Theoretical Approaches To Estimating Homolytic Bond Dissociation

Aug 27, 2012 - ... and §ARC Centre of Excellence in Free Radical Chemistry and Biotechnology, The University of Melbourne, Victoria 3010, Australia...
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Theoretical Approaches To Estimating Homolytic Bond Dissociation Energies of Organocopper and Organosilver Compounds Nicole J. Rijs,†,‡,§ Nigel J. Brookes,⊥ Richard A. J. O’Hair,*,†,‡,§ and Brian F. Yates*,⊥ †

School of Chemistry, ‡Bio21 Institute of Molecular Science and Biotechnology, and §ARC Centre of Excellence in Free Radical Chemistry and Biotechnology, The University of Melbourne, Victoria 3010, Australia ⊥ School of Chemistry, University of Tasmania, Private Bag 75, Hobart TAS 7001, Australia S Supporting Information *

ABSTRACT: Although organocopper and organosilver compounds are known to decompose by homolytic pathways among others, surprisingly little is known about their bond dissociation energies (BDEs). In order to address this deficiency, the performance of the DFT functionals BLYP, B3LYP, BP86, TPSSTPSS, BHandHLYP, M06L, M06, M06-2X, B97D, and PBEPBE, along with the double hybrids, mPW2PLYP, B2-PLYP, and the ab initio methods, MP2 and CCSD(T), have been benchmarked against the thermochemistry for the M−C homolytic BDEs (D0) of Cu−CH3 and Ag−CH3, derived from guided ion beam experiments and CBS limit calculations (D0(Cu−CH3) = 223 kJ·mol−1; D0(Ag−CH3) = 169 kJ·mol−1). Of the tested methods, in terms of chemical accuracy, error margin, and computational expense, M06 and BLYP were found to perform best for homolytic dissociation of methylcopper and methylsilver, compared with the CBS limit gold standard. Thus the M06 functional was used to evaluate the M−C homolytic bond dissociation energies of Cu−R and Ag−R, R = Et, Pr, iPr, tBu, allyl, CH2Ph, and Ph. It was found that D0(Ag−R) was always lower (∼50 kJ·mol−1) than that of D0(Cu−R). The trends in BDE when changing the R ligand reflected the H−R bond energy trends for the alkyl ligands, while for R = allyl, CH2Ph, and Ph, some differences in bond energy trends arose. These trends in homolytic bond dissociation energy help rationalize the previously reported (Rijs, N. J.; O’Hair, R. A. J. Organometallics 2010, 29, 2282−2291) fragmentation pathways of the organometallate anions, [CH3MR]−.

■

INTRODUCTION

This threshold energy (E0) can be used to determine the M− C bond energy (D0) of the methylmetal via the following equation

Interest in the organometallic chemistry of the copper and silver compounds is undergoing a revival due to their promise in C−X bond coupling applications in organic synthesis and catalysis.1 A key challenge in the use of these organometallic reagents is that decomposition reactions can compete with the desired coupling reaction, thereby limiting the temperature range at which coupling reactions can be carried out.2 The condensed phase decomposition reactions of organocopper and organosilver reagents are complex and can give rise to a range of products that arise from different pathways including radical reactions.3 Given that homolytic decomposition reactions can operate, it is surprising that unlike organic compounds,4,5 very little is known about the bond dissociation energies (BDEs, eq 1) of simple RM compounds (where R = an organic ligand and M = Cu or Ag).6 RM → R• + M•

ΔH °rxn = BDE(RM)

