NMR Diffusion, Relaxation, and Spectroscopic Studies of Water

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J. Phys. Chem. B 2001, 105, 8801-8809

8801

NMR Diffusion, Relaxation, and Spectroscopic Studies of Water Soluble, Monolayer-Protected Gold Nanoclusters† Olaf Kohlmann, Wayne E. Steinmetz,‡ Xi-An Mao,§ W. Peter Wuelfing, Allen C. Templeton, Royce W. Murray, and Charles S. Johnson, Jr.* Department of Chemistry, UniVersity of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3290 ReceiVed: March 27, 2001; In Final Form: May 29, 2001

NMR spectroscopy and computer modeling were used to characterize tiopronin monolayer-protected gold clusters (MPCs). These MPCs contain gold cores with a distribution of radii ranging from 0.4 to 2.6 nm. NOESY and HMQC spectra yielded assignments for all NMR sensitive nuclei in the tiopronin ligands. DOSY and T2 experiments provided information about the particle size distribution as a function of proton frequency shift. Further information was obtained from hole-burning and amide-exchange experiments. The spectroscopic data reveal two classes of ligands, a network of hydrogen bonds, and considerable inhomogeneous and homogeneous line broadening. The methyl and methine protons clearly exhibit two components with separations that decrease strongly with the number of bonds separating the proton from the gold core. Spin-echo experiments clearly show that a range of T2 values is associated with each resonance frequency in both the upfield and downfield components for each type of proton but that the most probable value is larger for the upfield component. Various models that may be consistent with the NMR data and the properties of reported crystal structures were considered. It is suggested that bimodal frequency distributions result from chemical shifts that are associated with a mixture of primarily two gold cluster structure types that differ in the mode of core packing. It is suggested that the Knight shift contributes to the large downfield shift observed for the methine protons in the larger particles.

Introduction In the last two decades, nanometer-sized metallic and semiconducting particles have received considerable attention.1-3 The reason for the increasing interest in these clusters is that they represent an “intermediate” dimension between small molecules (∼300 atoms) and present unusual chemical, electronic, and physical properties.4,5 Following a publication by Brust et al. in 1994,6 it was shown that the synthesis of monolayer-protected gold clusters (MPCs) is simple and leads to materials with properties akin to those of large, robust molecules.7 Moreover, it was demonstrated that these nanoparticles can easily be functionalized with a wide variety of ligands.8,9 This paper addresses the characterization of water soluble MPCs with nanometer-sized gold cores that are protected by tiopronin (N-2-mercaptopropionylglycine) ligands as shown in Figure 1.7 Our research was motivated by striking 1H NMR spectra of tiopronin ligands reported for polydisperse MPC preparations with different average core sizes. These spectra showed downfield shifts of methine, methyl, and methylene protons relative to their positions in the tiopronin monomer, a splitting of the methyl resonance into two components, and †

Part of the special issue “Royce W. Murray Festschrift”. * To whom correspondence should be addressed. Fax: (919) 962-2388. Phone: (919) 966-5229. E-mail: [email protected]. ‡ On leave from Chemistry Department, Pomona College, Claremont, California 91711-6338, USA § On leave from Laboratory of NMR and Atomic Molecular Physics, Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, China

Figure 1. Covalent structure of tiopronin attached to a gold core.

considerable line broadening depending on proximity, through bonds, of the protons to the core.7 Our aim was to characterize these MPCs by means of modern NMR methods and to evaluate models for cluster structures, ligand configurations, and dynamics, taking into account core size distributions from electron microscopy, structural studies of gold clusters, and previous NMR studies of alkanethiolate MPCs. To this end, we completely assigned the proton, carbon, and nitrogen NMR spectra by means of NOESY and HMQC experiments. We were able to measure amide proton exchange rates and to determine the percentage of hydrogen-bonded amides. In addition, we have measured diffusion coefficients and transverse relaxation times (T2) as functions of frequency shift. To demonstrate inhomogeneous broadening, hole-burning experiments were performed. Various molecular models have been created for visualization and semiquantitative determination of interactions. In the discussion section, we consider models that may explain the observed distribution of shifts, line widths, relaxation times, and diffusion rates. Types of models to explain

10.1021/jp011123o CCC: $20.00 © 2001 American Chemical Society Published on Web 07/11/2001

8802 J. Phys. Chem. B, Vol. 105, No. 37, 2001

Figure 2. Space filling models of MPC structures. (a) A 75-atom core (m-Dh). (b) A 201-atom core (TO). (c) A 13-atom TO with 14 tiopronin ligands.

