Comprehensive Thermodynamics of Nickel Hydride Bis(Diphosphine

Article pubs.acs.org/Organometallics

Comprehensive Thermodynamics of Nickel Hydride Bis(Diphosphine) Complexes: A Predictive Model through Computations Shentan Chen, Roger Rousseau,* Simone Raugei, Michel Dupuis, Daniel L. DuBois, and R. Morris Bullock Center for Molecular Electrocatalysis, Chemical and Materials Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States S Supporting Information *

ABSTRACT: Prediction of thermodynamic quantities such as redox potentials and homolytic and heterolytic metal hydrogen bond energies is critical to the a priori design of molecular catalysts. In this paper we expound upon a density functional theory (DFT)-based isodesmic methodology for the accurate computation of the above quantities across a series of Ni(diphosphine)2 complexes that are potential catalysts for production of H2 from protons and electrons or oxidation of H2 to electrons and protons. Isodesmic schemes give relative free energies between the complex of interest and a reference system. A natural choice is to use as a reference a compound that is similar to the chemical species under study and for which the properties of interest have been measured with accuracy. However, this is not always possible, as in the case of the Ni complexes considered here, where data are experimentally available for only some species. To overcome this difficulty, we employed a theoretical reference compound, Ni(PH3)4, which is amenable to highly accurate electron-correlated calculations, which allows one to explore thermodynamic properties even when no experimental input is accessible. The reliability of this reference is validated against the available thermodynamics data in acetonitrile solution. Overall the proposed protocol yields excellent accuracy for redox potentials (∼0.10 eV of accuracy), for acidities (∼1.5 pK a units of accuracy), for hydricities (∼2 kcal/mol of accuracy), and for homolytic bond dissociation free energies (∼1−2 kcal/mol of accuracy). The calculated thermodynamic properties are then analyzed for a broad set of Ni complexes. The power of the approach is demonstrated through the validation of previously reported linear correlations among properties. New correlations are revealed. It emerges that only two quantities, the Ni(II)/Ni(I) and Ni(I)/Ni(0) redox potentials (which are easily accessible experimentally), suffice to predict with high confidence the energetics of all relevant species involved in the catalytic cycles for H 2 oxidation and production. The approach could be extended to other transition metal complexes. Scheme 1

1. INTRODUCTION The transition metal−hydrogen bond is of both fundamental and practical importance. From a fundamental perspective, this bond is the simplest possible bond to a transition metal. From a practical perspective, the cleavage and formation of M−H bonds (where M is a transition metal) are important in a large number of stoichiometric and catalytic reactions. These considerations have led to a long-standing interest in thermodynamic studies of M−H bonds, which can be cleaved either homolytically (MH → M• + H•) or heterolytically: (i) MH → M− + H+ and (ii) MH → M+ + H− (see Scheme 1). Early studies focused on the energies associated with the first two of these bond cleavage reactions, homolytic bond dissociation energies1−7 and measurements of acidity (pKa values).8−20 In the past decade quantitative thermodynamic measurements of hydride donor abilities have also been reported,21−26 and it is now possible in favorable systems to measure all three bond dissociation energies of the M−H bond in solution. © 2011 American Chemical Society

Advances in measuring these thermodynamic properties have recently led to comprehensive thermodynamic studies involving both hydride and dihydride complexes with the same ligand donor set,22,25,26 for example, [HPt(EtXantphos)2]+ and [(H)2Pt(EtXantphos)2]2+ (where EtXantphos is 9,9-dimethyl4,5-bis(diethylphosphino)xanthene). 25 For these systems, thermodynamic diagrams such as that shown in Figure 1a can be constructed. These diagrams are useful for summarizing the different thermodynamic properties of these dihydride systems Received: July 18, 2011 Published: October 25, 2011 6108

dx.doi.org/10.1021/om200645x | Organometallics 2011, 30, 6108−6118

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protons in acetonitrile solvent) for interconversion between species. This information can also be used to construct free energy maps or landscapes, such as the one shown in Figure 1b, that illustrate the relative free energies of the different species at a specific pH and H2 pressure. Note that while pH is traditionally considered in aqueous solutions, we use pH in the current work in the general sense of pH = −log[H+].29 These free energy landscapes allow the energetics of many possible reactions to be assessed by inspection. For example, the addition of H2 to [Pt(EtXantphos)2]2+ to form [(H)2Pt(EtXantphos)2]2+ can be seen from Figure 1b to be favorable by 9.3 kcal/mol (PH2 = 1 atm and pH = 7 in acetonitrile). More generally, these diagrams can be used to assess a series of reactions. The oxidative addition of hydrogen followed by deprotonation results in the heterolytic cleavage of H 2, and an entire reaction profile depicting the free energies of possible intermediates of a catalytic cycle for the electrocatalytic oxidation of H2 can be constructed as shown in Figure 1c. Such free energy diagrams can also be used to compare different catalysts under the same conditions or the same catalysts under different thermodynamic conditions, i.e., as a function of pH to determine which catalyst or set of reaction conditions might exhibit the best overall reaction profile. 30 There has been considerable effort computationally to calculate reliable and accurate thermodynamic properties for transition metal organometallic species31−34 including recent emphasis on hydrogenase minics for hydrogen activation.35−37 The current work builds on that of Qi et al.,38 who have recently shown that density functional theory methods combined with polarizable continuum models (PCM) of solvation are able to yield hydricities, pKa’s, and E°(II/0) redox potentials of transition metal complexes with a satisfactory level of accuracy: mean absolute errors of 2.0 kcal/mol, 1.9 pKa units, and 0.07 V for each of the three properties, respectively. However, the validity of this approach for the electron redox couples E°(II/I) and E°(I/0) has not been demonstrated, and we show here how those two couples are very important in their correlcations to other properties. The procedure of Qi et al. relies on knowledge of an accurate value of the property of interest for a reference system and on an isodesmic reaction scheme that maintains the number of bonds of each type. This approach benefits from a systematic cancellation of errors that arise in theoretical calculations by using systems of similar characteristics to provide reliable relative energetics. Equations based on isodesmic schemes to calculate hydricities, pKa’s, redox potentials, and homolytic M−H bond dissociation energies are given in Section 2 and show how the value of a property for a given system relies on the value for a reference system. A good reference system is one for which experimental data are available and for which the calculated properties are in accord with experiment within chemical accuracy (2 kcal/mol). In the present work we use such an isodesmic approach to evaluate a series of [Ni(diphosphine)2]2+ complexes and their interaction with H2 including all quantities as shown in Figure 2. The challenge of the prediction of the complete diagram is addressed by computing the desired absolute thermodynamic quantities from highly accurate correlated wave function calculations (and nonisodesmic reaction energies) of a hypothetical Ni(PH3)4 reference system for use in the isodesmic scheme. With the availability of a full set of computationally derived properties for a broad set of complexes, it becomes possible to put previously suggested correlations on

