced (OER) spe-cies is produced. The product obtained by continuous photolysis(>400 nm) of a CH3CN or dimethylformamide solution contain-ing ½RuðbpyÞ2ðpbnÞ�2þ and an amine was identified as ½RuðbpyÞ2ðpbnHHÞ�2þ by comparing the spectroscopic and other proper-ties (i.e, UV–visible, NMR, electrospray ionization MS, etc.) tothose of ½RuðbpyÞ2ðpbnHHÞ�2þ prepared by a Na2S2O4 reduction.Furthermore, both ½RuðbpyÞ2ðpbnÞ�2þ and ½RuðbpyÞ2ðpbnHHÞ�2þwere characterized by X-ray single-crystal diffraction.

We further investigated the mechanistic pathways of formationof the ½RuðbpyÞ2ðpbnHHÞ�2þ species from ½RuðbpyÞ2ðpbnÞ�2þ inan aqueous medium using pulse radiolysis and 60Co irradiation(8). Formation of the OER species as a result of reduction bya solvated electron (k ¼ 3.0 · 1010 M−1 s−1) or CO2

•− (k ¼ 4.6 ·109 M−1 s−1) is followed by protonation of the reduced speciesto form ½RuðbpyÞ2ðpbnH•Þ�2þ with pKa ¼ 11. Dimerization(kd ¼ 2.2 · 108 M−1 s−1) of the singly reduced protonatedspecies, ½RuðbpyÞ2ðpbnH•Þ�2þ, takes place at pH < 9, and thisis followed by disproportionation of the dimer in parallel withthe cross-reaction between the singly reduced protonated andnonprotonated species (kcross ¼ 1.2 · 108 M −1 s−1) at near pH 11resulting in the formation of the final ½RuðbpyÞ2ðpbnHHÞ�2þ pro-duct together with an equal amount of the starting complex,½RuðbpyÞ2ðpbnÞ�2þ. At 0.2 °C, a dimeric intermediate, most likelya π-stacked dimer, was observed that decomposes thermally toan equimolar mixture of ½RuðbpyÞ2ðpbnHHÞ�2þ and ½RuðbpyÞ2ðpbnÞ�2þ (pH < 9). We provided further evidence for theπ-stacked dimer mechanism by demonstrating stereospecifichydrogenation to give Λ-(S)- and Λ-(R)- ½RuðbpyÞ2ðpbnDDÞ�2þ{pbnDD ¼ 5,10-dideutero-2-(2-pyridyl)benzo[b]-1,5-naphthyridine}upon visible-light irradiation in a D2O∕CH3CN∕triethylaminesolution (9).

Author contributions: J.T.M. designed research; J.T.M., P.A., C.C., D.E.P., and E.F. performedresearch; J.T.M., P.A., C.C., D.E.P., and E.F. analyzed data; and J.T.M. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. E-mail: muckerma@bnl.gov.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1201026109/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1201026109 PNAS ∣ September 25, 2012 ∣ vol. 109 ∣ no. 39 ∣ 15657–15662

CHEM

ISTR

YSP

ECIALFEAT

URE

Recently, we have studied the reactivity of a Ru complexcontaining the iso-pbn ligand [iso − pbn ¼ 3-(pyrid-2′-yl)-4-azaa-cridine], which is a structural isomer of the pbn moiety (4, 10).In ½RuðbpyÞ2ðiso─pbnHHÞ�2þ the hydride center is not stericallyhindered compared to ½RuðbpyÞ2ðpbnHHÞ�2þ, which affects themechanism of its formation and reactivity toward hydride accep-tors. Reduction of ½RuðbpyÞ2ðiso─pbnÞ�2þ proceeds through theformation of an unstable C─C─bonded dimer and results in adoubly reduced, doubly protonated species. The rate of hydridetransfer to trityl cation was found to be approximately 25 timesfaster for ½RuðbpyÞ2ðiso─pbnHHÞ�2þ compared to ½RuðbpyÞ2ðpbnHHÞ�2þ (4). This difference was attributed to the more steri-cally hindered environment around hydride-donor center in½RuðbpyÞ2ðpbnHHÞ�2þ.ModelDuBois and coworkers (11–14) investigated the thermodynamichydride-donor abilities (i.e., hydricities) of transition-metal hy-drides, formyl complexes, and NADPH-model complexes, suchas 1-benzyl-1,4-dihydronicotinamide, in order to develop CO2-reduction catalysts in CH3CN. The thermodynamic hydricity ofa species AH− (or BH) is defined as the standard free energychange for the reaction:

AH− → A þH− [1A]

BH → Bþ þH− [1B]

in a specified solvent. We denote the hydricity of the reaction inEq. 1A to be:

ΔG�H−ðAH−Þ ¼ G�ðAÞ þG�ðH−Þ −G�ðAH−Þ; [2]

where ΔG�H− is the thermodynamic hydricity and the various

G� values correspond to absolute free energies of the species in-dicated. In this work we denote the standard state of one moleper liter in solution with the asterisk symbol to distinguish it fromone atmosphere of pressure in the gas phase, the quantumchemical standard state for all species, which we denote by thesymbol “o”. The thermodynamic hydricity defined in Eq. 2 can bedetermined experimentally by means of a thermodynamic cycle,as shown in SI Appendix, Fig. S1, but the difficulty in calculatingthe absolute standard free energy of the solvated hydride ionprecludes its direct theoretical estimation. Previous ab initio ap-proaches to calculating the thermodynamic hydricity of hydride-donor molecules have circumvented this problem in one of twoways. One is by calculating the free-energy change of isodesmicreactions (Of the several definitions of an isodesmic reaction inuse, here we use the term to refer to a chemical reaction in whichthe type of chemical bonds broken in the reactants is the same asthe type of bonds formed in the reaction products.) with a refer-ence hydride-donor molecule for which the thermodynamichydricity has been experimentally determined (15, 16). The otheris to employ a similar isodesmic reaction scheme to calculateΔΔG�

