3.1 Geometries of Au9 Clusters
Figure 1 shows the optimized geometries of Au9(PPh3)8GaCl22+ (1) and its derivatives, Au9(PMe3)8GaCl22+ (1Me) and Au9(PH3)8GaCl22+ (1H). Previous studies describe the core structure of 1 as a truncated Au-centered centaur polyhedron (Au9Ga) with one corner missing and another one occupied by the GaCl2-unit.13 Average bond lengths of 1, 1Me, and 1H are presented in Table 1. The average Au-Au bond length of Au9(PPh3)8GaCl22+ (1) is 2.90 Å which is in good agreement with experiment13, differing by only 2.84%.
To understand the role of ligand composition on geometry, we reduced the ligand from the phenyl group to methyl to hydrogen. We found that as the ligand is reduced, the core structure deviates only slightly. When the ligand is reduced from the phenyl group to methyl (1Me), the Au-Au bond length changes by 0.3% and when the ligand is reduced to hydrogen (1H), the bond length changes by 0.7%. The Au-P bond length also decreases slightly as the ligand is reduced, changing by 1.69% in both 1Me and 1H. As expected, the Au-Ga bond increases as the ligand is reduced. This can be attributed to less steric hinderance around the GaCl2 unit, causing it to move down away from the cluster core. The GaCl2 unit also rotates slightly as the ligand is reduced (Fig. 1). We believe this is also a result of less steric hindrance which gives the unit more freedom to move. This result illustrates the importance of the steric effect of the ligand on the cluster core and overall geometry. Similar changes in core bond distances can be observed in previous studies analyzing the change of ligand composition on other ligated gold nanoparticles.20
Table 1
Comparison of the Average Relaxed Bond Lengths (Å) of the Au9 System with Different Ligand Composition.
system
|
Au-Au
|
Au-Ga
|
Au-P
|
Ga-Cl
|
Expt. Values (1)
|
2.82
|
2.61
|
2.30
|
2.21
|
Au9(PPh3)8GaCl22+ (1)
|
2.90
|
2.62
|
2.37
|
2.25
|
Au9(PMe3)8GaCl22+ (1Me)
|
2.91
|
2.64
|
2.33
|
2.26
|
Au9(PH3)8GaCl22+ (1H)
|
2.88
|
2.71
|
2.33
|
2.21
|
In addition to investigating the effect of ligand composition on geometry, we also substituted the post transition metal atom (Ga to Al orIn) and the halide atom (Cl to F or Br) to determine the possible impact on the structure. To reduce computational cost, we used 1Me as the base structure instead of the full structure (1). The phenyl groups of 1 introduce hundreds of additional states which has the potential to extend computational time significantly. Figure 2 shows the optimized geometries of Au9(PMe3)8GaCl22+ (1Me) and its derivatives, Au9(PMe3)8AlCl22+ (2), Au9(PMe3)8InCl22+ (3), Au9(PMe3)8GaF22+ (4), Au9(PMe3)8GaBr22+ (5). The average bond lengths of these systems are represented in Table 2.
Table 2
Comparison of Average Relaxed Bond Lengths (Å) of 1Me and its derivates.
system
|
Au-Au
|
Au-M
M = Al, Ga, In
|
Au-P
|
M-X
X = F, Cl, Br
|
Au9(PMe3)8GaCl22+ (1Me)
|
2.91
|
2.64
|
2.33
|
2.26
|
Au9(PMe3)8AlCl22+ (2)
|
2.93
|
2.59
|
2.34
|
2.18
|
Au9(PMe3)8InCl22+ (3)
|
2.91
|
3.11
|
2.34
|
2.49
|
Au9(PMe3)8GaF22+ (4)
|
2.89
|
2.64
|
2.33
|
1.83
|
Au9(PMe3)8GaBr22+ (5)
|
2.91
|
2.64
|
2.33
|
2.42
|
Substitution of the Group III metal had little effect on the Au-Au bond length. The Au-Au bond length in Au9(PMe3)8AlCl22+ (2) differed from the original structure (1Me) by only 0.7% while it remained the same in Au9(PMe3)8InCl22+ (3). The most noticeable change in bond length occurs in the bonds that directly involve the post-transition metal. The Au-Al bond length was reduced by 1.89% and the Al-Cl bond length was reduced by 3.54% in structure 2 when compared to 1. The Au-In bond length increased significantly in comparison to 1Me, changing by 17.8% in structure 3. The In-Cl bond length also increased significantly by approximately 10.18%. These considerable changes indicate that substitution of the post transition metal from Ga to In not only induces substantial geometrical change within the core structure, but also that structure 3’s electronic structure may differ significantly.
