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Bond Dissociation Energies of Solvated Silver(I)-Amide Complexes: Competitive Threshold Collision-Induced Dissociations and Calculations Vladimir Romanov,† Chi-Kit Siu,‡ Udo H. Verkerk,† Alan C. Hopkinson,† and K. W. Michael Siu*,† Department of Chemistry and Centre for Research in Mass Spectrometry, York UniVersity, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3, and Department of Biology and Chemistry, City UniVersity of Hong Kong, 83 Tat Chee AVenue, Kowloon Tong, Kowloon, Hong Kong, China ReceiVed: March 18, 2010; ReVised Manuscript ReceiVed: May 20, 2010
Using competitive threshold collision-induced dissociation (TCID) measurements, experimental bond dissociation energies have been evaluated for the water, methanol, and acetonitrile adducts of silver(I)-amide complexes. The influence of the solvent molecules on the binding energy of silver(I) to acetamide, N-methylacetamide, and N,N-dimethylacetamide was investigated. Experimental results show that solvents decrease the amide binding energy by 4-6 kcal mol-1. Using density functional theory (DFT), binding energies were evaluated using nine functionals, after full geometry optimizations with the ECP28MWB basis set for silver and the 6-311++G(2df,2pd) basis set for the other atomic constituents of the ligands. In addition, calculations employing the DZVP basis set for Ag and DZVP2 for C, H, N, and O atoms at the B3LYP and MP2 levels of theory were used to investigate the influence of the basis set on the theoretical bond energies. A comparison of the experimental and theoretical silver(I)-ligand bond dissociation energies enables an assessment of the limitations in the basis sets and functionals in describing the energetics of the metal-solvent interaction and the metal-amide interaction. No single functional/basis set combination was found capable of predicting binding energies with a sufficiently high level of accuracy for the silver(I)-amide solvent complexes. Introduction Insight into the thermodynamics accompanying silver(I) coordination chemistry remains under-developed, although fields as diverse as nanotechnology,1 inorganic chemistry,2 and bioengineering3-6 would benefit from such thermodynamic data. Binding energies between Ag(I) and the ligands can be calculated using DFT theory, but a plethora of basis sets and functionals are available, making selection of the optimal combination a challenge. Experimentally determined bond dissociation energies of gas-phase Ag(I)-ligand complexes allow a direct comparison with DFT calculations but are limited to small ligands,7-17 while such a comparison is further complicated by the (n + 1)s0nd10 configuration for silver ions allowing for sdσ hybridization.18-24 In a previous study, we measured binding energies of gasphase silver(I)-amide and silver(I)-alcohol complexes.25 The computations using the B3LYP functional, and the ECP28MWB (for Ag) and 6-311++G(2df,2pd) (for C, H, N, and O) basis sets, reproduced the binding energies of the alcohols well but consistently overestimated the silver(I)-amide interactions. Although similar shortcomings in DFT calculations have received some exposure, the emphasis of such publications in general is not on transition metals and bond dissociation energies, but on main group elements and on the structures. Selection of the appropriate functional and basis set to be used in DFT calculations is, therefore, not routine.26 A comparison of DFT calculations employing different functionals and basis * To whom correspondence should be addressed. Telephone: (416)6508021. Fax: (416)736-5936. E-mail:
[email protected]. † York University. ‡ City University of Hong Kong.
sets with experimental data would provide an assessment of the most appropriate level of theory for the calculation of binding energies. Experimental binding energy data can be obtained using mass spectrometric techniques, including the equilibrium,27 bracketing,28 kinetic,29 and threshold collisioninduced dissociation (TCID)30,31 methods. The TCID method, as pioneered by Armentrout and co-workers,30,31 models the onset of the precursor ion fragmentation via curve-fitting of the product channel cross-section as a function of the center-ofmass collision energy. This onset yields the bond dissociation energy. In practice, for larger precursor ions, additional internal energy is required to ensure that significant fragmentation occurs while the ions are still inside the collision cell. A correction is applied to the apparent threshold; the magnitude of this correction can be estimated from the unimolecular rate constant of the dissociation according to the Rice-RamspergerKassel-Marcus (RRKM) theory.32-34 Further development of the data analysis model by the Armentrout group encompasses modeling of competitiVe dissociation in doubly ligated complexes of metal ions.35,36 Here we further investigate DFT binding energy calculations and experimental bond dissociation energies of silver-amide complexes [Ag(amide)(solvent)]+, where the solvent is water, methanol, or acetonitrile. We compare the theoretical binding energies calculated using nine different functionals with binding energies of the doubly ligated silver complexes determined using competitive threshold collision-induced dissociation. The TCID measurements were executed on a modified triple-quadrupole instrument using a ring ion guide as the collision cell.37