H− values and then empirically fit the value ofG�ðH−Þ, theabsolute free energy of the solvated hydride ion in a specifiedsolvent (usually acetonitrile), to obtain the best overall agreementbetween calculated and experimental values of ΔG�

H− . With this

assumption, the value of G�ðH−Þ was found to be −400.7 and−404.7 kcal∕mol (1 kcal ¼ 4.18 kJ) in two recent studies (16, 17).

In the thermodynamic cycle in SI Appendix, Fig. S1,ΔG�

heteroðH2Þ ¼ G�ðHþðSÞÞ þG�ðH−

ðSÞÞ −GoðH2ðgÞÞ is theheterolysis standard free energy, the acid-dissociation standardfree energy, and the hydricity of H2, and is assigned a value of76 kcal∕mol in acetonitrile by DuBois and others (18, 19). Thisis a difficult quantity to calculate or to measure because it in-volves the solvation of both the gas-phase proton and the gas-phase hydride ion. Any hydricity scale based on the value of76 kcal∕mol would be internally consistent, but would be in errorin the actual hydricities by any error in the value of 76 kcal∕mol.

The key feature of the isodesmic reaction approach is that thestandard free energy of reaction of a hydride donor (AH−) withthe hydride acceptor corresponding to a different hydride donor(BH−) is the difference between the two thermodynamic hydri-cities,

AH− þ B → A þ BH− [3A]

and

ΔG� ¼ ΔG�H−ðAH−Þ − ΔG�

H−ðBH−Þ: [3B]

This suggests defining, in analogy with redox couples, “hydri-city half-reactions” (HHR) of the form AH− → A (i.e., half ofa hydride-transfer reaction as in Eq. 3A), with correspondingstandard free-energy change:

ΔG�HHRðAH−Þ ¼ G�ðAÞ −G�ðAH−Þ

¼ ΔG�H−ðAH−Þ −G�ðH−Þ; [4A]

so that the standard free energy change of Eq. 3A is:

ΔG� ¼ G�HHRðAH−Þ − ΔG�

HHRðBH−Þ¼ ΔG�

H−ðAH−Þ − ΔG�H−ðBH−Þ: [4B]

The benefit of the half-reaction convention is that the values

ΔG�HHRðAH−Þ ¼ G�ðAÞ −G�ðAH−Þ [4C]

can be readily calculated because they do not involveG�ðH−Þ. Gi-ven a reference reaction and at least one value of ΔG�

H− ðAH−Þ−ΔG�

H−ðrefH−Þ, we can evaluate G�ðH−Þ and construct a scale oftheoretical thermodynamic hydricities based on the isodesmicreaction scheme expressed by Eq. 4B. The solvent (in the presentcase, acetonitrile) is defined as the reference hydride acceptorwith a zero value of ΔGo

H−ðSolvH−Þ so that, from Eq. 4A,ΔGo

HHRðSolvH−Þ ¼ −GoðH−Þ. Here, SolvH− represents thehydride ion in the solvent, often written as H−

ðsolvÞ or H−ðsÞ.

We mention in passing that, in the case of acetonitrile as thesolvent, we determined that a useful picture for describing thestructure of the solvated hydride ion is as a molecule of “hydridedacetonitrile,” CH3CHN−, that is, isoelectronic with and similar instructure to acetaldehyde, CH3CHO. The computed value(−404.5 kcal∕mol) of G�ðH−Þ ≈G�ð½CH3CHN−·ðCH3CNÞ�ðSÞÞ−2G�ðCH3CNðliqÞÞ, where the subscript “(S)” indicates thatthe CH3CHN− explicitly solvated by one acetonitrile moleculeis immersed in a polarizable continuum model (PCM) of the

Fig. 1. Structures of various Ru complexes, where [Ru] indicates RuðbpyÞ2.

15658 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1201026109 Muckerman et al.

surrounding bulk solvent, and the subscript “(liq)” refers tothe standard state of the pure liquid solvent (20), is quite closeto the previously fitted values, and reasonably close to the valueof ΔG�ðH−Þ ¼ −412.7 kcal∕mol that we obtain in this workfrom extrapolation of experimental ΔG�

H− values using ourhydricity half-reaction procedure (see below). The straightfor-ward calculation of the hydride ion in a PCM treatment (21–23)of the solvent with the methodology employed here gives−391.4 kcal∕mol.

The hydricity of 1-benzyl-1,4-dihydronicotinamide (BNAH) isreported to be 59� 2 kcalmol−1 (12). This species is about inthe middle of the hydricity scale defined by DuBois, with Ph3CHas the weakest hydride donor (99 kcalmol−1) and [HRhðdppbÞ2]as the strongest hydride donor [dppb ¼ 1,2-bis(diphenylphosphi-nato)benzene, 34� 2 kcalmol−1]. Metal hydrides such as½RuðbpyÞðtpyÞH�þ (tpy ¼ 2,2′:6′,2″-terpyridine) react with CO2

to form the formato complex (24, 25); however, ½RuðbpyÞ2ðpbnHHÞ�2þ does not react with CO2 (4). Although C─H hydridessuch as ½RuðbpyÞ2ðpbnHHÞ�2þ can be photoregenerated, they areexpected to be weak hydride donors. M─H hydrides can be stron-ger hydride donors, but their photogeneration may be difficult.