Substitution of the halide atom had a similar effect to the post-transition metal substitution in that it only significantly affected the bond lengths where the atom was directly involved. The Au-Au bond length in Au9(PMe3)8GaF22+ (4) decreased by only 0.7% in comparison to 1Me while it stayed the same in Au9(PMe3)8GaBr22+ (5). In structure 4, the Ga-F bond length shows the most notable change, decreasing by over 19.03%. This can most likely be attributed to the high electronegativity of F in comparison to Cl or Br. Fluorine’s desire for electrons causes it to get closer to the post transition metal. In structure 5, the Ga-Br bond length also changes in comparison to 1Me but not as drastically as structure 4. The Ga-Br bond length increases by about 7.08%. We also ran additional geometry optimization calculations following the same parameters on the molecules GaF2, GaCl2, and GaBr2. We found that these molecules followed the same trend witnessed in Au9 with an increasing bond distance between Ga and the halide atom as one travels down the periodic table.
3.2 Electronic Structure
The gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), the HOMO-LUMO gap, was calculated for each of the studied systems (Table 3). Table 3 shows the change in the HOMO-LUMO gap as the ligand in structure 1 is reduced from the phenyl group to methyl to hydrogen. We find that as the ligand is reduced, the HOMO-LUMO gap increases, indicating an increase in stability. When the ligand is reduced from the phenyl groups to methyl (1 to 1Me), the HOMO-LUMO gap increases by 0.21 eV or 11.35%. When the ligand is reduced down to hydrogen (1 to 1H), the gap increases by 0.57 eV or 30.81%. This result is in good agreement with previous studies where the size of the HOMO-LUMO gap decreased as the size of the cluster increased.21
Table 3
Comparison of HOMO-LUMO Gaps (eV) of the Studied Au9 Cluster with Different Composition.
system
|
HOMO
|
LUMO
|
HOMO-LUMO Gap
|
Au9(PPh3)8GaCl22+ (1)
|
-8.00
|
-6.15
|
1.85
|
Au9(PMe3)8GaCl22+ (1Me)
|
-8.61
|
-6.55
|
2.06
|
Au9(PH3)8GaCl22+ (1H)
|
-10.04
|
-7.62
|
2.42
|
Au9(PMe3)8AlCl22+ (2)
|
-8.57
|
-6.35
|
2.22
|
Au9(PMe3)8InCl22+ (3)
|
-8.53
|
-6.64
|
1.89
|
Au9(PMe3)8GaF22+ (4)
|
-8.58
|
-6.45
|
2.13
|
Au9(PMe3)8GaBr22+ (5)
|
-8.61
|
-6.59
|
2.02
|
Table 3 also shows the change in the HOMO-LUMO gap as the Group III metal and halide atoms are altered. We find that the change of the post transition metal reduced the HOMO-LUMO gap as one continues down the periodic table. When Ga is changed to Al (i.e, 1Me to 2), the HOMO-LUMO gap increases by 0.16 eV or 7.77%. When Ga is changed to In (1Me to 3), the HOMO-LUMO gap decreases by 0.17 eV or 8.25%. We observe a similar trend when the halide atoms are substituted. The substitution of the halide atom also reduces the HOMO-LUMO gap as one continues down the periodic table. When Cl is changed to F (1Me to 3), the HOMO-LUMO gap increases by 0.07 eV or 3.40%. When Cl is changed to Br (1Me to 4), the HOMO-LUMO gap decreases by 0.04 eV or 1.94%.
Previous studies by our group and others use quantum chemical calculations to shed light on the superatomic nature of 1.13,22,23 According to the superatom (complex) model, the molecular orbitals on the cluster core arise from the iterant valence electrons of the metal atom core.24 The electron counting rule for a superatom complex is
$${n}^{*}=N{v}_{A}-M-z$$
1
,
where n* is the number of iterant electrons of the system, N is the number of core metal atoms, vA is the number of valence electrons of the metal atom, M is the number of one-electron withdrawing ligands, and z is the overall charge of the system. Typically, n* satisfies one of the shell-closing numbers (2,8,18,34,58,92….) and is described as a superatom (complex) system. Phosphine is a neutral ligand.9 In the case of 1, the total number electrons contributing to the molecular orbital configuration is eight and its expected superatom electron configuration is 1S21P6. Therefore, the highest occupied molecular orbital (HOMO) is expected to have P-symmetry, while the lowest unoccupied molecular orbital (LUMO) should have D-symmetry. We find that our results are in good agreement with this model. Figure 3 shows the HOMO-1 (P) to LUMO + 2 (D) orbitals of both 1 and 1Me. Although the change in ligand composition alters the HOMO-LUMO gap significantly, the order and structure of the orbitals remains the same. This result can be seen for all changes in composition (i.e. post transition metal atom and halide atoms). Additional visualizations of the orbitals of all structures can be found in Table S1.