the bimodal appearance of signals include different conformations of ligands, different core densities, and truncated octahedral (TO) and Marks decahedral (m-Dh) geometries of the cores with two different kinds of binding sites. To anticipate the results, we have found the following. NMR analyses show that the proton and carbon resonances from the tiopronin ligands are split into two components and that the magnitude of the splitting decreases strongly with the number of bonds separating the nucleus from the gold core. In each case, the upfield component is narrower and has the smaller area. Both diffusion and T2 relaxation data show that significantly smaller average particle sizes are associated with the upfield components. However, the T2 data also reveal broad distributions of mobilities at all frequency shifts in both components. The polydispersity of the samples and the presence of both homogeneous and inhomogeneous broadening complicate the determination of the source of the dispersion in shifts. However, our analysis of the statistics of types of surface sites and in particular our finding that the two components are associated with different size distributions lead us to the conclusion that the structure of the gold core is the important factor. The presence of TO and m-Dh crystal types with different modes of packing is consistent with this interpretation. We suggest that Knight shifts are partly responsible for the observed splittings. Background Previous NMR studies of alkanethiolate MPCs have shown that line widths in 13C NMR spectra vary systematically with carbon site position relative to the Au core.10 Moreover, for the alkanethiolate MPCs the line widths increase with cluster size.11 These effects lead to substantial signal broadening, making carbons and protons closest to the Au core difficult to detect.11,12 For gold clusters, susceptibility differences and dipole-dipole broadening have been ruled out as significant contributions to line widths and positions.13 Badia et al. argued persuasively on the basis of solid-state 13C hole-burning and CPMAS experiments for inhomogeneous broadening as the principal source of the line widths.13 Inhomogeneous broadening has been suggested to result from a distribution of chemical shifts through differences in the Au-SR binding site.10,12 Also reported was a systematic displacement of the chemical shifts with carbon position; in particular, spins separated by the smallest number of bonds from the Au core yield the largest displacement.11 The structure of the gold cores present in MPCs has been investigated experimentally by powder X-ray diffraction (XRD) and theoretically by energy minimization methods.14,15 This work narrows down the likely candidates to two structural themes, the m-Dh and the TO, which are shown in Figure 2. It was observed for alkanethiolate MPCs that the structures in the

Kohlmann et al. TO family are favored for larger cores (0.8-1.8 nm radius). For smaller cores (0.5-1.5 nm radius), the m-Dh was found to predominate. In the initial article describing tiopronin MPCs, the bimodal character of the methyl signal was mentioned and the possible existence of a second methine component overlapping with the methylene was noted.7 The two components were suggested to result from different binding sites on the Au core. In the case of TO or m-Dh, these would correspond to tricoordinate and tetracoordinate bonding, respectively, of the sulfur to different faces, (111) and (100) faces in the case of TO and similar faces for the m-Dh. We will designate these as C3 and C4 sites, respectively. The geometry of these sites has been determined in extended X-ray absorption fine structure spectroscopy (EXAFS), and photoelectron spectroscopy (PES) studies of (111) and (100) surfaces of coinage metals.16,17 So far, the bimodal character of NMR signals has not been reported for any MPCs other than the ones protected by tiopronin ligands. Experimental and Computational Section Materials. We have primarily focused on samples of tiopronin MPCs synthesized at room temperature (298 K) with a 3:1 ligand:AuCl4- molar ratio before reduction, denoted by 3x, RT. These conditions yield the smallest average cluster sizes leading to the sharpest NMR lines. Racemic tiopronin was used to synthesize the MPCs. Further details are described elsewhere.7 The core-size radius of these tiopronin MPCs ranges between 0.4 and 2.0 nm, according to high-resolution transmission electron microscopy (HRTEM), with an average core radius of 0.9 ( 0.35 nm and ∼64% of the population falling in the range of 0.8 ( 0.3 nm. The number of gold atoms per cluster presumably ranges from 13 to about 1200. The average molecular weight, estimated from the core-size distribution, was found to be ca. 80 000 u. Unless otherwise indicated, the results cited here refer to the 3x, RT preparation. Measurements were also made on a 1/6x, RT preparation where a 1:6 ligand:AuCl4molar ratio was employed. The average core radius of this sample was 1.6 nm with a core-size radius ranging from 0.5 to 2.6 nm. D2O was the solvent unless otherwise noted, and MPC concentrations typically ranged from 5 to 30 g/L. The pD of the resulting solutions, typically 2.8, was not adjusted. Impurities varied from batch to batch, with the variation depending primarily on the duration of dialysis.7 The solubility of tiopronin MPCs was measured to be 168 g/L. However, all samples showed some insoluble material, typically about 5%, probably resulting from aggregation. Also, water-soluble impurities were visible in the NMR spectra. The sharp components in all spectra can be attributed to impurities. Their presence and intensity depend mostly on storage and age of the sample solution. The impurities can be monitored through suppression of the broad components with a Carr-Purcell-Meiboom-Gill (CPMG) sequence involving an evolution period of g1s.18 An impurity signal at 3.8 ppm is typical and was initially incorrectly attributed to the methine group.7 The relative area of this signal can be greatly reduced by increasing the length of the dialysis step in the synthesis. NMR Spectroscopy. 1H, 13C, and 15N NMR experiments were performed on a Bruker Avance 500 spectrometer at 500, 125.7, and 36.1 MHz, respectively. We obtained 800 MHz 1H spectra with a Varian Inova spectrometer. The spectra were acquired at 298 K and referenced to 3-(trimethylsilyl) tetradeutero sodium propionate (TSP; Wilmad) for 1H and 13C and 45% formamide as an external standard for 15N (-268 ppm). T2 relaxation times were measured with a CPMG pulse sequence.