Figure 1. Catalyst design using thermodynamic properties, with all energies in acetonitrile solution. (a) Thermodynamic diagram for the [Pt(EtXantphos)2]2+ system (free energies quoted at standard state in acetonitrile),25 (b) Map of relative free energies of all species derived from Pt−H bond cleavage (1 atm H2 and pH = 7 in acetonitrile). (c) Reaction (free) energy profile for the electrocatalytic oxidation of H2 (H2 + 2B → 2HB+ +2e−, where B denotes a base) by [Pt(EtXantphos)2]2+ catalyst. In (c) the energies (red lines) are accurate, but the blue lines are only a guide to the eye and do not represent the actual activation barriers.

(and even more complex systems) and for discerning relationships between the different thermodynamic properties. For example, there are linear relationships between the potentials of the [M(diphosphine)2]+/0 couples (where M = Ni, Pd, and Pt) and the pKa values of the corresponding [HM(diphosphine)2]+ complexes and between the potentials of the [M(diphosphine)2]2+/1+ couples and the hydride donor abilities of the corresponding [HM(diphosphine)2]+ complexes.27 In addition, it has been suggested, on the basis of a limited data set of three systems of complexes,22,25,26 that the homolytic bond dissociation free energies for the [(H)2M(diphosphine)2]2+ complexes are 1 to 2 kcal/mol smaller than those of the corresponding [HM(diphosphine)2]+ complexes and that the difference in redox potentials of the [M(diphosphine)2]1+/0 couples and [HM(diphosphine) 2]2+/1+ couples are constant. If these relationships could be confirmed, then it would be possible to predict entire thermodynamic diagrams such as that shown in Figure 1a from the values of the M(I/0) and M(II/I) couples, which can generally be obtained by a simple cyclic voltammetry experiment. Furthermore, none of the nickel systems have an experimentally determined comprehensive thermodynamic diagram such as that shown in Figure 1a because the thermodynamic properties of the [(H)2Ni(diphosphine)2]2+ complexes are not experimentally accessible. Most Ni(IV) dihydrides are too high in energy to be observed, though we reported the observation of a Ni(H) 22+ complex by low-temperature NMR in a complex where the diphosphine had a positioned pendant amine. This Ni(IV) dihydride was observed only at low temperature.28 Prediction of the complete thermodynamic diagram and confirmation of these relationships through computations is one of the major objectives of this work. Thermodynamic diagrams such as shown in Figure 1a provide the reaction free energetics (at the standard state, T = 298 K, P = 1 atm H2, 1 mol/L concentration of catalyst and 6109


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For the ab initio reference system mentioned earlier, coupled cluster CCSD(T) (with single and double excitations and a perturbative treatment of triple excitations) calculations were carried out at the B3P86/bse-optimized structures. For closed-shell states, the restricted Hartree−Fock (RHF) wave function was used as the reference wave function for the CCSD(T) calculations. For open-shell states, a restricted open-shell HF (ROHF) wave function was used as the reference. Two levels of correlation-consistent polarized n-tuple zeta basis sets47−49 were used, mainly the triple- and quadruple-ζ (n = 3, 4, respectively) basis sets for the CCSD(T) energy calculations. Hartree−Fock (HF) energies at the 5-tuple zeta (cc-pV5Z) basis set were also calculated in order to estimate the complete basis set limits of HF energies using the formula proposed by Feller,50 A + B/C n (n = 3, 4, 5), where A, B, and C are fitting constants. As for the correlation energies, their complete basis set limits were estimated using the extrapolation formula proposed by Helgaker and co-workers, 51 A′ + B′/n 3 (n = 3, 4), where A′ and B′ are additional fitting parameters distinct from those used to estimate the HF energies. Complete basis limits of CCSD(T) energies were obtained by summing the complete basis set limits of the HF energies and correlation energies. All the calculations involving the CCSD(T) method and correlated-consistent basis sets were performed using the NWChem software.52,53 Basis sets that were not internally stored in the NWChem code were obtained from the W. R. Wiley Environmental Molecular Science Laboratory basis set exchange.54,55 The zero-point energies (ZPE) and thermal contributions (298 K and 1 atm) to the free energies were calculated at the DFT(B3P86)/bse level of theory, the same as for geometry optimization. The solvation free energies were calculated as indicated above using the CPCM model and DFT(B3P86)/bse level of theory and Bondi radii.44 2.2. General Procedure for Calculating Thermodynamic Properties. In accord with the reported experimental free energies, all calculated reaction free energies in the work are quoted at the standard state (T = 298 K, p = 1 atm of H2, 1 mol/L concentration of all species in acetonitrile) unless otherwise stated. We used thermodynamic cycles and isodesmic reactions to extract the thermodynamic quantities of interest (Figure 2). We calculated the free energies of isodesmic reactions and combined them with the values of a reference system to predict the values of each thermodynamic property. For best results, and to maximize the systematic cancellation of errors and produce the most reliable relative energetics, the reference system should be similar chemically to the complexes for which we want to predict the properties. A detailed discussion of the reliability of this approach, the dominant energy terms, and the choice of the reference system is provided below. For the hydride donor strength (or hydricity), ΔG°H−, of complex [LnNiHx]m+, we used the scheme depicted in eqs 1a−c, calculating the free energy of reaction ΔG°r(H−) for the isodesmic reaction 1a and then using the known value of reference system (Δ refG°H−) to calculate the hydricity ΔG°H−.