3.3 Optical Properties
Figure 4 shows the overall spectroscopic profiles of the studied structures. Although the systems all have the same number of gold atoms and a similar core structure, there are clear differences in the optical absorption properties observed. The calculated absorption spectra of 1Me exhibits three prominent peaks at 366 nm, 430 nm, and 448 nm. This is in good agreement with the characteristic peaks observed in experiment and is also in the range of previously reported absorption maxima of gold clusters.13,25 At 366 nm, the transition originated from a state 0.15 eV below the highest occupied molecular orbital (HOMO-1), a superatomic 1P state, and transitions to a state 1.40 eV above the lowest unoccupied molecular orbital (LUMO + 6), a superatomic 1D state. The simulated peaks at 430 nm and 448 nm originate from the same state 0.26 eV below the highest occupied molecular orbital (HOMO-2), a superatomic 1P state, and transition to states 0.26 eV above the lowest unoccupied molecular orbital (LUMO + 1 and LUMO + 2), superatomic 1D states. The calculated spectra of 1H is in good agreement with the absorption spectra of 1Me however, the first peak exhibits a bathochromic shift (otherwise known as red-shift) while the last two peaks exhibit hypsochromic shifts (otherwise known as blue-shift). This type of shifting has been observed in previous studies of clusters where the ligand was reduced.26 The prominent peaks are now witnessed at 402 nm, 419 nm, and 441 nm. While the last two peaks (419 and 441 nm) originate from the same transitions as 1Me, the transition at 402 nm originates from a state 0.36 below the highest occupied molecular orbital (HOMO-2) and transitions to a state 0.26 eV above the lowest unoccupied molecular orbital (LUMO + 3). These changes in optical properties show that ligand composition plays a very important role on obtaining optical spectra. While reduction of the ligand is common practice to reduce computational time, according to the data found here, reducing the ligand of the structure could have substantial effect on the observed properties making it impossible to compare to experimental data.
Figure 4B shows that changing the group III atom has an effect on the optical properties of the studied system (1Me). When the Gallium atom is substituted for Aluminum (structure 2), we find that there is only one prominent peak in the spectra at around 441 nm. While there is only one pronounced peak, we find that several transitions contribute this peak. However, the transitions originate from the same state 0.01 eV below the highest occupied molecular orbital (HOMO-1) and transition to states 0.11 eV and 0.39 eV above the lowest unoccupied molecular orbital (LUMO + 1 and LUMO + 4). When the Gallium atom is substituted to Indium (structure 3), we find that there is a bathochromic shift (otherwise known as red shift) of all the peaks. Prominent peaks can now be observed at 378 nm, 440 nm, and 460 nm. At 378 nm, the transition originated from the highest occupied molecular orbital (superatomic 1P) and transitioned to a state 1.50 eV above the lowest unoccupied molecular orbital (LUMO + 6) (superatomic 1D). The peaks at 440 nm and 460 nm are in good agreement with 1Me, both originating from the same state 0.67 eV below the highest occupied molecular orbital (HOMO-2) and transitioning to states 0.17 eV and 0.34 eV above the lowest unoccupied molecular orbital (LUMO + 1 and LUMO + 3). Interestingly, we also find another noticeable peak at 416 nm that is not witnessed in any of the other spectra. The transition at 416 nm originates from a state 0.12 eV below the highest occupied molecular orbital and transition to a state 0.84 eV above the lowest unoccupied molecular orbital (LUMO + 4).
Lastly, we investigated the effects of changing the halide atoms on the optical properties. Figure 4C shows the transitions exhibited when the chlorine atom is replaced by both fluorine and bromine (Structures 4 and 5). In both structures 4 and 5, we witness a bathochromic shift of the peaks. We find that as one continues down the periodic table, the optical spectra exhibits greater red shifts. When the chlorine atoms are substituted for fluorine, the prominent peaks occur at 402 nm, 436 nm, and 458 nm. At 402 nm, the transition originates from a state 0.22 eV below the highest occupied molecular orbital (HOMO-2) and transitions to a state 0.34 eV above the lowest unoccupied molecular orbital (LUMO + 2). The transitions at both peak 436 nm and 458 nm both originate from a state 0.13 eV below the highest occupied molecular orbital (HOMO-1) and transition to states 0.42 eV and 0.21 eV above the lowest occupied molecular orbital (LUMO + 3 and LUMO + 1) respectively. When the chlorine atoms are substituted for bromine, the prominent peaks occur at 376 nm, 423 nm, and 454 nm. The transition at 376 nm originates from a state 0.14 eV below the highest occupied molecular orbital (HOMO-1) and transitions to a state 1.20 eV above the lowest unoccupied molecular orbital (LUMO + 5). The peak at 423 nm originates from a state 0.24 eV below the highest occupied molecular orbital (HOMO-2) and transitions to a state 0.55 eV above the lowest unoccupied molecular orbital (LUMO + 4).The peak at 454 nm originates from the highest occupied molecular orbital and transitions to the same state as the peak at 423 nm, 0.55 eV above the lowest unoccupied molecular orbital (LUMO + 4). While change in the halide atom did not have the same impact on the HOMO-LUMO gap as some of the other changes in composition, it still played a major role in the appearance of the optical spectra.