NMR Studies of Gold Nanoclusters

J. Phys. Chem. B, Vol. 105, No. 37, 2001 8803

TABLE 1: Frequency Shift Assignments and Line Widths for 3x, RT Samples (500 MHz) nucleus

group

H1 H2 H4 H5 C1 C2 C3 C5 C6 N

methyl methine amide methylene methyl methine carbonyl methylene carboxyl amide

monomer δ [ppm]

MPC upfield δ [ppm]

MPCa downfield δ [ppm]

fwhm upfield [Hz]

fwhma downfield [Hz]

1.48 3.65 8.39 4.01 23.5 39.3 175.8 44.1 179.7

1.6 4.3 8.3 4.0 26 48 177 45 179 -268

1.8 4.7

65 150 330 110 380 400

140 350

a

4.1b 27 51

210 150 b

No entry for the downfield components indicates that no second component could be resolved. The upper limit of splitting is based on deconvolution of the 800 MHz spectrum.

Diffusion data were acquired with a Bruker Avance 500 MHz spectrometer equipped with an AcuStar gradient driver and a Nalorac 5 mm diffusion probe (coil constant: 0.1007 T m-1 A-1). DOSY experiments were performed with bipolar gradient pulses and the LED pulse sequence (BPP-LED) illustrated in Figure 3.19 The shaped gradient pulses were of amplitude g and duration δ and were described by the function g[sin(2πt/δ)] for a pulse beginning at t ) 0. The Stejskal-Tanner attenuation factor for this function, computed by standard techniques,20 has the form ψ(q,∆eff) ) exp(-Dq2∆eff) where q ) 2γgδ/π and ∆eff ) ∆ - τ/2 - 5δ/16. Here D is the self-diffusion coefficient, γ is the gyromagnetic ratio, and the time delays are defined in Figure 3. For rectangular gradient pulses, q ) γgδ and the coefficient of δ in the last term of ∆eff is changed from 5/16 to 1/3.19 The sine shaped pulses were designed to minimize induced eddy currents, but because the gradient amplitude must be increased to counteract the factor of 4/π2, improvement is marginal at best. Computer Modeling. The models were created on an SGI O2 workstation with version 6.6 of SYBYL (Tripos, Inc., St. Louis, MO 63144). SYBYL coordinate files of two gold cores with a TO structure were constructed manually. The coordinates were determined by the Oh symmetry of the nanocrystal and the closest packing arrangement of the gold atoms. One TO contained 13 atoms which were arranged in three layers of 4, 5, and 4 atoms. The second TO contained 201 atoms arranged in nine layers of atoms with 9, 16, 25, 36, 49, 36, 25, 16, and 9 atoms. The sulfur atoms were then added to binding sites on the (100) and (111) faces. The remainder of the tiopronin ligand was attached using SYBYL drawing utilities. Additional structures of metal clusters were also downloaded from the Web site of the Cambridge Cluster Database and converted into the Tripos coordinate file format.21 NMR Analysis Assignment of Spectra. Figure 4 provides a comparison between the 1H NMR spectrum of the tiopronin monomer and the 3x, RT MPC sample. For the tiopronin MPC samples, a complete assignment of all observable nuclei can be established by using a combination of one-dimensional, NOESY, and HMQC techniques. The results are summarized in Table 1. The methine (H2), methyl (H1), and methylene (H5) protons all show broad resonances with no recognizable fine structure as illustrated in Figure 4b. In addition, with the exception of the amide proton signal, each peak consists of two resolved components. The two-dimensional spectra are particularly useful for demonstrating the presence of the two components. Correlations in the NOESY spectrum shown in Figure 5 permit one to associate all upfield components with the same chemical

Figure 3. BPP-LED sequence with sinusoidally shaped gradient pulses.

Figure 4. (a) 500 MHz 1H spectrum of 0.1 mM tiopronin monomer in D2O at 298 K. (b) 500 MHz 1H spectrum of 20 g/L 3x, RT tiopronin MPC in D2O at 298 K. The amide proton at 8.4 ppm comes from a sample prepared immediately before acquisition. The solvent peak has been presaturated.

species. The magnitude of the displacement of one spectral component with respect to the other decreases with distance (through bonds) from the Au core. Integration yields a 1:1 distribution for the methyl signal versus the combined methine/ methylene signal complex, confirming the assignment. The amide proton (H4) exchanges with the solvent and can be detected either in a 10% H2O/90% D2O solution or in pure D2O immediately after solvation. The amide proton yields a broad, Gaussian-shaped signal at 8.3 ppm as shown in Figure 4b. All carbon atoms are detectable in the one-dimensional 13C spectrum, including the R carbon (C2) that has not been observed before for tiopronin MPCs, but even with signal accumulation over 15 h, the spectrum remains very noisy. All protonated carbons can be observed in the 1H/13C HMQC spectrum shown in Figure 6. As in the case of the proton spectrum, the methyl and methine carbon signals are clearly

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Figure 5. 800 MHz 1H NOESY spectrum of 15 g/L 3x, RT tiopronin MPC in D2O at 298 K acquired with a TPPI NOESY pulse sequence (solvent presaturation 0.9 s and a mixing time of 0.45 s). The residual HOD signal appears at 4.8 ppm.

Figure 7. Examples of hole-burning (see text).