We have carried out calculations of the thermodynamic hydri-city of ½RuðbpyÞ2ðpbnHHÞ�2þ, ½RuðbpyÞ2ðiso-pbnHHÞ�2þ, andthe hydrided forms of possible hydride acceptor molecules forintermolecular H− transfer reactions related to CO2 reduction.Because we found that ½RuðbpyÞ2ðpbnHHÞ�2þ is not a sufficientlystrong hydride donor for such reactions, we pursued the possibi-lity of increasing the hydricity of ½RuðbpyÞ2ðpbnHHÞ�2þ. Here,our theoretical calculations predict that a further reduced½RuðbpyÞ2ðpbnHHÞ�þ species formed by another visible-lightMLCT excitation/reductive-quenching step starting from the½RuðbpyÞ2ðpbnHHÞ�2þ complex can create a species with a dra-matically increased hydricity that, in principle, could donate itshydride to M─CO species to form M─CHO−, the most difficultstep in CO2 reduction to methanol.

Computational MethodsAll calculations quoted here were carried out using DFTas imple-mented in the Gaussian 03 program package (26). Unless other-wise specified, they correspond to the use of a hybrid functionaland an all-electron double-zeta with polarization basis for eachatom, except for transition metal atoms for which an effectivecore potential (ECP) and at least a double-zeta with polarizationbasis was employed. All structure optimizations and vibrationalfrequency calculations were carried out using a PCM incorporat-ing the dielectric constant of the acetonitrile solvent. Furtherdetails of the calculations are provided in SI Appendix.

The approach described by Eq. 4A handles all cases consideredhere with one important exception: H2. In the case of the gas-phase H2 hydride donor, we employ the absolute free energy ofthe solvated proton in acetonitrile solution (−266.5 kcal∕mol)recommended by Kelly et al. (20). This value is based on thegas-phase free energy of the proton (−6.3 kcal∕mol) and itsexperimental solvation energy (−260.2 kcal∕mol) at standardconditions. The use of the experimentally derived value is proble-matic for the case of H2 because there is no solvation of the re-actant molecule to compensate for any error in G�ðH−Þ arisingfrom systematic errors in the implicit solvation model in the cal-culations from which its value was determined.

Results and DiscussionCalculation of Hydricities. According to Eqs. 2 and 4C, we wouldexpect the experimental thermodynamic hydricity, ΔG�

H− , tobe a linear function of the experimental hydricity half-reaction,ΔG�

HHR;expt, with a slope of unity and an intercept of G�ðH−Þ,the constant absolute free energy of the solvated hydride ion.Therefore, in the absence of any systematic error in the calculatedvalue of the standard free energy of the hydricity half-reaction,

ΔG�HHR;calc, we would expect the least-squares linear fit to be-

have in the same way. However, it is more convenient to invertthis relation, and plot the calculated ΔG�

HHR;calc, henceforthdenoted simply as ΔG�

HHR;ðSÞ, versus the experimental ΔG�H− ,

with intercept G�HHR;ðSÞðSolvH−Þ. Because the hydricity of

the hydride ion in the solvent is zero, this implies that thebest-fit value of G�ðH−Þ, denoted G�

lfitðH−Þ, is the negative ofG�

HHR;ðSÞðSolvH−Þ.Such a plot is shown in Fig. 2 for five hydride donors with

“known” experimental hydricity. Although the hydricities of thesespecies may depend on the hydricity of H2, we do not include H2

in this calibration because of the aforementioned difficulty incomputing its hydricity half-reaction, and also because, as will beshown below, it is an “outlier” in a plot such as Fig. 2. We see thatthe linear correlation between ΔG�

HHR;ðSÞ and the experimentalΔG�

H− is very good, with correlation coefficient r ¼ 0.9979.However, the slope of the line is 0.9300 rather than unity, imply-ing a small systematic dependence of ΔG�

HHR;ðSÞ on the value ofΔG�

H− , probably a differential solvation error in ΔG�HHR;ðSÞ

arising from deficiencies in the solvation model. The intercept(i.e., zero of ΔG�

H− ) is 412.7 kcal∕mol, giving a value of−412.7 kcal∕mol for G�

lfitðH−Þ, where the subscript “lfit” indi-cates a quantity with a value based on the linear fit shown in Fig. 2.We note that the donation of a hydride ion from type AH−, AH,or AHþ hydride donors results in the HHR’s involving A andAH−, Aþ and AH, or A2þ and AHþ, respectively. In all cases,one of the species of each pair will dominate the ΔΔG�

S of theHHR so that systematic error in the solvation free energy of thedominant species will not be canceled. There could also be resi-dual systematic error in the computed ΔGo

HHR;ðgÞ arising fromdeficiencies in the electronic structure method and basis, andfrom the fact that the hydride donor and its conjugate acceptordiffer by two electrons and a proton. It is therefore best to regardthe specific correlation between the experimental ΔG�

H− andcalculated ΔG�

HHR;ðSÞ in Fig. 2 as pertaining to the present treat-ment of the species considered here.

