Computational Study of 3d Metals and Their Influence on the Acidity of Methane C-H Bonds.

CCSD(T) methods in conjunction with correlation consistent basis sets are used to predict the pK a for the deprotonation of methane in a 3d metal ion adduct, [M···CH4]+ (M = Sc-Cu), in dimethyl sulfoxide solvent, which is modeled by the SMD continuum solvent model. Results show that the coordination of methane to different M+ ions has a substantial difference of ∼27 pK a units, from most to least acidic, and increases the acidity of the methane C-H bond from ∼8 to 36 pK a units. Furthermore, even with the omission of the more expensive quadruple and quintuple zeta basis sets in the prediction process, similar trends in pK a(C-H) as a function of 3d metal ions are exhibited. This research serves to illustrate the substantial effect that metal ion identity has on the acidity of a coordinated hydrocarbon and the utility that correlation consistent basis sets have in lowering the computational cost of modeling larger systems.

Introduction

Methane activation by organometallic catalysis remains a field of intense study, as it has significant technological implications. Methane is both plentiful, being the primary component of natural gas, and quite valuable. The process of methane conversion has a multitude of industrial applications, including the production of fuel that could serve as an alternative energy source to the conventional petroleum and coal. However, because of the thermodynamic strength of the C–H bonds in methane and its very low acidity and basicity, it is difficult for methane to react readily.

Previous studies by Olah and co-workers[1] have shown that methane only becomes reactive in superacidic systems, allowing for the protonation of methane as well as methane conversion.[2] Similarly, the work of Streitwieser and Taylor demonstrated that methane is only deprotonated in superbasic systems.[3] These works illustrate the significance that reaction conditions have on influencing methane activation. Superacid and superbasic systems still typically require forcing conditions and highly reactive reagents for methane conversion and, in most cases, are stoichiometric not catalytic.

Presently, the relationship between pKa of coordinated C–H bonds and metal identity is an under researched area of organometallic chemistry.[4] Whereas the acidic properties of a variety of organic carbon acids are reasonably well known,[5] particularly in dimethyl sulfoxide (DMSO) solvent, there have been few studies concerning the acidity of C–H bonds within transition-metal structures. Indeed, one rare study by Christman et al. investigates the enhancement of pKa for aromatic substrates by coordination to Pd(II).[4] In their experiments, these researchers estimated an increase in the acidity of arene C–H bonds by 40 orders of magnitude or more upon coordination to cationic Pd(II) complexes.

In the present study, a Brønsted–Lowry acid/base reaction was examined, involving 3d transition-metal methane adducts of the form of [M···CH4]+ and the solvent DMSO to gain more insights into the impact of the metal on the acid/base properties of aliphatic C–H bonds in the coordination sphere of a 3d metal ion. In the observed reaction (Figure ), initially, the methane adduct is loosely coordinated to the M(I) ion (Figure ). After the deprotonation of [M···CH4]+, a shorter M–C bond is formed along with a neutral methyl complex (Figure ), which maintains sp3 hybridization at the carbon. In one study, Fallah and co-workers found that deprotonation of a methyl C–H bond was a competing side reaction to methane functionalization.[6] Thus, investigating the acid/base properties of aliphatic C–H bonds of both hydrocarbon and hydrocarbyl complexes within the coordination sphere of a transition metal is important in catalyst design.

Figure 1

Acid/base reaction used to calculate methane pKa values: a 3d metal methane adduct and DMSO results in a metallic methyl complex and protonated DMSO.

Figure 2

Nickel(I) methane adduct, a representative example of the methane adducts modeled in this research. B3LYP/6-31+G(d)-optimized bond lengths are reported in angstroms.

Figure 3

Nickel(I) methyl complex, a representative example of the methyl complexes modeled in this research. B3LYP/6-31+G(d)-optimized bond lengths are reported in angstroms.