D0(M−CH3) = D0(R−CH3) + IE(R•) − IE(M•) − E0 (3)

where IE(R•) and IE(M•) are the ionization energies of R• and M•, respectively. The threshold energies (E0) are determined by modeling the experimental cross sections with the following expression σ(E) = σ0 ∑ gi(E + Ei − E0)n /E

where σ0 is a scaling factor, E is the relative kinetic energy, n is an adjustable parameter and the sum of the vibrational, rotational, and electronic states, where energy is denoted by Ei and populations by gi (∑gi = 1). This corrects for all sources of energy in the reactants, and therefore bond energies (D0) are obtained at 0 K. The original experimental determination of bond energy for Cu−CH3 did not include this treatment,7 and the authors subsequently reevaluated their data to include this correction to obtain D0(Cu−CH3).8 More detailed discussion of the assumptions made and approaches to optimizing the parameters may be

(1)

Using the guided ion beam technique, Armentrout and his co-workers have determined BDEs for many methylmetal complexes. Thermochemistry of neutral methylmetal species is determined experimentally by measuring the threshold energy (E0) of the reaction of a metal cation: +

+

[M] + RCH3 → [M−CH3] + R

© 2012 American Chemical Society

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Received: June 12, 2012 Revised: July 18, 2012 Published: August 27, 2012

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found elsewhere.8 The experimentally derived bond energies are the following: D0(Cu−CH3) = 223 ± 5 kJ·mol−1 and D0(Ag−CH3) = 134 ± 7 kJ·mol−1 (Table 1).7−9

was not possible. The bond lengths calculated with M06 and B3LYP are remarkably similar and are not significantly affected by the choice of basis set. Therefore B3LYP/SDD:6-31+G(d) optimized structures are also used for all the organosilver species, Ag−R, considered in this report. The optimized geometries for the species M−R, M = Cu and Ag, are available in the Supporting Information accompanying ref 17. The CBS LimitGold Standard and Comparison to Experimental Bond Energies. Dunning basis sets have been shown to exponentially converge with regard to molecular properties.23 Therefore, this property of these basis sets was utilized to extrapolate CCSD(T) single-point energies21 to the complete basis set (CBS) limit. By fitting the results obtained from calculations of aug-cc-pVnZ, where n = D, T, Q, and 5, the exponentially convergent behavior of the molecular energies may be used to derive a “gold standard” for the bond energy. The results obtained were fitted to

Table 1. Previously Reported Bond Dissociation Energies (kJ·mol−1, 0 K) for Neutral Methylcopper and Methylsilver M−CH3

experimental

theoretical

Cu−CH3 Ag−CH3

223(5)a,b 134(7)c

238,d 205,e 197,f 153,f 223,f 203,f 188,f 232g 177,d 158,e 157,g 167g

a

Georgiadis, Fisher, Armentrout, 1989.7 bArmentrout and Kickel, 1996.8 cChen and Armentrout, 1995.9 dLCAO-HFS (Becke, 1987).10 e MCPF (Barnes, 1989).11 fMP2, MP3, MP4, MP2, CCSD(T), respectively (Reetz, 1994).12 gMP2 (Frenking, 1995).13

Organometallic bond energies, D0, can also be obtained from electronic structure calculations via the following equation: D0(M−CH3) = E0(M•) + E0(CH3•) − E0(M−CH3)

A(n) = A(∞) + γ e−((n − n0)/ τ)

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Zero-point vibrational energy must be included to obtain E0, for example: E0(M•) = Eelec(M•)

E0(CH3•)

=

Eelec(CH3•)

where n is the cardinal number of the Dunning basis set used, n0 is a constant, A(n) is the value of a molecular property at basis set size n, A(∞) is the value of the molecular property at the CBS limit, and γ and τ are fitting parameters. Two sets of data points are examined to derive D0(Cu− CH3)CBS: (1) an all electron set utilizing aug-cc-pVnZ for all atoms22b−d and (2) a set with the all electron basis set on the light atoms and the aug-cc-pVnZ-PP basis set and pseudopotential for the metal center.22e,d As aug-cc-pVnZ basis sets were not available for silver, all electron calculation of D0(Ag− CH3)CBS was not possible. Therefore, the combination of an all electron basis set aug-cc-pVnZ on the light atoms and the augcc-pVnZ-PP basis set and pseudopotential for the metal center was used.22b−d The fitted data and parameters used are available in the Supporting Information, Figures S4 and S5, while the CBS extrapolated bond energies of Cu−CH3 and Ag−CH3 (derived from extrapolated data in Supporting Information, Table S1, and eq 5) are given in Table 2. The zero-point correction was calculated at the optimization level.