Figure 6. 1H 13C HMQC spectrum at 500 MHz of 20 g/L 3x, RT preparation of tiopronin MPC in D2O, (J ) 130 Hz, ∆ ) 3.8 ms). 13C dimension: methyl signals (26 and 27 ppm) and methine signals (48 and 51 ppm). 1H dimension: sharp impurity signal (3.8 ppm).

bimodal. The methylene signal at 45 ppm is not resolved into two components. In the 13C spectrum, the carbonyl and carboxyl signals can be found at 177 and 179 ppm, respectively. Evidence for their assignment comes from another 1H/13C HMQC experiment tuned to detect long-range couplings. There are signals indicating a connectivity of the group at 177 ppm with the methyl carbon. Because the interchain distance between the carbonyl and methyl groups is the shorter one, it is reasonable to assign it to the carbonyl. A further indication of the validity of this assumption is the comparison with the tiopronin monomer spectrum, in which the carbonyl and carboxyl groups yield signals at 175.8 and 179.7 ppm, respectively. The only nitrogen signal present was determined via a 1H/15N HMQC spectrum. All spectral lines are significantly broadened. Full width at half-maximum (fwhm) estimates are presented in Table 1. The peaks assigned to downfield components are systematically

broader than those of upfield components. Furthermore, the line width is greatest for the methine proton. In the case of overlapping signals, the line widths have been determined from deconvolutions carried out in XWINNMR (Bruker software). The clearly non-Lorentzian line shapes were approximated as Gaussian to yield better fits. The only signal that is not overlapped with the solvent peak or other groups is the methyl signal. The intensity ratio of its components was determined to be approximately 1.6:1, with the downfield component yielding the larger integral. As can be anticipated from the line shapes, the line widths cannot be explained by homogeneous broadening alone. T2 relaxation times have been determined to be longer than 20 ms and would only allow for line widths of 15 Hz or less. Additional evidence for inhomogeneous broadening comes from a hole-burning experiment, carried out over the frequency range of the methyl signal in steps of 30 Hz. This experiment was performed with a continuous wave irradiation (γB1/2π ) 320 Hz) of 10 s duration for saturation. It is possible to burn “holes” into the broad signals over the entire frequency range as shown in Figure 7, indicating that the broad signals consist of particle families with different frequency shifts. Two Components in the Spectrum. To demonstrate that the existence of two components is a feature not unique to tiopronin MPC spectra, NOESY spectra have been acquired for two different alkanethiolate MPCs, i.e., butanethiolate and hexanethiolate MPCs, as well as the 1/6x, RT tiopronin MPC preparation (Figure 8). In all cases, the R protons show two overlapping components. The R protons of alkanethiolate MPCs

NMR Studies of Gold Nanoclusters

Figure 8. 500 MHz 1H NOESY spectrum of a 20 g/L 1/6x, RT tiopronin MPC sample (all sharp components are impurities). Two components are visible for the R protons. The upfield component is found between 3 and 5 ppm, and the downfield component is found between 5 and 10 ppm. The NOE of the upfield component can only be attributed to a connectivity between methyl and methine protons. The frequency shift of the downfield component relative to the monomer is significantly larger in comparison to the 3x, RT tiopronin MPC sample.

J. Phys. Chem. B, Vol. 105, No. 37, 2001 8805 Interchain/Intrachain Connectivities. The NOESY crosspeaks in Figure 5 arise from dipole-dipole interactions that indicate proximities between groups. The intensity of a NOESY cross-peak depends inversely on the sixth power of the distance between protons. For tiopronin MPCs where the considerable line widths greatly reduce the S/N ratios, the presence of a crosspeak can be taken as a proof that the distance between the two groups involved is smaller than 0.4 nm. In Figure 5, the three groups of cross-peaks are labeled A, B, and C. First, there is an apparent connectivity between methylene protons (A). The conspicuous bulge flanking the methylene peak is shown to be a legitimate cross-peak by the use of a modified NOESY pulse sequence that suppresses the diagonal peaks.22 The large intensity of this peak probably originates from intrachain interactions as the intrachain interproton distance for the methylene group is found to be 0.18 nm. Second, a connectivity exists between methyl and methine (B). This peak, primarily caused by an intrachain connectivity, shows that the upfield methine and methyl components belong to the same chemical species. Third, a connectivity between methyl components and the methylene group (C) is evidently caused by interchain interactions, because the intrachain distance between those groups again exceeds the 0.4 nm limit. In summary, A indicates the anisotropic environment of the methylene protons, B allows us to correlate the upfield/downfield components, and C an interchain interaction contains information about the packing of the chains. DOSY. The polydisperse nature of the samples requires careful analysis of the DOSY data. The Stejskal-Tanner attenuation factor ψ(q,∆eff) is adequate for describing a monodisperse sample. For polydisperse samples such as those encountered in this study, the signal intensity at frequency ν can be expressed by23

I(q,ν) ) Figure 9. 500 MHz 1H spectrum of butanethiolate MPC in CDCl3. The spectral region of the R proton is expanded in a 40× inset.

