1

Calculation of Thermodynamic Hydricities and the

Design of Hydride Donors for CO2 Reduction

James T. Muckerman,* Patrick Achord, Carol Creutz, Dmitry E. Polyansky, and Etsuko Fujita

Chemistry Department, Brookhaven National Laboratory, Upton, 11973-5000

Supporting Information

Text S1 providing details of the computational methods Text S2 describing why the isomers of [Ru(bpy)2(pbnHH)]2+ and [Ru(bpy)2

•−(pbnHH)]+ aren’t even stronger hydride donors

Text S3 providing details of experimental procedures Fig. S1showing a thermodynamic cycle for determining the hydricity of a hydride donor from

experimental data Fig. S2 showing calculated TD-DFT spectrum of [Ru(bpy)2(pbnHH)]2+, its frontier orbitals, and

transition assignments Fig. S3 of the singly-occupied molecular orbital (SOMO) of [Ru(bpy)2

•−(pbnHH)]+ showing delocalization of the electron from the third reduction to be delocalized over the two bpy ligands

Fig. S4 showing Mulliken atomic spin densities in the [Ru(bpy)2(pbnH•)]2+ species Fig. S5 showing the structures of the species in the reaction of [Ru(bpy)2

•−(pbnHH)]+ with CpRe(NO)(CO)3

+ Table S1 listing calculated free energies relevant to the disproportionation reaction of

[Ru(bpy)2(pbnH•)]2+

Table S2 listing calculated enthalpies and free energies of activation and reaction for four intermolecular

hydride-transfer reactions Table S3 listing selected calculated geometric parameters of species involved in the same four hydride-

transfer reactions

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Text S1. Details of the Computational Methods

Unless otherwise specified, all quoted calculations used the Gaussian 03 program package(1) and the

hybrid B3LYP DFT method(2-4), using the MWB28+f ECP and basis for Ru(5, 6), the LANL2DZ+f

ECP and basis for Re(7-9) and 6-31+G(d,p) basis(10-19) for all other atoms. Extensive preliminary

calculations were carried out using the LANL2DZ ECP and basis for metals(7-9) and the D95V basis

for all other elements(20). The results reported here for the iso-pbn complexes were obtained with this

basis. We used a self-consistent reaction field (SCRF) treatment with a polarizable continuum model

(PCM) with UAHF radii to simulate the solvation of all species in acetonitrile solution(21-23). All

structure optimizations and vibrational frequency calculations were carried out in this model of an

acetonitrile solution. While we have previously published TD-DFT spectra of [Ru(bpy)2(pbn)]2+ and of

[Ru(bpy)2(pbnHH)]2+(24), here we discuss assignments of the UV-vis spectrum of [Ru(bpy)2(pbnHH)]2+

based on new TD-B3LYP calculations.

Most hydride donor or acceptor molecules have a standard state defined as one molar in the solution

phase, and a standard state correction has to be made to the quantum chemical convention of one

atmosphere partial pressure in the gas phase. Some donor (e.g., H2) or acceptor (e.g., CO or CO2)

molecules have gas-phase standard states, so we do not apply the ∆Go→* of 1.89 kcal/mol correction to

convert them to a 1 M solution phase standard state.

Text S2. Why aren’t the isomers of [Ru(bpy)2(pbnHH)]2+

and [Ru(bpy)2••••−−−−(pbnHH)]

+ even

stronger hydride donors?

Donation of a hydride ion from [Ru(bpy)2(pbnHH)]2+ causes the active pbn ring to gain aromaticity,

and presumably more stability. On the other hand, the elimination of the remaining proton on

[Ru(bpy)2(pbnH+)]3+ is considerably exergonic, and if the loss of this proton is not concerted with the

donation of the hydride, the full energy of the two photons required to make the [Ru(bpy)2(pbnHH)]2+ is

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not recovered. The analogous reaction starting from the [Ru(bpy)2•−(pbnHH)]+ species does not confer

aromaticity on the pbnH• ligand, which is also stable with respect to proton loss.

Text S3. Details of Experimental Procedures

UV-vis spectra were measured in dry acetonitrile in a 1 cm quartz cuvette using an Agilent 8453 UV-

vis Diode Array spectrophotometer. The concentration of [Ru(bpy)2(pbnHH)]2+ was ca. 50 µM in all

experiments. Na/Hg reduction of an acetonitrile solution of [Ru(bpy)2(pbnHH)]2+ was performed under

vacuum using a high vacuum line and custom glassware. The progress of the reduction was followed

spectroscopically during gradual reduction of the starting material. The formation of the one-electron-

reduced product was assumed to be completed after deviation from isosbestic behavior of the UV-vis

spectrum was observed. The transient spectra of the excited state of [Ru(bpy)2(pbnHH)]2+ were

measured in dry de-aerated acetonitrile after excitation by the third harmonic of a Nd3+YAG laser and

probed by a Xe pulsed lamp. The detailed description of the setup can be found elsewhere(24). The

excited state quenching experiments were conducted using similar conditions and using 100 mM of 1,4-

diazabicyclo[2.2.2]octane (DABCO) as a quencher.