(6)

+

EZPVE(CH3•)

E0(M−CH3) = Eelec(M−CH3) + EZPVE(M−CH3)

(9)

(7) (8)

A number of previous studies have used electronic structure calculations to estimate the bond energies of Cu−CH3 and Ag−CH3, as outlined in Table 1. The aims of this work are to (i) perform benchmark calculations to estimate D0(Cu−CH3) and D0(Ag−CH3) with a variety of computational methods; (ii) use this benchmark to estimate the BDEs of the following organometallic compounds: M−R where M = Cu and Ag and R = Et, Pr, iPr, tBu, PhCH2, allyl, and Ph. Theoretical Methods. Electronic Structure Calculations. All reported calculations were performed with the Gaussian 09 package.14 Structures were confirmed to be minima by analysis of the vibrational frequency and the stability of the wave function.15 Zero-point energies were calculated at the level of geometry optimization and are unscaled. Where basis set superposition error (BSSE) has been corrected for, the counterpoise method was applied.16

Table 2. CCSD(T) aug-cc-pVnZ D0 Derived from CBS Limit Extrapolation and Experimental Data D0 (kJ·mol−1)

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RESULTS AND DISCUSSION Geometry Optimization and Comparison with Experimental Structure. As an accurate gas phase structure for methylcopper is available,17 a benchmark of the geometry optimization was possible. Both M0618 and B3LYP19 with SDD:6-31+G(d)20 yielded structures close to the experimentally determined structure (within 0.01 Å of experimental value, Supporting Information Figure S1). There is little geometry change with increasing basis set size, and when the energy difference is calculated at CCSD(T)/aug-cc-pVTZ (Supporting Information Figure S2), no significant difference was found due to this change in bond length.21,22b−d Thus, B3LYP/SDD:631+G(d) optimized structures are used for all other organocopper species, Cu−R, examined in this report.19,20 A comparative study of methylsilver was carried out (Supporting Information Figure S3). However, as there is no experimentally available data, benchmarking of the geometry

Cu−CH3 Ag−CH3

basis set

CBS calcd

exptl

aug-cc-pVnZa aug-cc-pVnZb aug-cc-pVnZc

215 223 169

223(5) 134(7)

a

All electron basis set for heavy and light atoms, n = D, T, Q, 5. bAll electron basis set for light atoms, aug-cc-pVnZ-PP pseudopotential and basis set for Cu, n = D, T, Q, 5. cAll electron basis set for light atoms, aug-cc-pVnZ-PP pseudopotential and basis set for Ag, n = D, T, Q, 5.

The results of these CBS limit values reveal a close agreement between experiment and theory for both of the D0(Cu−CH3)CBS values. The pseudopotential extrapolation gives the closest result to experiment, within 1 kJ·mol−1 of the experimental value (D0(Cu−CH3)CBS = 223 kJ·mol−1, Table 2); thus, this is used as the benchmark value. However, disagreement emerges between the experimental results for D0(Ag−CH3) and D0(Ag−CH3)CBS. The D0(Ag−CH3)CBS is 8911

