Journal of Organometallic Chemistry 949 (2021) 121957 Contents lists available at ScienceDirect Journal of Organometallic Chemistry journal homepage: www.elsevier.com/locate/jorganchem How acid can become a dihydrogen complex in water? A DFT study Manuel A. Ortuño a,∗, Agustí Lledós b,∗ a Centro Singular de Investigación en Química Biolóxica e Materiais Moleculares (CIQUS), Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain b Departament de Química, Universitat Autònoma de Barcelona, 08193 Cerdanyola del Vallès, Barcelona, Catalonia, Spain a r t i c l e i n f o a b s t r a c t Article history: To accurate know the acidity of a dihydrogen molecule coordinated to a transition metal ion in water Received 30 April 2021 medium is an issue of interest in many areas, from electrochemistry to enzymes and catalysis. However, Revised 16 June 2021 experimental determination of this magnitude is challenging, and very few values have been reported. In Accepted 17 June 2021 this article we describe a computational protocol, based on DFT calculations and employing a discrete- Available online 21 June 2021 continuum solvent representation, to estimate pKa water of transition metal dihydrogen complexes. In this Keywords: approach the number of solvent molecules explicitly included in the calculations is determined by the Dihydrogen complexes convergence with the solvation Gibbs energy of the proton in the solvent. The approach has been initially pKa validated with experimental data in tetrahydrofuran (THF) solvent. Using (THF)3 clusters a mean absolute Water solvent deviation from experiments of only 1.4 pKa unit is achieved. In water the convergence is reached with DFT calculations (H2 O)10 clusters. Using them in a discrete-continuum model, the pKa water of twelve dihydrogen complexes Discrete-continuum solvation methods experimentally characterized in water have been computed. pKa water values span a wide range, from 23 to -4, illustrating how coordination to a transition metal modifies the dihydrogen acidity. Decomposition of the G of the acid-base equilibrium in two contributions, one intrinsic to the complex and another one accounting for solvent effects enables a deeper analysis of the dihydrogen acidities. © 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) 1. Introduction Consequently, the M–H2 bonding situation can lead to a H–H bond splitting via either homolytic or heterolytic cleavages (Scheme 1). Given the imminent consumption of fossil fuels, alternative en- In the homolytic process, the H2 ligand is oxidatively added to the ergy sources such as the hydrogen economy should receive the ba- metal yielding the corresponding dihydride species. Otherwise, in ton. Dihydrogen molecules are not only the feedstock in several the heterolytic pathway one hydrogen from the H2 ligand is ab- hydrogenation processes, but also arise as a potential fuel [1]. Back stracted as a proton forming a hydride complex [13]. The participa- in the 80s, Kubas et al. reported that transition metals can indeed tion of dihydrogen hydrogen bonded intermediates in this mecha- form σ -complexes binding dihydrogen molecules in a η2 fashion nism has been proposed [14-16]. Depending on the location of the [2,3]. Since then, a wide variety of dihydrogen complexes have base, such a proton transfer can occur intra- or intermolecularly been characterized [4]. In this matter, the production and storage [5-9]. In addition, the heterolytic mechanism is involved in rele- of molecular H2 are essential concerns that must be addressed, in vant bio-inspired processes such as those concerning hydrogenases which transition metals (M) can play a major role [5-9]. [17-19]. The M–H2 bonding in σ -complexes is usually described using These heterolytic processes are easily interpreted as acid–base the Dewar-Chatt-Duncanson model, i.e., involving a three-center reactions; thus, the evaluation of acid constants Ka (normally ex- two-electron interaction stabilized by back donation from a d or- pressed as pKa values) for the coordinated H2 ligand becomes an bital of M to a σ ∗ orbital of H2 [10]. The extent of back donation invaluable tool. The acidity of free dihydrogen is almost negligi- strongly