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Geometric and Electronic Structure of Au25(SPhX)18(X = H, F, Cl, Br, CH3, and OCH3) Christine M. Aikens* Department of Chemistry, Kansas State University, Manhattan, Kansas 66506
ABSTRACT Using density functional theory calculations, the geometric structure of Au25(SPh)18- is found to have S6 symmetry. The electronic structure of this particle is affected by a splitting of the superatom Pz orbital from the set of Px and Py orbitals; this leads to a double peak similar to the characteristic double peak of Au25(SCH2CH2Ph)18- and related compounds. Para substituents shift the HOMO and LUMO orbital energies, but the HOMO-LUMO gap remains constant. The shifts correspond with Hammett substituent constants, with the exception of OCH3. Calculated optical absorption spectra are mostly unaffected by ligand substitution, although slight (0.1 eV) changes are evident in ligand-based transitions. SECTION Nanoparticles and Nanostructures
Table 1. Relative Energies (eV) for Au25(SPh)18-
T
hiolate-protected nanoparticles in the 1-2 nm size regime are of significant interest due to their highly structured optical absorption,1-3 intense circular dichroism,4 luminescence visible to the eye,5,6 and sizable nonlinear optical properties,7 in addition to applications in catalysis.8 The pioneering X-ray crystal structure determination of Au102(SR)44 (R = para-mercaptobenzoic acid)9 showed that the cores of these particles are passivated by gold thiolate oligomers similar to the divide-and-protect motif proposed by H€ akkinen et al.10 The structures of Au25(SR)18- and Au25(SR)18 also contain similar gold thiolate units.11-14 A number of Au25(SR)18- systems have been synthesized experimentally, including R = SCH2CH2Ph, SC6H13, SG (HSG = glutathione), Spy (py = pyrene), SPh, and para-substituted SPhX.4,15-17 Density functional theory (DFT) calculations have proved useful for interpreting the electronic structure of these particles12,13,18-21 and have recently been employed to successfully predict22 the chiral structure of Au38(SR)24 in advance of X-ray crystal structure determination.23 DFT calculations have also been used recently to examine gold-phosphine binding24 and gold sulfide clusters.25 In the Au25(SCH2CH2Ph)18- crystal structure,11,12 the ligands are arranged in a (2 þ 1) configuration, where two of the thiolates are arranged in an eclipsed orientation across the Au(I) bond and the third thiolate lies in an anti orientation. In Au25(SH)18-, the flipping of a single SH group to the opposite side of the V-shaped oligomer has a barrier of 0.6 eV at the XR/TZP level of theory, which suggests that the ligand orientation may be dynamic in solution at room temperature and that the ligand orientation determined in the crystal structure of Au25(SCH2CH2Ph)18- may be needed for packing but could vary somewhat in solution. In addition, the most thermodynamically stable orientation could differ from ligand to ligand. Because of the importance of considering ligand orientation, a number of structures for the phenylthiolate-protected
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structure
XR/DZ
PBE//XR/DZ
1
0.00
0.00
2
0.41
0.23
3
0.68
0.42
4a 5
0.74 1.05
0.47 0.73
a
Analogous to crystal structure of Au25(SCH2CH2Ph)18-
nanoparticle have been considered in this work. The computational approach is described in the Computational Methods section. For Au25(SPh)18-, the orientation of the phenyl groups has been varied in pairs that preserve the center of symmetry from Au25(SCH2CH2Ph)18-. The relative XR/DZ energies of five low-energy structures (1-5) are shown in Table 1. The coordinates for structure 4 are analogous to those from the crystal structure of Au25(SCH2CH2Ph)18-. As shown in Table 1, structure 1 is 0.74 eV lower in energy than this structure and 0.41 eV lower in energy than the second lowest energy structure 2 at the XR/DZ level of theory. To check the relative energies, single-point PBE calculations were performed at the optimized XR geometries. The relative ordering of these five structures is predicted to be the same at this level of theory, although the differences in energy are up to 0.32 eV smaller. Structure 1 has a higher symmetry than structure 4. The point group of this system has idealized S6 symmetry, where the C3 axis is shown in Figure 1A. The relative stability of this system is likely due to the π-stacking arrangement of the phenyl groups. The phenyl groups are located in sets of three, in which the two outer phenyl groups (denoted 1 and 3 in Received Date: July 19, 2010 Accepted Date: August 12, 2010 Published on Web Date: August 16, 2010
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DOI: 10.1021/jz1009828 |J. Phys. Chem. Lett. 2010, 1, 2594–2599
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Figure 1. Geometric structure of Au25(SPh)18- showing (A) the C3 axis (top view) and (B) three π-stacked phenyl groups (side view). Gold atoms are shown in pink, sulfur in yellow, carbon in gray, and hydrogen in white.