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28 kJ·mol−1 above the upper error limit of the average experimental values, although it is closer to the “best” direct experimental value of 139 kJ·mol−1 determined for the reaction of Ag+ with isobutane.9 Given the close agreement for the copper systems, this suggests the silver experimental data might be somewhat underestimated. A possible explanation is that the experimental value is a lower limit due to the presence of a reverse activation barrier, as previously noted by Chen and Armentrout.9 Interestingly, inconsistencies in experimental and theoretical derived BDEs have been noted for other silver systems. For D0(Ag−CH2+), the experimental BDE was underestimated compared to CCSD(T) results,25 while for D0(Ag−O+) experiment overestimated BDE compared to CCSD(T).26 Disagreement also was observed for experiments versus a range of theoretical methods for the BDE of silver(I)− amide complexes; the authors suggested it is the basis sets for silver(I) that need improving.27 Additional CCSD(T) calculations with CBS limit extrapolation using the method described were carried out on D0(Ag−H) to test the reliability of the theory. The calculated D0(Ag−H)CBS = 224 kJ·mol−1, while experimentally determined values ranged between 199 and 222 kJ·mol−1. The CBS value lies in the upper limit of the experimental values (Supporting Information, Table S2). This trend is consistent with the slight overestimation of D0, which we suggest is due to the basis set and ECP on silver. Additionally, the experimental value for D0(Ag−H) = 199 kJ·mol−1 obtained from ref 9 is at the lower end of this range, suggesting that this set of experiments may underestimate BDE. This is the same set of experiments used to obtain D0(Ag− CH3) (Table 2). Thus, currently the CBS limit calculations are judged as the most appropriate benchmark for D0(Ag−CH3). Given that it is not clear whether the experimental BDEs need to be redetermined, the D0(Ag−CH3)CBS value is used as the benchmark.28 Benchmark Calculations on the BDEs of Cu−CH3 and Ag−CH3. Next a range of theoretical methods are utilized to calculate the D0(Cu−CH3) and D0(Ag−CH3) values to examine their accuracy. The results of these calculations are presented in the following sections. A series of calculations were carried out to test the dependency of each method on the basis set (as defined in Table 3 below).20,22

Benchmark Calculation for D0(Cu−CH3). Comparison of the 14 methods (Figure 1) to the benchmark value for D0(Cu− CH3) (dashed line in Figure 1, 223 kJ·mol−1) reveals they are neither consistently over- nor underestimated. The values for D0(Cu−CH3) and deviation from the benchmark are shown in Table 4. As expected, those most affected by basis set size appear to be the ab initio (CCSD(T), MP2) methods. Unexpectedly, the TPSSTPSS functional is also influenced by basis set size (e.g., compare basis set i to ii). With increasing basis set size CCSD(T) appears to approach the benchmark BDE value, while MP2 approaches an overestimate of this value. The double hybrids (B2-PLYP and mPW2-PLYP) appear to be significantly improved by the use of basis set v (aug-ccpVTZ-PP:6-311+G(2d,p)), approaching within 1 and 3 kJ·mol−1 of the benchmark value (224.2 and 220.6 kJ·mol−1), respectively. However, both these combinations of basis set and double-hybrid method represent a significant increase in computational demand. BLYP and M06, while overestimating the value with basis set v, give consistent results across the range of other basis sets, which are the closest to the benchmark value. TPSSTPSS also yields a close result (within 3 kJ·mol−1) for basis sets ii, iii, and iv. The popular B3LYP functional underestimates the D0 by around 20 kJ·mol−1 and yields similar results to PBEPBE, and the double hybrids for basis sets i−iv. BHandHLYP and M06-2X drastically underestimate the D0 value by around 50 kJ·mol−1. B97D, BP86, and M06-L all overestimate the value by around 10−20 kJ·mol−1. Thus M06 and BLYP appear to be a good compromise between accuracy and computational expense for a variety of basis sets. Benchmark Calculation for D0(Ag−CH3). Comparison of the same basis sets (Table 3) and 14 methods (Figure 2) for D0(Ag−CH3) against the CBS limit benchmark value (dashed line, 169 kJ·mol−1) reveals that the value is more likely to be underestimated in this case compared to the previously benchmarked copper system. The calculated D0 values for each method, along with deviations from the benchmark value, are shown in Table 5. A number of trends common to those in the previous benchmark calculations emerge. The ab initio methods (CCSD(T) and MP2) plus the TPSSTPSS functional are the most affected by basis set, with CCSD(T) converging toward the benchmark and MP2 toward an overestimate. The double-hybrid methods (B2-PLYP and mPW2-PYLP) approach the benchmark value with increasing basis set size, to within 4 and 6 kJ·mol−1, respectively for the largest basis set (v) examined. The closest calculated values to the benchmark are BLYP and M06, showing minimal basis set dependence, again representing a good compromise between computational demand and accuracy. B3LYP underestimates the value by ∼10 kJ·mol−1, as do the double-hybrids with smaller basis sets, PBEPBE, and CCSD(T) with basis set v. B97D, BP86, and M06-L all overestimate the value by around 10−20 kJ·mol−1. BHandHLYP and M06-2X underestimate the D0 value; however, the former (∼40 kJ·mol−1) is significantly worse than the latter (∼20 kJ·mol−1). Thus, M06 and BLYP were also found to be effective at determining D0(Ag−CH3). Summary of Benchmark Comparisons. Thus, both these sets of benchmark calculations are consistent with the observation that M06 and BLYP are effective methods for determining BDE of organocopper(I) and organosilver(I) compounds, with the smallest average deviation from the benchmark value across a series of different basis sets. Several other methods gave good results with specific basis sets. For example, B2-PLYP with a large basis set gave a BDE within 2−4

