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 Academic Journal of Science, Engineering and Technology 

Vol.6, Issue 5; September - October 2021; 

1252 Columbia Rd NW, Washington DC, United States 

https://topjournals.org/index.php/TAJES/index; mail: topacademicjournals@gmail.com 

  

 

 

1 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

INTEGRATING THERMODYNAMIC AND KINETIC INFORMATION: INSIGHTS 

FROM POURBAIX DIAGRAMS IN ELECTROCHEMISTRY  
 

Dr. Emily Anne Mitchell and Dr. Alexander James Patel 
Department of Chemistry, York College, City University of New York 

 

 

Abstract: In the pursuit of sustainable energy solutions and environmental preservation, the need to meet the 

growing energy demands of the modern world has become increasingly pressing. This challenge has ignited a 

concerted effort to identify and harness renewable energy sources. Fuel cells have emerged as a promising avenue 

in this endeavor, primarily due to their ability to derive energy from solar power and the readily available supply 

of water. This paper delves into the quest for efficient catalysts to facilitate the reversible process of water splitting, 

a critical step in hydrogen production. Furthermore, we explore the cathodic process of hydrogen oxidation in 

hydrogen fuel cells. This work draws inspiration from nature's hydrogenase enzymes, which exhibit remarkable 

efficiency in catalyzing both of these processes. The insights gained from studying hydrogenase enzymes offer 

valuable guidance in the design and development of hydrogenase-like catalysts, paving the way for cleaner and 

more sustainable energy production. 

Keywords: Renewable energy, Fuel cells, Water splitting, Hydrogen production, Hydrogenase enzymes  
 

 

1.  Introduction 

The challenge of meeting the energy demands of the modern age while preserving environmental quality is driving 

a push towards finding renewable energy sources.1-5 Fuel cells are one such target because the energy source can 

be garnered from solar power and the naturally abundant water supply.6 We are exploring ways to design efficient 

catalysts for reversibly carrying out the water splitting process. Hydrogen production is a fundamental step in 

water splitting, and hydrogen oxidation is the cathodic process in a hydrogen fuel cell.7 Hydrogenase enzymes 

catalyze both processes with extreme efficiency and are thus useful as a learning tool to help in the design of 

hydrogenase-like catalysts.8   

In this paper, computational methods are applied to explore features of catalysts, inspired by hydrogenase 

enzymes, and evaluate their contributions to overall catalytic ability. The role of the ligand architecture and the 

influence of solvent on the catalysts’ ability to function in a thermodynamically realizable regime for 

protoncoupled electron-transfer processes are the primary focus.  We adopt a systematic approach of describing 

a set of possible mechanistic routes for H2 production and oxidation and characterize the intermediates in order 

to elucidate the most energetically favored reaction mechanism. In the vast potential energy landscape of these 

model systems, this approach could reveal starting structures that can be used to explore transition states at critical 

junctures along the reaction coordinate. Insight gained from understanding the mechanism of how these catalytic 

models function can be correlated with the electrochemical operating conditions of the experiments. Together, the 

information offers the opportunity to recommend more efficient designs. This paper is organized as follows: 

Section II (Background/Motivation) introduces two crystal structures and corresponding data for experimentally 

characterized hydrogenase-inspired model catalysts that motivated this work; Section III (Method) describes the 

computational approach of using free energy profiles and coupled Pourbaix diagrams as a tool for understanding 

the reaction mechanism and determining the electrochemically tunable aspects of catalyst design; Section IV 

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2 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

(Results) first introduces the proposed mechanistic routes of H2 oxidation and production and describes the 

intermediates. Using these intermediates as the reference compound, free-energy profiles are calculated to 

establish the favored mechanistic route.  

Next this section summarizes the properties of calculated coupled Pourbaix diagrams which illustrate the optimal 

electrochemical operating regimes for the catalyst. Section V (Conclusion) summarizes the work and attempts to 

identify trends in the results.  

2. Background/Motivation   

Catalysts for hydrogen production and oxidation which utilize metal centers coordinated by diphosphine ligands 

with nitrogen pendent bases have been explored by several experimental groups.9-14 A recent review summarizes 

a series of hydrogenase mimics utilizing nickel and cobalt transition metals.15 These catalysts bear some structural 

resemblance to the active site of hydrogenase enzymes; they employ a nickel metal center as in the Ni-Fe 

hydrogenase, but only a single metal center at which hydrogen oxidation and production occurs. Crystal structures 

have been characterized for these catalysts that indicate that the nickel center is in a 4-coordinate configuration 

with the two diphosphine ligands, indicative of the NiII oxidation state.10,14,16-19 The diphosphine ligands and alkyl 

group substituents are oriented to place nitrogen atoms at a distance of around 3.4 Å from the metal center. Fig.1.   

Compound A, [Ni (PPh
2N

Ph
2)2(CH3CN)](BF4)2 where PPh

2N
Ph

2 is 1,3,5,7tetraphenyl-1,5-diaza-3,7 

diphosphacyclooctane, has phenyl groups attached to the phosphorous and nitrogen base sites and an explicit 

acetonitrile ligated to the metal center.20,21 Compound A has been shown to perform best as an H2 production 

catalyst. Compound B, [Ni (PCy
2N

Bz
2)2](BF4)2, has cyclohexyl (Cy) groups on phosphorous and benzyl (Bz) 

groups on the nitrogen base sites and has been shown to perform best as an H2 oxidation catalyst. However, the 

turnover frequency for these models is still well below that of the Ni-Fe Hydrogenase enzyme.  

The natural enzyme has turnover rates of 700 s-1,20,22 while compound A has a turnover rate of 350 s-1 and 

compound B has a turnover rate of 10 s-1.20,21 The availability of the experimental structural and some kinetic data 

offers a good opportunity for theoretical methods to be used to characterize the effect of various features, or design 

principles, for such catalysts, and to understand which effects are likely to have the greatest influence in the 

reversibility and efficiency of future designs. Using density functional theory coupled to implicit solvation 

schemes,23 the freeenergy profiles of proposed mechanistic routes, as well as the associated pKa values and 

reduction potentials (E1/2), have been calculated for computational models of A and B.  

 
Fig.  1:  Crystal  structures  from  DuBois  references  are:  (A)  

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3 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

[Ni(PPh
2N

Ph
2)2(CH3CN)](BF4)2 PPh

2N
Ph

2 = 1,3,5,7-tetraphenyl-1,5-diaza-3,7diphosphacyclooctane, shown to 

work in the H2 production direction; and (B)  

[Ni(PCy
2N

Bz
2)2] shown to work in the H2 oxidation direction.  