Figure 1B) are attached to the same -SR-Au-SR-Au-SRligand unit and the central intercalating phenyl group (2 in Figure 1B) is connected to a neighboring unit. The nanoparticle possesses six sets of three stacked phenyl groups. The electronic structure of the nanoparticle is affected by the geometric arrangement of the gold thiolate units. As shown in Figure 2, the three highest occupied orbitals have superatom P-like character, as previously noted for Au25(SCH3)18- (ref 13) and Au25(SH)18- (ref 19). Unlike Au25(SH)18-,19 these three orbitals are not essentially degenerate. Instead, the highest occupied orbital corresponds to a Pz orbital that lies 0.12-0.13 eV higher in energy than the Px and Py orbitals; the Px and Py orbitals are essentially doubly degenerate at the LB94/DZ level of theory. In addition, the five superatom D orbitals are not split into doubly and triply degenerate sets as they are in Au25(SH)18-. Rather, the first four orbitals form two essentially doubly degenerate sets that are split by 0.53 eV. In the S6 point group, these would correspond to (Dxz, Dyz) and (Dx2-y2, Dxy) sets; however, the axes are somewhat mixed in the nanoparticle and cannot be clearly assigned. The Dz2 orbital lies the highest in energy at -5.728 eV, which is 0.17 eVabove the second degenerate set. These orbital splittings are due to a ligand-field splitting of the P and D sets within the S6 symmetry created by the phenyl group arrangement. Related ligand-field splitting has been noted for Au25(SR)18-.13,19 The splitting of the Pand D orbitals in Au25(SPh)18- leads to dramatic effects on the LB94/DZ optical absorption spectrum (Figure 3). The peaks at 1.21 and 1.22 eV arise from the HOMO (i.e., Pz) f (LUMO, LUMOþ1) transitions (Table 2). The peaks between 1.31 and 1.37 eV originate from the (Px, Py) f (LUMO, LUMOþ1) transitions. Overall, this splitting of the P orbitals leads to a double peak similar to the characteristic double peak previously observed for Au25(SCH2CH2Ph)18- and Au25(SPh)18- (ref 16) as well as for Au25(SR)18- with other ligands such as glutathione and nhexylthiol4 [note that the compound originally identified as Au38(SR)24 in ref 16 was later reassigned as Au25(SR)18-]. However, it should be noted that the peaks predicted at the LB94/DZ level of theory underestimate the energy by approximately 0.4 eV relative to experiment, which is significantly greater than the 0.15 eV previously reported for Au25(SH)18at the SAOP/TZP level of theory.20 The LB94/DZ absorption
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Figure 2. Electronic structure of Au25(SPh)18-. Kohn-Sham orbitals (contour value 0.17) are shown from the z-axis (top); additional views oriented to best display the superatom orbital are shown in wireframe.
Figure 3. LB94/DZ optical absorption spectra of Au25(SPhX)18(X = H, Br, Cl, F, CH3, OCH3). The vertical red lines represent the TDDFT-calculated excitations for X = H. For all X, the peaks are broadened by Gaussian functions with a full-width at halfmaximum of 0.125 eV.
spectrum for Au25(SH)18- is presented in the Supporting Information for comparison (Figure S1). The double peak is
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DOI: 10.1021/jz1009828 |J. Phys. Chem. Lett. 2010, 1, 2594–2599
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Table 3. AuSPhX Bond Distances (Å) at the XR/DZ Level of Theory
Table 2. Excitation Energy, Oscillator Strength, Single-Particle Transitions, and Their Weights state
E (eV)
f
from
to
weight
X
S-C1
a
C1-C2
C2-C3
C3-C4
C4-X
1
1.212
0.014
HOMO
LUMO
0.9049
H
1.769
1.396
1.385
1.390
1.097
2
1.220
0.013
HOMO
LUMOþ1
0.8951
H
1.843
1.394
1.393
1.395
1.097
3
1.311
0.001
HOMO-1
LUMO
0.3974
Br
1.839
1.394
1.394
1.389
1.940
HOMO-2
LUMOþ1
0.2656
Cl
1.840
1.395
1.394
1.385
1.821
HOMO-1
LUMOþ1
0.1791
F
1.839
1.396
1.393
1.381
1.399
HOMO-2
LUMO
0.1381
CH3
1.839
1.394
1.392
1.398
1.495
HOMO-1 HOMO-2
LUMO LUMOþ1
0.4279 0.3850
OCH3
1.832
1.397
1.389
1.396
1.378
LUMOþ1
0.4474
4
1.349
0.022
5
1.351
0.021
HOMO-1 HOMO-2
LUMO
0.3744
6
1.368
0.037
HOMO-2