Table 3. Basis Sets Used for Method Benchmarking of D0(Cu−CH3) and D0(Ag−CH3) basis set number

basis set descriptiona

i ii iii iv v

SDD:6-31+G(d) SDD:6-311+G(2d,p) SDD(f):6-311+G(2d,p) SDD-ecp-def2-QZVP:6-311+G(2d,p) aug-cc-pVTZ-PP:6-311+G(2d,p)

a

This nomenclature describes the effective core potentials and basis sets used for the transition metals (before the colon) followed by the basis set used for C and H.

BSSE between the metal and methyl fragments was found to be significant for a number of methods tested and thus has been corrected for in both Figures 1 and 2. The uncorrected energies may be found in the Supporting Information (Figure S6), along with the magnitude of the BSSE for the various functionals (Figure S7). Supporting the generally accepted notion, the DFT functionals were found to be less affected by BSSE, while the ab initio methods were more affected.29 8912

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Figure 1. Calculated D0(Cu−CH3) energies (kJ·mol−1), using B3LYP/SDD:6-31+G(d) optimized geometries. Energies include zero-point energy calculated at the optimized level and are corrected for basis set superposition error. Dashed line is both experimental and CBS benchmark D0(Cu− CH3) value, 223 kJ·mol−1 (Table 2).

Figure 2. Calculated D0(Ag−CH3) energies (kJ·mol−1), using B3LYP/SDD:6-31+G(d) optimized geometries. Energies include zero-point energy calculated at the optimized level and are corrected for basis set superposition error. Dashed line is CBS benchmark D0(Ag−CH3) value, 169 kJ·mol−1 (Table 2).

kJ·mol−1 of the benchmark, but with a considerable increase in computational expense compared with the DFT methods. This method also requires BSSE to be taken into consideration. TPSSTPSS also gave good results for specific basis sets, but does not give consistent results between basis sets. It seems that the experimental value for D0(Ag−CH3) needs to be reexamined, as the computational results here for Ag−CH3 seem consistent with the CBS limit value. Two of the DFT functionals examined, BHandHLYP and M06-2X, performed particularly poorly and are thus not recommended for determining accurate BDEs of alkyl organometallics. Where kinetic barriers are to be compared to BDEs, further

benchmarking of these outcomes should be undertaken. The trends may be predicted very well by the methods examined here despite chemical accuracy not being met. It seems that the underestimation of BDE suggested previously24 is borne out by these results, the calculated B3LYP energetics being consistently below the benchmark BDE value with a variety of basis sets. Thus, it is concluded that M06 is a good choice for determining the BDEs of Cu−R and Ag−R. Theoretical Predictions of BDEs of Cu−R and Ag−R, Where R = Et, Pr, iPr, tBu, allyl, CH2Ph, and Ph. In the previous section we showed that the M06/SDD:6-31+G(d) level of theory is a useful compromise between computational 8913