affects the H–H bond distance (0.74 Å in free H2 ) giving ble. A first determination of pKa in tetrahydrofuran (THF) gave a rise to different stages of dihydrogen species, namely true (0.8–1.0 value of 35-37 for dihydrogen [20]. However, more recent estima- Å), elongated (1.0–1.3 Å), and compressed dihydride (>1.3 Å) [11,12]. tions are consistent with a pKa THF of approximately 50 [21]. This value dramatically changes in the presence of transition metals. As pioneering study, Chinn and Heinekey firstly measured the pKa in ∗ Corresponding authors. acetonitrile of a ruthenium dihydrogen complex, resulting in 17.6 E-mail addresses: manuelangel.ortuno@usc.es (M.A. Ortuño), agusti@klingon.uab.es (A. Lledós). [22]. Since then, a vast collection of experimental values has been https://doi.org/10.1016/j.jorganchem.2021.121957 0022-328X/© 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) M.A. Ortuño and A. Lledós Journal of Organometallic Chemistry 949 (2021) 121957 trans-derivatives [24,32] likely due to the strong trans influence exerted by the two hydride ligands. The estimation of pKa values in water is performed after testing the computational protocol in THF, with the final aim of providing valuable information to design transition metal complexes capable of tune the coordinating and splitting properties of H–H bonds. 2. Computational details Scheme 1. Transition metal-mediated H–H bond splitting mechanisms 2.1. Geometries and energies Geometries have been fully optimized at the DFT level in gas reported in organic solvents [21, 23-33]. Interestingly, some mono- phase using the M06 density functional [63] (with an ultrafine cationic rhenium [34], dicationic ruthenium [34,35] and osmium grid) [64] as implemented in Gaussian 09 [65]. This functional cor- [36] species exhibit a remarkably acidic behavior, with pKa values rectly accounts for dispersion interactions and is recommended for ranging from −6 to −2. Morris has proposed an empirical, simple transition metal chemistry [66,67] and water clusters [68]. Fe, Ru, equation, based on ligand acidity constants, to estimate the pKa THF and Os atoms were described by means of an effective core po- or pKa DCM values of hydride and dihydrogen species [37]. This sim- tential SDD for the inner electrons and its associated double-ζ ple model has been very successful in accounting and systematiz- basis set for the outer ones [69], complemented with a set of f- ing over 450 reported acid-base reactions involving such species polarization functions [70]. The 6-31G(d,p) was used on H atoms, [21]. Density Functional Theory (DFT) calculations have been per- 6-31G(d) on C, N, F, P, and Cl atoms, and 6-31G+(d) on O atoms formed to validate the additive nature of ligand contributions to [71-73]. This setup is now called BI. Geometries were optimized the pKa of metal hydride complexes [38-40]. Despite the evident without any symmetry restrictions and the nature of the min- success of the method, it breaks down when specific solvation ef- ima has been verified with analytical frequency calculations. All fects are important as it happen in methanol solvent [21]. transition metal complexes present closed shell electronic struc- Water is a desirable solvent due to its economics and envi- tures (singlet spin state). Gibbs energy calculations have been per- ronmental advantages. Despite dihydrogen complexes in organic formed at 298.15 K and 1 atmosphere. Single point calculations media have been extensively surveyed [4], these species are diffi- were performed on previous gas-phase (g) geometries (computed cult to be synthesized and characterized in aqueous environment, at M06/BI level) using 6-311++G(d,p) on H, C, N, O, F, P, Cl atoms hence literature is rather scarce [41]. pKa measurements in wa- [74-76], namely, setup BII. Ggp (BII) was obtained by adding the ter are neither easy nor straightforward because of solubility is- BI-entropic contribution to Egp (BII): sues as well as the leveling effect of the solvent. In those cases in which experimental data are difficult to acquire, theoretical calcu- Gg (BII) = Eg (BII) + [Gg (BI) – Eg (BI)] (1) lations come into play. The computation of acid constants can be performed by