LUMO
0.4143
22
24
26
30 31
1.899
1.927
1.950
2.012 2.070
0.016
0.041
0.053
0.054 0.024
HOMO-2
LUMOþ1
0.2265
HOMO-1
LUMOþ1
0.2138
HOMO-1
LUMO
0.0906
HOMO-1 HOMO-1
LUMOþ3 LUMOþ2
0.3612 0.2575
HOMO-2
LUMOþ2
0.1151
HOMO-2
LUMOþ3
0.0348
HOMO-2
LUMOþ2
0.3125
HOMO-2
LUMOþ3
0.1847
HOMO-1
LUMOþ4
0.1806
HOMO-2
LUMOþ4
0.2153
HOMO-2 HOMO-1
LUMOþ3 LUMOþ3
0.1771 0.1634
HOMO-1
LUMOþ2
0.1382
HOMO
LUMOþ4
0.4881
HOMO
LUMOþ5
0.1550
HOMO-2
LUMOþ4
0.6589
32
2.082
0.029
HOMO-1
LUMOþ4
0.6423
34
2.132
0.022
HOMO-11
LUMOþ1
0.3781
HOMO-1 HOMO-2
LUMOþ5 LUMOþ5
0.3024 0.1148
35
2.133
0.027
HOMO-11
LUMO
0.6346
HOMO-11
LUMOþ1
0.1914
a
Geometries for related AuSPhX compounds have been optimized at the XR/DZ level of theory, and the carbon-carbon distances computed are relatively constant. As shown in Table 3, the carbon-carbon distances for AuSPh and Au25(SPh)18differ by at most 0.008 Å. The sulfur-carbon distance is significantly shorter in the nanoparticle, which is understandable because the sulfur atom bridges two gold atoms in this system. However, the carbon-hydrogen distance is unchanged. In general, the carbon-carbon distances are reasonably insensitive to the substituent on AuSPhX. These values differ by less than 0.01 Å compared to the Au25(SPh)18- values. Consequentially, coordinates for the Au25(SPhX)18- complexes are constructed by replacing the para hydrogens with the X substituents at the appropriate C4-X distances without further optimization. Average Voronoi deformation density (VDD) and Hirshfeld charges for the AuSPhX and Au25(SPhX)18- systems are shown in Table 4. Although averages are shown in Table 4, X substituents of the intercalating phenyl groups (2 in Figure 1B) tend to be slightly more electropositive than those of the outer phenyl groups. As may be expected, Au and S possess more electron density when an electron-donating ligand is employed in the para position for AuSPhX, whereas they are more positive when electron-withdrawing ligands are utilized. However, this trend does not hold for Au25(SPhX)18-. In this nanoparticle, the charges on the gold and sulfur atoms are remarkably constant regardless of X for both charge distribution methods. This behavior has been calculated previously for a chlorinated Au25 nanoparticle.26 The HOMO-LUMO gaps for AuSPhX and Au25(SPhX)18at the LB94/DZ level of theory are shown in Table 5. The HOMO-LUMO gaps for AuSPhX vary with a range of 0.05 eV between 1.334 and 1.386 eV depending on substituent X, whereas the HOMO-LUMO gaps for Au25(SPhX)18- lie between 1.131 and 1.139 eV, with the exception of 1.122 eV for X = OCH3. The HOMO-LUMO gap of Au25(SPhX)18- is less sensitive to the X substituent than AuSPhX. The orbital energies for 10 HOMOs and LUMOs of Au25(SPhX)18- are presented in Table 6. In general, the orbital energies become more negative as the Hammett constant σpara increases, and the shift is similar in magnitude for orbitals near the HOMOLUMO gap. This behavior has been observed previously in electrochemical measurements.16 It should be noted that in both the theoretical results presented here and the electrochemical measurements from ref 16, the HOMO
also predicted at the PBE/DZ level of theory (Figure S2, Supporting Information) at similar (but slightly lower) energies relative to LB94/DZ. The weak states between 1.72 and 1.79 eV for Au25(SPh)18- primarily originate from transitions out of ligandbased orbitals into the LUMO and LUMOþ1 (Table S1, Supporting Information). The moderately strong ( f > 0.01) states between 1.89 and 1.95 eV arise from the (Px, Py) f (LUMOþ2, LUMOþ3) transitions. The Pz f Dz2 (HOMO f LUMOþ4) transition is computed to fall at 2.01 eV ( f = 0.054). Again, the LB94/DZ level of theory underestimates the energy of the second peak observed in the experimental spectrum.16 The higher-energy peaks arise primarily from transitions out of ligand-based orbitals. In order to examine the effect of substituents in the para position on the phenyl groups, a series of Au25(SPhX)18- (X = H, F, Cl, Br, CH3, and OCH3) coordinates have been constructed.