are difficult to detect both because of their large line widths and overlapping spectral components. To our knowledge, the R protons of butanethiolate and hexanethiolate MPCs have not previously been observed. The butanethiolate MPC 1H spectrum (Figure 9) shows a broad peak between 3 and 5 ppm that is assigned to the R proton. The weak cross-peak between the R and β protons in a NOESY spectrum recorded at 500 MHz with a mixing time of 400 ms is barely resolved into two components. Similar results were obtained for a hexanethiolate MPC sample, although the deconvolution of the R/β cross-peak in its NOESY spectrum is tenuous. The 1/6x, RT tiopronin MPC NOESY spectrum displayed in Figure 8 shows two methine components, one between 3.3 and 4.7 ppm and a second at 7 ( 2 ppm. Amide Exchange Rate Constant. To determine the exchange rate of the amide proton, the integrals of amide signal intensities versus time have been fitted to a single-exponential decay. The exchange rate constant was determined as (2.0 ( 0.2) × 10-3 s-1 at 298 K and pD ) 2.80. The excellent fit is consistent with a first order dependence on the amide proton concentration. An extrapolation of the signal intensity at time t ) 0 yields an initial ratio between CH3 and amide of 1:0.18 which translates to 53% of amide protons displaying a slow decay. This result indicates the presence of two classes of amide protons, suggesting 53% hydrogen-bonded versus 47% non-hydrogenbonded protons.

∑n An(ν) exp(-Dnq2∆eff)

(1)

where An(ν) is the intensity of the 1D-NMR spectrum of the nth diffusing species at frequency ν when q is small and Dn is the associated diffusion coefficient. In general I(q,ν) for polydisperse samples will be nonexponential, i.e., a plot of ln[I(q,ν)] versus q2∆eff will not be linear. However, we have found that I(q,ν) curves for the MPCs investigated here deviate only slightly from exponentials, and at least the initial part of the decay can be used to obtain the average diffusion coefficient at each frequency. The average diffusion coefficients can be related to hydrodynamic radii rH of the MPCs by means of the Stokes-Einstein equation D ) kBT/(6πηrH) where kB is the Boltzmann constant, T is the temperature, and η is the viscosity. This equation, based on “stick” boundary conditions, is appropriate at low concentrations for particles that are much larger than the solvent molecules.24 For nanometer sized rough particles, e.g., proteins, some slip effects are expected; however, the roughness works in the opposite direction, and stick boundary conditions turn out to be a good approximation.25 We note that the weak dependence of D on rH explains the almost exponential attenuation for MPC samples. The attenuation curves are completely consistent with simulations based on the distributions of core sizes determined by electron microscopy.7 The plot of the average diffusion coefficients versus frequency shifts in Figure 10 shows two signal regions arising from the methyl and methine/methylene groups. The average diffusion coefficients range from 1.4 × 10-10 to 1.7 × 10-10 m2/s. In both signal groups, the diffusion coefficients decrease mono-

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Figure 10. 1H DOSY display at 500 MHz of 15 g/L 3x, RT tiopronin MPC in D2O. The bipolar LED pulse sequence with presaturation was employed with ∆ ) 0.3 s and sixteen exponentially spaced q values ranging from 3.4 × 104 to 3.1 × 105 m-1.

tonically in both the upfield and downfield directions, but values lower than 1.4 × 10-10 m2/s should be treated as potential artifacts because of their small S/N ratios. Although the average radii have to be treated as estimates, they do agree fairly well with the particle size range expected from HRTEM values.7 The shape of the two signal regions indicates a tendency for the upfield components to display larger average diffusion coefficients. However, we can detect no simple relationship between particle size and frequency shift within the upfield and downfield components for methine, methyl, or methylene protons. This analysis is, of course, complicated by the unknown amounts of homogeneous and inhomogeneous broadening. The maxima at 1.6 and 3.9 ppm could be slightly affected by impurities. The solvent (HOD) peak at 4.8 ppm, despite being partly suppressed and displaying only a small signal in the projection, has a substantial effect on the average diffusion coefficient in the region of the downfield methine component (4.4-5.0 ppm). Additional DOSY experiments have been performed using the bipolar LED sequence in Figure 3 followed by a CPMG filter with different evolution periods. As expected, the longer the relaxation evolution period, the more the average diffusion coefficients are shifted toward larger values. Transverse Relaxation (T2) Data. The CPMG experiment was performed with the goal of determining the size distribution of the MPC particles. In terms of the total transverse evolution period t, the attenuation for a nucleus of type X, e.g., methyl or methylene proton, in the nth species is described by exp(-t/ T2n,X). The decay for a polydisperse sample is analogous to that found for diffusion and can be written as

I(t,ν) )

An(ν) exp(-t/T2n,X) ∑ n,X

(2)

The intensities at various frequencies show a marked deviation from exponential dependence on the evolution time t, i.e., plots of ln[I(t,ν)] versus t are not linear. Inspection of the data seems to show two exponential components, but careful analysis with the program CONTIN26,27 demonstrates that the data can be fitted to a continuous distribution of decay constants, 1/T2n,X. The origin of the distribution of transverse relaxation rates must be sought in the relaxation mechanisms that affect the protons. Consider an X type proton, e.g., a methyl proton, in the nth size particle. The transverse relaxation rate will have contributions from secular and nonsecular terms. Because T1 is much larger than T2 for the samples of interest, we neglect the

Figure 11. Transverse relaxation distribution functions g(1/T2) in the methyl region: Upfield component (b); downfield component (O).