Figure 2. Thermodynamic diagram for the [Ni(diphosphine)2]2+ system. E°(I/0), E°(II/I), and E°(III/II) are the electrochemical potentials for the Ni(I)/Ni(0), Ni(II)/Ni(I), and HNi(III/II) redox couples, respectively; ΔG°H•(II), ΔG°H•(III), and ΔG°H•(IV) are the homolytic bond dissociation free energies of Ni(II) and Ni(III) monohydrides and Ni(IV) dihydride, respectively; pK a(II) and pKa(III) are the pKa values for the Ni(II) and Ni(III) monohydrides, respectively, and pKa(IV) is the pKa of the Ni(IV) dihydride; ΔG°H−(II) is the Ni(II) monohydride hydride donor strength (hydricity). Quantities shown by solid lines are those that have been measured experimentally for Ni complexes; quantities shown by dashed lines are those that currently have not been determined experimentally.

a firm theoretical footing. Further analysis has revealed other correlations not previously reported. The most important and general result of these computational studies and correlations is that all of the thermodynamic properties shown in Figure 2 can be predicted from the redox potentials for the Ni(II)/Ni(I) and Ni(I)/Ni(0) couples and, consequently, the relative energetics of all of the species. This provides a powerful tool for catalyst design and for understanding thermodynamic relationships.

2. METHODOLOGY 2.1. Structures and Energies. Molecular structures were optimized at the DFT level of theory with the hybrid B3P8639,40 exchange and correlation functional using the Stuttgart-Dresden relativistic ECP and associated basis set (SDD) for Ni41 and 6-31G* for all nonmetal atoms. We include an additional polarization p function on hydride hydrogen atoms. Hereafter, this basis set will be referred to as bse. Harmonic vibrational frequencies were calculated at the optimized geometries using the same level of theory to estimate the zero-point energy (ZPE) and the thermal contributions (298 K and 1 atm) to the gas-phase free energy. Free energies of solvation in acetonitrile (which include the change of thermodynamic conditions of P = 1 atm in the gas phase to 1 M solution) were then computed using a self-consistent reaction field (SCRF) model at the same level of theory as for the other steps. The conductor-like polarizable continuum model (CPCM)42,43 was used with Bondi radii.44 All the calculations were carried out with Gaussian 09.45 The hybrid B3P86 functional was shown to yield two-electron redox potentials, hydride donor strengths, and pKa’s with good accuracy for a set of complexes with varied metals and ligands.38 Additionally our earlier characterization of the energy profile for H 2 oxidation with a nickel bis(diphosphine) complex46 showed that the B3P86 functional in conjunction with the bse basis set compared favorably with CCSD(T) calculations. All geometries were optimized without any symmetry constraint and were verified by vibrational analyses at the same level of theory to ensure that they are minima on the potential energy surface. For some complexes, several conformations were considered, and the lowest energy conformer was chosen for the calculation of the thermodynamic properties. It is stressed that the calculated properties could vary significantly due to the different energies of the conformers (see Supporting Information).

Similarly, for the pKa of complex [LnNiHx]m+, we used the scheme depicted in eqs 2a−c, calculating the free energy of reaction 2a, ΔG°r(H+), and then using the reference value (pKaref) to calculate the pKa:

For the one-electron redox potential E° of complex [LnNiHx]m+, we used the scheme depicted in eqs 3a−c. Calculating the free energy of reaction 3a, ΔG°, one can convert a redox potential via division by a conversion constant, 23.06 mol/kcal·V. In a subsequent step the redox couple E° is found by using the corresponding value of the redox 6110


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potential of the reference system:

For the homolytic Ni−H bond dissociation free energy (BDFE) of complex [LnNiHx]m+, we used the scheme of eqs 4a−c to calculate the free energy of reaction 4a, ΔG°r(H•), and then used the value of the reference system to calculate the bond dissociation free energy: Figure 5. Ligands of the extended set of Ni bis(diphosphine) complexes.

3. RESULTS AND DISCUSSION The prediction of thermodynamic properties through isodesmic schemes requires a reference system. We report on two different choices of the reference system. First, we used as a reference system a Ni(dmpp)2 complex for which experimental data, namely, the ΔG°H−(II), pKa(II), ΔG°H•(II), E°(II/I), and E°(I/0), are available. Our investigation focused on these calculations initially, and we show that a very good level of accuracy (∼0.05 V for one-electron redox potentials, ∼1.5 pKa units for pKa’s, and ∼1.5 kcal/mol for hydride donor strengths) is obtained. Second, we developed an ab initio protocol, which uses the simple Ni(PH3)4 complex as the reference system. This reference system is amenable to highly accurate electroncorrelated CCSD(T) calculations. The use of this reference system allowed us to extend the computations to additional thermodynamic properties shown in Figure 2, namely, the pKa(III), pKa(IV), ΔG°H•(III), ΔG°H•(IV), and E°(III/II), and to assess their quantitative prediction. Once this absolute thermodynamic scale was established, we examined and extracted correlations between thermodynamic properties based on an expanded data set of complexes. This analysis corroborates many of the correlations previously reported in the literature and also reveals additional relationships. The latter observations allow us to show that the entire free energy landscape can be estimated with good accuracy solely from the potentials of the Ni(II/I) and Ni(I/0) couples, E°(I/0) and E°(II/I). 3.1. Predictions with an Experimentally Characterized Ni Complex As a Reference System. We are interested in assessing the errors afforded by the isodesmic schemes and the reliability of the calculated properties. Isodesmic schemes yield relative free energies between complexes of interest and a reference system. The knowledge of the experimental thermodynamic property for the reference system places the relative energies on an absolute scale, and the derived thermodynamic properties for the systems of interest are then directly comparable to experimentally determined values. In the following we discuss in detail quantities calculated using Ni(dmpp)2 as a reference system. As discussed in the Supporting Information, different choices among the ligands shown in Figure 3 provide similar results. Calculated and experimental values for ΔG°H−(II), pKa(II), ΔG°H•(II), E°(II/I), and E°(I/0) are given in Table 1. Correlations between calculated and experimental values for all the properties are displayed in Figure 4; all data are for acetonitrile solutions, and all E° values in this paper are referenced to Cp2Fe+/0 at 0 V. Note that we are dealing here with a subsection of the full thermodynamic map shown in Figure 2, as experimental values for these Ni(diphosphine) 2 complexes are available only for these properties and the