computing solvation Gibbs energies [42-45], albeit the proper handling of solvent becomes mandatory to obtain fairly Tetrahydrofuran (THF, ε = 7.43) and water (ε = 78.36) solvents reliable results. Very recently, a data set containing the pKa of ca. (sol) have been described as a continuum using the SMD method 200 transition metal hydrides, computed with low level, semiem- [77]. Single point calculations in solvent were carried out using the pirical DFT methods, was used to construct an automated machine BII setup and Gsol (BII) values were deduced by adding the BI- learning approach for the rapid estimation of pKa of transition entropic contribution to Esol (BII): metal hydride complexes [46]. In transition metal chemistry, some examples of pKa calculations including both implicit and explicit Gsol (BII) = Esol (BII) + [Gg (BI) – Eg (BI)] (2) descriptions of the solvent have been reported in organic [47,48] and water [49,50] solvents. Recently, the acidity of methane coor- dinate to transition metal ions has been investigated with compu- 2.2. pKa computation tational methods [51]. Because of the above-mentioned reasons, the acid- Acid constants can be estimated by computing the standard ity of water-soluble transition metal dihydrogen com- Gibbs energy in solution of the corresponding deprotonation pro- plexes appears as quite interesting feature to get in- cess. To deal with solvation of species, the proper description of sight into. This work focuses on the experimentally re- the solvent becomes crucial. Especially when solute–solvent inter- ported water-soluble η2 -H2 species: trans-[Fe(H2 )(H)(dRpe)2 ]+ actions may be decisive, such as water [78,79], solvent is described 1 [52] and trans-[Fe(H2 )(Cl)(dRpe)2 ]+ 2 [53] (R = 3- in both implicit (continuum) and explicit (discrete molecules) methoxypropyl), [CpRu(H2 )(PTA)2 ]+ 3 and [Cp∗ Ru(H2 )(PTA)2 ]+ ways. These methods are commonly known as cluster–continuum 4 (PTA = 1,3,5-triaza-7-phosphaadamantane) [54,55], trans- [80-82] and implicit–explicit [83]. [Ru(H2 )(H)(dRpe)2 ]+ 5 (R = p-3-methoxypropylphenyl) [56], Several procedures to compute acid constants by means of DFT trans-[Ru(H2 )(H)(dmpe)2 ]+ 6 [57], trans-[Ru(H2 )(H)(dppe)2 ]+ 7 calculations can be found in literature [42-46]. A recent report [57], trans-[Ru(H2 )(P(OH)3 )(dppe)2 ]2+ 8 [58], [Ru(H2 )(H2 O)5 ]2+ showcases the improvement provided by discrete-continuum sol- 9 [59], [Os(H2 )(NH3 )5 ]2+ 10 [60,61], trans-[Os(H2 )(Cl)(NH3 )4 ]+ vation methods in the pKa calculations. There are cases where the 11 [60,61], and trans-[Os(H2 )(Cl)(en)2 ]+ 12 (en = ethylenedi- root mean squared error is as large as 7 pKa units with pure con- amine) [62]. The corresponding conjugated species are: cis- tinuum solvation model and becomes around 1 pKa unit with the [Fe(H)2 (dRpe)2 ] 1’, trans-[Fe(H)(Cl)(dRpe)2 ] 2’, [CpRu(H)(PTA)2 ] 3’, hybrid approach [84]. Accordingly, herein, the calculations are per- [Cp∗ Ru(H)(PTA)2 ] 4’, cis-[Ru(H)2 (dRpe)2 ] 5’, cis-[Ru(H)2 (dmpe)2 ] formed by means of a hybrid cluster–continuum approach [81] as 6’, cis-[Ru(H)2 (dppe)2 ] 7’, trans-[Ru(H)(P(OH)3 )(dppe)2 ]+ 8’, shown in Scheme 2 in THF and water. Solvent (S) is treated as clus- [Ru(H)(H2 O)5 ]+ 9’, [Os(H)(NH3 )5 ]+ 10’, trans-[Os(H)(Cl)(NH3 )4 ] 11’, ter configurations of n molecules (Sn and H+ Sn ). Go g,deprot stands and trans-[Os(H)(Cl)(en)2 ] 12’. It must be pointed out that the con- for the deprotonation Gibbs energy in gas phase. The term Go→ ∗ , jugated bases of 1 and 5–7 are cis-dihydride species rather than which is the conversion factor from an ideal gas standard state of 2 M.A. Ortuño and A. Lledós Journal of Organometallic Chemistry 949 (2021) 121957 Table 1 Computed and experimental G∗ THF (H+ ) val- ues n G∗ THF (H+ ) / kcal mol−1 1 −242.8 2 −258.8 3 −260.5 Exp. [47,90] −256.3 the accepted G∗ water (H+ ) is −265.9 kcal mol−1 as reported by Scheme 2. Cluster-type thermodynamic cycle for deprotonation Gibbs energies in Tissandier et al. [87-89]. This result has been confirmed by several solution theoretical studies using cluster–continuum (−266.7 kcal mol−1 ) [82] and implicit–explicit (−266.1 kcal mol−1 ) [83] models. Un- fortunately, accurate data in