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Thiolate Ligand Exchange Mechanisms of Au1 and Subnanometer Gold Particle Au11† Allison Hadley and Christine M. Aikens* Department of Chemistry, Kansas State UniVersity, Manhattan, Kansas 66506 ReceiVed: NoVember 20, 2009; ReVised Manuscript ReceiVed: March 1, 2010
Density functional theory is employed to examine the thiolate-for-thiolate ligand exchange mechanism of the undecagold Au11(SR′)3(PH3)7 particle with several incoming thiols HSR′′ (R′ ) H, CH3; R′′ ) H, CH3, CH2CH3, CH2CH2CH3, CH2CH(NH2)COOH). The reaction with cysteine is investigated as a representation for undecagold-protein binding. BP86 calculations using double-, triple-, and quadruple-ζ basis sets on a model Au1 system show that the triple-ζ basis set predicts reaction energies and geometries in good agreement with the larger quadruple-ζ basis set, while barrier heights are underestimated by ∼9 kJ/mol. Ligand exchange reaction on Au11 is more endothermic than Au1, and longer organic chains on the incoming thiol lead to increases in the reaction energy of up to 0.8 kJ/mol. The reaction of cysteine is more favorable than other ligands, and the reaction energy is predicted to be -5.0 kJ/mol with the Au11(SCH3)3(PH3)7 particle. Barrier heights are essentially constant for aliphatic ligands, while the barrier height is 10 kJ/mol higher for the incoming cysteine molecule. I. Introduction Gold nanoparticles are finding use in the field of medicine because they possess certain qualities such as size-dependent optical and electronic properties, biocompatibility, large surface areas, and ease of functionalization.1 Proteins containing cysteine amino acids can irreversibly bind gold nanoparticles, whereas proteins without cysteine do not.2 Because this binding most likely occurs through a thiolate-thiolate exchange mechanism, an understanding of this mechanism will improve our knowledge of how gold nanoparticles attach to proteins, which could aid in areas such as the design of particles for better cancer detection and therapy. Undecagold (Au11) subnanometer particles are examined in this study because of their potential biological applications. Undecagold particles have been employed in biological imaging for decades.3-5 The atomic structure of these particles is wellestablished. X-ray crystal structures of phosphine-stabilized Au11(PPh3)8X2+ (X ) halide),6 Au11(PPh3)7X3 (X ) halide or SCN),7,8 and [Au11(PPh3)10+3]9 systems show that the core can be described as an incomplete icosahedron. The crystal structure of a partially thiolate-protected Au11(S-4-NC5H4)3(PPh3)7 cluster has recently been resolved, and the core structure was found to be an incomplete icosahedron with approximate C3V symmetry.10 Several previous experimental studies have examined thiolatefor-phosphine or thiolate-for-thiolate ligand exchange reactions in gold nanoparticles.11-20 However, to date no quantum mechanical investigations have been performed to determine the atomic mechanism of these processes. Thiolate-for-thiolate ligand exchange reactions have been shown to occur in an associative rather than dissociative manner, and the displaced thiolate is present in solution as a thiol.11 The reaction is initially rapid but then slows significantly for 1.6 and 2.2 nm diameter nanoparticles, which has been attributed to ligand exchange at different binding sites.11,12 For the smaller Au25(SR)18- nano† Originally intended for publication in the special issue “Protected Metallic Clusters, Quantum Wells and Metal-Nanocrystal Molecules Symposium”, published as the September 30, 2010, issue of J. Phys. Chem. C (Vol. 114, issue 38; URL: http://pubs.acs.org/toc/jpccck/114/38). * To whom correspondence should be addressed.