To the extent that the slope of the line in Fig. 2 differs fromunity, it reflects the degree of breakdown of any isodesmicscheme based on taking differences between ΔG�

HHR;ðSÞ values.Also, the straightforward estimation of experimental hydricities(denoted by the addition of a prime to the superscript) based oncalculated ΔG�

HHR;ðSÞ values,

ΔG� 0H− ≈ ΔG�

HHR;ðSÞ þG�lfitðH−Þ; [5]

Fig. 2. Correlation between the calculated value of ΔG�HHR;ðSÞ and ΔG�

H−

based on five species with known experimental hydricity in acetonitrile (redpoints): formate anion, Cp�ReðNOÞðCOÞ2ðCHO−Þ, CpReðNOÞðCOÞ2ðCHO−Þ,BNAH, and Ph3CH. The equation of the least-squares linear fit, the correla-tion coefficient, and the intercept are also indicated. (Inset) Blow-up of thefitted region.

Muckerman et al. PNAS ∣ September 25, 2012 ∣ vol. 109 ∣ no. 39 ∣ 15659

CHEM

ISTR

YSP

ECIALFEAT

URE

would similarly break down. We therefore seek to incorporate theempirically derived correction to the slope of the correlation inFig. 2. We should point out that there should be no error arisingfrom differential solvation for the case ofΔG�

H− ¼ 0 because thehydride donor and hydride acceptor are the same (the solvent) onboth sides of the isodesmic relation—i.e., the best-fit line shouldyield the correct value of G�

lfitðH−Þ.The plot in Fig. 2 can be inverted to yield the predicted value of

the experimental hydricity as a function of the calculated hydri-city half-reaction as

ΔG�H− ;lfit ¼ 1.0752 · ΔG�

HHR;ðSÞ − 443.7586 kcal∕mol; [6]

where the linear correlation is used to obtain the “lfit” approx-imation to the hydricity of a given hydride donor from the calcu-lated free-energy change of its hydricity half-reaction and theextrapolated value of the absolute free energy of the solvated hy-dride ion. This line is shown in a plot of Eq. 6 for the experimentalcalibration points corresponding to the five species in Fig. 2 as thered line and points, respectively, in Fig. 3.

The dashed line in Fig. 3 shows the ΔG� 0H− values obtained by

application of Eq. 5. This prediction is seen to deviate from thebest-fit red line at high values of ΔG�

HHR;ðSÞ. Taking the differ-ence between Eqs. 5 and 6, we find the correction term, denotedΔG�

corr;lfit, between ΔG�H−;lfit and ΔG� 0

H− values owing to thesystematic dependence of ΔG�

HHR;ðSÞ on ΔG�H− is:

ΔG�corr;lfit ¼ 0.0753 · ΔG�

HHR;ðSÞ − 31.0631 kcal∕mol: [7]

The computed thermodynamic hydricities, ΔG�H− ;lfit, of var-

ious hydrides in acetonitrile are listed in Table 1, where theyare compared to experimental values in the cases where theyare available. For comparison, the value of ΔG� 0

H− in acetoni-trile from Eq. 5 is also given. The values for all entries includingthe five calibration species (red points) are also plotted in Fig. 3(blue points), and, of course, they all lie along the red line. Theexperimental and calculated values for H2 are represented inFig. 3 by the black square and the black point, respectively.

The value of G�lfitðH−Þ obtained by extrapolation in Fig. 2 of

−412.7 kcal∕mol is somewhat more negative that previous values(−400.7 and −404.7 kcal∕mol) of G�ðH−Þ obtained as a fittingparameter in isodesmic schemes (16, 17). This can be understoodby comparing the “Expt.” and “ΔG� 0

H−” columns in Table 1. IfG�ðH−Þ were used as a fitting parameter to bring the averageerror in ΔG� 0

H− to zero, the resulting value of G�ðH−Þ would

be −406.6 kcal∕mol, in much better agreement with the previousestimates. This higher value of an isodesmic G�ðH−Þ compen-sates (on the average) for the correction term given by Eq. 7.

The most hydridic species have the smallest (most negative) hy-dricity values. One important feature of Table 1 is that, analogousto standard reduction potentials, any entry for a hydride donor inthe table is predicted to have an exergonic reaction with the reversehydricity half-reaction (i.e., the conjugate acceptor) of any entry inthe table below it. For example, for the CpReðNOÞðCOÞ2þ specieswith opposite direction −ΔGo

H− of −56 kcal∕mol, any hydridedonor above it in the table should, in principle, be able to donatea hydride to it to form CpReðNOÞðCOÞðCHO−Þ. These results areconsistent with the experimental result of Koizumi and Tanaka (3),that the Ru─pbnHH complex can reduce acetone to isopropanolin acidic acetonitrile solution because the reaction is predicted tobe essentially thermoneutral. We see that the Ru─pbnHH com-plex should be (within the expected error in the calculations) cap-able to transfer a hydride to protonated acetone, but not toacetone itself, indicating that the mechanism likely proceeds byprotonation followed by hydride transfer.

It is noteworthy that the formyl anion is the strongest hydridedonor listed in Table 1, indicating that it is extremely difficult totransfer a hydride ion to free CO. However, it is also apparent inthe table that binding CO to a transition metal leads to a greatlyreduced CHO− hydricity in M─CHO− complexes. Furthermore,the data in the table indicate that the addition of another electronto ½RuðbpyÞ2ðpbnHHÞ�2þ is predicted to be the key to openingthe door to new opportunities for hydride-transfer reactions lead-ing to CO2 reduction by producing a species with much increasedhydricity (see below). Finally, we see that the computed hydricityvalues are in fairly close agreement (i.e., within the expected com-bined error of the electronic structure method and solvationmodel used, with the exception of H2 as mentioned above) withexperimental values in the cases where they are known, includingour preliminary value for the hydricity of ½RuðbpyÞðtpyÞðHÞ�þ(green open circle in Fig. 3).