The hydride transfer reaction from [Ru(bpy)2(pbnHH)](PF6)2 to [CpRe(NO)(CO)2](BF4) was carried

out in CD3CN using custom glassware under vacuum. After a [Ru(bpy)2(pbnHH)]+ solution was

prepared from 3.5 mg [Ru(bpy)2(pbnHH)](PF6)2 using glassware equipped with a 0.5 mm optical cell, a

Na/Hg chamber and a break seal by the process described above, the camber containing the resulting

[Ru(bpy)2(pbnHH)]+ solution was separated by flame sealing. The glassware containing

[Ru(bpy)2(pbnHH)]+ was connected to another custom-made glassware with a chamber containing 3 mg

[CpRe(NO)(CO)2](BF4) solid and an NMR tube. The [Ru(bpy)2(pbnHH)]+ solution was added to the

[CpRe(NO)(CO)2](BF4) via a break seal, and the resulting mixture was transferred to the NMR tube,

which was separated by flame sealing. Gas samples were taken from the resulting reaction mixture in

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another part of the glassware for analysis using a Agilent 6890N GC equipped with TCD and FID

detectors, however, the quantification of the evolved CH4 (and CO) was difficult owing to the use of

liquid N2 during part of the procedure (i.e., some of the produced CH4 may have remained in the NMR

tube).

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D−H → D+ + H− ∆G*H− (D−H), hydricity of D−H (S1)

D−H → D− + H+ ∆G*H+ (D−H), acidity of D−H (S2)

D+ + 2e− → D− −2FE*(D+/D−), 2e− reduction of the conjugate acceptor (S3)

H2 → H− + H+ ∆G*hetero(H2), H2 heterolysis (S4)

2H+ + 2e− → H2 −2FE*(NHE), reduction of H+ (S5)

(S1) = (S2) − (S3) + (S4) + (S5)

∆G*H− (D−H) = ∆G*H

+ (D−H) + 2FE*(D+/D−) + ∆G*hetero(H2) − 2FE*(NHE) (S6)

Figure S1. Determination of the thermodynamic hydricity, eq. (S1), of the hydride donor (D-H) from

thermodynamic cycles based on the processes involving the acidity of D-H, eq. (S2), the two-electron reduction

of the conjugate hydride acceptor, eq. (S3), the acidity or heterolysis of H2, eq. (S4), and the reduction of H+, eq.

(S5).

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Orb 154 HOMO–3 Orb 155 HOMO–2 Orb 156 HOMO–1 Orb 157 HOMO

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Orb 158 LUMO Orb 159 LUMO+1 Orb 160 LUMO+2

Figure S2. TD-B3LYP/LANL2DZ (SCRF-PCM in CH3CN) calculations of [Ru(bpy)2(pbnHH)]

2+ indicate multiple d → π*pbn and d → π*bpy transitions in the visible

region of the spectrum. The HOMO–3, HOMO–2, and HOMO–1 are mostly ruthenium d orbitals, while the LUMO and LUMO+1 are π* orbitals delocalized over

the two bpy ligands. Most of the transitions are thus between Ru d and the π* bpy orbitals. The strong absorption at 431nm is mostly HOMO–1 → LUMO+2.

The HOMO → LUMO+2 excitations (highlighted in green) correspond to πpbn → π*pbn and make only a small contribution to the overall transition.

Experimentally, it has been determined that such π – π* transitions are difficult to quench because they fluoresce too rapidly. Structures that lack bpy ligands

are poor candidates for MLCT transitions. Thus it appears that [RuII(bpy)2pbnHH]

2+ is a candidate for visible-light excitation and reductive quenching.

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Figure S3. The singly-occupied molecular orbital (SOMO) of [Ru(bpy)2•−

(pbnHH)]+ showing delocalization

of the electron from the third reduction to be delocalized over the two bpy ligands.