particle, the initial rate constants are similar to the larger diameter nanoparticles but the biphasic kinetics process is less pronounced.13 Future theoretical studies will potentially elucidate the binding sites involved in this process. Computational studies also have the potential to elucidate factors such as core growth during ligand exchange reactions. Phosphine-stabilized nanoparticles with diameters ∼1.3-1.5 nm have been shown to undergo core growth during thiolatefor-phosphine ligand exchange.14,15 Investigations of the reverse phosphine-for-thiolate exchange mechanism with the Au25(SR)18- nanoparticle (originally assumed to be Au38(SR)24) show that the nanoparticle core size decreases during the reaction, and the authors suggest that thiolates are initially removed as a Au(I)SR species.16 For smaller nanoparticles, Woehrle, Warner, and Hutchison find that the core of Au11(PPh3)8Cl3 remains intact,17 whereas Tsukuda et al. have observed core growth in related phosphine-stabilized undecagold clusters.18 Thiolate-for-phosphine ligand exchange in Au11(PPh3)8Cl3 (core ∼0.8 nm) occurs more slowly than exchange in larger gold particles; in order for ligand exchange to occur in Au11(PPh3)8Cl3, the temperature must be elevated to approximately 55 °C and the reaction time is double that for 1.5 nm nanoparticles.17 If Au11(PPh3)8Cl3 particles do not experience core size changes, these systems may follow a different exchange mechanism than larger nanoparticles during their reaction with thiols.19 One difference between undecagold and larger nanoparticles is the metal-ligand binding arrangement. In the crystal structure of Au11(SR)3(PPh3)7,10 thiolate groups are bound to a single Au atom, whereas they bridge two Au atoms in Au25(SR)1821-23 and Au102(SR)44.24 In this research, the thiolate-for-thiolate ligand exchange mechanism is examined for the subnanometer Au11(SR)3(PH3)7 system as a first step toward development of a fuller understanding of the ligand exchange mechanism in gold nanoparticles. II. Computational Details Initial structures for reactants, products, and transition states were created using the MacMolPlt v7.1 program.25 Several
10.1021/jp911054e 2010 American Chemical Society Published on Web 03/23/2010
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Figure 2. Transition state structures in the reaction of AuSH with HSCH3.
TABLE 1: BP86 Reaction Energies and Barrier Heights for Au1 Ligand Exchange (kJ/mol)
Figure 1. Reactants and products for the AuSH + HSCH3 f AuSCH3 + H2S reaction.
different nuclear configurations were examined for each system in an effort to ensure that the global minimum is reached; however, the size of the system makes full configurational sampling unfeasible. Initial structures were built from the known crystal structure coordinates of Au11(SR)3(PPh3)710 using multiple configurations of the incoming ligands (including anti and gauche configurations for each alkane). The Amsterdam density functional (ADF) program was used for all calculations.26 The optimized structures were calculated at the density functional (DFT) level of theory using the gradient-corrected Becke-Perdew (BP86) exchange-correlation functional.27,28 This functional often yields harmonic frequencies that are close to experimental values.29 Double-ζ (DZ) and triple-ζ with polarization functions (TZP) basis sets were employed with a frozen core for all elements (4f for Au, 2p for S and P, 1s for C and O). A full core triple-ζ basis set (TZP-full) has been employed for calculations where noted. A full core quadruple-ζ with polarization functions (QZ4P) basis set was also used for calculations on Au1 structures. To account for scalar relativistic effects, the zeroth-order regular approximation (ZORA) was utilized in the calculations.30 Frequencies have been calculated numerically for all stationary points. Reaction energies and barrier heights have been corrected for zero-point vibrational energy (ZPE). III. Results and Discussion Au1 Ligand Exchange. Using Au1 as an initial model for Au11, two general reaction mechanisms have been explored in this work. Mechanism 1 involves breaking a covalent S-H bond, whereas mechanism 2 involves ligand exchange at the Au atom. Although the Au-S bond is weaker and would therefore be expected to exchange more easily than S-H, steric considerations with larger gold nanoparticles suggest examination of both mechanisms. Converged structures of the reactants and products of Au1 at the BP86/TZP level of theory are shown in Figure 1. For all of the figures, black represents gold, yellow represents sulfur, dark gray represents carbon, white represents hydrogen, and green represents phosphorus. One transition state structure (TS1) was found for the first reaction mechanism and three transition state structures (TS2, TS3, TS4) were found for the second reaction mechanism, where these structures vary in the relative configurations of the SH and SCH3 groups (Figure 2). The structures determined with the DZ, TZP, and QZ4P basis are compared in Figure S1 (see the Supporting Information). Table 1 displays the reaction energies and barrier heights for the four transition state structures using the DZ, TZP, and QZ4P basis sets. Values for several density functionals are compared in Table S1. The first transition state explored is much higher in energy than the other three, which indicates that the breaking