Previously, we have determined that ½RuðbpyÞ2ðpbnHHÞ�2þ isformed by two ½RuðbpyÞ2ðpbnH•Þ�2þ molecules undergoingbimolecular disproportionation (8). We can therefore think of½RuðbpyÞ2ðpbnHHÞ�2þ as being a doubly reduced, doubly proto-nated species that “pools” the two electrons and two protonscarried by the two ½RuðbpyÞ2ðpbnH•Þ�2þ molecules. Our calcula-tions predict that the triply reduced, doubly protonated species,½RuðbpyÞ2 •−ðpbnHHÞ�þ, and other complexes containing theðbpyÞ2 •−ðpbnHHÞ or pbnHH•− ligands can be produced by anadditional reduction. These highly reduced species can donatehydrides to become singly reduced, singly protonated complexeswith the pbnH• ligand. Calculations of the electronic spectra andspin density indicate that these are the same ½RuðbpyÞ2ðpbnH•Þ�2þspecies that disproportionate to form the corresponding pbnHHcomplexes (see below).

An Additional Reduction. The ½RuðbpyÞ2ðpbnHHÞ�2þ complexexhibits a visible absorption peak between 400 and 450 nm ina region where the parent ½RuðbpyÞ2ðpbnÞ�2þ complex does notstrongly absorb. Our TD-B3LYP/LANL2DZ calculations (SIAppendix, Fig. S2) show that this transition is primarily of theMLCT type. This may be followed by reductive quenching to pro-duce a ligand anion radical in which the unpaired electron isdelocalized over the π� system of the two bpy ligands, as shownin SI Appendix, Fig. S3. Thus, it may be possible to generate atriply reduced, doubly protonated ½RuIIðbpyÞ2 •−ðpbnHHÞ�þ spe-cies, as indicated in Eq. 8:

½RuIIðbpyÞ2ðpbnHHÞ�2þ þ e−→hv½RuIIðbpyÞ2 •−ðpbnHHÞ�þ: [8]

When the triply reduced, doubly protonated structure donatesa hydride, it reforms Ru─pbnH•. Our Mulliken atomic spin den-

Fig. 3. Predicted values of ΔG�H− ;lfit as a function of the computed

ΔG�HHR;ðSÞ for the five calibration species from Fig. 2 (red points), the least-

squares fit to the five calibration points (red line), the predicted values of theadditional hydride donors listed in Table 1 (blue points), and the straightfor-ward ΔG� 0ðH−Þ prediction based on Eq. 5 (dashed line). The equation of theleast-squares linear fit and the “experimental” (black square) and predictedvalues (black point) of ΔG�

H− (H2) are also indicated. The experimental valueof RuðtpyÞðbpyÞðHÞþ is indicated by the green open circle. (Inset) Blow-up ofthe fitted region.

15660 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1201026109 Muckerman et al.

sity results (SI Appendix, Fig. S4), are consistent with this; theunpaired electron is on the hydride carbon. Importantly, the exactlocation of the unpaired electron in ½RuðbpyÞ2 •−ðpbnHHÞ�þ doesnot matter, as it supplies the driving force for hydride transfer, andthe ½RuðbpyÞ2ðpbnH•Þ�2þ product following that hydride transferis the species that can be “recycled” into ½RuðbpyÞ2ðpbnHHÞ�2þ.With regard to that, our calculations (SI Appendix, Table S1) in-dicate that disproportionation of ½RuðbpyÞ2ðpbnH•Þ�2þ is energe-tically favorable.

In the case of the iso-pbnHH complex, the reduction by a thirdelectron and the “recycling” to iso-pbnH are similar to those forpbnHH [Eq. 9]. The excited state may be reductively quenched toproduce an anion radical. TD-DFT analysis shows that πpbn →π�

pbn transitions are in the minority.

½RuIIðbpyÞ2ðiso-pbnHHÞ�2þ

þ e−→hv½RuIIðbpyÞ2 •−ðiso-pbnHHÞ�þ: [9]

Intermolecular Hydride Transfer. It was mentioned above that metalhydride complexes such as ½RuðbpyÞðtpyÞðHÞ�þ are strong hy-dride donors, and this is corroborated by the position of ½RuðbpyÞðtpyÞðHÞ�þ near the top of Table 1, with a predicted hydricity inexcellent agreement with the experimental value. Interestingly,we predict the hydricities of ½RuðbpyÞ2 •−ðpbnHHÞ�þ and½RuðbpyÞ2 •−ðiso-pbnHHÞ�þ to approach that of ½RuðbpyÞðtpyÞðHÞ�þ, and even that of ½ReðpbnHH•−ÞðCOÞ3ðClÞ�−, in whichwe calculated the unpaired third electron to be localized onthe bpy part of the pbn ligand, which we predict to be an evenstronger hydride donor.