3. Method 

A.   Computational Method  

Density Functional Theory (DFT) was employed using the hybrid functional B3LYP24-26 and a 6-31G(d,p) (5D, 

7F) basis set in the Gaussian 03 program package.27,28 Frequency calculations were performed at the optimized 

geometries to confirm minimum geometries and obtain the sum of electronic and thermal free energies for each 

species. Atomic charge and spin populations were calculated at the optimized geometry to confirm the oxidation 

state of the metal center and charge state of the ligands. To obtain the free energy of solvation, a conductor-like 

polarizable continuum model (CPCM)29-32 was used to mimic the solvent, and the radii around the solute were 

carefully selected in such a way that charged species achieved greater interaction with the continuum through the 

use of smaller solvation radii.32,33 In this case, Bondi radii34 were used, and two parameters were adjusted to 

provide the lowest solvation free-energy possible for the model.35,36   

A sphere overlap index of 0.8Å and minimum radius for added spheres of 0.5Å were used based on a series of 

tests using the same functional and basis set. Both adjustments result in a smaller number of added spheres. 

Without these adjustments, the solvation free-energy remains too high and contributes to extremely acidic pKa 

values, not in the range of the known experimental values.35,36 Lowering the solvation free-energy by adjusting 

these parameters calibrates our method with the experimental values of the crystal structures provided. The only 

solvent considered throughout this paper is acetonitrile, as used in the experimental conditions.  

1. Pourbaix Diagrams Used For Proton Management.  
With the goal of understanding the mechanism for H2 oxidation and production in hydrogenase-inspired 

compounds, theory and experiment align to gain valuable insight into fundamental processes in these catalysts.7,37 

The Pourbaix diagram shows the thermodynamically stable form of a chemical species as a function of applied 

potential and pH, spanning all oxidation states accessible by redox reactions and/or acid/base reactions. The 

horizontal and diagonal lines plotted on the diagram are the half-potentials, i.e., the reduction potentials for all 

redox couples at the condition of equal concentration of the reduced and oxidized forms of the species, as a 

function of the solution pH. The vertical lines are the pKa values of protonated forms of the species.  

  
Fig. 2: Schematic illustration of coupled Pourbaix diagram. Shaded region (green) is the overlap between the 

PCET regions of the NII/I and NiIII/II(H-) redox couples that must align at the same pH conditions to promote 

optimal catalyst performance for H2 oxidation or production. The red and blue Pourbaix diagrams are coupled by 

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4 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

oxidative addition or reductive elimination reactions between intermediates connected by purple double-headed 

arrows and heterolytic cleavage or association reactions between intermediates connected by green double-headed 

arrows. 

For mechanisms that involve thermal reactions to produce intermediates not reached by redox processes, Pourbaix 

diagrams can be combined in order to provide an effective description of the process, as in Fig. 2. An example of 

such a thermal reaction is the rapid intramolecular proton transfer between a reduced metal center and a pendent 

base (i.e., reductive elimination or oxidative addition). Coupled Pourbaix diagrams can provide crucial 

information about the performance of a given catalyst. For example, if the mechanism operates by way of an 

oxidative addition reaction that transforms a NiI to a NiIII(H-) species that is the precursor to further redox 

chemistry, these two species must be able to coexist at similar pH and potential. Furthermore, such a reaction 

would ideally have ∆G° = 0. A more detailed explanation of coupled Pourbaix diagrams has been given in our 

previous paper.42 More fundamental details of the method are described in the supporting information. 

2. p Ka Calculation.  
To be able to compare to experiments, the pKa is calculated by constructing a thermodynamic cycle as shown in 

Scheme 1 and similar in approach to ref 37.39,43   

Gg 

 HA A-(g) + H+(g) 
G

s(HA) Gs(H ) 

 HA(sol) A-(sol) + H+(sol)   
  

Scheme 1 General thermodynamic cycle used to calculate pKa in acetonitrile 

solvent.  

∆Gg is the free-energy change of the acid dissociation reaction in the gas phase where  

∆Gg = Gg(A
-) + Gg(H

+) – Gg(HA) calculated with DFT at 1 atm standard state.32,44   

  
G

solo ΔGo * pKa  

 2.303RT  (1)  

DGs
o
ol =DGg +DDGs

o (2)  

In this construct, equations (1) and (2) are used to solve for the pKa. ∆Go
sol is the free-energy change of the acid 

dissociation reaction in solution where ∆∆Gsol = ∆Gsol(A
-) + ∆Gsol(H

+) – ∆Gsol(HA).45 The solvation free energy 

was approximated with a polarizable continuum model (PCM) solvation model.30,39 The difference between 

standard states of the gas phase and solution phase is reconciled by the ∆Go→* term, taken to be 1.89 kcal/mol.39 

The solvation free-energy of the proton in acetonitrile solvent is taken from the literature to be -260.2 kcal/mol.46 

The gas-phase free energy of the proton is also taken from the literature as a value of -6.28 kcal/mol, calculated 

from the Sakur-Tetrode equation.46  

3.  Reduction Potential Calculation.  
To calculate the standard reduction potential, a second thermodynamic cycle is constructed as shown in Scheme 

2. In this construct, the Nernst equation represented by equations (3) and (4) is used to solve for the reduction 

potential.46,47  

Gg 

( g ) 

) ( A s  
 G 

o 
sol G  

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5 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

 + - 

 Ox(g) + mH (g) + ne HRed(g) 
Gs(Ox) Gs(H ) G 0 Gs (HR ed) 

Ox(sol) + mH+(sol) + ne (sol) HRed(sol)   
  

Scheme 2 General thermodynamic cycle used to calculate the reduction potential in acetonitrile solvent.  

(DGOox|Red - DGRoHE ) 

 E
Oox|Red =-   (3)  

nF 

  

E=EOox|Red - RT lnæça Red ÷ö- m×0.0591×pH (4)  

nF èaOx ø n  

The absolute free energy of the normal hydrogen electrode DGR
o
HEin  

acetonitrile solution was calculated to be 4.63V and is very close to the value of 4.48V reported in ref 37. EO
o

x|Red 

is at unit (i.e., 1 molar) activity of oxidant and reductant (at pH 0). The reduction potential is related to the free 

energy that the catalyst needs to obtain n electrons from the normal hydrogen electrode via the reaction as in 

equation (5).  

H++e-
g ® (1/2) H2  (5) 

As illustrated in the thermodynamic cycle, the number of protons is designated by m and the number of electrons 

is designated by n. As such, the slope of the reduction potential with respect to pH is governed by the ratio m/n.    

The solvation free-energy of H2 is calculated in acetonitrile solution using the same optimization parameters as 

in the model systems. The inherent error arising from the approximations introduced by the implicit solvation 

model is estimated to be on the order of 0.09-0.13V. This error corresponds to pKa differences of around 2 pH 

units with respect to the experiments.  