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+ +→→→→ →→→→

Figure S5. Calculated structures of the reactants (left), transition state (center), and products (right) of

the reaction [Ru(bpy)2•−

(pbnHH)]+ + [CpRe(NO)(CO)3]

+ → [Ru(bpy)2(pbnH

•)]

2+ +

[CpRe(NO)(CO)2(CHO)]0. The transferring hydride ion is highlighted in pink. The ∆G* for the reaction is

predicted to be −6.7 kcal/mol from the ∆G*H−

,lfit values in Table 1. The calculated ∆H‡ is −0.6 kcal/mol,

and the calculated ∆G‡ is 12.6 kcal/mol. The [Ru(bpy)2

•−(pbnHH)]

+ reactant has 3 translational, 3

rotational and 267 vibrational degrees of freedom, and the [CpRe(NO)(CO)3]+ reactant has 3

translational, 3 rotational and 45 vibrational degrees of freedom for a total of 6 translational, 6

rotational and 216 vibrational reactant degrees of freedom, and a grand total of 273 reactant degrees of

freedom. The transition state (center) has 3 translational, 3 rotational and 267 vibrational degrees of

freedom (one and only one of which has an imaginary frequency and corresponds to translation along

the reaction coordinate), also for a grand total of 273 degrees of freedom. The loss of 3 translational and

3 rotational contributions to the entropy in the reactants when they are transformed into the transition

state is not compensated by the entropy gain from the 5 additional vibrational degrees of freedom of

the TS, so there is a large (13.2 kcal/mol) entropic contribution to the activation free energy.

N

N

N

H H

H

N

N

N

H

H

0.06

0.04

0.10

0.02

-0.11 -0.08

0.11

-0.05

0.13

-0.04

0.110.43

0.09

0.18

+ CpReINO(CO)2+ CpReINO(CHO)(CO)

0.00

[RuII(bpy)2pbnHH.−]+1 [RuII(bpy)2pbnH

.]+2

Figure S4. Mulliken atomic spin densities, [RuII(bpy)2pbnHH

•−]

+ → [Ru

II(bpy)2pbnH

•]

+2, in

acetonitrile.

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Table S1. Calculated standard free energies (kcal/mol) associated with the disproportionation reaction of [Ru(bpy)2pbnH•]2+ and [Ru(bpy)2(iso-pbnH•)]2+ in CH3CN solution.

Species or Reaction ∆G* relative to Ru(pbn)

Species or Reaction ∆G* relative to Ru(iso-pbn)

[Ru(bpy)2(pbn)]2+ 0.0 [Ru(bpy)2(iso-pbn)]2+ 0.0

[Ru(bpy)2(pbnH•)]2+ −371.8 [Ru(bpy)2(iso-pbnH•)]2+ −374.3

[Ru(bpy)2(pbnHH)]2+ −751.1 [Ru(bpy)2(iso-pbnHH)]2+

−753.8

Disproportionation ∆G* = −7.6 Disproportionation ∆G* = −5.2

Table S2. Calculated enthalpies and free energies (kcal/mol) for four intermolecular hydride transfer reactions.

Hydricity Half-Reactions Energy change in CH3CN

CpReI(NO)(CO)2 → CpReI(NO)(CHO)(CO) ∆Η ∆G ∆Η‡ ∆G‡

Ru(bpy)2•−(pbnHH)+ → Ru(bpy)2(pbnH•)2+ -8.2 -6.7 6.9 12.6

Ru(bpy)2(pbnHH)2+ → Ru(bpy)2(pbnH+)3+ 29.7 29.3 42.3 50.0

Cp*ReI(NO)(CO)2 → Cp*ReI(NO)(CHO)(CO) ∆Η ∆G ∆H† ∆G

†

Ru(bpy)2•−(pbnHH)+ → Ru(bpy)2(pbnH•)2+ -5.1 -3.1 10.2 17.3

Ru(bpy)2(pbnHH)2+ → Ru(bpy)2(pbnH+)3+ 32.8 35.3 37.3 44.4

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Table S3. DFT calculated geometrical parameters for intermolecular reactions at the B3LYP/LANL2DZ level of theory.

Property [Ru(bpy)2(pbnHH)]2+ [Ru(bpy)2•−(pbnHH)]+ [Ru(bpy)2(iso-pbnHH)]2+ [Ru(bpy)2

•−(iso-pbnHH)]+

React. TS Cp

TS Cp* React.

TS Cp

TS Cp* React.

TS Cp React.

TS Cp

TS Cp*

Ru-N, (pbn) Å 2.191 2.158 2.172 2.193 2.168 2.168 2.168 2.161 2.167 2.161 2.162

Ru-N, (pbn) Å 2.088 2.086 2.089 2.087 2.090 2.090 2.090 2.086 2.092 2.089 2.091

Re-CO, Å 2.074 2.050 2.050 2.053 2.053 2.050 2.045

C-O, Å 1.235 1.226 1.232 1.234 1.224 1.230 1.233

C-Hydride, Å 1.429 1.489 1.409 1.422 1.484 1.402 1.397

Hydride-CO, Å 1.318 1.277 1.349 1.344 1.272 1.342 1.343

νCO, Cp, cm-1 2040 2040 2040 2040

νCO, Cp*, cm-1 2021 2021 2021 2021

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