10.1021/jp102470x 2010 American Chemical Society Published on Web 06/15/2010
Bond Dissociation Energies of Solvated Silver(I)-Amides
J. Phys. Chem. A, Vol. 114, No. 26, 2010 6965
Experimental Method and Data Treatment Computational Method. Initial DFT calculations employed Becke’s three-parameter hybrid functional formalism (B3LYP), involving Hartree-Fock exchange and Becke’s exchange functionals38,39 and the Lee-Yang-Parr correlation functional.40 For these calculations, the Stuttgart/Dresden quasi-relativistic effective core potential basis set ECP28MWB41,42 was used for the metal, and for the other elements Pople’s 6-311++G(2df,2pd) basis set was used. Optimized geometries and vibrational frequencies of the ligands and their metal complexes were calculated using the Gaussian 03 program that was also employed for further calculations (vide infra).43 All structures were characterized to be at minima by harmonic frequency calculations. + The binding energy at 0 K, ∆H°, 0 between the metal ion, M , and the ligand, L, is the standard enthalpy change of the reaction M+-L f M+ + L at 0 K. ∆H°0 was calculated as follows:
∆Ho0 ) ∆Eelec + ∆EZPVE
(1)
where ∆Eelec and ∆EZPVE were the changes in electronic energies and zero-point vibrational energies, respectively, between the product(s) and the reactant of the dissociation reaction. The initial geometries were further optimized using the following DFT functionals: MPW1PW91, PBE1PBE, B98, B972, HCTH407, BMK, TPSSTPSS, and B1B95. As a consequence of using a large Gaussian basis set, basis set superposition errors (BSSE) were significantly smaller than the differences in bond energies obtained using different functionals (maximum standard deviation 2.9 kcal mol-1, typical 2.2 kcal mol-1, see ref 25 and Table 2 for details); therefore, no BSSE corrections44 were applied. In addition, the double-ζ plus polarization basis setssDZVP for Ag and DZVP2 for C, H, N, and O atoms45swere also employed with the aforesaid functionals. All structures were also optimized at MP2 (frozen core) using these DZVP basis sets.45 Attempts at locating transition states (TSs) for removal of a ligand from [Ag(amide)(solvent)]+ complexes were all unsuccessful. The transition states were therefore assumed to be loose and product-like (the phase-space limit, PSL) and the TS rovibrational frequencies taken to be those of the ionic and neutral products52 as approximated by the DFT calculations. Each transition state was assumed to be variationally located at the centrifugal barrier, and the adiabatic 2D rotational energy was calculated using the statistical average approach detailed by Rodgers et al.46 Mass Spectrometry. TCID measurements were conducted on a PE SCIEX API 365 triple-quadrupole mass spectrometer (Concord, Ontario, Canada) that had previously been modified by having its second quadrupole (q2) replaced with a reversibly mounted ring ion guide. Construction and operating details can be found in ref 25. Sample solutions were 100 µM in ligand and 40 µM in metal (silver, copper, potassium, or sodium) nitrate in 20/80 water/methanol. All chemicals were obtained from Sigma-Aldrich, St. Louis, MO, and were used as received. The sample solutions were introduced into the ion source at atmospheric pressure using a syringe pump (Harvard Apparatus, South Natick, MA) at a typical flow rate of 3 µL/min and ionized by means of pneumatically assisted electrospray, using a potential of 5 kV with nitrogen being the nebulizer gas. Collision-induced dissociation in the ring ion guide was performed with argon (Air Liquide Canada Inc., Brampton, Ontario, Canada) as the neutral gas. Dissociation cross sections
σ(E) were determined as a function of the center-of-mass collision energies at three collision-gas pressures: 0.05, 0.1, and 0.15 mTorr. To eliminate the effects of multiple collisions, E0 values were obtained from threshold curves constructed from σ(E) at zero pressure. The latter data were determined by linear extrapolation of the σ(E) measured at those three pressures to zero pressure. Background ions can result from dissociations occurring outside the collision cell. To account for background ion generation, collision gas was diverted from the collision cell to the vacuum chamber. Collisional cross sections were measured with and without diverting the gas, and the difference for each data point was used to construct the backgroundsubtracted TCID curve.37,47 All E0 values were determined four times, except for [Ag(CH3CONH2)]+ and [Ag(CH3CN)]+, which were measured six times. The kinetic energy distributions of the ions entering q2 were determined using time-of-flight (TOF) analysis; the typical fullwidth-at-half-maximum (fwhm) values for the complexes investigated in this paper were approximately 0.54-0.96 V, translating to center-of-mass energy distributions of 0.08-0.22 eV. In a previous publication, experimental evidence was obtained indicating that ions underwent collisional cooling in the q0 region, thereby yielding a thermal translational temperature for the ions.25 The extent of RF-heating and vibrational and rotational temperatures in our apparatus have not been characterized. In this study, an ion temperature of 298 ( 5 K is assumed. To give this assumption the best chance to work, low-resolution conditions in Q1 (typically fwhm g0.8 amu) were used to minimize RF heating and the smallest possible potential gradient was used to transfer ions. The threshold energy for the CID of a given complex was determined using the curve-fitting and modeling program CRUNCH developed by Armentrout and co-workers.48-52 CRUNCH curve-fits the dissociation cross section σ(E) versus the center-of-mass collision energy E using eq 2:
σ(E) ) σ0
∑
giP(E, Ei, t)(E + Ei - E0)n E
(2)
where σ0 is a scaling factor, E0 is the threshold energy, Ei is the internal energy of a given vibrational state with a relative population of gi, n is an adjustable parameter, and P is the probability that a precursor ion of collision energy E and internal energy Ei will fragment within an experimental time t. For a precursor ion with many vibrational degrees of freedom, a considerable kinetic shift is present and can be estimated from the unimolecular rate constant of the dissociation according to the RRKM theory.32-34 This correction term is contained in the term P(E,Ei,t). For a metal complex containing two ligands, two fragmentation channels can compete, thus requiring the modified eq 3 for modeling:35,36
σj(E) )
( )∑ nσ0,j E
gi
∫EE -E 0,j
i
[
]
kj(E*) × ktot(E*) -ktot(E*)t
[1 - e
](E - ε)n-1 d(ε) (3)
where σ0,j is a scaling factor for channel j, t is the experimental time for dissociation, E* (E* ) ε + Ei) is the internal energy of the energized molecule after the collision, ε is the energy deposited in the complex by the collision with argon, and kj(E*) is the unimolecular rate constant for dissociation by channel j. RRKM theory defines kj(E*) and ktot(E*) as follows:
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ktot(E*) )
∑ kj(E*) ) ∑ j
j
djNj†(E* - E0,j) hF(E*)
Romanov et al.
(4)
where dj is the reaction degeneracy, Nj†(E* - E0,j) is the sum of ro-vibrational states of the transition state (TS) for channel j at an energy (E* - E0,j), and F(E*) is the density of states of the energized molecule at the energy available for bond dissociation, E*. Experimental Uncertainties. The total standard deviation of a given E0 determination is the root-sum-of-squares of the sample standard deviations of all the steps or stages. In Table 1, E0 (with kinetic-shift modeling) is reported with the standard error of the mean at the 90% confidence level.53-55 All reported E0 values were background and kinetic-shift corrected. Details may be found in Table S1 of the Supporting Information. In our calculations, we assumed an ion temperature of 298 ( 5 K, based upon ion thermalization in q0 and the temperature of the vacuum chamber, resulting in an uncertainty in E0 of (0.01 eV. The uncertainty in the zero-point correction as calculated using TOF data was based on an assumed absolute error of (1 cm in the effective length. As a result of TCID data scatter and range of the collision energies, the threshold and RRKM model fits some reactions better than others. To take curve-fitting and energy-range errors into account, threshold energies were determined over an Ecm optimization range varied by +0.5 and -0.5 eV (laboratory frame). The threshold energies thus obtained differ by ((0.01-0.15) eV from the energies obtained without varying the range for the optimization of the data set.25 Contributions to the sample standard deviation of E0 from uncertainties in the vibrational frequencies of the precursor ions and products, the time available for dissociation of the complex, the kinetic shift, the distribution of the kinetic energies, and the zero-point potential were estimated by determining threshold energies within the error margin of individual factors. The sample standard deviations for the minimum and maximum absolute values for the uncertainties are different for the average experimental time available for dissociation (100 µs), distribution of kinetic energy, frequency, and temperature as a result of the nonlinear relationship between input and output variables in CRUNCH. A conservative approach was therefore adopted by incorporating the larger uncertainty for any given factor or stage. Altering the vibrational frequencies of the precursor ions and the products systematically by (10% resulted in a change of E0 by ((0.01-0.09) eV, which became more noticeable for complex systems with many degrees of freedom. The estimated uncertainty in the experimental time (between 50 and 200%) resulted in a relatively small error in E0 of ((0.01-0.05) eV. The kinetic-energy distribution contribution as determined by TOF method was ((0.02-0.16) eV in the laboratory frame) and resulted in an uncertainty in E0 of ((0.0-0.04) eV. The zero-point uncertainty, based on a range of ((0.05-0.11) eV in the laboratory frame, was estimated to give an error in E0 of ((0.01-0.02) eV. Results and Discussion Structures. The geometries of the doubly ligated silver complexes are essentially linear with respect to the silver-ligand bonds with the metal ion being in the center. The effect of the functionals and basis sets on the optimized geometries was insignificant;thestructuresobtainedfromtheB3LYP/ECP28MWB/ 6-311++G(2df,2dp) level of theory are used for discussing the geometry. The silver(I)-acetamide complex ligated with one