4.  Results  

A.  Mechanistic Routes for H2 Oxidation/Production.  
Based on several studies on hydrogenase enzymes,19,48 the mechanism for H2 oxidation/production is thought to 

proceed via a heterolytically cleaved intermediate in which the hydride ion is attached to the metal center, forming 

a metal hydride, and the proton is attached to the base. We define this as Type-I H2 bond cleavage. An alternative 

to this Type-I H2 bond cleaved intermediate is the second heterolytically cleaved intermediate, which has been 

observed experimentally by NMR spectroscopy in some characterized catalyst models, in which both protons 

from the hydrogen molecule attach to different pendent base groups while the two electrons reduce the NiII metal 

center to Ni0. We define this as Type-II H2 bond cleavage.  

The ability to reach higher or lower oxidation states of the metal and to change the basicity of the pendent base(s) 

can be tuned by the choice of substituent on the catalyst as shown in our previous studies.42 In this paper, we 

describe possible mechanistic routes for H2 oxidation and production which involve Type-I and TypeII H2 bond 

cleaved intermediates. Analysis of the intermediates appearing in nonelectrochemical and electrochemical 

reactions and the free-energies along these two main routes, Type-I and Type-II H2 bond cleaved intermediates, 

can be linked to the experimental operating regime and offers insight into which conditions can be tuned for 

optimal catalyst performance.  

The possible mechanistic routes for both [Ni(PPh
2N

Ph
2)2(CH3CN)] and [Ni(PCy

2N
Bz

2)2] models have been 

generically summarized in Fig. 3. Starting from the bare catalyst with the metal in the 2+ oxidation state, 

intermediate (0), upon addition of the H2 molecule leads to two main branches considered herein. The first branch 

( g ) 

- 
o 

Red | Ox G  

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6 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

leads to intermediate (1a) in which a Type-II bond cleaved H2 symmetrically protonates both nitrogen base sites 

and the electron reduces the metal to the Ni0 state. In a recent publication, the Ni0 intermediate is described as 

being important to intramolecular proton exchange processes in the cycle.49 The second branch leads to 

intermediate (1b) in which a Type-I bond cleaved H2 asymmetrically protonates the nitrogen base site and adds a 

hydride (H-) to the metal center. The H2 addition reaction from intermediates 0  1 is considered a non-

electrochemical reaction and relies on a reasonable activation free energy needed to form either (1a) or (1b). The 

next step towards H2 oxidation is the first of the two electrochemical reactions shown in the chemical equation 

H2  2H+ + 2e-.50  

These electrochemical reactions depend on the potential applied to the electrodes and the pH of the solution. The 

balance between pH and potential will dictate whether the proton and electron transfers occur sequentially or in 

a concerted manner described as proton-coupled electron transfer (PCET). As shown in Fig. 3, if sequential 

electrochemical reactions occur then intermediates (2a), (2b), (3a), and (3b) can be isolated and characterized 

depending on whether intermediate (1a) or (1b) prevails after H2 addition. A key factor in H2 oxidation processes 

is the formation of a metal-hydride intermediate along the mechanistic route. In the case where intermediate (1a) 

is formed upon H2 addition, an additional non-electrochemical reaction is needed from intermediate 2  3 to form 

the key metal-hydride intermediate. In this oxidative addition, the proton on the nitrogen base gets donated to the 

Ni0 as a hydride and oxidizes the metal to NiII.  

In the case where intermediate (1b) is formed, the oxidative addition reaction is unnecessary because the metal-

hydride intermediate is already present. The next step towards H2 oxidation is another non-electrochemical 

reaction from intermediate 4  5.   

This reductive elimination is an intramolecular transfer where the hydride donates a proton the nitrogen base and 

an electron to reduce the metal from NiIII to NiI. Lastly, the final step to complete H2 oxidation is the second of 

the two electrochemical reactions in the process. 

 
Fig. 3. Summary of mechanistic routes leading to H2 oxidation for Nickel diphosphine model catalysts. 

Intermediates along this direction are classified as reaction steps producing intermediates in the order, 0   1  

2  3  4  5  6  0.  The H2 production direction for the model is exactly the reverse process where the 

intermediates in the reaction steps are ordered by 0  6  5  4  3  2  1  

 0.  

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7 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

Again there will be a dependence on the applied potential and pH in determining if the reactions will be sequential 

or PCET. If sequential then intermediates (6a) or (6b) can be isolated and characterized. Catalysis in the H2 

production direction involves the 2H+ + 2e-  H2 reaction which allows us to consider the possible mechanistic 

routes as the reverse of the H2 oxidation direction previously described. For the non-electrochemical reactions, 

reductive elimination is the reverse of the oxidative addition reaction and H2 release is the reverse of the H2 

addition reaction. These non-electrochemical processes are similarly governed by the kinetics of those reactions. 

For the electrochemical reactions, sequential or PCET processes are governed by the applied potential and pH of 

the reaction conditions. Therefore, for ease in describing the intermediates in these mechanistic routes, we 

subdivide them into two categories, those encountered in the non-electrochemical reactions and those encountered 

in the electrochemical reactions.   

One reason is that the two categories of reactions can be controlled differently. The behavior of species involved 

in the non-electrochemical reactions can be controlled by knowing the structure and energy of the transition states 

and by tuning the ligands such that the intermediates are close in energy (i.e. ∆G = 0). The species involved in 

the electrochemical reactions can be controlled by tuning the ligands to control the pH in which they operate and 

tuning the metal to control the oxidation states reached when a potential is applied. We discuss these two 

categories next and discuss the calculated results of [Ni(PPh
2N

Ph
2)2(CH3CN)] and [Ni(PCy

2N
Bz

2)2] model 

compounds.  

B.   Non-electrochemical intermediates  

Non-electrochemical intermediates in H2 oxidation/production reactions are dominated by kinetic processes so it 

becomes important to describe the activation energy barrier in these reactions which can ultimately be compared 

to the rates achieved in the experiments. The two non-electrochemical intermediates for which we attempt to 

determine the transition states occur in Fig. 3 between intermediates 0   

1, which we define as the H2 adduct, and intermediates 4  5 which we define as a thermal reaction common to 

all mechanistic routes shown in Fig. 3.  

1.   H2 adduct  

The energy of the intermediate formed upon H2 addition is one marker for the catalytic direction that the molecular 

catalyst favors. If the energy of the cleaved intermediate is favored (i.e. -∆G) with respect to the H2 adduct, the 

catalyst is likely to function as an H2 oxidation catalyst. Otherwise, the catalyst prefers scavenging available 

electrons and protons from the reservoir, combining them to produce H2. As such we explored several possible 

conformers of the H2 adduct and quantified their energies with respect to the Type-I or Type-II H2 bond cleaved 

intermediates. This will be a useful starting structure to use for transition state searches.  Beginning from different 

conformers of the H2 adduct to [Ni(PCy
2N

Bz
2)2], three stable intermediates were located as shown in Fig. 4(i), 4(ii) 

and 4(iii).  