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Table 4. BSSE Corrected D0(Cu−CH3) Data Calculated with Various Computation Methods and Basis Sets (i−v) and Deviation from Benchmark Value of D0(Cu−CH3)CBS (Bold) (kJ·mol−1)

Table 5. BSSE Corrected D0(Ag−CH3) Data Calculated with Various Computation Methods and Basis Sets (i−v) and Deviation from Benchmark Value of D0(Ag−CH3)CBS (Bold) (kJ·mol−1)

calcd D0(Cu−CH3) and deviation from benchmark (kJ·mol−1)

calcd D0(Ag−CH3) and deviation from benchmark (kJ·mol−1)

basis set (as defined in Table 3) method B2-PLYP B3LYP B97D BHandHLYP BLYP BP86 CCSD(T) M06 M06-L M06-2X MP2 mPW2-PLYP PBEPBE TPSSTPSS

basis set (as defined in Table 3)

i

ii

iii

iv

v

204.4 −18.6 206.0 −17.0 236.3 13.3 170.4 −52.6 225.2 2.2 236.6 13.6 173.6 −49.4 222.7 −0.3 243.3 20.3 184.9 −38.1 198.1 −24.9 202.1 −20.9 208.5 −14.5 189.2 −33.8

209.0 −14.0 205.4 −17.6 237.3 14.3 169.6 −53.4 224.8 1.8 236.4 13.4 187.3 −35.7 221.6 −1.4 240.2 17.2 183.2 −39.8 215.3 −7.7 206.2 −16.8 208.2 −14.8 223.1 0.1

211.4 −11.6 205.9 −17.1 237.8 14.8 170.4 −52.6 225.2 2.2 236.9 13.9 193.3 −29.7 222.3 −0.7 240.7 17.7 184.0 −39.0 221.4 −1.6 208.6 −14.4 208.9 −14.1 223.6 0.6

210.1 −12.9 201.4 −21.6 239.4 16.4 165.1 −57.9 221.0 −2.0 233.0 10.0 194.5 −28.5 218.7 −4.3 241.1 18.1 175.1 −47.9 226.5 3.5 206.8 −16.2 204.4 −18.6 220.5 −2.5

224.2 1.2 213.4 −9.6 245.0 22.0 176.9 −46.1 233.4 10.4 245.7 22.7 209.6 −13.4 230.7 7.7 253.1 30.1 187.1 −35.9 243.0 20.0 220.6 −2.4 216.7 −6.33 233.1 10.1

avg

method B2-PLYP

−11.2 B3LYP −16.6 B97D 16.1 BHandHLYP −52.6 BLYP 2.9 BP86 14.7 CCSD(T) −31.4 M06 0.2 M06-L 20.7 M06-2X −40.2 MP2 −2.2 mPW2-PLYP −14.2 PBEPBE −13.7 TPSSTPSS −5.1

ii

iii

iv

v

145.9 −23.1 153.2 −15.8 187.2 18.2 123.1 −45.9 167.9 −1.1 181.2 12.2 126.1 −42.9 169.2 0.2 175.2 6.2 146.8 −22.2 134.2 −34.8 145.1 −23.9 158.4 −10.6 135.6 −33.4

150.5 −18.5 152.6 −16.4 187.6 18.6 122.1 −46.9 167.6 −1.4 180.8 11.8 140.0 −29.0 167.6 −1.4 173.8 4.8 145.0 −24.0 152.0 −17.0 149.3 −19.7 157.7 −11.3 169.2 0.2