∆Eelec ∆EZPE ∆E0 barrier height
basis set
DZ
TZP
QZ4P
TS1 TS2 TS3 TS4
1.1 -1.6 -0.5 206.5 15.1 13.8 10.9
-0.5 -2.1 -2.6 250.1 45.0 45.1 44.0
-1.0 -2.3 -3.2 258.7 54.1 54.0 52.6
of the covalent S-H bond is less favorable than substitution at the Au atom. Transition state four is found to have the lowest energy for Au1. As the basis set increases from DZ to TZP to QZ4P, the difference in electronic energies (∆Eelec) for reactants and products becomes more negative. In addition, the predicted zeropoint energy corrections (∆EZPE) increase in magnitude from -1.6 to -2.3 kJ/mol. The zero-point corrected reaction energies (∆E0) for basis sets DZ, TZP, and QZ4P are -0.5, -2.6, and -3.2 kJ/mol respectively, which indicates that the reaction is slightly exothermic but is almost thermoneutral. The barrier height increases for each transition state as the basis set increases. Using the QZ4P basis set, TS1 has the largest barrier height of 258.7 kJ/mol. TS4 has the lowest barrier height of 52.6 kJ/mol, whereas TS2 and TS3 are slightly higher at 54.1 and 54.0 kJ/mol, respectively. The barrier heights for TS2 and TS3 are very close to the barrier height for TS4 because these structures only differ in the orientation of the methyl group. The predicted TS1-TS4 barrier heights with the TZP basis set are approximately 9 kJ/mol lower in energy than those calculated with the QZ4P basis. Overall, the frozen core TZP basis set predicts reaction energies and barrier heights in reasonable agreement with the full core QZ4P basis set, so the TZP basis set will be used in the subsequent Au11 calculations. TABLE 2: BP86 Bond Lengths for TS4 basis set bond lengths (Å)
DZ
TZP
QZ4P
1-2 1-5 2-4 5-4 2-3 5-6
2.664 2.572 1.731 1.777 1.398 1.929
2.585 2.482 1.705 1.730 1.360 1.843
2.568 2.449 1.704 1.716 1.353 1.829
TABLE 3: BP86 Bond Angles for TS4 basis set bond angles (deg)
DZ
TZP
QZ4P
1-5-4 1-2-4 5-4-2 5-1-2 3-2-4 4-5-6
66.3 64.3 149.0 80.4 94.1 98.6
65.4 62.9 149.9 81.8 89.4 97.6
65.6 62.6 149.5 82.2 89.9 96.8
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Figure 3. BP86/TZP stationary points for ligand exchange reactions on undecagold.
TABLE 4: BP86/TZP Reaction Energies and Barrier Heights (kJ/mol) for Ligand Exchange Reaction Au11(SR′)3(PH3)7 + HSR′′ f Au11(SR′)2(SR′′)(PH3)7 + HSR’ SR′ SH
SCH3
SR′′
∆Eelec
∆EZPE
∆E0
barrier height
SCH3 SCH2CH3 SCH2CH2CH3 cysteinate SH SCH2CH3 SCH2CH2CH3 cysteinate
14.0 15.3 15.9 6.0 -12.4 0.2 0.7 -4.9
-3.8 -4.9 -5.0 -3.5 3.8 -0.3 -0.7 -0.1
10.1 10.4 10.9 2.5 -8.6 -0.1 0.0 -5.0
42.9 41.1 41.2 50.5 34.4 N/A N/A 47.7
For TS4, the bond lengths predicted with basis sets DZ, TZP, and QZ4P are shown in Table 2 and the bond angles are presented in Table 3. Geometrical parameters for the other transition states are available in the Supporting Information. All of the bond lengths for TS4 decrease with increasing size of the basis set. Overall, the bond lengths predicted with the QZ4P basis set are approximately 0.026-0.096 Å shorter than the DZ values and 0.001-0.033 Å shorter than the TZP values. Angles 1-5-4 and 5-4-2 are relatively insensitive to basis set, whereas angle 1-2-4 decreases by 1.7° and angle 5-1-2 increases by 1.8° upon changing the basis set from DZ to QZ4P. The angles between the R groups (H and CH3) and the transferring hydrogen decrease more noticeably (4.2° and 1.8° for angles 3-2-4 and 4-5-6, respectively) as the basis set is increased. Au11 Ligand Exchange. Using the geometrical parameters from Au1 as starting coordinates for Au11, the stationary points for the Au11(SH)3(PH3)7 + HSCH3 f Au11(SH)2(SCH3)(PH3)7 + H2S reaction have been determined. The reactants, products, and transitions states for mechanisms 1 (TS1) and 2 (TS2) are shown in Figure 3. The Au11(SH)3(PH3)7 reactant shown in Figure 3 has a small imaginary frequency (15.8i cm-1) corresponding to rotation of the top PH3 group around the z-axis; the global minimum for this system lies only 0.1 kJ/mol lower in energy so PH3 rotation does not substantially affect isomer energies. The zero-point corrected reaction energy is predicted to be 10.1 kJ/mol at the BP86/TZP level of theory (Table 4), so the Au11 reaction is 12.7 kJ/mol more endothermic than the Au1 reaction. The predicted barrier heights for TS1 and TS2 are 241.6 and 42.9 kJ/mol, respectively. The imaginary frequencies for TS1 and TS2 are 410 and 233 cm-1, which arise from