 Cy Bz 

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|  https://topjournals.org/index.php/AJSET 

Fig. 4. Intermediates of the H2 adduct to [Ni(P 2N 2)2] model. (i) loosely bound dihyrogen[NiII…H2]
2+; (ii) strongly 

bound dihydrogen [NiII(H2)]
2+; and (iii) dihydride [NiIV(H-)2]

2+ trans axial the plane of the metal center and 

phosphorous atoms.  

Table 1: Intermediates of the H2 adduct for the [Ni(PCy
2N

Bz
2)2] model.  

  [NiII…H2]2+  [NiII(H2)]2+  [NiIV(H-

)2]2+ trans 

axial  

Bond Length 

(Å)  

(i)  (ii)  (iii)  

H1---H2  0.8  0.8  3.0  

Ni---H1  2.9  1.7  1.5  

N---H1  2.4  2.4  2.8  

  

Angle (degrees) 

P1---Ni---P2  

  

  

81.5  

  

  

81.2  

  

  

82.8  

P3---Ni---P4  81.5  81.2  82.8  

P1---Ni---P3  158.6  169.2  105.1  

P2---Ni---P4  156.8  141.3  105.1  

H1---Ni---H2  14.6  25.8  180.0  

P2---Ni---P3  102.9  102.5  149.8  

P1---Ni---P4  102.9  102.4  150.0  

These intermediates, labeled (i), (ii), (iii), ordered energetically from lowest to highest are [NiII∙∙∙H2]
2+, 

[NiII(H2)]
2+ and [NiIV(H¯)2]

2+, respectively. Bond distances shown in Table 1 confirm the assignment of (i) as a 

dihydrogen loosely bound to the catalyst and (ii) as a dihydrogen strongly bound to the metal center, given the 

short HH bond of around 0.8 Å.   

The (i) and (ii) intermediates have similar distances from the nearest H atom to the nitrogen base sites of 

approximately 2.4 Å, a reasonable PT distance under the appropriate acid/base conditions.  

The third H2 adduct, (iii), is a trans axial dihydride across the plane of the metal center and the four phosphorous 

atoms, and has longer distances between the hydride and nitrogen of around 2.8 Å. The trans axial positioning of 

the hydrides across the metal phosphide plane was the only possible dihydride complex that could be found for 

this catalyst model given the low flexibility of the boat/boat configuration of the diphosphine rings with respect 

to the metal center. 

On the other hand, starting from many different conformers, the H2 adduct to [Ni(PPh
2N

Ph
2)2(CH3CN)] converged 

to four stable intermediates, ordered energetically from lowest to highest in Fig. 5. Similar to the [Ni(PCy
2N

Bz
2)2] 

model, intermediates (i’), (ii’) and (iii’) are the loosely bound dihydrogen, strongly bound dihydrogen and trans 

axial dihydride respectively, as shown by the bond distance and angles in Table 2. However, an additional H2 

adduct found for this system is a complex with the dihydride atoms on the same face of the metal-diphosphine 

plane, third highest in energy from the other H2 adducts, as shown in figure 6. For this case, both hydride ions 

remain on the same side of the metal phosphide plane because the boat/chair conformation of the diphosphine 

rings offers more flexibility at the metal center.  

This dihydride intermediate [NiIV(H¯)2(CH3CN)]2+ has Nickel hydride bond lengths of 1.5Å, similar to the 

dihydride of the [Ni(PCy
2N

Bz
2)2] model. Figure 6 summarizes the comparison of the energies of the various H2 

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|  https://topjournals.org/index.php/AJSET 

adducts with respect to the Type-II H2 bond cleaved (1a) and Type-I H2 bond cleaved (1b) intermediates for the 

two models. Figure 6(A) for the [Ni(PPh
2N

Ph
2)2(CH3CN)] model shows that the dihydride intermediate (iv’) is 

nearly isoenergetic with the Type-II H2 bond cleaved  intermediate (1a), differing in energy by 0.06 eV. Figure 

6(B) for the [Ni(PCy
2N

Bz
2)2]  model shows that the energies of the loosely bound dihydrogen complex (i) and the 

Type-I H2 bond cleaved [NiII(H-)-NH+]2+ intermediate (1b) are nearly isoenergetic, differing by only 0.023 eV.  

Likewise, the energies of the dihydride (iii) and the TypeII H2 bond cleaved intermediates (1a) are relatively 

similar, differing by 0.14 eV. The H2 adduct nearest in energy to the Type-I or Type-II H2 bond cleaved species is 

a good starting point for locating the transition state of this initial step and efforts are underway in this search. 

The trend in Figure 6 shows that formation of the Type-II H2 bond cleaved intermediate (1a) will likely be 

preceded by a dihydride intermediate, and similarly, formation of the Type-I H2 bond cleaved intermediate (1b) 

will likely be preceded by the dihydrogen complex.  

 
  

Fig. 5: Intermediates of the H2 adduct to [Ni(PPh
2N

Ph
2)2(CH3CN)] model. (I’) loosely bound dihydrogen 

[NiII…H2]
2+; (ii’) strongly bound dihydrogen [NiII(H2)]

2+; (iii’) trans axial dihydride [NiIV(H-)2]
2+ and (iv’) 

[NiIV(H¯)2]
2+ dihydride intermediate.  

Table 2: Intermediates of the H2 adduct for the [Ni(PPh
2N

Ph
2)2(CH3CN)] model ordered energetically from lowest 

to highest. 

  [NiII...H2]2+  [NiII(H2)]2+    [NiIV(H-

)2]2+  

[NiIV(H-

)2]2+ trans 

axial  

Bond Length 

(Å)  

(i’)  (ii’)  (iv’)  (iii’)  

H1---H2  0.8  0.8  1.9  3.0  

Ni---H1  2.8  1.8  1.5  1.5  

N---H1  2.5  2.5  2.2  2.6  

Ni---NCCH3  

  

4.8  

  

4.8  

  

5.8  

  

4.6  

  

Angle (degrees)  
  

P1---Ni---P2  

  

83.5  

  

83.6  

  

84.8  

  

84.1  

P3---Ni---P4  83.6  83.5  84.8  84.1  

P1---Ni---P3  171.7  171.7  161.1  150.9  

P2---Ni---P4  137.8  137.8  109.3  153.4  

H1---Ni---H2  16.4  25.6  81.4  180.0  

) ii' ( ) iii’ ( iv’ ( ) ( i ') 

  

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P2---Ni---P3  99.6  99.3  106.3  102.6  

P1---Ni---P4  99.3  99.6  106.3  102.6  

  

The stability of these H2 adduct intermediates, as confirmed by gas phase frequency calculations, may offer insight 

into the nature of the transition state needed to reach the Type-I or Type-II H2 bond cleaved intermediate.  