non-aqueous solvents is less accessi- ble. For THF solvent, the G∗ THF (H+ ) value has been estimated by adding a correction term to G∗ water (H+ ), resulting in −256.3 kcal mol−1 [47,90]. The number of THF and water molecules considered in this study will be discussed next. 3. Results and discussion 3.1. Estimating the cluster size Scheme 3. Cluster-type thermodynamic cycle for the solvation Gibbs energy of pro- Prior to the calculation of pKa values, one should evaluate the ton number of solvent molecules, n, required to properly compute Gibbs energies in Scheme 2. As mentioned before, such number 1 atm “o ” to a standard state of 1 M “∗ ” [85], cancels out since should reproduce the experimentally reported value of G∗ sol (H+ ). the molecularity of the reaction is zero. G∗ sol (X) terms represent Several cluster structures Sn and H+ Sn are computed for THF and standard solvation Gibbs energies of species X, and RT•ln([sol]/n) is water solvents. the correction term for the Gibbs energy change of 1 mol of [sol]/n Small clusters up to 3 molecules are considered for THF solvent. M liquid state to 1 M [86]. Among the several conformations explored, Fig. 1a displays the According to the thermodynamic cycle illustrated in Scheme 2, most stable (THF)2–3 structures. Starting from the dimer (THF)2 , the deprotonation Gibbs energy in solution is derived as the fol- the approaching of a third THF molecule generates two main sub- lowing equation: classes of conformations for (THF)3 , namely, stacked and non- stacked configurations. The non-stacked structure is finally consid- ered, being 0.5 kcal mol−1 more stable than the stacked one. On G∗ sol,deprot = G°g,deprot + G∗ sol (M– ) + G∗ sol (H+ Sn ) – the other hand, Fig. 1b depicts the most relevant H+ (THF)2–3 clus- G∗ sol (MH) – G∗ sol (Sn ) – RT ln ([sol]/n) (3) ters. The proton in species H+ (THF)2 appears strongly solvated by the oxygen atoms, showing O•••H distances of ca. 1.19 Å. The in- and the pKa can be expressed as: clusion of a third THF molecule as in H+ (THF)3 forms a weaker interaction with a O•••H distance of 2.651 Å. Consequently, no ad- ditional molecules were further considered in order to simplify the pKasol = G∗ sol,deprot / 2.303 RT (4) conformational space. The G∗ THF (H+ ) values computed using (5) are collected in It can be easily deduced from (4) that Gibbs energy errors of Table 1 for clusters containing 1–3 THF molecules. As expected, 1.4 kcal mol−1 entail errors in pKa of 1 unit at room temperature, the description using only one molecule is not appropriate, but it being 2 units an acceptable discrepancy [43]. Detailed G values significantly improves with the dimer structures. The calculation can be found in the Supporting Information. using clusters with 3 molecules slightly decreases the Gibbs en- ergy by 1.7 kcal mol−1 with respect to those with 2, thus conver- 2.3. Number of solvent molecules gence is assumed for n = 3. The values of G∗ sol (H+ (THF)3 ) and G∗ sol ((THF)3 ) used in the pKa computation via (3) are −43.9 and The number of solvent molecules explicitly included in the cal- −9.4 kcal mol−1 , respectively. culations, n, is that which properly accounts for the solvation Gibbs The same protocol is adopted to estimate the number of water energy of the proton, G∗ sol (H+ ) in Scheme 3 [82]. molecules. Previous work on water clusters stated that, for even Accordingly, the G∗ sol (H+ ) term is evaluated using: numbers of molecules, (H2 O)n can be divided into two subclasses, (H2 O)4m and (H2 O)2+4m (m = 1, 2, …), being the latter more stable [82]. For m > 2, the complex network of hydrogen bonds provides G∗ sol (H+ ) = G°g,bind – G°→ ∗ – G∗ solv (Sn ) + G∗ sol (H+ Sn ) a clustering scenario difficult to deal with [91,92]. Since the full ex- – RT ln ([sol]/n) (5) ploration of water configurations is not the goal of this study, only 1–4, 6 and 10 molecules are considered. Fig. 2a shows selected For the cluster-type thermodynamic cycle (Scheme 3), the ac- (H2 O)n clusters for n = 4, 6 and 10. Although the cyclic structure is tual value of G∗ sol (H+ ) is obtained when n→∞ [82]. Thus, n is the most stable conformation for (H2 O)4 , it is less clear for (H2 O)6 . estimated as