Calculations (Table 1) indicate that the triply reduced, doublyprotonated ruthenium complex is sufficiently hydridic to reduce ametal-bound carbonyl on CpReðNOÞðCOÞ2, as indicated inEq. 10:

½RuðbpyÞ2 •−ðpbnHHÞ�þ þ CpReðNOÞðCOÞ2þ→ ½RuðbpyÞ2ðpbnH•Þ�2þ þ CpReðNOÞðCOÞðCHOÞ: [10]

The transition state (TS) for the ½RuðbpyÞ2 •−ðpbnHHÞ�þ com-plex (SI Appendix, Fig. S5) shows the hydride being transferredfrom the ½RuðbpyÞ2 •−ðpbnHHÞ�þ complex to the acceptor mole-cule. Both the ½RuðbpyÞ2 •−ðpbnHHÞ�þ and ½RuðbpyÞ2 •−ðiso-pbnHHÞ�þ species show promise for transferring a hydrideion to a metal-bound carbonyl group, because those reactionsare exothermic with small enthalpic barriers but substantial

free-energy barriers (SI Appendix, Table S2). Selected geometricparameters of the reactants and transition states are listed in SIAppendix, Table S3.

It is fortuitous that the two isomeric ½RuðbpyÞ2 •−ðpbnHHÞ�þcomplexes are both strong hydride donors and donate a hydrideto form ½RuðbpyÞ2ðpbnH•Þ�2þ, which can disproportionate into½RuðbpyÞ2ðpbnHHÞ�2þ and ½RuðbpyÞ2ðpbnÞ�2þ. If the formationof ½RuðbpyÞ2 •−ðpbnHHÞ�þ could successfully be demonstrated, itwould establish a second catalytic cycle that is interconnectedwith the one elucidated previously for the formation of the½RuðbpyÞ2ðpbnHHÞ�2þ species (SI Appendix).

Fig. 4. (Bottom) UV–visible spectrum of ½RuðbpyÞ2ðpbnHHÞ�2þ in acetonitrile;(Top) difference spectra of the excited state of ½RuðbpyÞ2ðpbnHHÞ�2þ(red)measured after 355 nm excitation, ½RuðbpyÞ2 •−ðpbnHHÞ�þ from quenchingof the excited state by DABCO (blue), and ½RuðbpyÞ2 •−ðpbnHHÞ�þ fromNa∕Hg reduction of ½RuðbpyÞ2ðpbnHHÞ�2þ (green). The transient spectra ofthe excited state of ½RuðbpyÞ2ðpbnHHÞ�2þ were measured in dry deaeratedacetonitrile after excitation by the third harmonic of a Nd3þYAG laser andprobed by a Xe-pulsed lamp. The excited-state quenching experiments wereconducted using similar conditions and using 100 mM of DABCO as a quench-er (SI Appendix).

Table 1. Calculated and experimental* thermodynamic hydricities (kcal/mol) in CH3CN solution

Hydride donor Conjugate hydride acceptor Expt. ΔG� 0H− ΔG�

H− ;lfit

CHO− CO −10.0 −10.8CH3CðOÞHCH−

3 CH3COCH3 18.5 19.8½ReðpbnHH•−ÞðCOÞ3ðClÞ�− ½ReðpbnH•ÞðCOÞ3ðClÞ�0 32.4 34.9½RuIIðbpyÞðtpyÞðHÞ�þ ½RuIIðbpyÞðtpyÞðNCMeÞ�2þ 39† 36.0 38.7HCOO− CO2 43 39.1 42.1½RuIIðbpyÞ2 •−ðpbnHHÞ�þ ½RuIIðbpyÞ2ðpbnH•Þ�2þ 46.6 50.1½RuIIðbpyÞ2 •−ðiso-pbnHHÞ�þ ½RuIIðbpyÞ2ðiso-pbnH•Þ�2þ 47.1 50.7½Cp�ReIðNOÞðCOÞðCHOÞ�0 ½Cp�ReIðNOÞðCOÞ2�þ 52.6 49.7 53.4MNAH MNAþ 52.0 55.8½CpReIðNOÞðCOÞðCHOÞ�0 ½CpReIðNOÞðCOÞ2�þ 55 52.8 56.8BNAH BNAþ 59 53.3 57.2p −monohydroquinone− p-benzoquinone 58.9 63.3H2 Hþ 76 61.2 65.8½ReðpbnHHÞðCOÞ3ðClÞ�0 ½ReðpbnHþÞðCOÞ3ðClÞ�þ 76.5 82.2CH3CðOHÞHCH3 CH3CðOHÞCH3

þ 81.6 87.7½RuIIðbpyÞ2ðpbnHHÞ�2þ ½RuIIðbpyÞ2ðpbnHþÞ�3þ 82.6 88.7½RuIIðbpyÞ2ðiso-pbnHHÞ�2þ ½RuIIðbpyÞ2ðiso-pbnHþÞ�3þ 85.2 91.5Ph3CH Ph3Cþ 99 92.0 98.9

*Experimental data taken from refs. 12 and 14 unless otherwise indicated.†Value from our preliminary work.