All 3d metal ions were assumed to have a formal oxidation state of 1+ in order to facilitate comparison among the various methane adducts. Highly accurate coupled cluster (CCSD(T)) calculations are performed to assess how metal identity impacts the intrinsic acid/base properties of a methane C–H bond within the coordination sphere of a first-row transition-metal ion (Sc through Cu). Furthermore, CCSD(T) simulations, in conjunction with correlation consistent basis sets, can serve as a benchmark for future studies using more approximate density functional theory (DFT), which may be applied to larger, more experimentally relevant catalyst candidates.

Results and Discussion

pKa Values for 3d Metal(I) Methane Adducts

Given the simplicity of the present models, our main goal is to assess trends—rather than absolute values as a function of metal upon the Brønsted–Lowry acidity of a methane C–H bond within the coordination sphere of a 3d metal ion. Calculating the deprotonation of free methane with several complete basis set (CBS) extrapolation methods outlined in Computational Methods, it is less acidic than coordinated methane with an average pKa(C−H) of 49.5 and a standard deviation of ±0.3 pKa units

The predicted ground-state multiplicities of the cationic 3d metal methane adducts studied (Table ) all agreed with experimental data reported in the National Institute of Standards and Technology (NIST) database for the “naked” metal monocations, except that of Cr(I), where single point CCSD(T) calculations predicted that [Cr(I)···CH4]+ was a quartet ground state, but the NIST database suggested that the naked chromium cation should be a sextet.[7] Likewise, the predicted multiplicities of the studied methyl complexes also agreed with the findings of Rinaldo et al. and McKee.[8,9]

Table 1

Lowest Energy Multiplicities of Methane Adducts and Methyl Complexes Predicted from CCSD(T) Computations

	Sc	Ti	V	Cr	Mn	Fe	Co	Ni	Cu
[M···CH4]+ multiplicity	1	4	5	4	7	6	3	2	1
M–CH3 multiplicity	1	4	5	6	7	6	3	2	1

In Table , the average estimated pKa of extrapolation methods is displayed along with the standard deviation in pKa values for each respective metal. Figure shows that the pKa(C–H) values as a function of the 3d transition metals follow a trend, in which the acidity rises and falls twice, peaking at Ti+ and Mn+.

Table 2

Average and Standard Deviation of Methane Adduct pKa(C–H) Values for Each Metala

	Sc	Ti	V	Cr	Mn	Fe	Co	Ni	Cu
pKa average	31.1	39.4	34.2	28.6	41.4	36.3	26.7	14.0	16.5
pKa standard dev.	1.0	1.1	1.0	1.0	0.9	0.8	2.1	1.9	2.0

Averages and standard deviations were calculated with the values obtained from the extrapolation methods of each respective metal, excluding the DZ, TZ, QZ, and 5Z values obtained from the cc-pVXZ energies.

Figure 4

Bactrian camel trend exhibited by the pKa values of 3d transition metals using CCSD(T) methods and correlation consistent basis sets (cc-pVXZ for X = 2 (DZ), 3 (TZ), 4 (QZ), and 5 (5Z)) at the B3LYP/6-31+G(d)-optimized geometries.

Initially, the basis sets cc-pVDZ, cc-pVTZ, cc-pVQZ, and cc-pV5Z were utilized in calculating single point energies. However, as the study progressed, it became apparent that the quintuple zeta basis set was not critical to determine accurate pKa(C–H) estimates, as all extrapolation schemes yielded values within ±2.1 pKa units (Table ). Because the deviation in predicted pKa values is quite small (Table ), one could argue that the quadruple zeta basis set may also be unnecessary in approximating pKa values. Figure further implies that the least expensive DZ and TZ basis sets show the same trends as the CBS extrapolations as well as the more expensive QZ and 5Z basis sets. Only utilizing the cc-pVDZ and cc-pVTZ basis sets, which are less computationally expensive, would enable larger organometallic complexes to be studied as well.