nonsecular contributions and focus on slow motions and in particular rotational diffusion. In methyl and methylene groups, the dominant relaxation mechanism is provided by the direct nuclear magnetic dipole-dipole interaction between adjacent protons. According to the Bloembergen-Purcell-Pound theory (BPP) the rotational contribution from a single pairwise contribution is given by28

() 1 T2

rot

)

( )( )

9 µ0 γ4p2 τ 20 4π R6 rot

(3)

where R is the internuclear distance and τrot is the rotational correlation time. The effect of the additional spin in a methyl group can be approximated by a factor of 2 if correlated motions are neglected. Of course, the effective dipole interaction strength is reduced because of averaging over restricted angles by highfrequency wagging and torsional motions in the ligands. However, the following lines of evidence suggest that the motion of the ligands is quite restricted: (a) computer modeling shows that the chains are tightly packed, (b) interchain hydrogen bonds are indicated by amide proton exchange rates and computer modeling, (c) intrachain methylene NOEs suggest that the methylene protons are not equivalent, and (d) T2 values computed with eq 3 are of the correct order of magnitude. In any event, the form of eq 3 is preserved and the relaxation rate is proportional to the rotational correlation time. We note that, according to Debye’s theory of rotational diffusion, τrot ) Vη/ (kBT) where the volume of the particle is given by V ) 4πrH3/3 and “stick” boundary conditions are assumed for the reasons outlined above. The polydisperse character of the tiopronin MPC samples is clearly demonstrated by our measurements of T2. Data sets of intensity versus evolution time were extracted at frequencies representative of each component and proton type from the CPMG data acquired for the 3x, RT and 1/6x, RT preparations. In each case, the CONTIN analysis yielded a broad, asymmetric probability distribution function g(1/T2). Plots of the CONTIN distribution function versus 1/T2 are shown for both components of the methyl group in Figure 11. In this case, the input data were integrated intensities for each component obtained from a deconvolution of the methyl signal. Even the smallest T2 values found yield line widths that are considerably narrower than the broad signals in the proton spectrum. This confirms the conclusion of the hole-burning experiment that inhomogeneous broadening is primarily responsible for the width and shape of the observed components. At each frequency shift, we imagine

NMR Studies of Gold Nanoclusters

Figure 12. Methyl signal of 3x, RT tiopronin MPC in D2O in a CPMG experiment. Total evolution times: (a) 4 and (b) 300 ms.

a sum of homogeneous Lorentzian components. The narrow components are responsible for the dips seen in the hole-burning experiment, whereas the broad components contribute to the signals at the upfield and downfield edges of the multiplet. The relaxation data also demonstrate that the two components are associated with two distinct populations of particles. Qualitatively, the differences between these populations are indicated by the proton spectrum in the methyl region where the relative intensity of the two components changes remarkably as a function of CPMG evolution time as shown in Figure 12. We conclude from this change that the more abundant downfield component relaxes faster and is therefore associated with larger average particle sizes. In particular, the most probable values of 1/T2 for the upfield and downfield components are 6.4 and 18 s-1, respectively. Furthermore, the downfield component has a significantly narrower distribution and therefore is comprised of a narrower range of particle sizes. This is a counterintuitive result as the downfield component consistently has the broader peak in both 1H and 13C spectra. Our interpretation of the relaxation data as a direct consequence of a size distribution of MPCs is supported by simulations of the CONTIN distribution function and the ln[I(t,ν)] versus t plots. The simulations were based on the number of particles versus core radius reported by Templeton et al.7 In particular, simulations show that the cubic dependence of 1/T2 on rH required by the Debye model accounts for the nonlinearity of the ln[I(t,ν)] versus t plot. Computer Modeling Molecular Modeling of MPCs. The development and evaluation of the three hypotheses that were considered for the MPCs were informed by the construction of molecular models. TO structures with 13 and 201 gold atoms provided a visual assessment of the packing of the ligands on the gold core. Templeton et al. determined from an elemental analysis that an average gold nanocrystal contains 2.4 ligands per gold atom.7 Our models show that it is possible to achieve or slightly exceed this average stoichiometry without incurring steric repulsion but only if the orientation of each ligand with respect to the gold