Muckerman et al. PNAS ∣ September 25, 2012 ∣ vol. 109 ∣ no. 39 ∣ 15661

CHEM

ISTR

YSP

ECIALFEAT

URE

Chemical and Photochemical Reduction of ½RuðbpyÞ2ðpbnHHÞ�2þ.Photoexcitation into the MLCT transition of ½RuðbpyÞ2ðpbnHHÞ�2þ results in an excited state with a lifetime of about70 ns (Fig. 4, Top: red difference spectrum) in acetonitrile.The excited state is readily quenched by an amine [0.1 Mtriethylamine (TEA) or 1,4-diazabicyclo[2.2.2]octane (DABCO)]producing a long-lived (half-life above 50 μs) one-electron-re-duced species (Fig. 4, Top: blue difference spectrum). However,Na∕Hg-amalgam reduction of ½RuðbpyÞ2ðpbnHHÞ�2þ yields theone-electron-reduced species (Fig. 4, Top: green difference spec-trum) with the absorption band blue-shifted by about 50 nm. Thisblue shift can possibly be attributed to a corresponding red shiftin the absorption of ½RuðbpyÞ2 •−ðpbnHHÞ�þ arising from the in-teraction between the ½RuðbpyÞ2 •−ðpbnHHÞ�þ and an amine.The DABCO radical cation itself has no significant absorptionabove 520 nm (27). The one-electron-reduced species obtainedby pulse radiolysis showed an identical spectrum to that obtainedby Na/Hg reduction (4).

Irradiation of a solution containing ½RuðbpyÞ2ðpbnÞ�2þ, TEAas a sacrificial electron donor, and ½CpReðNOÞðCOÞ2�þ did notproduce ½CpReðNOÞðCOÞðCHOÞ�0. However, Na∕Hg-amalgamreduction of ½RuðbpyÞ2ðpbnHHÞ�2þ produced ½RuðbpyÞ2ðpbnHHÞ�þ (experimental details in SI Appendix). The productsof the reaction of ½RuðbpyÞ2ðpbnHHÞ�þ with ½CpReðNOÞðCOÞ2�þ in dry acetonitrile showed no NMR signal for Re─CHOdespite the fact that the reaction is predicted to have a ΔG� of−6.7 kcal∕mol. However, the products of electron- and hydride-transfer reactions, ½RuðbpyÞ2ðpbnHHÞ�2þ and ½RuðbpyÞ2ðpbnÞ�2þ, were observed. Furthermore, CO and CH4 (but no H2)were reproducibly detected by GC, suggesting that the Re─CHOspecies may have been further reduced to CH4, accompanied bythe release of CO from the 19e− species ½CpReðNOÞðCOÞ2�0produced by the electron-transfer reaction. The electron-transferreaction is probably caused by the large driving force (ΔE1∕2 ¼0.9 V), which causes it to compete with the kinetically impeded(ΔG�‡ ¼ 12.6 kcal∕mol) hydride transfer.

ConclusionsWe have investigated through DFT calculations the hydride-donating power, or hydricity, of various catalysts that incorporatethe pbnHH ligand to model the function of NADH. These visiblelight-generated, photocatalytic complexes show promise for usein reducing CO2 and converting that pollutant molecule into fuelssuch as methanol. We examined potential catalysts based on themetals ruthenium and rhenium. The modification of the previ-ously characterized ½RuðbpyÞ2ðpbnHHÞ�2þ that showed the mostpromise was the addition of a third electron to form the triplyreduced, doubly protonated isomeric ½RuðbpyÞ2 •−ðpbnHHÞ�2þspecies. These species are predicted to donate hydrides to pro-duce the pbnH• intermediate, which has been shown to formthe active species pbnHH through a disproportionation reaction.The calculations indicate that the reaction of the ½RuðbpyÞ2 •−ðpbnHHÞ�2þ species with carbonyl ligands bound to transition-metal centers may provide a promising route to producing theformyl anion and beyond. Experimental evidence that the ex-cited-state lifetime of photoexcited ½RuðbpyÞ2ðpbnHHÞ�2þ isabout 70 ns, and that this excited state can be reductivelyquenched by TEA or DABCO to produce the one-electron-reduced ½RuðbpyÞ2ðpbnHHÞ�þ species with half-life exceeding50 μs, is presented, thus opening the door to new opportunitiesfor hydride-transfer reactions leading to CO2 reduction byproducing a species with much increased hydricity. A preliminaryexperimental exploration indicated that the reaction of the stronghydride donor ½RuðbpyÞ2ðpbnHHÞ�þ with ½CpReðNOÞðCOÞ2�þmay be complicated by the competition between electron- andhydride-transfer reactions.

ACKNOWLEDGMENTS. We thank Dr. Jonathan Skone for valuable discussionsand Professor Koji Tanaka at the Institute for Molecular Science, Japan, forproviding ½RuðbpyÞ2ðpbnÞ�ðPF6Þ2 samples. The work at Brookhaven NationalLaboratory (BNL) was carried out under contract DE-AC02-98CH10886 withUS Department of Energy and supported by its Division of Chemical Sciences,Geosciences, Biosciences, Office of Basic Energy Sciences. We also thank theUS Department of Energy for funding under the BES Solar Energy UtilizationInitiative. Calculations were carried out in part at the US Department ofEnergy National Energy Research Scientific Computing Center (NERSC).

1. Morris AJ, Meyer GJ, Fujita E (2009) Molecular approaches to the photocatalyticreduction of carbon dioxide for solar fuels. Acc Chem Res 42:1983–1994.

2. Polyansky D, et al. (2007) Photochemical and radiolytic production of an organichydride donor with a Ru(II) complex containing an NADþ model ligand. Angew ChemInt Ed 46:4169–4172.

3. Koizumi T, Tanaka K (2005) Reversible hydride generation and release from the ligandof ½RuðpbnÞðbpyÞ2 �ðPF6Þ2 driven by a pbn-localized redox reaction.Angew Chem Int Ed44:5891–5894.

4. Cohen BW, et al. (2012) Steric effect for proton, hydrogen-atom, and hydride transferreactions with geometric isomers of NADH-model ruthenium complexes. Faraday Dis-cuss 155:129–144.