molecule of water, methanol, or acetonitrile is shown in Figure 1; see Figure S2 in the Supporting Information for other structures with N-methylacetamide and N,N-dimethylacetamide as a ligand. Previous calculations on silver-amide monocoordination indicated a bonding situation largely determined by electrostatic interaction.25 Coordination only occurs through the carbonyl oxygen and results in weakening of the CdO bond and strengthening of the C-N bond. On addition of a second ligand (water, methanol, or acetonitrile), the structure of the amide relaxes slightly toward that of the free amide, but the Ag-O distance in the bis-coordinated complex is consistently slightly shorter than that in the [Ag(amide)]+ complex (see Table S3). Calculated Bond Dissociation Energies. Silver ion complexes have higher binding energies than potassium ion complexes although the two elements have similar ionic radii (see Table 1). The increase in bond dissociation energy cannot be rationalized by a purely electrostatic interaction; instead, using a valence-bond description, sdσ hybridization of the transition metal ion occurs and results in an improved overlap with the ligand that reduces the interatomic distance and increases the binding energy relative to the potassium-amide interaction.48,49 This effect is even more pronounced in a Group IB metal ion complex with two of the same ligands, as a result of the symmetry of the sdσ hybrid orbital. For example, the energies required to remove the first and second ligand from [Cu(L)2]+ (L ) water,50 acetonitrile,57 ammonia,58 acetone,59 dimethyl ether60) complex are nearly identical. To estimate the effect of sdσ hybridization on the metal ion-ligand bond energy, experimental dissociation energies and calculated interatomic distances were compared for [M(acetamide)(acetonitrile)]+ complexes, with M ) K, Na, Cu(I) and Ag(I), see Table 1. A purely electrostatic contribution from the sodium (ionic radius: 0.97 Å) and potassium (ionic radius: 1.33 Å) bond energies is supported by increases in experimental bond dissociation energies for both acetamide (0.29 eV) and acetonitrile (0.41 eV) from potassium to the smaller sodium, see Table 1. The complex with Cu(I) ion (a radius of 0.96 Å and comparable to that of sodium(I)) deviates considerably in bond length and dissociation energies from the sodium complex, indicating the presence of a nonelectrostatic bonding contribution of around 0.93 eV. A similar comparison of bond lengths and energies between the complexes with potassium and Ag(I) reveals a similar trend but of a smaller magnitude. The observed differences have been attributed to both the effect of the ionic radius and the energy required to move an electron from a s0d10 to a s1d9 electron configuration (Ag, 4.86; and Cu, 2.72 eV).16,18,61 Further insight into the type of bonding was obtained using a natural population analysis (NPA),62,63 (see Table 1) yielding the charge of metal ions and occupancies of the (n + 1)s and nd orbitals. The charges on Na and K in the complexes are close to one, indicating an almost pure electrostatic interaction between the metal ion and the two ligands. For Cu and Ag, significant charge transfer from the metal ions to the ligands occurs in the [M(acetamide)(acetonitrile)]+ complexes. The charges on Cu+ and Ag+ are 0.83 and 0.87, respectively. The NPA analysis also showed there to be a significant population in the (n + 1)s orbitals, 0.42 for Cu+ and 0.22 for Ag+, in agreement with the sdσ hybridization (vide supra). Figure 2 shows the highest occupied molecular orbital (HOMO) of [M(acetamide)(acetonitrile)]+ for Na+, K+, Cu+ and Ag+. Unlike complexes of Na+ and K+, in which the metal ion does not participate in the HOMO, extensive contributions from both
Bond Dissociation Energies of Solvated Silver(I)-Amides
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TABLE 1: Comparison of Bond Lengths, Energies, and Results of Natural Population Analysis (NPA) of Acetamide and Acetonitrile Binding to Doubly Coordinated Sodium, Potassium, Copper(I), and Silver(I) Ions M+(acetamide)(acetonitrile) metal ion M+
ionic radiusa (Å)
M-Ob (Å)
M-Nb (Å)
Na K Cu Ag
0.97 1.33 0.96 1.26
2.137 2.567 1.850 2.097
2.301 2.771 1.823 2.067
E0(ACE) (eV)c,d 1.36 1.07 2.29 1.64
( ( ( (
0.21 0.11 0.11 0.10
NPAe E0(ACN) (eV)c,d
charge
(n + 1)s
nd
( ( ( (
0.97 0.99 0.83 0.87
0.03 0.01 0.42 0.22
9.75 9.90
1.21 0.80 2.16 1.51
0.20 0.14 0.09 0.11
a Reference 56. b Calculated bond length based on DFT calculations using B3LYP/(ECP28MWB/6-311++G(2df,2dp)) level of theory. Experimental bond dissociation energy based on TCID measurements, see Table 2 this study. d ACE ) acetamide, ACN ) acetonitrile. e Charges and orbital occupancies evaluated using natural population analysis at B3LYP/DZVP/DZVP2 level of theory. c
Figure 1. Optimized structures of the [Ag(acetamide)(solvent)]+ ion where the solvent is water, methanol, or acetonitrile as optimized at the B3LYP/ECP28MWB/6-311++G(2df,2dp) level of theory. Interatomic distances are in Ångstrom (10-10 m).