the number that provides a fairly converged value of Binding energies computed using CCSD(T) and MP2 methods favor G∗ sol (H+ ). Experimental values of G∗ sol (H+ ) are here mandatory the prism structure [93]. According to the present level of theory in order to validate the theoretical predictions. In aqueous solution (see Computational Details), energies in gas-phase indeed support 3 M.A. Ortuño and A. Lledós Journal of Organometallic Chemistry 949 (2021) 121957 Fig. 1. Optimized structures of (a) (THF)n and (b) H+ (THF)n , n = 2, 3. Distances in Å. Table 2 Computed and experimental G∗ water (H+ ) val- ues n G∗ water (H+ ) / kcal mol−1 1 −249.8 2 −255.4 3 −262.4 4 −263.5 6 −264.5 10 −265.7 Exp. [87,88] −265.9 Fig. 2. Optimized structures of (a) (H2 O)n and (b) H+ (H2 O)n , n = 4, 6 and 10. Dis- 3.2. Calibrating the method: computing pKa in THF tance in Å. The present study pursues the pKa computation of dihy- drogen species in water, particularly 1–12. Although hybrid the prism hexamer, but Gibbs energies in solution claim for the cluster–continuum methods perform generally well for such cyclic form, being ca. 3–5 kcal mol−1 more stable than the prism calculations, no dihydrogen complexes have been analyzed so and cage counterparts. The geometry of (H2 O)10 is taken from lit- far, thus an initial validation with respect to experimental data erature [94]. Likewise, Fig. 2b displays the H+ (H2 O)n clusters for is recommended. Unfortunately, no experimental data of 1– n = 4, 6 and 10. The structure of H+ (H2 O)4 is interpreted as a 12 are available in aqueous solution. Instead, the pKa values H3 O+ ion solvated by 3 water molecules. Concerning H+ (H2 O)6 , have been evaluated in THF solution. Consulting the literature among the several configurations explored [95] we found that the of 1–12, only the pKa THF of 7 has been measured [31]. The disposition experimentally proposed by Reed and co-workers [96- analysis is then extended to include other complexes which 98] is preferred, showing a O•••O distance of 2.383 Å [99]. Analo- pKa THF values are reported (Fig. 3): trans-[Ru(H2 )(H)(dArpe)2 ]+ gous to (H2 O)10 , the geometry of H+ (H2 O)10 is collected from lit- (Ar = p-methoxyphenyl) 13, trans-[Fe(H2 )(H)(dppe)2 ]+ 14, erature [83]. trans-[Os(H2 )(H)(dppe)2 ]+ 15, [CpRu(H2 )(dppm)]+ 16, and The G∗ water (H+ ) values computed using (5) are collected in [Cp∗ Ru(H2 )(dppm)]+ 17 [31]. The conjugated bases are: cis- Table 2 for clusters of 1–10 water molecules. Structures with one [Ru(H)2 (dArpe)2 ] 13, cis-[Fe(H)2 (dppe)2 ] 14, cis-[Os(H)2 (dppe)2 ]+ and two molecules poorly describe the experimental value, al- 15, [CpRu(H)(dppm)] 16, and [Cp∗ Ru(H)(dppm)] 17. though a quite improvement is obtained for n = 3, 4. After ex- The pKa THF values of 7 and 13–17 are computed according to panding the cluster up to 6 and 10 molecules, the result becomes (3) and (4) using clusters with 3 THF molecules as depicted in quite better. The difference between G∗ water (H+ ) values for 6 and Scheme 4. The results are collected in Table 3. The calculations 10 molecules is only 1.2 kcal mol−1 , thus convergence is assumed are in fair agreement with the experimental ones [21,37], show- for n = 10. Previous calculations considered 4 [82] and 10 wa- ing absolute differences in the range of 0.0–2.8 units. This DFT- ter molecules [83]. The present computed value of −265.7 kcal based protocol is recommended when the subtle influence of re- mol−1 is in agreement with the experimental one, −265.9 kcal mote groups, such as the p-OMe groups in 13, needs to be cap- mol−1 [87,88]. The corresponding values of G∗ sol (H+ (H2 O)10 ) and tured. These positive results suggest that the present computa- G∗ sol ((H2 O)10 ) used in the pKa computation via (3) are −64.3 and tional protocol can be successfully applied to dihydrogen species −23.4 kcal mol−1 , respectively. in THF. 4 M.A. Ortuño and A. Lledós Journal of Organometallic Chemistry 949 (2021) 121957 Fig. 3. Dihydrogen complexes studied in THF. 3D pictures of the optimized dihydrogen complexes, as well their related hydrides can be found at the Supporting Information. tributions are negative and relatively small in the range of 2–14 kcal