5. Tanaka H, Tzeng BC, Nagao H, Peng SM, Tanaka K (1993) Comparative study on crystalstructures of ½RuðbpyÞðCOÞ2�ðPF6Þ2 , ½RuðbpyÞðCOÞðCðOÞOCH3Þ�BðC6H5Þ4·CH3CN, and½RuðbpyÞ2ðCOÞ�ðη1-CO2Þ� · 3H2O (bpy ¼ 2,2′-bipyridyl). Inorg Chem 32:1508–1512.

6. Ooyama D, Tomon T, Tsuge K, Tanaka K (2001) Structural and spectroscopic character-ization of ruthenium(II) complexes with methyl, formyl, and acetyl groups as modelspecies in multi-step CO2 reduction. J Organomet Chem 619:299–304.

7. Sweet JR, Graham WA (1982) Stepwise reduction of coordinated carbon monoxide.J Am Chem Soc 104:2811–2815.

8. Polyansky DE, et al. (2008) Mechanism of hydride donor generation using a Ru(II) com-plex containing an NADþ model ligand: Pulse and steady-state radiolysis studies. InorgChem 47:3958–3968.

9. Fukushima T, et al. (2009) Photochemical stereospecific hydrogenation of a Ru com-plex with an NADþ∕NADH-type ligand. Inorg Chem 48:11510–11512.

10. Cohen BW, et al. (2010) Differences of pH-dependent mechanisms on generation ofhydride donors using Ru(II) complexes containing geometric isomers of NADþ modelligands: NMR and radiolysis studies in aqueous solution. Inorg Chem 49:8034–8044.

11. Curtis CJ, Miedaner A, Ellis WW, DuBois DL (2002) Measurement of the hydride donorabilities of ½HMðdiphosphineÞ2 �þ complexes (M ¼ Ni, Pt) by heterolytic activation ofhydrogen. J Am Chem Soc 124:1918–1925.

12. Ellis WW, Miedaner A, Curtis CJ, Gibson DH, DuBois DL (2002) Hydride donor abilitiesand bond dissociation free energies of transition metal formyl complexes. J Am ChemSoc 124:1926–1932.

13. Price AJ, et al. (2002) HRhðdppbÞ2, a powerful hydride donor. Organometallics21:4833–4839.

14. Ellis WW, Raebiger JW, Curtis CJ, Bruno JW, DuBois DL (2004) Hydricities of BzNADH,C5H5MoðPMe3ÞðCOÞ2H, and C5Me5MoðPMe3ÞðCOÞ2H in acetonitrile. J Am Chem Soc126:2738–2743.

15. Qi XJ, Fu Y, Liu L, Guo QX (2007) Ab initio calculations of thermodynamic hydricities oftransition-metal hydrides in acetonitrile. Organometallics 26:4197–4203.

16. Kovács G, Pápai I (2006) Hydride donor abilities of cationic transition metal hydridesfrom DFT-PCM calculations. Organometallics 25:820–825.

17. Nimlos MR, et al. (2008) Calculated hydride donor abilities of five-coordinate transi-tion metal hydrides ½HMðdiphosphineÞ2 �þ (M ¼ Ni, Pd, Pt) as a function of the biteangle and twist angle of diphosphine ligands. Organometallics 27:2715–2722.

18. Berning DE, Noll BC, DuBois DL (1999) Relative hydride, proton, and hydrogen atomtransfer abilities of HMðdiphosphineÞ2 PF6 complexes (M ¼ Pt, Ni). J Am Chem Soc121:11432–11447.

19. Tilset M, Parker VD (1989) Solution homolytic bond dissociation energies of organo-transition-metal hydrides. J Am Chem Soc 111:6711–6717.

20. Kelly CP, Cramer CJ, Truhlar DG (2007) Single-ion solvation free energies and the nor-mal hydrogen electrode potential in methanol, acetonitrile, and dimethyl sulfoxide.J Phys Chem B 111:408–422.

21. Klamt A, Schüürmann G (1993) COSMO: A new approach to dielectric screening insolvents with explicit expressions for the screening energy and its gradient. J ChemSoc, Perkin Trans 2 799–805.

22. Barone V, Cossi M (1998) Quantum calculation of molecular energies and energygradients in solution by a conductor solvent model. J Phys Chem A 102:1995–2001.

23. Cossi M, Rega N, Scalmani G, Barone V (2003) Energies, structures, and electronicproperties of molecules in solution with the C-PCM solvation model. J Comput Chem24:669–681.

24. Konno H, et al. (2000) Synthesis and properties of ½RuðtpyÞð4; 4 0-X2bpyÞH�þ(tpy ¼ 2,2′:6′,2′′-terpyridine, bpy ¼ 2,2′-bipyridine, X ¼ H and MeO), and their reac-tions with CO2. Inorg Chim Acta 299:155–163.

25. Creutz C, Chou MH (2007) Rapid transfer of hydride ion from a ruthenium complex toC1 species in water. J Am Chem Soc 129:10108–10109.

26. Frisch MJ, et al. (2004) Gaussian 03, Revision B.04 (Gaussian, Inc., Wallingford, CT).27. Halpern AM, Forsyth DA, Nosowitz M (1986) Flash photolysis of saturated amines in

acetonitrile solution at 248 nm: Formation of radical cations. J Phys Chem90:2677–2679.

15662 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1201026109 Muckerman et al.