metal ion and ligand orbitals are observed for complexes containing Cu+ and Ag+. According to Figure 2, the contribution to the HOMO by the acetonitrile solvent is much smaller than that by the acetamide ligand, supporting the observation that changing the solvent molecule has only a small effect on the metal-ligand bond energy calculated (Table 2). Unlike the geometries, the calculated binding energies of the silver(I) complexes were strongly dependent on the type of theory and the basis set employed (see Table 2, rows 1 to 9). To separate the effects of varying the functional and the basis set, one series of calculations, all using the quasirelativistic basis set ECP28MWB41,42 for Ag and the 6-311++G(2df,2dp) basis set for C, H, N, and O atoms, was performed while varying the type of DFT functional. The average of the binding energies calculated using nine different functionals is given in the last column of Table 2; individual binding energies from the different functionals are given in Table S2, Supporting Information. For complexes containing silver and copper, two of the functionals gave binding energies that deviate significantly from the average. The HCTH407 functional values were consistently lower while the BMK values were higher than the average (Table S2). The functionals B3LYP, PBE1PBE, and TPSSTPSS produced binding energies slightly above the average, whereas B98, B972, and B1B95 values were marginally but consistently below the average. The resulting standard deviation of the average for the binding energies of silver-containing complexes (∼2 kcal mol-1) is markedly different from that obtained for similar complexes containing potassium and sodium (Table 2, rows 10 and 11). For the latter complexes, standard deviations of 0.3-0.6 kcal mol-1 and maximum deviations of 1.0-1.6 kcal mol-1 were obtained over the whole range of functionals. Summarizing the trend in calculated binding energies, the amide binding energy is always higher than that of the solvents. Comparing the solvent effect for [Ag(acetamide)]+ and [Ag(acetamide) (solvent)]+, the solvents decrease the amide binding energy by 4-6 kcal mol-1. The binding energies of the solvents in the complexes are H2O < CH3OH < CH3CN and for each solvent the binding energy
shows little dependence on the amide (0.6-0.8 kcal mol-1). By contrast, a larger effect (3-4 kcal mol-1) is seen on the silver-amide binding energy that increases with amide nitrogen methylation. A second basis set combination, involving the all electron DZVP basis set for Ag and DZVP245 for C, H, N, and O atoms at the B3LYP level of theory (Table 2, column 5) was also employed. To investigate the influence of the basis set on binding energies, these results were compared with those obtained using the other basis set combination: ECP28MWB for Ag and the 6-311++G(2df,2dp) basis set for C, H, N, and O (Table 2, column 6). Although BSSEs for the ECP28MWB/ 6-311++G(2df,2dp) basis set combination was negligible, and therefore not applied, those for the DZVP/DZVP2 combination were large, and therefore applied. The use of the latter basis set combination consistently gave lower binding energies compared to the former. The smallest difference (2.8-3.9 kcal mol-1) was obtained for Ag(I) binding to methanol and water, but increased to a difference of 5.8-6.4 kcal mol-1 for that to the amides and an even larger deviation (7.8-8.1 kcal mol-1) for binding to the nitrogen-coordinating acetonitrile, see Table 2. These variations resulting from the use of different basis sets do not improve upon using second-order many-body perturbation theory (MP2) calculations, see Table 2, column 7. The binding energies are consistently below those from B3LYP/ ECP28MWB/6-311++G(2df,2dp) with differences of 8.9-13.3 kcal mol-1 for the amide ligands, 11.5-14.4 kcal mol-1 for acetonitrile, 7.5-7.8 kcal mol-1 for water, and 0.7-4.4 kcal mol-1 for methanol. Experimental Bond Dissociation Energies. TCID bond dissociation energies were determined using competitive fitting of two dissociation channels: those of the amide and the solvent. This approach has been applied successfully to various systems, including measurement of the gas-phase acidities of phenols64 and alcohols,65 fragmentation of silver cluster anions,66 and complexation of Na+ with glycine67 and proline.68 Determination of E0 using TCID measurements requires the vibrational frequencies and rotational constants of the precursor ions and the transition states that are supplied by molecular orbital calculations. Because of the variation of theoretical results (vide supra), the bond energies of acetonitrile to Ag+ (Table S4) and of acetonitrile to [Ag(acetonitrile)]+ (Table S5) were calculated using frequencies from nine functionals; these, however, had only minimal effects on the calculated bond dissociation energy. Changing the vibrational frequencies of the precursor ions and products (as calculated by the B3LYP/ECP28MWB/6311++G(2df,2dp) level of theory) by (10% (see Experimental Uncertainties) results in an error margin that covers the variations in using different basis sets and functionals, to the effect that errors emanating from the use of different functionals and basis sets are covered by the uncertainty calculation.
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Figure 2. Contour plots for the HOMO of [M(acetamide)(acetonitrile)]+, for Na+, K+, Cu+ and Ag+ as determined using DFT calculations at the B3LYP/DZVP/DZVP2 level of theory. The bottom half of the HOMOs (isosurface value ) 0.03) are also shown with positive values in red and negative values in green. The, dx2, dy2, and dz2 orbitals (in a 6D formalism) are largely involved in the HOMO of the complexes of Cu and Ag.