2.3. Nickel Complexes of Interest. To establish the accuracy of the proposed approach, we investigated a set of Ni bis-diphosphine complexes for which a large number of the quantities of interest are available from experimental data.21,23,27,56 Diverse diphosphine ligands comprised this set (see Figure 3). They differ in both the nature of the

Figure 3. Diphosphine ligands for Ni(diphosphine)2 complexes whose thermodynamic properties have been determined experimentally. substituents on the P atoms and the chemical structure of the linkers. The acidities and hydride donor abilities of nickel complexes of these ligands span a range of approximately 15 kcal/mol. With this set we also assessed previously discussed correlations27 among selected thermodynamic properties, such as redox potential E°(II/I) and ΔG°H− and redox potential E°(I/0) and pKa(II). The correlations were then consolidated across a larger set of complexes and ligands on the basis of computations solely, in the absence of experimental data (see Section 3.3). The ligands included in the extended data set are shown in Figure 5.

Figure 4. Correlation between calculated and experimental thermodynamic properties for the Ni complexes studied here. Ni(dmpp) 2 has been used as reference. 6111


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Table 1. Calculated Thermodynamic Properties of Ni[(L)2Hn]m+ (where L is the associated diphosphine ligand) Using the DFT(B3P86)/bse Level of Theory and the Isodesmic Schemes in Section 2a ΔG°H−(II) (kcal/mol)

pKa(II) pKa units

ΔG°H•(II) (kcal/mol)

E°(II/I) (V)

E°(I/0) (V)

L

calcd

expt

calcd

expt

calcd

expt

calcd

expt

calcd

expt

dmpeb dmppb depeb deppc dppvb dppeb pnpd MAE

52.0 61.2 58.3 63.0 65.9 63.2 64.7 1.4

50.7 61.2 56.0 66.2 66.4 62.7 66.0

23.8 24.0 25.6 22.8 12.8 15.7 22.0 0.7

24.4 24.0 23.8 23.3 13.2 14.2 22.2

57.3 55.6 57.1 53.0 53.1 55.9 55.3 1.1

55.7 55.6 56.3 54.5 52.5 52.7 55.3

−1.36 −0.89 −1.08 −0.70 −0.58 −0.82 −0.73 0.06

−1.35 −0.89 −1.16 −0.61 −0.52 −0.70 −0.64

−1.25 −1.33 −1.36 −1.37 −0.78 −0.82 −1.22 0.05

−1.35 −1.33 −1.29 −1.34 −0.83 −0.88 −1.24

a

Ni[(dmpp)2Hn]m+ is the reference system. Redox potentials are given with respect to the ferrocenium/ferrocene couple. bExperimental values taken from ref 27. cExperimental values taken from ref 23. dExperimental values taken from ref 56.

Table 2. Mean Absolute Error for Quantities Calculated Using Free Energies (full model) and Approximate Free Energies (minimal model)a MAE

E°(I/0) (V)

E°(II/I) (V)

pKa(II) pKa unit

ΔG°H−(II) (kcal/mol)

ΔG°H•(II) (kcal/mol)

full model eq 5 minimal model eq 6

0.05 0.04

0.06 0.10

0.7 0.5

1.3 1.6

1.1 1.1

a

Ni(dmpp)2 reference system.

E°(III/II) couple has been estimated only for a few systems based on irreversible cyclic voltamograms.56 As can be inferred from Table 1 and Figure 4, the calculated trends across this series of compounds agree well with the experiment for all the measured quantities. For the seven nickel complexes studied here, the calculated values of ΔG°H−(II) and pKa(II) have a mean absolute error (MAE) of 1.4 kcal/mol and 0.7 pKa units, respectively, comparable to the uncertainty in the experimental measurements. Calculated homolytic Ni−H bond dissociation free energies show a MAE of only 1.1 kcal/mol, although the error for the Ni(depp)22+ system was 3.2 kcal/ mol. The MAEs are slightly lower than those reported by Qi et al.,38 presumably due to our choice of the reference system, which is itself a Ni complex with its electronic structure similar to all other complexes (see Supporting Information for further discussion). The one-electron redox potentials, E°(I/0) and E°(II/I), are in excellent agreement with experiment, with a MAE of 0.06 and 0.05 V, respectively. When the two oneelectron potentials E°(I/0) and E°(II/I) are known, the twoelectron redox potential, E°(II/0), can be readily calculated as their average. The calculated E°(II/0) has a MAE deviation of 0.03 V. It is of interest to understand why the isodesmic methodology used here yields small MAEs. To this end, we decomposed the calculated values along various energy components. For the change in free energy (ΔG°) of each half reaction we can write

CPCM model of solvation allows us to resolve ΔG°sol into an electrostatic contribution, ΔG°sol,el, and a nonelectrostatic contribution, ΔG° sol,nonel. As shown in the Supporting Information, it is found that the change in the electrostatic term suffices to explain the overall trends in the results. Thus, a minimal model (6)

can also reproduce the observed trends with only a slightly increased error, as can be seen in Table 2. The above analysis explains why the relative values obtained by the isodesmic scheme are highly accurate. Indeed, the changes in electronic energy of similar bond types across a series and the change in the electrostatic contribution to solvation free energies are properties that can be calculated with good accuracy, even by a relatively modest level of electron structure theory. 3.2. Characterization of an ab Initio Ni Complex to Serve As a Reference System: [HxNi(PH3)4]m+. In principle, thermodynamic properties can be calculated using any complex with similar electronic structure characteristics as a reference. Qi et al.38 used a Pt complex as a reference. Improved accuracy is obtained in the present work, as we chose a complex with stronger similarity in electronic structure with the set of complexes of interest (see Supporting Information). Ideally, the reference system should preserve the core electronic structure characteristics of the set of complexes of interest, but need not necessarily be characterized experimentally. In principle the reference system may be relatively small in number of atoms such that it is amenable to highly accurate electron-correlated molecular theory calculations, such as CCSD(T) in conjunction with large basis sets. If these calculations are able to yield the required thermodynamic properties of the model system with an accuracy of 1−2 kcal/mol, one may end up with a fully “ab initio” protocol for free energy map prediction (see Supporting Information for further discussion).57,58 The nickel complex Ni(PH3)4, which possesses a similar first coordination sphere to the nickel center to the compounds