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Bond distances in
Au25(SPh)18-.
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DOI: 10.1021/jz1009828 |J. Phys. Chem. Lett. 2010, 1, 2594–2599
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Table 6. LB94/DZ Orbital Energies (eV) for 10 HOMOs and 10 LUMOs of Au25(SPhX)18-
Table 4. Averaged LB94/DZ Charge Distribution for AuSPhX and Au25(SPhX)18-
OCH3
Voronoi Deformation Density AuSPhX Br
Cl
F
CH3
H
Br
Cl
F
-8.27
-8.16
-8.31
-9.07
-9.22
-9.45
-8.12
-8.01
-8.17
-8.92
-9.07
-9.30
OCH3
CH3
H
Au
-0.018
-0.010
-0.001
0.005
0.009
0.013
S
-0.028
-0.027
-0.025
-0.022
-0.021
-0.019
-0.065 0.091
-7.96
-8.13
-8.86
-9.02
-9.25
0.057 -0.011
-0.032 0.069
-8.02
Ph X
0.087 -0.070
0.094 -0.082
0.167 -0.161
-8.01
-7.95
-8.11
-8.86
-9.01
-9.24
-7.99 -7.67
-7.91 -7.56
-8.07 -7.71
-8.82 -8.48
-8.97 -8.63
-9.20 -8.85
-7.66
-7.55
-7.70
-8.47
-8.62
-8.84
-7.53
-7.42
-7.58
-8.34
-8.49
-8.71
Au25(SPhX)18Au(core)
-0.019
-0.018
-0.019
-0.020
-0.020
-0.020
Au(ligand)
-0.045
-0.043
-0.043
-0.044
-0.044
-0.044
S Ph
-0.009 0.048
-0.010 -0.050
-0.009 -0.087
-0.004 0.077
-0.003 0.079
-0.002 0.150
X
-0.051
0.046
0.082
-0.085
-0.088
-0.159
Hirshfeld AuSPhX OCH3
CH3
H
Br
Cl
F
Au
0.003
0.011
0.020
0.026
0.030
S
0.002
0.004
0.006
0.010
0.011
0.012
Ph
0.013
-0.057
-0.080
-0.026
-0.006
0.131
-0.018
0.043
0.053
-0.009
-0.034
-0.177
X
0.034
0.009
0.010
0.010
0.009
0.009
0.009
Au(ligand)
0.025
0.026
0.027
0.027
0.027
0.027
S
0.047
0.046
0.047
0.052
0.053
0.054
Ph
-0.054
-0.137
-0.173
-0.111
-0.092
0.043
X
-0.072
0.010
0.044
-0.020
-0.041
-0.177
Table 5. LB94/DZ HOMO-LUMO Gaps (eV) X
AuSPhX
Au25(SPhX)18-
OCH3
1.386
1.122
CH3
1.345
1.135
H
1.334
1.138
Br Cl
1.364 1.365
1.131 1.134
F
1.369
1.139
of Au25(SPhOCH3)18- lies lower in energy than the HOMO of Au25(SPhCH3)18-. Thus, the OCH3 data do not exactly correspond with values expected from Hammett substituent constants. As shown in Table S2 (Supporting Information), the shift in orbital energies with the Hammett substituent constant and the slight exception of OCH3 from the general trend are also observed for AuSPhX, which suggests that calculations on individual ligands could provide useful information about expected orbital energy and HOMO-LUMO gap behavior in a nanoparticle.
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-7.98
-8.14
-8.89
-9.04
-9.27
-7.97
-8.13
-8.88
-9.03
-9.26
-6.40
-6.29
-6.44
-7.21
-7.35
-7.57
-6.40
-6.28
-6.44
-7.21
-7.35
-7.57
-5.89
-5.76
-5.91
-6.70
-6.84
-7.06
-5.87
-5.75
-5.90
-6.69
-6.83
-7.05
-5.70 -5.57
-5.58 -5.45
-5.73 -5.60
-6.51 -6.39
-6.65 -6.53
-6.87 -6.74
-5.39
-5.26
-5.41
-6.19
-6.33
-6.55
-5.33
-5.21
-5.36
-6.15
-6.29
-6.51
-5.21
-5.08
-5.24
-6.03
-6.17
-6.37
-5.03
-4.78
-4.91
-5.71
-5.85
-6.06
The LB94/DZ optical absorption spectra of Au25(SPhX)18(X = H, F, Cl, Br, CH3, and OCH3) are presented in Figure 3. The first double peak does not shift with the electron-withdrawing nature of the para substituent. As discussed above, the shift in the orbital energies for both the HOMO and the (LUMO, LUMOþ1) set is approximately the same; therefore, the gap remains constant. Very slight changes (