Eliminations of solvent or ligand molecules from [Ag(N(methyl)nacetamide)(solvent)]+ complexes were observed in the CID (see Figure S1). The experimental results showed initial loss of the solvent molecule at low energies and loss of the amide ligand at higher energies. Simultaneous loss of both was also observed, but in low abundance. Curve fitting was performed using CRUNCH with independent scaling factors for the two channels. This approach was better able to fit experimental data than using a common scaling factor, especially when the bond energy of the ligand was much higher than that of the solvent.67,68 Direct curve fitting of the first channel yielded the same bond dissociation energy as obtained from the competitive fitting of the two fragmentation channels; however, direct fitting for the second, higher energy channel, always overestimated its bond dissociation energy. This observation is in keeping with those of previous studies.67,68 The experimental cross sections were well reproduced by the CRUNCH program over the energy range of 0-4 eV (Figure S1; for fitting parameters see Table S1, Supporting Information). Previously we have shown that replacing a hydrogen by a methyl group on the amide nitrogen of [Ag(RCONH2)]+ complexes increases the strength of interaction between silver ion and carbonyl oxygen;25 here, the same trend occurs for mixed complexes of amides with various solvents. In general, variation of the solvent does not have much effect on the silver ion-amide binding energy, resulting in a minor decrease in binding energy with increasing polarizability of the solvent. The presence of the solvent decreases the bond energy between the silver ion and amide by approximately 9% (bond energies for silver amides are taken from ref 25). Similarly, the binding energy of the solvent molecule in the complex is reduced by attachment of an amide ligand by ∼17%. Losses of the solvent and ligand molecules can be represented in a thermodynamic cycle, see Figure 3. Published individual binding energies of Ag(I)-solvent (E0(III)) and Ag(I)-amide
(E0(II)),25,37 and bond dissociation energies obtained using direct fitting of the lower-energy channel (E0(I)) (see Table S1 in Supporting Information) can be combined with the thermodynamic cycle to yield the value for the second, higher-energy channel (E0(IV)), the loss of the amide ligand from the complex using:
E0(IV) ) E0(I) + E0(II) - E0(III)
(6)
The bond dissociation values, E0, as obtained from the competitive fitting and indirectly from the thermodynamic cycle are supplied in Table 3. With the possible exception of dissociation 5 (Table 3), there is excellent agreement, indicating an internal consistency of the results. Even for that dissociation, the bond dissociation energy from competitive fitting falls within the error margins of that from the thermodynamic cycle. Comparison of Calculated and Experimental Bond Dissociation Energies. A comparison of the theoretical binding energies using B3LYP/DZVP/DZVP2 (Table 2, column 5) with the experimental values (column 4) shows a consistent underestimation of the silver(I)-solvent interaction, with silver(I)water/methanol and silver(I)-acetonitrile bond energies lower by 1.7-3.5 kcal mol-1 and 1.1-3.2 kcal mol-1, respectively. The same underestimation, but with a more pronounced variation (between 0.2 and 3.1 kcal mol-1), is observed for the silver(I)-amide interaction. In a previous study on monoligated silver(I), this combination of functional and basis sets was shown to reproduce experimental silver(I)-amide binding energies well, but again consistently underestimated silver(I)-alcohol binding energies.25 Also in the aforementioned study, a combination of ECP28MWB basis set for silver and 6-311++G(2df,2pd) basis set for C, H, N, and O atoms was able to reproduce silver(I)-alcohol binding energies, but overestimated silver(I)-amide binding energies by 5 kcal mol-1.25 The same