(5)

where ΔE° is the change in gas-phase electronic energy, ΔZPE is the change in zero-point energy, ΔG°thermo is the change in thermal contributions to the free energy (as estimated from harmonic vibrations, rotations, and translational partition functions), and ΔG°sol is the change in free energy of solvation. Examination of these terms for all the properties reported in Table 1 shows that only ΔE° and ΔG°sol exhibit any significant variations (see Supporting Information). Furthermore, the 6112


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studied here, represents an excellent candidate as model reference compound. In this section we describe the accurate calculation of the thermodynamic properties of the [HxNi(PH3)4]m+ system. Since the various species reported in the thermochemical diagram of Figure 2 are connected through thermodynamic cycles, it is not necessary to calculate from first principles all of the thermodynamic properties. For instance, with the knowledge of only the three pKa values and the three homolytic bond dissociation energies shown in Figure 2, it is possible to obtain all of the other quantities (three redox potentials and one hydricity). In what follows we report calculated pKa’s and homolytic bond dissociation energies (ΔG°H•) using well-established proton transfer and hydrogen atom transfer reactions of organic molecules and converged electronic energies obtained at the CCSD(T) level of theory. This allows us to exploit the accurate energetics provided by the high-level electronic structure theory, even when dealing with nonisodesmic reactions, in this case weighting the relative strengths of C−H bonds and Ni−H bonds. For pKa(II) of [HNi(PH3)4]+, we considered reaction 7 (where py = pyridine),

the redox potentials by exploiting various thermochemical cycles. For instance E°(I/0) can be obtained using the thermodynamic cycle shown in Scheme 2. Scheme 2

The free energy of the half reaction (11d) can be calculated on the basis of the reaction free energies obtained from eqs 8 and 10 with the formula derived from the thermochemical cycle, eq 12, (12)

where 53.6 kcal/mol is the experimental free energy for reaction 11c in acetonitrile.61 The redox potential E°(I/0) then can be determined through the equation E°(I/0) = −G°(I/0)/ 23.06, where 23.06 is a conversion constant for converting from volt coulombs to kcal/mol. With the thermodynamic properties determined for the reference complex, we were able to calculate all the thermodynamic properties of the seven trial complexes. Results and mean absolute errors are given in Table 3. The agreement between predicted and experimental pK a(II), ΔG°H•(II), E°(I/0), and E°(II/I) is excellent. The small errors of the known quantities give us confidence that for pKa(III), pKa(IV), ΔG°H•(III), ΔG°H•(IV), and E°(III/II), the absolute quantities obtained from this method are likely to have similarly small errors, on the order of 1−2 kcal/mol for bond strengths and 0.1 V for redox potentials. 3.3. Correlations between Thermodynamic Properties. In the previous sections we showed that it is possible to compute reliably the thermodynamic properties needed to predict free energy landscapes, for example those for the activation of H2 by [Ni(diphosphine)2]2+ complexes. We next examine correlations between the properties in order to determine the minimal set of parameters (experimental or computed) needed to derive the free energy landscapes for these reactions. Such correlations are extremely useful, owing to the difficulties in measuring many of these quantities experimentally. We extended the set of compounds to include a series of species for which experimental thermodynamic properties have

(7)

and calculated the reaction free energy Δ rG°, which was then used to compute the pKa by the formula (8)

where 1.364 is the conversion factor for converting from pKa units to kcal/mol and 12.53 is the experimental pKa value of the protonated pyridine (Hpy+) in acetonitrile.59 Likewise, for ΔG°H•(II) of [HNi(PH3)4]+, we calculated the free energy of reaction 9,

(9)

and obtained the homolytic bond dissociation free energy from the formula (10)

where 87.0 kcal/mol is the homolytic bond dissociation free energy of toluene (PhCH2−H) in acetonitrile.60 Similarly, we calculated pKa(III), pKa(IV), ΔG°H•(III), and ΔG°H•(IV). From the pKa values and the homolytic bond dissociation free energies, we can easily calculate the hydricities, ΔG°H−, and

Table 3. Thermodynamic Properties of [NiL2Hn]m+ (L = diphosphine ligand) in Acetonitrile Predicted Using the “ab Initio” Reference Systema

a

L

pKa(II)

pKa(III)

pKa(IV)

ΔG°H•(II)

ΔG°H•(III)

ΔG°H•(IV)

E°(I/0)

E°(II/I)

E°(III/II)

ΔG°H−

PH3 dmpe dmpp depe depp dppv dppe pnp MAE

9.4 24.9 25.0 26.6 23.8 13.9 16.7 23.0 1.3

−16.7 −0.8 −1.5 −1.0 −2.6 −12.8 −8.6 −4.3

−13.0 0.9 −0.8 −0.2 −1.1 −10.1 −7.3 −4.4

50.4 56.1 54.4 56.0 51.8 52.0 54.7 54.2 1.2

21.4 20.5 30.5 26.7 33.4 22.2 22.4 30.3

55.5 58.6 55.4 57.1 53.8 55.7 56.5 54.1

−0.70 −1.37 −1.45 −1.48 −1.49 −0.90 −0.94 −1.34 0.10

−0.41 −1.39 −0.92 −1.11 −0.73 −0.60 −0.84 −0.75 0.08

0.85 0.16 0.13 0.16 0.08 0.69 0.56 0.28

67.0 50.2 59.4 56.4 61.1 64.0 61.3 62.8 2.1

The units are volts for redox potentials and kcal/mol for homolytic bond dissociation free energy and hydricity. Compare with Tables 1 and 2. 6113


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Table 4. Thermodynamic Properties of [Ni[L2Hn]m+ (L = diphosphine ligand) Predicted for an Extended Set of Complexes with the Ligands Shown in Figure 5 Using the “ab Initio” Reference Systema

a

L

pKa(II)

pKa(III)

pKa(IV)