mol−1 . Due to the systematic effect of G∗ sol , the Go g,deprot term mainly governs the acidity. Conversely, dicationic species 8–10 Scheme 4. Model deprotonation reaction of dihydrogen species in THF (n = 3) behave the other way around, i.e., they exhibit negative values Table 3 of Go g,deprot ; in other words, the deprotonation of such dica- Calculated and experimental [37] pKa THF tionic complexes is thermodynamically favored. The solvation term G∗ sol also works in the opposite direction with respect to Species pKa THF (calc) pKa THF (exp) |pKa THF | monocations; positive values indicate that the solvation of dica- 7 14.1 14.1 0.0 tionic dihydrogen reactants becomes more relevant than that in- 13 17.9 17.4 0.5 volving monocationic hydride and H+ (H2 O)10 products. The scarce 14 14.3 11.5 2.8 15 14.1 12.1 2.0 number of reported dicationic species hampers a proper analysis 16 9.6 7.2 2.4 of general trends. 17 9.9 9.2 0.7 The G∗ sol term seems to be rather similar for the monoca- MADa 1.4 tionic species under study. As a consequence, a direct correlation a Mean absolute deviation from experiments. between pKa water and Go g,deprot can be found. The corresponding plot of pKa water against Go g,deprot is shown in Fig. 6. The calcu- lated regression line (R2 = 0.863) affords a slope of 0.59. Assum- ing G∗ sol as a constant in (6), the resulting ideal slope shall be 0.73 (298 K), which is close to the present value of 0.59. Overall, for these monocationic species the acidity of the dihydrogen ligand Scheme 5. Model deprotonation reaction of dihydrogen species in water (n = 10) can be roughly estimated in the basis of the gas-phase deprotona- tion term Go g,deprot . 3.3. Computing pKa in water 3.4. Discussing pKa in water The computational protocol has been previously tested against similar dihydrogen complexes in THF solution. Since the water This section is devoted to discuss the pKa water results obtained clusters seem to be adequate (they do reproduce the proton solva- for the transition metal complexes 1–12. As regards the geometri- tion value G∗ water (H+ )), we hypothesize that the present discrete- cal parameters, one important feature may be the H–H bond dis- continuum protocol could also be applied to dihydrogen complexes tance of dihydrogen ligands (Fig. 4), although no global correlation in water. The pKa water values of 1–12 have been estimated accord- toward the acidity is found. That is, the elongated nature of dihy- ing to (3) and (4) using clusters with 10 water molecules as de- drogen ligands apparently does not influence the acidic behavior in picted in Scheme 5. The values for each complex are collected in a systematic way. Complexes 1–12 will be analyzed regarding the Fig. 4, ranging from 23.0 in 12 to −3.5 in 8. The corresponding H–H transition metal as follows. bond distances have also been gathered in Fig. 4. Complexes 1–10 For the Fe-based species trans-[Fe(H2 )(X)(dRpe)2 ]+ , the pKa water display values of 0.8–0.9 Å, whereas 11 and 12 behave as elongated of 1 (X = H) and 2 (X = Cl) are 20.4 and 12.8, respectively. The dihydrogen species, showing distances of 1.2–1.3 Å. difference results in 7.6 units and mainly comes from the gas- To gain further insight into the acidic properties, Equations (3) phase deprotonation term (Go g,deprot of 8.4 kcal mol−1 ). Notably, and (4) can be combined to express pKa water (4) according to two 1 adopts a cis rearrangement of phosphines whereas 2 maintains main terms, G°g,deprot and G∗ sol : the trans stereochemistry. Morris and co-workers have reported similar results for a set of trans-[Os(H2 )(X)(dppe)2 ]+ complexes in dichloromethane solution. For X = H [24] Cl, and Br ligands [25], pKa water = (G°g,deprot + G∗ sol + constant) / 2.303 RT (6) the pKa values are 13.6, 7.4, and 5.4, respectively. The pKa be- tween the Os-based complexes with H and Cl ligands is 6.2, in line G°g,deprot represents the thermodynamics of the deprotona- with the 7.6 units previously mentioned for the Fe-derivatives 1 tion reaction in gas phase, i.e., the intrinsic acidity of the H2 lig- and 2. and in the transition metal complex. On the other hand, G∗ sol Moving forward to Ru-based species 3–7, some differences are