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TABLE 2: Calculated and Experimental Solvent and Ligand Bond Dissociation Energies (kcal mol-1) for Ag(I), Cu(I), Na, and K Complexes at 0 K No. 1
2
3
4
reactant
∆H°0 Expa B3LYP/DZVPb B3LYP/ECP28MWBc MP2/DZVPb
ionic product
[Ag(CH3CONH2)(H2O)]+
[Ag(CH3CONH2)]+
[Ag(CH3CONHCH3)(H2O)]+
+
24.9 ( 2.1
[Ag(H2O)]
+
38.7 ( 1.8
[Ag(CH3CONHCH3)]+
24.9 ( 3.2
[Ag(H2O)]+
39.7 ( 4.6 +
[Ag(CH3CON(CH3)2)(H2O)]
[Ag(CH3CONH2)(CH3OH)]+
[Ag(CH3CON(CH3)2)]
25.6 ( 2.3
[Ag(H2O)]
+
44.3 ( 5.8
[Ag(CH3CONH2)]+
28.8 ( 1.8
[Ag(CH3OH)]+ 5
6
[Ag(CH3CONHCH3)(CH3OH)]
+
[Ag(CH3CON(CH3)2)(CH3OH)]+
[Ag(CH3CONHCH3)]
27.2 ( 1.6
[Ag(CH3OH)]+
40.1 ( 2.1
[Ag(CH3CON(CH3)2)]+
28.1 ( 4.2
[Ag(CH3OH)] 7
8
[Ag(CH3CONH2)(CH3CN)]
+
[Ag(CH3CONHCH3)(CH3CN)]+
37.1 ( 2.8 +
+
41.7 ( 4.8 +
[Ag(CH3CONH2)]
34.8 ( 2.5
[Ag(CH3CN)]+
37.8 ( 2.3
[Ag(CH3CONHCH3)]+
34.8 ( 3.7
+
9
10
[Ag(CH3CON(CH3)2)(CH3CN)]+
+
[K(CH3CONH2)(CH3CN)]
[Ag(CH3CN)]
40.6 ( 3.9
[Ag(CH3CON(CH3)2)]+
36.2 ( 4.4
[Ag(CH3CN)]+
42.4 ( 5.8 +
[K(CH3CONH2)] +
11
12
[Na(CH3CONH2)(CH3CN)]+
+
[Cu(CH3CONH2)(CH3CN)]
18.4 ( 3.2
[K(CH3CN)]
24.7 ( 2.5
[Na(CH3CONH2)]+
27.9 ( 4.6
[Na(CH3CN)]+
31.4 ( 4.8 +
[Cu(CH3CONH2)]
49.8 ( 2.1
[Cu(CH3CN)]+
52.8 ( 2.5
22.5 [-2.4] 37.6 [-1.1] 22.2 [-2.7] 39.9 [+0.2] 22.1 [-3.5] 41.3 [-3.0] 25.8 [-3.0] 36.9 [-0.2] 25.5 [-1.7] 39.2 [-0.9] 25.2 [-2.9] 40.4 [-1.3] 33.7 [-1.1] 36.0 [-1.8] 33.4 [-1.4] 38.1 [-2.5] 33.0 [-3.2] 39.3 [-3.1] 18.6 [+0.2] 23.4 [+1.3] 26.1 [+1.8] 31.8 [+0.4] 53.7 [+3.9] 54.6 [+1.8]
25.6 [+0.7] 43.4 [+4.7] 25.3 [+0.4] 45.8 [+6.1] 25.0 [+0.6] 47.2 [+2.9] 28.7 [-0.1] 42.8 [+5.7] 28.3 [+1.1] 45.2 [+5.1] 28.0 [-0.1] 46.5 [+4.8] 41.8 [+7.0] 42.3 [+4.5] 41.2 [+6.4] 44.5 [+3.9] 40.8 [+4.6] 45.7 [+3.3] 19.1 [+0.7] 23.2 [-1.5] 26.6 [-1.3] 31.8 [+0.4] 56.4 [+6.6] 56.4 [+3.6]
17.8 [-7.1] 30.6 [-8.1] 17.6 [-7.3] 32.7 [-7.0] 17.5 [-8.1] 33.9 [-10.4] 24.3 [-4.5] 30.1 [-7.0] 24.2 [-3.0] 32.2 [-7.9] 27.3 [-0.8] 37.6 [-4.0] 29.6 [-5.2] 32.7 [-5.1] 26.8 [-8.0] 31.2 [-9.4] 29.3 [-6.9] 36.6 [-5.8] 18.9 [+0.5] 22.2 [-2.5] 23.5 [-4.4] 28.7 [-2.7] 48.4 [-1.4] 50.6 [-2.2]
average of nine functionalsd 25.2 ( 2.0 42.9 ( 2.1 24.9 ( 2.0 45.4 ( 2.2 24.6 ( 2.0 46.7 ( 2.5 28.1 ( 2.1 42.4 ( 2.1 27.7 ( 2.1 44.7 ( 2.2 27.4 ( 2.3 46.0 ( 2.6 41.6 ( 2.2 41.8 ( 2.2 41.1 ( 2.2 44.1 ( 2.3 40.8 ( 2.2 45.3 ( 2.5 18.9 ( 0.3 22.7 ( 0.5 26.0 ( 0.5 31.0 ( 0.6 55.8 ( 2.6 55.4 ( 2.9
a Experimental data, competitive TCID measurements. b DZVP for Ag and DZVP2 for C, H, N, and O atoms; differences between calculated and experimental values are shown in brackets. c ECP28MWB for Ag and 6-311++G(2df,2pd) for C, H, N, and O atoms; differences between calculated and experimental values are shown in brackets. d Functionals employed: B3LYP, MPW1PW91, PBE1PBE, B98, B972, HCTH407, BMK, TPSSTPSS, and B1B95. Uncertainties are shown as standard deviations. Individual bond dissociation energies are available in Table S2 in the Supporting Information.
Figure 3. complex.