ΔG°H• (II)

ΔG°H•(III)

ΔG°H•(IV)

E°(I/0)

E°(II/I)

E°(III/II)

ΔG°H−

(PH3)2 dmpe dmpp depe depp npn dppv dppe dmpv mpnp df3mpe df2mpe dfmpe dfmpp df3mpp dfmpv

9.4 24.9 25 26.6 23.8 23 13.9 16.7 22.3 23.5 −14.1 1.7 11.7 10.8 −13.9 7.7

−16.7 −0.8 −1.5 −1 −2.6 −4.3 −12.8 −8.6 −4.6 −2.3 −41.8 −23.6 −15.7 −14.3 −41.2 −21.3

−13 0.9 −0.8 −0.2 −1.1 −4.4 −10.1 −7.3 −2.8 −2 −38.2 −21.5 −15.5 −14.7 −36.3 −16.2

50.4 56.1 54.4 56 51.8 54.2 52 54.7 55.5 55 52.1 51.3 57.1 55.2 50.7 52.8

21.4 20.5 30.5 26.7 33.4 30.3 22.2 22.4 20.7 29.7 33.6 25.9 24.3 35 36.7 21.1

55.5 58.6 55.4 57.1 53.8 54.1 55.7 56.5 58.1 55.3 57.1 54.1 57.4 54.7 57.5 59.8

−0.7 −1.37 −1.45 −1.48 −1.49 −1.34 −0.9 −0.94 −1.24 −1.34 0.76 −0.21 −0.55 −0.58 0.69 −0.5

−0.41 −1.39 −0.92 −1.11 −0.73 −0.75 −0.61 −0.84 −1.15 −0.91 1.61 0.19 −0.34 0.04 1.7 −0.15

0.85 0.16 0.13 0.16 0.08 0.28 0.69 0.56 0.36 0.19 2.41 1.3 1.08 0.91 2.31 1.23

67 50.2 59.4 56.4 61.1 62.8 64 61.3 55 60.1 115.3 81.7 75.3 82 116 75.4

The units are volts for redox potentials and kcal/mol for the homolytic bond dissociation free energies and hydricities, ΔG°H−.

Table 5. Correlations between Thermodynamic Properties (see text for discussion)a pKa(II) = −18.01E°(I/0) − 0.89 ΔG°H−(II) = 21.72E°(II/I)) + 79.27 E°(III/II) = 1.02E°(I/0) + 1.60 pKa(III) = −18.38E°(I/0) − 27.82 pKa(IV) = −16.90E°(I/0) − 24.78 ΔG°H•(II) = −1.34E°(II/I)) + 53.27 ΔG°H•(III) = −25.05E°(I/0) + 23.06E°(II/I) + 15.65 ΔG°H•(IV) = 0.47E°(I/0) + 56.7

R2

σb

0.990 0.992 0.993 0.985 0.991

0.37 pKa units 0.41 kcal/mol 0.08 V 0.46 pKa units 0.34 pKa units 0.4 kcal/mol 0.5 kcal/mol

previously discussed in the literature. The correlations revealed from our calculations are summarized in Table 5. As previously discussed, the experimental values of pK a(II) should be inversely linearly correlated to E°(I/0),27 as both properties rely on the electron richness of the Ni center that is, the more electron rich the Ni center, the easier the oxidation, and the Ni−H bond will be less acidic. As indicated by eq 13, such a correlation is observed from our data set (see Figure 6 and Table 5) with a reasonable confidence level: (13)

Our fit indicates that one can estimate pKa(II) within ±0.37 pKa units (0.50 kcal/mol) based on knowledge of E°(I/0). It is noted that the value of the slope obtained from the subset of the six experimentally determined compounds27 is −20.8 with an intercept of −3.6, which differs appreciably from the larger set fit and hence would affect the prediction of the thermodynamic quantities significantly. Note, in this and all the correlations described below only the intercept depends on the choice of reference species, whereas the slope depends only on the relative energetics across the series. In a similar spirit, E°(II/I) should be linearly correlated with the hydricity ΔG°H−, as both depend on the ability of a Ni(d8) species to act as an electron acceptor.27 Such correlation is indeed observed (Figure 6b) with the best-fit line given by eq 14.

2.2 kcal/mol

a

The confidence of the estimate σ and, where appropriate, the correlation coefficient are also given. Redox potentials are in volts and free energies in kcal/mol; the constants have consistent units. bFor each correlation the associated error

is also reported, where N is the number of points in the data set, σ y is the standard deviation of the dependent variable, and R 2 is the correlation coefficient. Assuming that the ab initio values have a normal distribution about the correlation line, σ gives the accuracy of the estimate. The errors associated with the quantities obtained from thermochemical cycles are obtained from standard error propagation.

not been measured, but rather calculated with the protocols presented above. Specifically we have chosen R = CFxHy (x + y = 3) groups on the diphosphines in several cases to extend the data set to include strong electron-withdrawing ligands, thus expanding the range of thermodynamic quantities. In this way we could increase the size of the data set in order to examine correlations between properties in a statistically meaningful way over a much wider range of values than available from just the experimentally characterized species. The extended set of ligands (Figure 5 and Table 4 for computed thermodynamic properties) offers the opportunity to verify and validate the experimentally observed correlations between E°(II/I) and ΔG°H−, and E°(I/0) and pKa(II),27 as well as look for correlations between other properties that have not been

(14)

Compared with the parameters derived from the smaller “experimental” set with values of 17.5 (kcal/mol)/V for the slope and 75.7 kcal/mol for the intercept, both parameters derived from the more extensive computed data set are larger. It is noticeable that our estimated error of ±0.41 kcal/mol for this correlation is smaller than for the correlation between E°(I/0) and pKa(II) discussed above, implying that the underlying relationship between these properties holds to a stronger degree. The underlying structural/electronic reasons for the above two correlations have been discussed previously27,62 in terms of the influence of the diphosphine dihedral twist angle on 6114


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Figure 6. Linear correlations between thermodynamic properties as obtained from the simulated data set: (a) pK a(II) and E°(I/0), (b) ΔG°H− and E°(II/I), (c) E°(III/II) and E°(I/0), (d) pKa(III) and E°(I/0), (e) pKa(IV) and E°(I/0). See Figure 2 for definitions.