Table 3

Average and Standard Deviation of Methane Adduct pKa(C–H) Values of Each Metal Utilizing Only Double and Triple Zeta Basis Set Extrapolation Methods

	Sc	Ti	V	Cr	Mn	Fe	Co	Ni	Cu
pKa average	31.6	37.5	32.6	28.5	40.1	35.3	24.7	14.3	16.6
pKa standard dev.	0.7	0.3	0.3	0.2	0.3	0.3	0.4	0.3	0.3

Conclusions

The goal of this study was to examine the effect metallic identity has on the acidity of a coordinated aliphatic C–H bond using highly accurate CCSD(T) simulations in conjunction with correlation consistent basis sets and several CBS extrapolation techniques. It is clear from the present research that there is a very noticeable impact of the metal ion, as the highest and lowest pKa values differ by ∼27 pKa units (Table ). Furthermore, coordination of methane to the 3d metal ion results in a dramatic increase in acidity as compared to that of free methane, ranging from ∼8 to 36 pKa units.

It was observed that less expensive basis sets may be utilized to obtain an accurate estimate of acidic properties (cc-pVTZ and cc-pVQZ) or reproduce trends as a function of metal (cc-pVDZ). Employing just the cc-pVDZ and cc-pVTZ basis sets (Table ), the resultant pKa values vary only slightly when compared to those that also utilize the cc-pVQZ and cc-pV5Z basis sets (Table ). This is an important point to consider for further research, especially when dealing with larger metal complexes. Future studies could be worthwhile in investigating whether similar trends exist in more complex systems, pKa values other than DMSO, or complexes with more realistic ligands. Furthermore, CCSD(T) simulations, in conjunction with correlation consistent basis sets, can serve as a benchmark for future studies using more approximate DFT, which can be applied to larger, more experimentally relevant catalyst candidates. Another intriguing result of this research is the fact that pKa correlates surprisingly well not just with metal ion identity but also with C–H bond lengths and vibrational frequencies (see the Supporting Information), which appears to be an additional point of interest for further investigation. Ultimately, while this study has made it clearer the impact that 3d metals have on the pKa(C–H), there remains much to be uncovered about what other chemical effects impact acidity, for example, the ligand environment as well as “outer sphere” effects such as hydrogen bonding, electrostatic and dispersion forces, and so forth.

Computational Methods

Geometry optimizations were performed with the Gaussian09 software package using the B3LYP/6-31+G(d) level of theory.[10] Single point energies were calculated with the Gaussian16 software package using the UCCSD(T) technique and the following basis sets: cc-pVDZ, cc-pVTZ, cc-pVQZ, and cc-pV5Z.[11] Tests with restricted open-shell CCSD(T) calculations for the titanium and nickel complexes did not appreciably change the predicted pKa(C–H) values nor did the computed ⟨S2⟩ expectation values suggest issues from spin contamination. Likewise, tests with larger, more expensive core-valence correlation treatments (the “Full” and “FreezeInnerNobleGasCore” options in Gaussian16) and consideration of scalar relativistic effects (Douglas–Kroll–Hess second-order scalar relativistic calculation) changed estimated pKa(C–H) values by less than 1 pKa unit. Additionally, the use of augmented correlation consistent basis sets was tested on methane adducts of Sc+, Ti+, and Ni+, changing pKa estimates by only as much as 0.3 pKa units.

The energies obtained from the UCCSD(T) technique paired with correlation consistent basis sets were used to extrapolate to the CBS limit by employing various extrapolation schemes gathered by Vasilyev:[12] exponential (eq ),[13] power function (eq ),[14] mixed Gaussian (eq ),[15] eq 11 in the paper by Vasilyev[9] (eq ),[16] three parameters (eq ),[13] two parameters with integer exponent 4 (eq ),[13] and two parameters with integer exponent 3 (eq ).[11] The extrapolations were applied with the following equationswhere n represents the cardinal number of the xth basis set used and E denotes the electronic energy obtained from the xth basis set used. Obtaining the electronic energies at the basis set limit, the Gibbs free energy correction of each respective structure (obtained from DFT geometry optimization and vibrational frequency calculation) was then applied to calculate the Gibbs free energy at the basis set limit (GCBS). From the GCBS free energies, the ΔGCBS of deprotonation was computed for each of the 3d metals. In order to estimate the pKa of each metal, the following formula was usedto obtain an initial pKa value. A linear correction derived from the published work of Nazemi and Cundari[17] was then applied to the pKa calc. to get the final estimated pKa of the methane adduct, [M···CH4]+ (M = Sc–Cu).