  
Fig. 6. Energetics of the H2 adduct with respect to the Type-I and Type-II H2 bond cleaved intermediates. Energy 

differences are taken with respect to the free catalyst and H2.   

2.  Thermal reaction common to all mechanistic routes – Intermediates and Transition States  

The second non-electrochemical reaction along the H2 production mechanistic route is an oxidative addition 

involving intermediates 5 → 4 of Fig. 3, the reverse of which is considered a reductive elimination. In an optimal 

catalyst, the freeenergy for this step should be nearly isoenergetic (i.e. ∆G  0) and the free-energy of activation 

(∆G ) should be low. We calculate the transition state at this reaction step to understand the structure and 

energetics of the reacting species. Fig. 7 shows the structures of the transition states characterized by the negative 

eigenvalue of the hessian matrix along the donor/acceptor mode between the metal center and the nitrogen base 

site of compounds A and B. Distances and angles of the reacting species are shown in table 3 for the 

[Ni(PPh
2N

Ph
2)2(CH3CN)] model and table 4 for the [Ni(PCy

2N
Bz

2)2]  model. The tables show that the transferring 

proton is approximately midway between the donor atom (Ni) and the acceptor atom (N) for both compounds.  

  

  

 
  

A B 

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Fig. 7. Oxidative addition  transition state, between intermediates 5 → 4, for compound A, 

[Ni(PPh
2N

Ph
2)2(CH3CN)] model and compound B, [Ni(PCy

2N
Bz

2)2] model.  

The transferring proton is midway between the donor atom (Ni) and acceptor atom (N).    

Table 3 Oxidative Addition 5 → 4 in the [Ni(PPh
2N

Ph
2)2(CH3CN)] model for H2 production.  

  

   Intermediate (4) Transition State Intermediate (5)  

Bond Length (Å)  P  TS  R  
Ni---H1  1.46  1.67  2.86  

N---H1  2.31  1.46  1.03  

Ni---NCCH3  5.78  5.75  5.47  

        

frequency of   

Ni—H—N mode  

(cm-1)  

 ---    

921.01i  

 ---  

        

Angle (degrees)        

P1---Ni---P2  86.07  82.52  85.51  

P3---Ni---P4  83.54  82.92  86.44  

P1---Ni---P3  159.78  157.99  145.20  

P2---Ni---P4  109.77  112.92  121.54  

P2---Ni---P3  107.39  105.56  111.98  

P1---Ni---P4  106.49  106.54  110.48  

        

∆Go
s (R & P) (eV)  

∆G  (TS) (eV) relative 

to reactant  

0.32    

0.60  

0.00  

 
In the [Ni(PPh

2N
Ph

2)2(CH3CN)] model, the flexibility of the boat/chair configuration allows for large 

rearrangements of the angles around the diphosphine plane. For example, the P1---Ni---P3 and P2---Ni---P4 

angles undergo the largest changes between the reactant (R), transition state (TS) and product (P) configurations, 

shown in table 3. The constraint of the boat/boat configuration in the [Ni(PCy
2N

Bz
2)2]  model shows much less 

rearrangement of the angles between the (R), (TS) and (P), as seen in Table 4.    

Comparing the transition states of the two compounds, Table 3, shows that the P---Ni---P angles of the (TS) have 

more product character than reactant character while Table 4 shows the opposite behavior for the [Ni(PCy
2N

Bz
2)2]  

model. In other words, both transition states have diphosphine bite angles similar to intermediate (4) of Fig. 3.  

This implies that the barrier for oxidative addition will be higher than the barrier for reductive elimination. Given 

nature of the transition state structurally appears to be associated with the bite angle and is therefore impacted by 

the amount of steric bulk from the ligands. As such, consideration should be given to designing the catalyst with 

some flexibility in the first coordination shell to the metal center.   

Table 4: Reductive Elimination 4 → 5 in the [Ni(PCy
2N

Bz
2)2] model for H2 oxidation.  

 

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   Intermediate (4) Transition State Intermediate (5)  

Bond Length 

(Å)  

R  TS  P  

Ni---H1  1.46  1.74  2.91  

N---H1  2.79  1.68  1.03  

        

frequency of   

Ni—H—N 

mode   

(cm-1)  

 ---    

654.89i  

 ---  

        

Angle (degrees)        

P1---Ni---P2  82.07  82.06  82.49  

P3---Ni---P4  82.06  82.07  83.62  

P1---Ni---P3  152.66  152.66  147.20  

P2---Ni---P4  147.62  147.02  146.35  

P2---Ni---P3  105.80  105.79  105.94  

P1---Ni---P4  105.79  105.80  107.08  

        

∆Go
s (R & P) 

(eV)  

∆G  (TS) (eV) 

relative to 

reactant  

0.00    

0.48  

-1.07  

 
C.   Electrochemical intermediates  

The second category of intermediates along H2 oxidation/production mechanistic routes are the electrochemical 

intermediates, those involving redox and acid/base reactions. In Fig. 3, the first of the two electrochemical steps 

in the 2H+ + 2e- → H2 reaction occurs between intermediates (1) and (4), and the second occurs between 

intermediates (5) and (0). The electrochemical reactions can be sequential PT and ET or concerted PCET. If 

sequential, the order of ET followed by PT or vice versa is not easily determined a priori and depends on the pH 

of the experimental conditions, along with the potential needed to reach redox species along the mechanistic route.   

Therefore, we calculate the free-energy profile along various mechanistic routes to understand which species are 

energetically likely to dominate.   

D. Free-energy Comparison of Type-I and Type-II H2 bond cleaved mechanistic routes      

The characterized catalyst (A), has been shown to operate as an H2 production catalyst while (B) has been shown 

to operate as an H2 oxidation catalyst. As such, we explore the free-energy profiles of each calculated model 

catalyst along the catalytic direction in which they are thought to operate. An important component in determining 

the mechanism is the formation of the H2 adduct as the first step in the H2 oxidation direction. As such, this 

importance is highlighted by using a proposed adduct as the reference compound in the free energy profiles, 

instead of the bare catalyst plus a gas phase hydrogen molecule. In doing so, the magnitude of the free energy of 

key steps (i.e. PCET and electrochemical steps) is similar to the corresponding free energy steps of our previous 

paper.42 Efforts are underway to determine the true transition state of these key steps.  