accounts for the solvation Gibbs energy difference between prod- revealed according to the ligands presented. Within the same fam- ucts and reactants. This means that the relative stability of species ily, more electron-donating ligands correlate to larger pKa water . For mainly comes from implicit solvation effects (as the proton in gas instance, the pKa water of Cp-derivative 3 is 1.3 units lower than that phase is already solvated with explicit solvent molecules). of Cp∗ -derivative 4 [100]. This trend shown by Cp and Cp∗ ligands The G°g,deprot and G∗ sol contributions for each complex are has been experimentally detected for 16 and 17 (pKa THF of 2.0 in illustrated in Fig. 5 as blue and red bars, respectively. For mono- Table 3) [21,37] and other related species [23]. A similar but more cationic species 1–7, 11, and 12, the positive values of Go g,deprot stressed trend is observed for the pKa water values of bis(phosphine) show the difficulty to deprotonate the dihydrogen complexes to complexes trans-[Ru(H2 )(H)(dXpe)]+ , being 7 (X = Ph, 12.3) quite form the hydride derivatives. For the other term, G∗ sol , all con- more acidic than 6 (X = CH3 , 19.3), and 6 more acidic than 5 5 M.A. Ortuño and A. Lledós Journal of Organometallic Chemistry 949 (2021) 121957 Fig. 4. pKa water and H–H bond distances (in Å) of dihydrogen species 1–12. 3D pictures of the optimized dihydrogen complexes, as well their deprotonated hydrides (1’-12’), are collected in the Supporting Information. Fig. 5. Bar chart showing G contributions for species 1–12, including pKa water values. (X = (CH2 )3 OCH3 , 22.0). In these cases the steric and electronic The dicationic nature is indeed a key factor, but it is worth not- properties are not fully separated. As computational exercise, some ing that dicationic complexes do not entail a strong acidic char- complexes of the type [Ru–(dmpe)] are calculated substituting acter systematically, see for instance the Os-derivatives 9 (9.3) methyl groups by H 18, CF3 19 and F 20 (Scheme 6), where steric and 10 (21.1). Other dihydrogen complexes acting as strong acids contributions are rather similar among them but electronic effects have been reported, e.g., monocationic [Cp∗ Re(H2 )(CO)(NO)]+ (pKa are not. In this scenario, electron-withdrawing groups clearly en- ca. −2) [34] and dicationic trans-[Os(H2 )(CO)(dppp)2 ]2+ (pKa ca. hance the acidity of dihydrogen complexes. The pKa water values −5.7) [35] and trans-[Os(H2 )(CH3 CN)(dppe)2 ]2+ (pKa ca. −2) [36]. range from 19.3 in 6 (X = CH3 ) to −4.4 in 20 (X = F). In other To further investigate the case of 8, taking into account the influ- words, the more electron-donating the ligands are, the less acidic ence of the ligand L trans to the dihydrogen ligand in the acid- the complex behave [30]. The chelating size of the bis(phosphine) ity, the pKa water values of hypothetical species calculated with ligands may also influence [101,102]. other ligands L are displayed in Scheme 7. Inspired by the pre- An interesting scenario arises for complex 8, which exhibits su- vious reports [35,36] the P(OH)3 ligand in 8 has been substi- peracidic properties according to the calculated pKa water of −3.5. tuted by CH3 CN 21 and CO 22. In line with above-mentioned 6 M.A. Ortuño and A. Lledós Journal of Organometallic Chemistry 949 (2021) 121957 ues, displaying a mean absolute deviation from experiments of ca. 1 pKa unit. The same protocol has been adopted to estimate the number of water molecules. Convergence on the proton solvation has been achieved for (H2 O)10 clusters. Therefore, introducing these clus- ters in the discrete-continuum model, the pKa water of twelve ex- perimentally characterized transition metal-dihydrogen complexes have been computed. pKa water values obtained in this way span a broad range, from 23 to −4, illustrating how coordination to a transition metal is modifying the dihydrogen acidity. Neverthe- less, no global correlation between the H–H bond distance of di- hydrogen ligand and acidity has been found. To further analyze the acidic properties, we have decomposed G of deprotonation in water of all the complexes in two contributions, one describ- ing the intrinsic acidity of