J. Phys. Chem. B, Vol. 105, No. 37, 2001 8807 surface is allowed to be flexible. Visual examination of the structures in a space-filling format shows that the gold surface is well covered (cf. Figure 2c). A maximum of 88 ligands can be attached to the 201-atom cluster by binding four ligands to C4 sites on each of the six (100) faces and eight ligands to C3 sites on each of the eight (111) faces. Guided by the normalincidence X-ray standing wave (NIXSW) studies of alkanethiols bound to a (111) face of single crystals of Ag,29 the first six tiopronin ligands on each (111) face were attached as in a 71/2 × 71/2 structure. Space was available on the interior of each hexagonal (111) face for placing the final two ligands in C3 sites. The models also enabled us to examine the conformational consequences of the tight packing on the gold cores. The interproton distances generated by a TO structure with 13 gold atoms and 14 ligands provided the basis for the assignment of the NOESY spectrum. For example, in this structure, methyl protons were separated by less than 0.4 nm from methylene protons when they were on separate chains and NOESY crosspeak C was confidently assigned to an interchain interaction. Molecular dynamics runs with the Tripos force field were conducted at 1000 K for free tiopronin and a 201-atom cluster with 88 ligands. A visual comparison of the trajectories clearly demonstrated a striking reduction in the mobility of side chains enforced by packing on the gold core. To explore conformational space, the structures generated by these runs were reminimized and hydrogen bonding to the amide nitrogen was located using a SYBYL utility. The structures examined contained 5-13 hydrogen bonds per MPC which were scattered throughout the structure. The limited number of molecular dynamics runs provide a lower bound on the actual number of hydrogen bonds because no attempt was made to locate the global minimum with an exhaustive search of conformational space. Discussion Summary of Findings. We have performed a variety of experiments on polydisperse tiopronin-MPC samples of two types: 3x, RT and 1/6x, RT, with average radii in the ranges 0.9 ( 0.35 nm and 1.6 ( 0.6 nm, respectively. These polydisperse samples were carefully selected to represent different average particle sizes because the overlap of the size distributions is quite small. Any models advanced to describe structure and bonding in these MPCs must at least be consistent with our experimental results, reported structures of the gold cores, and the conclusions of computer modeling. In particular, we list major experimental findings for these MPCs that are supported by this work: (1) The resonances are shifted downfield relative to those of the tiopronin monomer. (2) The methyl and methine protons have bimodal frequency distributions, and the peak separations depend strongly on the number of bonds separating the nuclei from the gold core. (3) 13C methyl and methine resonances are also bimodal. (4) The splitting appears to be larger for larger particles. The size dependence is most striking for the downfield component of the methine proton. (5) NOEs show connectivities of the upfield components for the methyl and methine protons and also for the downfield components, i.e., upfield components are associated with the same chemical species as are the downfield components. (6) The ratio of the number of downfield to upfield ligands is approximately 1.6 from methyl deconvolution and integration. (7) DOSY experiments indicate that the upfield components are associated with smaller average hydrodynamic radii.

8808 J. Phys. Chem. B, Vol. 105, No. 37, 2001 (8) CPMG experiments show that the most probable T2 values are larger for the upfield components, suggesting smaller particle radii and/or more mobile ligands. These results are supplemented by computer modeling results that show (1) the ligands must be tightly packed on the gold surface to conform with elemental analysis results and (2) the hydrogen bonds are more or less uniformly distributed over the surface of the particle. In view of these findings and previous reports concerning structures of the gold cores, we have considered three types of models for the structure and properties of the MPCs. Binding Site Model. High-resolution PES has demonstrated the presence of different sulfur species and hence different binding sites in alkanethiols bound to silver and gold surfaces.30 The electronic factors that influenced the PES chemical shift may also affect the NMR chemical shift. Both TO and m-Dh nanocrystals contain faces that support C3 and C4 binding, and the two spectral components are assigned to ligands bound to different sites on the same particle. The signal width in this model would be attributed to a distribution of particle sizes and shapes. This model, although attractive, is incompatible with the DOSY display and T2 relaxation rates and the relative amounts of the two components. The DOSY spectrum and the relaxation data indicate that the two components are due to ligands on different particles. Furthermore, an examination of typical nanocrystals belonging to the TO and m-Dh families showed that the relative number of C4 to C3 binding sites is too small to account for the relative amounts of the two components determined from the integration of the 1H spectrum. The 13 structures examined ranged in size from 13 to 102 gold atoms, and the average fraction of C4 sites was 0.27. For nine of the structures, the fraction was less than 0.3, which should be compared with the experimental value of 1/1.6 ) 0.63. Conformational Model. Second, we considered a model in which the ligands on an MPC would form a mosaic with patches of ordered and disordered ligands. Hydrogen bonding demonstrated by the amide-exchange data would provide the physical basis for organization of the ligands. This model is ruled out by two lines of evidence. First, all proton spectra recorded over the temperature range 298-368 K showed both components and no evidence of their merging. Second, the modeling calculations demonstrated that the network of hydrogen bonding was distributed randomly throughout the MPC surface. Gold Core Structure Model. Our third model follows from the DOSY spectrum and the relaxation measurements that support the assignment of the components to two populations of particles. It is tempting to associate the bimodal frequency distributions with the presence of primarily two types of core structures, but a mechanism must be associated with the observed shifts. Chemical shifts are expected to be influenced by the proximity of the gold cores.13 The association of upfield and downfield spectral components with the two core types, of course, depends on differences in electron density and possibly on the presence of conduction electrons in the two cores. It is reasonable to assume that the closest packed arrangement of gold atoms in the TO cores is associated with the higher density and conductivity. Accordingly, we tentatively assign the larger shifts of the downfield components to the TO gold cores. A particularly interesting finding is the increase in downfield chemical shift for the methine protons with increase in core size. The separation of the two methine components also increases, and the shift of the downfield component is striking. This result has led us to consider the possibility of a contribution