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1.   H2 Production in [Ni(PPh
2NPh

2)2(CH3CN)].     
Free-energy calculations on the [Ni(PPh

2N
Ph

2)2(CH3CN)] model were performed, and will be discussed here in the 

catalytic direction for H2 production. Figure 8 illustrates the calculated free-energy versus the reversible hydrogen 

electrode (RHE) along the proposed H2 production mechanistic routes at pH = 0. Intermediates along the reaction 

coordinate, emphasizing the distinction between the two Type-II H2 bond cleaved (Paths 1 and 2) and two Type-

I H2 bond cleaved (Paths 3 and 4) routes are explained in the caption.  

  
Fig. 8: Summary of mechanistic routes leading to H2 production of  

[Ni(PPh
2N

Ph
2)2(CH3CN)] at conditions of pH = 0. Energy differences are taken with respect to the first point, the 

H2 adduct, and normalized to the reversible hydrogen electrode (RHE). Intermediates involved in each route are:  

Type-II  Path 1(blue): 0  6a  5  4  3a  2a  1a  0.   

Type-II  Path 2(orange): 0  6a  5  4  3b  2b  1a  0.   

Type-I Path 3(green): 0  6b  5  4  3a  1b  0.   

Type-I Path 4(purple): 0  6b  5  4  3b  1b  0.  

In figure 8, the Type-II H2 bond cleaved routes are the ones in which intermediate (1a) is involved in the 

mechanism and Type-I H2 bond cleaved routes involve intermediate (1b). Panel (a) illustrates that when the two 

Type-II H2 bond cleaved routes are compared, path 1 (blue), which follows intermediates 0  6a  5  4  3a 

 2a  1a  0, is a lower energy route than path 2 (orange). The Ni0NH+ (2a) and NiII(H-)-N (3a) are lower in 

energy than +HN-NiI-NH+ (2b) and NiIII(H-)-NH+ (3b). 

Panel (b) illustrates that when the Type-I H2 bond cleaved routes are compared, path 3 (green) which follows 

intermediates 0  6b  5  4  3a  1b  0, is a lower energy route than path 4 (purple). Again, the difference 

here is that NiII(H-)-N (3a) is lower in energy than NiIII(H-)-NH+ (3b). Panel (c) then compares the lowest energy 

route for both Type-I and Type-II H2 bond cleaved routes, paths 1 and 3, and is a key feature in this energy 

analysis. The comparison shows that the first electrochemical step, involving intermediates 0 → 5 is nearly 

isoenergetic. Viability of this first electrochemical step becomes important for the discussion in Section IV C 

about the appropriate pH regime at which the experiment should be operated.   

The subsequent electrochemical step leads to the [NiI-NH+]2+ reduced metal, protonated base defined as 

intermediate (5). If PCET conditions prevail, then intermediate (6) is not observed, otherwise intermediate (6a) 

would be favored. The oxidative addition that follows, common to all four proposed mechanistic routes, in which 

the base loses the proton to the metal center as a hydride forming the [NiIII(H)-N]2+ intermediate (4), has an 

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associated free-energy change of 0.324 eV (7.47 kcal/mol). The second electrochemical reaction involving 

intermediates 4 → 1, show significant deviation between Type-I and Type-II H2 bond cleaved routes. Focusing 

on the H2 adduct that is formed in intermediate 1, before release of the H2 molecule, intermediate 1a is 0.369 eV 

higher in energy than intermediate (1b). However, since the intermediate (1a) is higher in energy than the 

dihydrogen complex (iii) then H2 release is favored, making this route consistent with the experimentally 

characterized results of the H2 production catalyst. The dihydrogen H2 adduct was chosen as the reference 

compound for this comparison.  

  
Fig. 9. Type-II H2 bond cleaved path 1 for H2 production of the  

[Ni(PPh
2N

Ph
2)2(CH3CN)] model catalyst.  The intermediates along this Path are 0  6a  

 5  4  3a  2a  1a  0.   
Fig. 9 summarizes the Type-II H2 bond cleaved mechanistic route 1 for the [Ni(PPh

2N
Ph

2)2(CH3CN)] model. Under 

the appropriate pH conditions, a proton from the solution can attach to the catalyst at a nitrogen base site (6b), or 

an electron from an applied potential can reduce the metal center, from NiII to NiI (6a).  Depending on whether 

intermediate (6a) or (6b) is formed, a subsequent electron transfer (ET) or proton transfer (PT) leads to the reduced 

metal with a protonated base, intermediate (5). The increased basicity of the metal center then causes the proton 

to transfer from the pendent base to the metal to form the metal-hydride, intermediate (4), through an oxidative 

addition reaction (Fig. 3, step 5 → 4).   

The next step (Fig. 3, step 4 → 3), is again determined by the pH of the solution or the applied potential. If the 

pH allows for the availability of protons, the base becomes protonated, forming the metal-hydride with a 

protonated base (3b). Otherwise, an appropriate applied potential forms the reduced metal-hydride (3a). Of the 

two intermediates formed in step 4 → 3, (3a) and (3b), each has two alternatives along the reaction coordinate to 

H2 production. If the reduced metal-hydride (3a) is formed, it can undergo PT immediately or as a second step 

after reductive elimination.   

If the PT from the solution to the catalyst is favored, the Type-I H2 bond cleaved intermediate (1b) is formed. If 

reductive elimination is favored, the hydride transfers from the metal to form a proton on the pendent base as 

intermediate (2a).  Then under the appropriate pH conditions, a second pendent base becomes protonated forming 

the Type-II H2 bond cleaved intermediate (1a). If the metalhydride with the protonated base, intermediate (3b), is 

formed, it can either undergo a one-electron reduction immediately or as a second step after reductive elimination. 

If the reduction occurs immediately, the Type-I H2 bond cleaved intermediate [NiII(H-)NH+]2+ intermediate (1b) 

is formed. If the reduction occurs as a second step, reductive elimination forms [+HN-NiI-NH+]3+ as intermediate 

(2b) first, then forms the Type-II H2 bond cleaved [+HN-Ni0-NH+]2+ as intermediate (1a). In the last step 0  

→ 1, the two hydrogen ions on the molecular catalyst combine with two electrons from the metal to release an 

H2 molecule.  

2.  H2 Oxidation in [Ni(PCy
2NBz

2)2].  
Free energy calculations of similar Type-I and Type-II H2 bond cleaved pathways in the catalytic direction for H2 

oxidation with the [Ni(PCy
2N

Bz
2)2] model were performed. Experimentally, the [Ni(PCy

2N
Bz

2)2] catalyst was 

observed to favor H2 oxidation, so here we explore comparisons to the experimental system in that catalytic 

direction.  Figure 10 shows the calculated free-energy profile of this model at pH = 0. 

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Fig. 10. Summary of mechanistic pathways leading to H2 oxidation with the [Ni(PCy

2N
Bz

2)2] model at conditions 

of pH = 0. Energy differences are taken with respect to the first point and normalized to the reversible hydrogen 

electrode (RHE).  