the H2 ligand (G°g,deprot , thermody- Fig. 6. Plot of pKa water against Go g,deprot for monocations 1–7, 11, and 12. Regres- namics of the deprotonation reaction in gas phase) and the other sion line in dashed red. one accounting for implicit solvent effects in the relative stabilities of acid and conjugate basis forms of each complex (G∗ sol ). For monocationic species, G°g,deprot term mainly governs the acidity, being the G∗ sol term rather similar for all the monocationic species considered. To separate steric and electronic effects, we have varied a X ligand in a series of complexes structurally equiv- alent, finding a marked influence of the electron-donating prop- Scheme 6. pKa water of complexes 18–20 derived from 6. 3D pictures of the opti- erties of X in pKa water , changing from 19.3 for X = Me to −4.4 for mized dihydrogen complexes, as well their deprotonated hydrides (’), are collected X = F. Within the same family, more-electron donating ligands cor- in the Supporting Information. relate to higher pKa water . Dicationic complexes behave in a different way; for them, the deprotonation is intrinsicality favored (negative G°g,deprot term). However, the solvation term works in opposite direction, against deprotonation. As a result of the two factors operating in oppo- site directions, dicationic complexes do not systematically entail a strong acidic character. However, the scarce number of dicationc Scheme 7. pKa water of complexes 21–23 derived from 8. 3D pictures of the opti- species reported in water hampers a deeper analysis of general mized dihydrogen complexes, as well their deprotonated hydrides (’), are collected in the Supporting Information. trends. With the current computational means, the calculations de- scribed in this paper can be easily performed to large data set acids, the computed pKa water values of 2.5 for 21 and −0.2 of compounds, enabling for an accurate estimation of their acid- for 22 clearly account for strong acidic properties. As a mat- base properties. Moreover, discerning their different energy con- ter of fact, a solvent water molecule is also considered as lig- tributions to the pKa values would prove essential to understand and forming 23. This complex does conserve the acidity, with their intrinsic acidity and tune it by modulating their ligand envi- a pKa water of −0.5. One can suggest that the acidic behavior of ronment. bis(phosphine) complexes mainly comes from their dicationic and phosphine-based nature, since the superacidic behaviour is ab- Declaration of Competing Interest sent in the dications 9 and 10 containing O- and N-donor lig- ands, respectively. The type of ligand L also influence but to a less The authors declare that they have no known competing finan- extent. cial interests or personal relationships that could have appeared to As concerns the Os-based complexes 10–12, the resulting influence the work reported in this paper. pKa water values are rather similar and fewer conclusions can be made. Curiously, the dicationic species 10 exhibit a similar acidic Acknowledgements behaviour than monocations 11 and 12. The latter 12 is slightly less acidic than 11 (0.9 units), presumably due to the better electron- A. L. acknowledges financial support from Spanish Ministry of donor properties of primary amine ligands with respect to ammo- Science and Innovation (project PID-2020-116861GB-I00). M.A.O. nia. acknowledges Xunta de Galicia (Investigador Distinguido program ED431H 2020/21, Centro singular de investigación de Galicia ac- 4. Conclusions creditation 2019-2022, ED431G 2019/03) and the European Union (European Regional Development Fund - ERDF). We employed a computational protocol, based on DFT calcula- tions, to estimate pKa of transition metal dihydrogen complexes in Supplementary materials water solvent. We used a discrete-continuum solvation approach, in which the number of solvent molecules explicitly included in Supplementary material associated with this article can be the calculations properly accounts for the solvation Gibbs energy found, in the online version, at doi:10.1016/j.jorganchem.2021. of the proton in the solvent at choice. 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