155.8 −13.2 154.9 −14.1 189.7 20.7 125.2 −43.8 169.4 0.4 182.8 13.8 146.9 −22.1 170.0 1.0 176.2 7.2 147.9 −21.1 161.4 −7.6 154.4 −14.6 160.5 −8.5 171.5 2.5

162.2 −6.8 157.9 −11.1 192.0 23.0 128.3 −40.7 172.5 3.5 185.9 16.9 155.6 −13.4 173.1 4.1 179.9 10.9 150.3 −18.7 173.0 4.0 160.5 −8.5 163.5 −5.5 175.0 6.0

165.2 −3.8 159.6 −9.4 193.8 24.8 130.2 −38.8 174.1 5.1 187.7 18.7 160.8 −8.2 175.3 6.3 182.1 13.1 152.6 −16.4 178.8 9.8 163.3 −5.7 165.4 −3.6 176.6 7.6

avg −13.1 −13.4 21.0 −43.2 1.3 14.7 −23.1 2.0 8.5 −20.5 −9.1 −14.5 −7.9 −3.4

organometallic bond). This explanation is borne out by NBO calculations that clearly predict the trend in M−C bonds for Ag−R to be more ionic than those of Cu−R (see Supporting Information Table S3). Compared to H−alkyl, the Cu−alkyl bond energies are ∼225 kJ·mol−1 lower and the Ag bond energies are ∼275 kJ·mol−1 lower. This is a direct reflection of (1) the difference in bond type: strong covalent bonding in the C−H sp3-bond of H−R, versus σ s-3d and s-4d hybridized organometallic bonds of Cu− R and Ag−R, and (2) the stability of the radicals (H• versus M•). The effect on BDE of changing the R group shows a reasonably consistent trend between Cu−R and Ag−R and also reflects the changes in H−R bond energies for R = alkyl, decreasing bond strength with increasing substitution of the carbon. This pattern is likely to correspond to the stability of the corresponding radical R•. The effect of increasing electron donation due to higher substitution of the alkyl groups (e.g., tBu > iPr > Et > Me) should also play a role in the bond strength. The net effect of this BDE pattern on decomposition will be obscured in most experiments due to competitive βhydride elimination.24 The R groups with different hybridizations (R = allyl, CH2Ph, and Ph) deviate from the trends mentioned for the alkyl groups (decreasing bond strength with increasing

resources and reliability in reproducing experimentally determined BDEs. Here we use this level of theory to estimate the BDEs of a range of organometallics Cu−R and Ag−R, where R = an organo ligand. The results of these calculations are presented in Figure 3. In Figure 3, the experimental bond energies (measured enthalpies at 298 K, which should be within 10 kJ·mol−1 of D0(0 K)5) for the homolytic bond dissociation (eq 10) of H− R5,30 are plotted with the calculated energies for D0(M−R), M = Cu and Ag, R = Me, Et, Pr, iPr, tBu, allyl, CH2Ph, and Ph.

R−H → R• + H•

i

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The trends show that Ag−R bonds are more susceptible to bond homolysis than the Cu−R bonds, due to a consistently lower BDE (∼50 kJ·mol−1) across the range of R groups examined. This prediction is consistent with the unimolecular fragmentation reactions reported previously,24 where the organoargentates, [CH3AgR]−, were observed to more readily fragment via bond homolysis than the corresponding organocuprates. This trend in copper and silver bond strengths has also been observed for carbonyl complexes, where the degrees of covalency for the bonds of silver(I) complexes were lower those that of copper(I) complexes, decreasing the bond strength.31 Thus, the lower degree of covalency is a possible explanation of the lower BDEs of Ag−R (i.e., a more ionic 8914

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Figure 3. Calculated BDE at the M06/SDD:6-31+G(d) level for Cu−R and Ag−R, plotted with experimental values H−R, (kJ·mol−1, measured at 298 K) obtained from the literature.5,30

basis set v was compared to the values derived from M06. The results of these additional calculations are given in Supporting Information Figure S8. While there is little deviation from the alkyl series (