Intermediates involved in each route are:  

Type-II Path 1 (blue): 0  1a  2a  3a  4  5  6a  0.   

Type-II Path 2 (orange): 0  1a  2b  3b  4  5  6a  0.   

Type-I Path 3 (green): 0  1b  3a  4  5  6b  0.  

Type-I Path 4 (purple): 0  1b  3b  4  5  6b  0.   

In figure 10, the reference compound for which the energies are plotted is the dihydrogen adduct (ii), chosen for 

its low energy stability compared to the other calculated H2 adducts. Panel (a) shows that the Type-II H2 bond 

cleaved intermediate (1a) is 0.151 eV (3.48 kcal/mol) higher in energy than the H2 adduct. The first 

electrochemical reaction follows, between intermediates 1 → 4. In this model, special attention is paid to 

intermediates 1a and 3a because these have both been observed with NMR spectroscopy using the characterized 

compounds.21 Following the route of the NMR observed intermediates, path 1 (blue) traverses intermediates 0  

1a  2a  3a  4  5  6a  0. However, intermediate (2a) is 0.753 eV (17.37 kcal/mol) higher in energy than 

intermediates (1a). 

The next step is a non-electrochemical, reductive elimination reaction, consistent in all four mechanistic routes 

between intermediate 4 → 5. The energy of which is downhill by 0.585 eV (13.49 kcal/mol). The second 

electrochemical reaction occurs between intermediate 5 → 0. Panel (b) shows that the Type-I H2 bond cleaved 

intermediate (1b) is -0.203 eV (4.68 kcal/mol) lower in energy than the H2 adduct reference compound which is 

consistent with this model as an H2 oxidation catalyst. In the next electrochemical reaction between 1 → 4, if 

PCET conditions prevail, then intermediate 3 is not observed, otherwise intermediate (3a) would be favored. A 

schematic description of this energetically favored TypeI H2 bond cleaved Path 4 is shown below in Fig. 11.  

  

  

 

 

 

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|  https://topjournals.org/index.php/AJSET 

 

  

 

 

 

 

 
 

 

 

   

Fig. 11. Energetically favored Type-I H2 bond cleaved Path 4 for H2 oxidation of the  

[Ni(PCy
2N

Bz
2)2] model catalyst.  The intermediates along this Path are 0  1b  3b   

4  5  6b  0. 

C.  Electrochemical perspective from calculated Pourbaix diagrams 

One criterion for molecular catalyst design is energy matching in the nonelectrochemical reaction steps. However, 

an additional condition to improve the efficiency of the catalyst is to control the electrochemical reactions so that 

the energy cost of sequential proton and electron transfer is circumvented by steering the reduction to proceed by 

PCET.     

The goal then becomes to align all intermediates involved in the nonelectrochemical reaction steps such that they 

are available at similar pH ranges. Hence, for the electrochemical reactions, an applied potential, at a pH, will 

facilitate the most efficient mechanistic route due to the availability of the most relevant species. We demonstrate 

this idea using the coupled Pourbaix diagram, a plot of potential versus pH where the identity of the various 

species has been described in the methods section above. A schematic of an expanded Pourbaix diagram 

illustrating all intermediates in both Type-I and Type-II H2 bond cleaved routes is shown in Fig. 12.  

The Type-II H2 bond cleaved route shown in purple arrows in Fig. 12 is expanded schematically in Fig. 13. The 

ideal, most efficient mechanism would involve only PCET reactions which overlap in the pH ranges of the 

protoncoupled electron-transfer steps, PCET12, PCET34 and PCET56, and occur at similar potentials. The 

schematic Pourbaix diagram in Fig. 12 is broadly applicable to both catalysts models. 

Having mapped out two relevant mechanistic routes, Type-I and Type-II H2 bond cleaved, of these molecular 

catalyst models, a connection must be made to the operational pH and potential where the intermediates are 

accessible. We turn to the calculated coupled Pourbaix diagrams to make this necessary connection and attempt 

to draw correlations to the operational regimes used in the experimental setup. Fig. 14 is the coupled Pourbaix 

diagram of model  

[Ni(PCy2NBz2)2]. 

Intermediates involved in the Type-II H2 bond cleaved routes are shaded in purple, and intermediates involved in 

the Type-I H2 bond cleaved routes are shaded in green. pKa’s  for the H2 adducts correspond to the single 

deprotonation of the (i), (ii) and (iii) intermediates to [NiII(H-)-N]. 

  

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Fig. 12. Schematic of an expanded coupled Pourbaix diagram. Red lines signify the NiII/NiI couple, blue lines are 

the NiIII/II(H-) couple, and purple lines are the NiI/0 couple. Numbered intermediates followed by purple arrows 

travel along the Type-II H2 bond cleaved pathway. The intermediates labeled with circled numbers follow the 

Type-II H2 bond cleaved pathway as an illustration that free-energy mechanistic routes can be mapped onto the 

Pourbaix diagram at a way to interpret findings from electrochemistry experiments.  

  
Fig. 13. Type-II H2 bond cleaved pathway of H2 oxidation with [Ni(PCy

2N
Bz

2)2] model.   

Focusing first on the PCET overlap region highlighted in purple which represents the Type-II H2 bond cleaved 

route, the results show that this route operates in a basic region of the pH scale and with relatively large 

overpotentials. Interestingly, the experiment is performed in the presence of triethylamine, a strong base buffer, 

which could explain why the [+HN-Ni0-NH+] intermediate is observed by NMR spectroscopy under these basic 

conditions. Now focusing on the PCET overlap region highlighted in green, representing the Type-I H2 bond 

cleaved route, the result shows that this route operates in an acidic region of the pH scale with much lower 

overpotentials than the Type-II H2 bond cleaved route.   

Interestingly, the H2 adduct represented by (ii) and (iii) in Fig. 14 falls within this pH range which is consistent 

with the similarity in energy to the Type-I H2 bond cleaved intermediate. Comparing the operating regimes of 

both Type-I and Type-II H2 bond cleaved routes, this Pourbaix diagram of [Ni(PCy
2N

Bz
2)2], indicates that if the 

solution can be tuned to more acidic conditions, the intermediates reached will traverse a lower energy, thus a 

more favorable mechanistic route.  

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 Cy Bz 

Fig. 14. Coupled Pourbaix diagram of model [Ni(P 2N 2)2]. Intermediates involved in the Type-II H2 bond cleaved 

pathway are shaded in purple, and intermediates involved in the Type-I H2 bond cleaved pathway are shaded in 

green.  

Figure  15  is  the coupled Pourbaix  diagram  of  model  

[Ni(PPh
2N

Ph
2)2(CH3CN)]. Focusing on the PCET overlap region highlighted in purple in Fig. 15 which represents 

the Type-II H2 bond cleaved route, a largely acidic pH range is involved with accompanying large overpotentials. 