hydrogen-transfer modes as expected. Both transition states also have five or six small imaginary frequencies under 50i cm-1 that correlate to low-frequency motions such as PH3 rotation. Because the potential energy surface for PH3 rotation is essentially flat and these small imaginary frequencies do not affect the zero-point energy, imaginary frequencies corresponding to PH3 rotation are ignored. In Au11 as in Au1, the preferred reaction pathway involves breaking the weaker Au-S bond rather than the stronger S-H bond, even though this pathway is somewhat more sterically hindered. To account for use of an incomplete basis set, the reaction energies and barrier heights have been computed using singlepoint calculations with full core triple-ζ and quadruple-ζ basis sets. As the frozen core TZP set is replaced by the full core TZP set, the reaction energy increases by 0.1 to 14.1 kJ/mol and the barrier height increases by 1.0 to 45.0 kJ/mol. Relative to the frozen core TZP set, use of the QZ4P basis set increases the reaction energy by 0.7 to 14.7 kJ/mol; the barrier height increases by 6.8 to 50.8 kJ/mol. This increase is in reasonable agreement with the 8-9 kJ/mol increase in barrier height observed for the Au1 system. Basis set superposition errors have also been computed for the frozen core TZP basis set using a counterpoise correction method. For the transition state, the barrier height is predicted to be 3.5 kJ/mol too low due to basis set superposition error; this may account for some of the 6.8 kJ/mol increase noted in the QZ4P single point calculations. Since TS1 has the highest barrier, it is not likely that Au11 will take this pathway during the reaction. Thus, only ligand exchange at gold is considered in the remainder of this study. In order to ascertain the effects of ligands on reaction energies and barrier heights, several organic groups are explored in the reaction Au11(SR′)3(PH3)7 + HSR′′ f Au11(SR′)2(SR′′)(PH3)7 + HSR′
where R′ ) H and CH3 and R′′ ) H, CH3, CH2CH3, CH2CH2CH3, and CH2CH(NH2)COOH. The cysteinate ligand (SCH2CH(NH2)COOH) is employed as a model for protein binding via cysteine amino acids. The reaction energies and barrier heights for this series of reactions are shown in Table 4. As the length of the organic chain on the incoming thiol increases the reaction energy becomes slightly more positive, which indicates that nanoparticles with shorter chain lengths will generally be preferred, although the change in predicted reaction energies is less than 1 kJ/mol. In contrast to the endothermic reaction predicted for aliphatic thiols, the ligand exchange reaction with cysteine is approximately thermoneutral (+2.5 kJ/mol) for R′ ) H or slightly exothermic (-5.0 kJ/mol) for R′ ) CH3. Because ethyl and propyl thiols have comparable ligand exchange reaction energies to the methyl thiol, exothermic reactions are also expected for ligand exchange of cysteine for these longer chain thiols, which suggests that binding of undecagold to proteins is favorable. For R′ ) H, the barrier heights are essentially constant (41.1-42.9 kJ/mol) regardless of the incoming aliphatic ligand, but the barrier is about 10 kJ/mol higher for the incoming cysteinate ligand, which may be due to steric effects. These barrier heights are about 3-8 kJ/mol lower when R′ ) CH3. The increased barrier height for the cysteinate ligand relative to aliphatic thiols means that the reverse reaction will also have a larger barrier height, so it will be more difficult to remove undecagold from proteins once it binds. The (R′ ) H, R′′ ) CH3) reaction is almost the reverse of the (R′ ) CH3, R′′ ) H) reaction, although these systems vary
Thiolate Ligand Exchange Mechanisms slightly due to the presence of two differing thiolate groups not involved in the exchange mechanism. The reaction energies are approximately equal and opposite (10.1 vs -8.6 kJ/mol). The expected barrier height for the reverse (R′ ) H, R′′ ) CH3) reaction is predicted to be 32.8 kJ/mol (calculated by subtracting the forward reaction energy of 10.1 kJ/mol from the forward barrier height), which is similar to the 34.4 kJ/mol barrier height computed for the (R′ ) CH3, R′′ ) H) reaction. Differences in zero-point vibrational energies are approximately 3.5-5.0 kJ/mol for reactions involving H2S, so it is important to include ZPE in the calculated reaction energies for these species. The ZPE corrections for other reactions are