E°(II/I), ligand bite angle on E°(I/0), and the relationships between these properties and the HOMO and LUMO orbital energies of these complexes.62 We observe similar structural trends in our computed data.27,62 We now consider the relationship between the half-wave potentials E°(I/0) and E°(III/II). It was found that a linear correlation exists between these two potentials, as shown in Figure 6c. The best-fit line is given by

that for the protonated species H has a net positive charge; particularly revealing is the electrostatic potential map shown in Figure 7. As such, both E°(III/II) and E °(I/0) represent the

(15)

with an error estimate of ±0.08 V. The correlation indicates that the two half-wave potentials E°(I/0) and E°(III/II) differ, to a very good approximation, by a constant of 1.60 V, as was noted previously by DuBois and co-workers.22,25,26 To explain the correlation of eq 15, we first note that the low pKa(II) values suggest that the Ni−H bonds of all the [HNi(diphosphine)2]+ species are more like protons than hydrides. Consequently, these species should be best thought of as Ni(0)/H+ (d10) species as opposed to a Ni(II)/H− (d8) as assigned by formal oxidation state arguments. This description is supported by an analysis of the electronic structure, which shows

Figure 7. Electrostatic potential projected onto an iso-electron density surface (an isovalue of 0.02 e/Å2) of [HNi(PH3)4]+ and [Ni(PH3)4] complexes.

reduction of a Ni(d9) species to a Ni(d10) species, where the former has an electronic environment similar to the latter with the exception of the presence of an extra proton, which provides an electrostatic stabilization of the Ni d electrons. As such, the constant of 1.60 V in eq 15 can be ascribed the physical meaning of an energetic stabilization of the Ni d electrons by a proton. 6115


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The above observations have an implication for our ability to estimate pKa(III) and pKa(IV) in terms of redox potentials. The constant shift between E°(III/II) and E°(I/0) implies that there is also a constant shift between pKa(III) and pKa(II), as can be established through thermodynamic cycles. Since pKa(II) is proportional to E°(I/0), a linear correlation with E°(I/0) must also hold for pKa(III). Through similar arguments to those used for the relationship between pKa(II) and E°(I/0), pKa(IV) must be related to E°(III/II) and thus also E°(I/0). As shown in plots d and e of Figure 6, these correlations are indeed observed. It was previously hypothesized, based on measurements obtained on a small set of complexes containing Co, Rh, and Pt complexes, that pKa(II) and pKa(IV) may be correlated.22,25,26 The current calculations not only support this hypothesis but also provide an estimate of the difference between the two pKa values for Ni-based species. The implication is that for these species all the pKa values needed for free energy maps can be derived solely from the knowledge of E°(I/0) within a reasonable approximation (0.5 pKa units). Correlations between the homolytic bond dissociation energies and any of the redox potentials are less reliable. This can be a consequence of the small range of values spanned by ΔG°H•(II) and ΔG°H•(IV), which vary by 6 and 4 kcal/mol, respectively. However, we have reliable estimates for the pK a, hydride donor strength, and redox potentials, as discussed above. One can thus infer homolytic bond energies from thermodynamic cycles. For instance ΔG°H•(II) is best inferred from the thermodynamic cycle of Scheme 3 involving E°(II/I)

Figure 8. Example of catalyst design using thermodynamic properties. (a) Thermodynamic diagram for the [Ni(depp)2]2+ system in acetonitrile, calculated from the experimental values of two oneelectron redox potentials, E°(I/0) and E°(II/I), using the correlations from Table 5. (b) Map of relative free energies of all species derived from Ni−H bond cleavage (1 atm H2 and pH = 8.5 in acetonitrile). (c) Reaction free energy profile for the electrocatalytic oxidation of H2 (H2 + 2B → 2HB+ +2e−, where B denotes a base) by [Ni(depp)2]2+ catalyst. In (c) the energies (red lines) are accurate, but the blue lines are only a guide to the eye and do not represent the actual activation barriers.

E°(I/0) and E°(II/I), quantities that are often easily accessible from cyclic voltammetry experiments.

Scheme 3

4. CONCLUSIONS We have developed a theoretical protocol that is capable of predicting with high accuracy the thermodynamic properties of molecular catalysts, such as pKa, hydricities, redox potentials, and homolytic bond dissociation free energies of metal hydride bonds. The protocol has been validated against Ni catalysts for H2 oxidation/evolution and can be extended to other metals. The proposed approach involves isodesmic reactions coupled with accurately known values, either from experiment or from high-level calculations on a reference system. In the latter approach complete free energy maps for all species involved in catalytic cycles can be generated without requiring a complete set of experimental data for all properties of interest. Previous studies of [HM(diphosphine)2]+ complexes computed their pKa values and hydride donor abilities and the M(II/0) couple of the corresponding [M(diphosphine) 2]2+ complexes. Our calculations have been extended to 10 thermodynamic properties, five of which cannot be directly measured experimentally for nickel complexes. Analysis of the calculated properties reveals a number of important correlations, some of which have not been recognized due to a lack of detailed experimental data. Linear correlations were extracted between pKa(II) and E°(I/0), between pKa(IV) and E°(III/II), and between hydricity and E°(II/I). The half-wave potentials E°(I/0) and E°(III/II) were found to differ by a constant value of ∼1.60 V for the nickel diphosphine complexes calculated here. Similarly, pKa(II) and pKa(III) differ by a constant value of 27 pK a units for [HNi(diphosphine) 2 ] + vs [HNi(diphosphine)2]2+. Such correlations are exceedingly important because they allow one to easily calculate thermodynamic diagrams, such as those shown in Figures 1a and 8a, from the

and ΔG°H−(II), for which our confidence in the correlations is the highest (see above): It follows that

(17)

From the thermodynamic cycle shown in Scheme 3 and correlations between E°(II/I) and ΔG°H−(II), the homolytic bond dissociation energy ΔG°H•(II) can be calculated from E°(II/I) with an error of ∼0.4 kcal/mol: (18)

Similarly, ΔG°H•(III) and ΔG°H•(IV) can be calculated from the knowledge of E°(I/0) and E°(II/I) through eqs 19 and 20, respectively.