Thermodynamic cycle for the [Ag(ligand)(solvent)]+
trend is present for bis-ligated silver(I) (Table 2, column 6), with silver-water/methanol bond energies deviating 0.1-1.1 kcal mol-1, and silver(I)-acetonitrile bond energies deviating 4.6-7.0 kcal mol-1 above the experimentally determined values. The silver(I)-amide binding energies in the present data set are
consistently 2.9-6.1 kcal mol-1 above the experimental values. The average calculated from the nine functionals (Table 2, last column) is almost identical in value to the binding energies obtained using the B3LYP functional with the same ECP28MWB/ 6-311++G(2df,2pd) basis sets (Table 2, column 6), so that the same binding energy trend is present in the averages as well. Limiting further discussion to the HCTH407 functional (Table S2, Supporting Information), silver(I)-water/alcohol bond energies are consistently 3.1-4.7 kcal mol-1 lower than the experimental bond energies, whereas the silver(I)-acetonitrile bond energy is 0.8-3.2 kcal mol-1 higher than the experimental values. The calculated silver(I)-amide bond energies are nearer to the experimental values, randomly deviating from 0.1 to 2.5 kcal mol-1. Although the performance of the various combinations of functionals and basis sets are marginal in describing the binding energies in the silver(I) complexes, replacing the
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Romanov et al.
TABLE 3: Comparison of Experimental Ag(I)-L Bond Dissociation Energies E0 (eV) Determined Using Competitive Fitting or from Thermodynamic Cycle (Figure 3) reactant [Ag(L)(S)]+ No. 1 2 3 4 5 6 7 8 9
L CH3CONH2 CH3CONHCH3 CH3CON(CH3)2 CH3CONH2 CH3CONHCH3 CH3CON(CH3)2 CH3CONH2 CH3CONHCH3 CH3CON(CH3)2
E0 (eV) S
H2 O H2 O H2 O CH3OH CH3OH CH3OH CH3CN CH3CN CH3CN
ionic product +
[Ag(H2O)] [Ag(H2O)]+ [Ag(H2O)]+ [Ag(CH3OH)]+ [Ag(CH3OH)]+ [Ag(CH3OH)]+ [Ag(CH3CN)]+ [Ag(CH3CN)]+ [Ag(CH3CN)]+
silver with sodium or potassium results in a good correlation between theory and experiment (Table 2, rows 10 and 11), which indicates that the source of bias lies outside of the experiments. The described misalignment between DFT calculations and experimental results is also relevant for copper-containing complexes, in which sdσ hybridization is more pronounced due to the smaller ionic radius of copper. DFT calculations on [Cu(CH3CONH2)(CH3CN)]+ (Table 2, row 12) indicate that copper(I) is following the trends described for silver(I), as previously reported.57,69,70 The theoretical values for [Cu(CH3OCH3)n]+ determined at the MP2/aVDZ (a frozen core metal basis set) level of theory were 48.4 kcal mol-1 for the monoligated, and 50.6 kcal mol-1 for the bis-ligated complex in a study70 from the Feller group, which is consistently 4 kcal mol-1 higher than experimental results obtained by the Armentrout group.64 A better agreement between theory (MP2/aVQZ)69 and experimental results was obtained for copper(I) water complexes.69,50 In a study from the Rodgers group,57 the experimental binding energy of Cu(I)-acetonitrile, 57.0 ( 0.7 kcal mol-1, was matched by a calculated value of 56.6 kcal mol-1 at the B3LYP/6-311+G(2d,2p)//B3LYP/6-31G(d) level of theory with a BSSE correction. A comparison of the calculated binding energy (63.3 kcal mol-1) using the B3LYP/ ECP28MWB/6-311++G(2df,2dp) level of theory with the published Cu(I)-acetonitrile binding energy (57.0 ( 0.7 kcal mol-1) yields a value higher by 6.3 kcal mol-1. Conclusions TCID with competitive dissociation has permitted determinations of the bond dissociation energies of [silver(I)(amide)(solvent)]+ complexes. The experimental results show that a solvent molecule reduces the strength of the amide/silver ion binding energies by 4-6 kcal mol-1, with little dependence on the nature of the solvent. In combination with our earlier study on the silver(I)-amide complexes, these results provide a quantitative measure of the effect of one solvent molecule on the silver(I)-amide binding energy. The quality of these measurements allowed evaluation of the computational accuracies of DFT functionals and basis sets. No single combination of functional and basis sets was found to reproduce all data as obtained for the silver-acetamide complexes within a 1-2 kcal mol-1 error margin. On the basis of the observed excellent fit between experimental and predicted bond dissociation energies for sodium and potassium complexes, further development of silver(I) and, by extension, copper(I) basis sets is required. Acknowledgment. We thank Professor Peter Armentrout for making his CRUNCH program available to us. This work was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada and MDS Analytical Technologies
competitive fitting
thermodynamic cycle
1.68 ( 0.08 1.72 ( 0.20 1.92 ( 0.25 1.61 ( 0.12 1.74 ( 0.09 1.81 ( 0.21 1.64 ( 0.10 1.76 ( 0.17 1.84 ( 0.25
1.62 ( 0.15 1.71 ( 0.25 1.87 ( 0.35 1.57 ( 0.18 1.59 ( 0.25 1.76 ( 0.39 1.57 ( 0.16 1.66 ( 0.26 1.85 ( 0.38
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