Kohlmann et al. from Knight shifts for particles containing more than about 300 Au atoms that are known to show metallic properties.10 The literature concerning NMR of molecules on metal surfaces suggests that Knight shifts, resulting from the interaction of conduction electrons with nuclei, are likely to be present for nuclei on or close to the gold surface.28 Knight shifts have the following features: (1) the shifts are downfield (for nuclei in metals) and tend to be larger than chemical shifts in diamagnetic molecules, (2) the shifts are proportional to the applied static magnetic field strength as are conventional chemical shifts, (3) the shifts are propagated through bonds by exchange interactions and result from Fermi contact interactions with the nuclei; therefore, Knight shifts are expected to attenuate strongly with the number of bonds, and (4) the shifts will increase as the gold clusters becomes more metal-like, a property that will depend on core density, shape, and size. Knight shifts are commonly confirmed by measuring the temperature dependence of T1 values for comparison with predictions of the Korringa relation.28 Unfortunately, the small magnitudes of the shifts observed here correspond to very small contributions to longitudinal relaxation rates that cannot be distinguished in the presence of other relaxation mechanisms, e.g., dipole-dipole interactions between protons. However, the features of Knight shifts match well with our observations, in particular the downfield shifts and the dependence on particle size. We have not found previous experimental or theoretical studies to inform us about the magnitudes expected of the Knight shifts for nuclei separated from the metallic core by two or more bonds. However, numerous studies of adsorbed molecules, e.g., CO,31,32 show large Knight shifts for atoms directly bonded to the metallic surface which can be confirmed by T1 studies. We note that Badia et al. concluded that Knight shifts are not significant for 13C nuclei in alkanethiolated gold clusters on the basis of (a) comparisons with the chemical shifts in [Au(I)SR]n complexes and (b) the absence of Korringa behavior for measured T1 values.13 In view of point (a), it is likely that conventional chemical shifts including the effects of the nearby gold atoms in the two types of cores account for most of the shifts found in smaller particles and for nuclei far from the metal core. Also, Kolbert et al. failed to find evidence for Knight shifts for 13C and 31P in ligands attached to Au55 clusters.33 However, this result is not relevant to our situation because the small Au55 clusters fail to exhibit metallic properties.1 Our finding that the shifts and broadening for the methine protons increase dramatically when the average number of atoms in the gold core increases from 200 to 550 adds credibility to the suggestion that Knight shifts are present. Sources of Line Broadening. The methyl and methine resonances are characterized by broad bimodal frequency distributions that have been shown to be primarily inhomogeneous in nature. However, the homogeneous contribution may be considerable and may contribute to the intensity in the upfield and downfield wings of the distribution, thus, providing a rational for the small diffusion coefficients measured in the wings. This is possible because the CPMG experiment may well miss extremely fast relaxing components. The origin of the inhomogeneous broadening is not certain. A likely source, at least for the methyl and methine resonances, would be the distribution of chemical shifts and Knight shifts associated with the variety of crystal shapes, sizes, and defects expected for both TO and m-Dh type gold cores. The Cambridge Cluster Database is particularly informative concerning the rich

NMR Studies of Gold Nanoclusters variety of particle shapes.21 Also, Knight/chemical shifts may well vary with binding sites, e.g., the C3 and C4 sites discussed above. A contribution to the chemical shifts is also expected from the variety of conformations available to the ligands. This contribution is expected to dominate for the methylene protons. Our modeling calculations of TO with 13 and 201 gold atoms show that the tiopronin ligands can adopt a wide range of torsional angles and diverse states of hydrogen bonding. A tiopronin MPC is comparable to a spherical protein, and the protein NMR literature is instructive. It is well-known that the chemical shifts of spins in a protein depend on the torsional angles and hydrogen bonding.34 The Biological Magnetic Resonance Bank database (BMRD) provides distributions of chemical shifts for each type of amino acid residue.35 The associated histograms for the alpha and amide protons of glycine show that conformation alone would be sufficient to explain the widths of the methylene and amide proton resonances. Conclusions The characterization of extremely polydisperse samples rarely leads to a single, definitive model. Yet robust conclusions can be drawn from our NMR data that any successful model must address. Both proton and carbon spectra of tiopronin MPCs demonstrate the existence of two chemical components. This bimodal feature is not limited to tiopronin MPCs as it was also observed in the proton NOESY spectra of alkanethiolate MPCs. DOSY and relaxation measurements associate the two components with two populations of particles. We have proposed that the unusual NMR properties reflect differences in the gold cores and have tentatively identified gold cores of the two components with m-Dh and TO. The two populations are characterized by different average particle sizes, but each population spans a broad range of sizes. We have also suggested that the core types influence chemical shifts for nuclei close to the gold surfaces and that Knight shifts make a contribution at least for the larger particles. We hope in the future to have access to more monodisperse samples so that these studies can be refined. Also, the study of MPCs with different metals in the core, e.g., silver, would be helpful in verifying our suggestion that Knight shifts can be significant for nuclei separated by three or four bonds from the metallic core. In addition, we plan to undertake electrophoretic NMR (ENMR) studies of MPCs in an attempt to resolve the NMR spectra on the basis of the net charges of the particles. It is also possible that simultaneous diffusion and mobility measurements will permit the correlation of sizes with electrophoretic mobilities of the particles. Acknowledgment. This work was supported under National Science Foundation Grants CHE-9903723 (C.S.J.) and CHE97-26171 (R.W.M.). We thank Anthony A. Ribeiro at the DUKE NMR Spectroscopy Center for providing 800 MHz spectra, Mu-Hyan Baik for chemical shift calculations, and Tao Huang and Mike Leopold for the preparation of MPC samples.

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