In this case, the experiment is performed in the presence of triflic acid, which correlates with the strongly acidic 

pH range calculated. Unlike the [Ni(PCy
2N

Bz
2)2] case, this case appears to be more difficult to disentangle. From 

the free-energy profiles, the favored mechanism for this case appears to be along the Type-I H2 bond cleaved 

pathway because of the 0.354 eV lower energy of the Type-I H2 bond cleaved intermediate. However, the Type-I 

H2 bond cleaved route falls in a narrow, even more acidic region of the Pourbaix diagram but equally close to the 

acidic region of the Type-II H2 bond cleaved route, although with much lower overpotential. It may be that under 

the acidic conditions required by both routes, PCET reactions dominate and optimal conditions for the reactions 

prevail. 

  
Fig. 15: Coupled Pourbaix diagram of model [Ni(PPh

2N
Ph

2)2(CH3CN)].  

Comparing the  Pourbaix diagrams of this [Ni(PPh
2N

Ph
2)2(CH3CN)] model and the previous [Ni(PCy

2N
Bz

2)2] model, 

lower potentials are needed to drive the reaction in this case and may be one contributing factor to the higher 

turnover frequency (TOF) of 350 s-1 of this catalyst as opposed to the TOF of 10 s-1 of the previous one. The other 

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contributing factor being the lower change in free-energy of the oxidative addition reaction involving 

intermediates 5→ 4.  

5.   Discussion     

In our previous paper42, explicit emphasis was placed on matching the pKa’s of intermediates 4 & 5 (the oxidative 

addition step) such that the free energy of this step is thermoneutral in an ideal catalyst. Our exploration of these 

actual catalysts shows that there are pKa regions of overlap for each catalyst, favoring the Type-II route. While 

the pKa’s overlap, the reduction potentials do not and may be a source of explanation for why these two catalysts 

have less than ideal turnover frequencies in their H2 oxidation/reduction directions. The pKa’s for intermediates 

4 and 5 are shown in Figures 14 and 15. While the previous work also postulated a second reduction to the Ni0 

species before the oxidative addition step, this was not observed for these real catalyst systems. In fact, we show 

the calculated pKa of the Ni0 species in Figures 14 and 15 (labeled in purple as the intermediates around PCET56).    

One of the strengths of the Pourbaix diagram is the opportunity to explore the mechanism in terms of the pH 

dependence of various routes. So far the results have presented the simple case, at pH = 0 conditions, of proton 

transfers being coupled to electron transfers in what is usually defined as intermolecular PCET.    

However, a second, more complex process can be considered involving the coupling of oxidative additions to 

electron or proton transfers in a way that is traditionally defined as intramolecular PCET. 

One paper argues that B3LYP is not in qualitative agreement with coupledcluster expansion calculations on a 

model system of the nickle-diphosphine compound.51 The choice of using  DFT with a B3LYP functional for 

these calculations is based on seeking a qualitative understanding of how Pourbaix diagrams can be used to design 

molecular catalysts at the low computational cost of calculating pKa’s and reduction potentials of the full system, 

not a truncated model.  

6.   Conclusion     

In search of renewable energy sources as a way of preserving the environment, nature’s energy producers have 

become an attractive instructor. Hydrogenase enzymes, for example, are capable of turning over hydrogen at high 

rates using readily available and cost effective nickel and iron metals. While recognizing the complexity with 

which hydrogenases function, a few design features have been taken as a start towards building molecular 

catalysts which can function at comparable efficiencies. Experimentalists have characterized such compounds, 

two of which we chose to model in this paper, one for H2 oxidation and the other for H2 production. Using these 

models, we explored three aspects of catalytic function which can influence the choices made in designing the 

catalyst. The goal is to elucidate how to tune design features on the catalyst to improve efficiency, and to formulate 

a computational protocol which predicts how the changes ultimately affect catalyst behavior. By first mapping 

the free energy along a proposed reaction coordinate, we illustrate that we can decipher the mechanistic routes of 

the characterized catalyst and project ways to improve the catalyst by designing it to traverse more favorable 

routes. We then target the H2 adduct as a critical intermediate by which the pathway can be controlled and suggest 

design features that coerce the catalyst into forming certain low energy intermediates. 

 Lastly, we correlate the free-energy routes with electrochemical mapping of the intermediates as a way to project 

optimal electrochemical conditions for improving catalyst behavior. 

The key result from analyzing the free-energy profiles is that the heterolytic route is favored for both models, 

[Ni(PPh
2N

Ph
2)2(CH3CN)] and [Ni(PCy

2N
Bz

2)2]. This suggests that using ligands to make one of the two nitrogens 

in the upper plane of the catalyst more basic than the other can bias the reaction to reach the heterolytically cleaved 

intermediate. When both nitrogens have the same ligand, homolytic cleavage is more difficult to avoid.   

  The synthetic challenge of course becomes how to construct a catalyst with an asymmetric [Ni(PPhNPh) (PPhNBz)] 

configuration. However, if this can be overcome, this new asymmetric catalyst may traverse the optimal 

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heterolytically cleaved route. In analyzing the H2 adduct intermediate, structure appears to have a large 

contribution in controlling whether the homolytic or heterolytic intermediate is formed. Formation of a loosely 

bound dihydrogen complex is nearly isoenergetic with the heterolytically cleaved intermediate and is best 

achieved by the complex that has diphosphine rings in the boat/boat configuration. Lastly, since potential is 

proportional to the free-energy, lower potentials correlate with smaller cost in free-energy. From the perspective 

of the Pourbaix diagrams, the results indicate that lower potentials are needed in acidic pH regions. Thus, if the 

asymmetric catalyst can be stabilized in acidic solution through the phenyl ligands, all optimal conditions should 

prevail.  

While concepts of proton management have been considered by many investigators in the catalysis community,52 

we are unaware of another study which hinges on the connection between free-energy profiles and Pourbaix 

diagrams as a tool to design more efficient H2 oxidation and production catalysts. Our paper is the second in this 

direction and hopes to gain greater appeal based on the electrochemical insight that it offers.  

Further studies of this nature will of course rely on the availability of experimental data in the initial stages. 

However, the outcome of this study shows great promise in the future of designing efficient catalysts having a 

larger electrochemical component.  

Acknowledgements 

The work at BNL was supported by DOE under contract DE-AC0298CH10886 (Division of Chemical Sciences 

and its Scientific User Facilities Division). This research utilized resources at the New York Center for 

Computational Sciences (NYCCS) at Stony Brook University/Brookhaven National Laboratory which was 

supported by the U.S. Department of Energy under Contract No. DE-AC02-98CH10886 and by the State of New 

York, and at the BNL Center for Functional Nanomaterials (CFN). 

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