(19) (20)

The important correlations discussed above are summarized in Table 5. Indeed, using these correlations, it is possible to predict all of the properties in the thermodynamic scheme of Figure 2 from knowledge of only two half-wave potentials, 6116


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(14) Moore, E. J.; Sullivan, J. M.; Norton, J. R. J. Am. Chem. Soc. 1986, 108, 2257. (15) Nataro, C.; Angelici, R. J. Inorg. Chem. 1998, 37, 2975. (16) Nataro, C.; Chen, J.; Angelici, R. J. Inorg. Chem. 1998, 37, 1868. (17) Nataro, C.; Thomas, L. M.; Angelici, R. J. Inorg. Chem. 1997, 36, 6000. (18) Pearson, R. G.; Kresge, C. T. Inorg. Chem. 1981, 20, 1878. (19) Siclovan, O. P.; Angelici, R. J. Inorg. Chem. 1998, 37, 432. (20) Wang, D.; Angelici, R. J. Inorg. Chem. 1996, 35, 1321. (21) Berning, D. E.; Noll, B. C.; DuBois, D. L. J. Am. Chem. Soc. 1999, 121, 11432. (22) Ciancanelli, R.; Noll, B. C.; DuBois, D. L.; DuBois, M. R. J. Am. Chem. Soc. 2002, 124, 2984. (23) Curtis, C. J.; Miedaner, A.; Ellis, W. W.; DuBois, D. L. J. Am. Chem. Soc. 2002, 124, 1918. (24) Ellis, W. W.; Miedaner, A.; Curtis, C. J.; Gibson, D. H.; DuBois, D. J. Am. Chem. Soc. 2002, 124, 1926. (25) Miedaner, A.; Raebiger, J. W.; Curtis, C. J.; Miller, S. M.; DuBois, D. L. Organometallics 2004, 23, 2670. (26) Raebiger, J. W.; Dubois, D. L. Organometallics 2005, 24, 110. (27) Berning, D. E.; Miedaner, A.; Curtis, C. J.; Noll, B. C.; Rakowski DuBois, M. C.; DuBois, D. L. Organometallics 2001, 20, 1832. (28) Yang, J. Y.; Bullock, R. M.; Shaw, W. J.; Twamley, B.; Fraze, K.; DuBois, M. R.; DuBois, D. L. J. Am. Chem. Soc. 2009, 131, 5935. (29) Appel, A. M.; Lee, S. J.; Franz, J. A.; DuBois, D. L.; DuBois, M. R. J. Am. Chem. Soc. 2009, 131, 5224. (30) Rakowski DuBois, M.; DuBois, D. L. Chem. Soc. Rev. 2009, 38, 62. (31) Niu, S.; Hall, M. B. Chem. Rev. 2000, 100, 353. (32) Wright, J. S.; Rowley, C. N.; Chepelev, L. L. Mol. Phys. 2005, 103, 815. (33) Gossens, C.; Dorcier, A.; Dyson, P. J.; Rothlisberger, U. Organometallics 2007, 26, 3969. (34) Liu, S.; Schauer, C. K.; Pedersen, L. G. J. Chem. Phys. 2009, 131, 164107. (35) Siegbahn, P. E. M.; Tye, J. W.; Hall, M. B. Chem. Rev. 2007, 107, 4414. (36) Surawatanawong, P.; Tye, J. W.; Darensbourg, M. Y.; Hall, M. B. Dalton Trans. 2010, 39, 3093. (37) Felton, G. A. N.; Vannucci, A. K.; Chen, J.; Lockett, L. T.; Okumura, N.; Ptro, B. J.; Zakai, U. I.; Evans, D. H.; Glass, R. S.; Lichtenberger, D. L. J. Am. Chem. Soc. 2007, 129, 12521. (38) Qi, X.-J.; Fu, Y.; Liu, l.; Guo, Q.-X. Organometallics 2007, 26, 4197. (39) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (40) Perdew, J. P. Phys. Rev. B 1986, 33, 8822. (41) Andrae, D.; Häußermann, U.; Dolg, M.; Stoll, H.; Preuß, H. Theor. Chem. Acc. 1990, 77, 123. (42) Barone, V.; Cossi, M. J. Phys. Chem. A 1998, 102, 1995. (43) Cossi, M.; Rega, N.; Scalmani, G.; Barone, V. J. Comput. Chem. 2003, 24, 669. (44) Bondi, A. J. Phys. Chem. 1964, 68, 441. (45) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09; Revision B.01 ed.; Gaussian, Inc.: Wallingford, CT, 2009.

knowledge of only E°(I/0) and E°(II/I), through experimental measurement or computations. These diagrams are very powerful, as they allow construction of free energy landscapes, such as that shown in Figure 1b. This in turn allows the prediction of the free energies of all intermediates for numerous reaction profiles for selected stoichiometric and catalytic reactions. As an illustrative example, we show in Figure 8 a thermodynamic diagram calculated from E°(I/0) and E°(II/I) for the Ni(depp)2 complex and possible free energy profile for the electrocatalytic oxidation of H2. Note that there are several significant differences between this free energy profile for Ni and that for Pt (Figure 1c), such as the much higher energy of the nickel dihydrides. The fundamental electronic structure characteristics that underlie these correlations will be the subject of future research. The approach developed here can be extended to other catalysts and metals.

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ASSOCIATED CONTENT

S Supporting Information *

This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. ACKNOWLEDGMENTS We thank Karol Kowalski for the help with CCSD(T) calculations. This research was carried out in the Center for Molecular Electrocatalysis, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, FWP 56073. Pacific Northwest National Laboratory is operated for the U.S. Department of Energy by Battelle under Contract No. DE-AC06-76RLO 1830. Computational resources were provided at W. R. Wiley Environmental Molecular Science Laboratory (EMSL), a national scientific user facility sponsored by the Department of Energy’s Office of Biological and Environmental Research located at Pacific Northwest National Laboratory, and the National Energy Research Scientific Computing Center (NERSC) at Lawrence Berkeley National Laboratory.

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Comprehensive Thermodynamics of Nickel Hydride Bis(Diphosphine

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