Atomically precise nanoclusters have excited the science community in part because they possess specific geometric, 1-3 optical 4,5 and photoluminescent [6][7][8] properties that depend sensitively on the various sizes and shapes of the nanoclusters (NCs). The demand for these NCs is increasing, as they can be controlled with atomic precision, and therefore, they provide an alternative to bulk materials or larger nanomaterials because they have precise electronic and geometric structure. 9-12 A well-known example of this is [Au25(SR)18] 1-, which was structurally determined by the Murray and Jin groups in 2008. 13,14 Since 2008, experimental and theoretical groups have showed that the properties of this cluster can be tuned for different applications such as photodynamic therapy, 15,16 small molecule activation, [17][18][19] biosensing, 20,21 and more. The immense applicability of [Au25(SR)18] 1-has further trigged a variety of theoretical and experimental studies benchmarking the properties of thiolate-protected nanoclusters with different sizes, shapes, ligands, and charge states. [22][23][24][25][26] In addition to changing the ligand shell or surface structure of the nanocluster, controlled modification of the metal core via doping has become an exciting new progression of this work. Au24M(SR)18 clusters (M = dopant) have become star models in understanding the role of the dopant in thiolate-protected clusters, 27 largely because the parent cluster, [Au25(SR)18] 1-, has been thoroughly studied. [28][29][30][31][32] Out of the immense number of transition metal dopants, Au24Pt(SR)18 stands out, as it is an exceptional catalyst 33 as well as a robust oxidizer. 34 Despite initial difficulties to structurally characterize this cluster, which arises in part due to the similarities between Pt and Au, 34,35 the crystal structure was accomplished by Jin and coworkers in 2012. 36 Since that time, several structures of Au24Pt(SR)18 have been used to theoretically and experimentally describe the Au-Pt bonding, 37 the cluster stability, 31 the large catalytic activity, 34 the optical properties, and more. As the electronic structure of a doped cluster is dictated by the type of dopant, the precise dopant location, and synthetically, by the dopant concentration, [38][39][40] Au24Pt(SR)18 is a perfect model to examine how the properties change with a heteroatom dopant.
One of the reasons that thiolate-protected clusters stand out is their high stability, which can be traced back to geometric and electronic effects that can be understood from the superatom model. 41,42 Analogous to atomic theory, superatomic electrons occupy a set of delocalized superatomic orbitals that possess the symmetries of spherical harmonic functions. 43 For instance, similar to an atomic p orbital, there would be a set of three superatomic P molecular orbitals (MOs) that would be energetically degenerate if the nanocluster has perfect spherical symmetry. 44 These molecular orbitals are usually comprised of 6s contributions from the gold atoms in the core of the nanocluster. In the case of [Au25(SR)18] 1-, there are eight superatomic electrons that create a S 2 P 6 configuration. 45 This configuration is equivalent to the atomic configuration of a noble gas, which is one reason why the cluster is so stable. Neutral Au24Pt(SR)18, on the other hand, has a S 2 P 4 configuration as a result of the six superatomic electrons present in this system, which results in one empty superatomic P orbital. 19,46 Because that first unoccupied orbital is empty, the first two excited state transitions (P→P) are dipoleforbidden, and hence, Au24Pt(SR)18 clusters have shown to have similar absorption trends to [Au25(SR)18] 1+ , as well as similar electron dynamics to the open shell neutral Au25(SR)18 cluster. 47 The Pt dopant is thought to accelerate the core-shell coupling, which results in a faster relaxation to the ground state as compared to [Au25(SR)18] 1-. 48,49 While there is some literature on how the Pt dopant changes the electron dynamics mechanisms compared to the parent cluster based on 2DES and TA measurements, no experimental photoluminescence (PL) emission peak is present in the range of 600-1600 nm. 50 The reason for the missing emission in Pt-doped clusters is unclear, perpetuating the need for theoretical studies. Further, among the Au24Pt(SR)18 literature, several different ligands have been used. Negishi and coworkers showed in 2019 that there is a large difference in geometry as well as optical absorption spectra when R=PET (PET = 2-phenylethanethiolate) and R=TBBT (TBBT = 4-tert-butylbenzenethiolate) in Au24Pt(SR)18. 35 While some gold nanoclusters with the same core size have shown similar optical properties between ligands, 51 small nanoclusters such as Au24Pt(SR)18 experience a larger influence from the bulkiness of the ligand shell. 40 This paper will therefore provide a theoretical look into the electronic structure, optical, and photoluminescent properties of Au24Pt(SH)18 and Au24Pt(C3H7)18 and examine how the dopant changes the properties compared to [Au25(SR)18] 1-.
All calculations with Au24Pt(SH)18 were performed using the Amsterdam Density Functional (ADF) 2016.101 package, and all calculations of Au24Pt(C3H7)18 and [Au25(SC3H7)18] 1-were completed using the ADF 2018.105 package. 52 Several experimental crystal structures of [Au25(PET)18] 1-(Refs. 13,14,29,53,54 ) with removed phenyl groups were used as initial input structures for the theoretical calculations of [Au25(SC3H7)18] 1-. The lowest energy isomer was initially used with single atom Pt replacements as initial input structures to optimize Au24Pt(C3H7)18. The core structure was later edited with a more flattened-oblate structure to help the calculation converge. For Au24Pt(SH)18, the crystal structure of [Au25(SR)18] 1-(Refs. 3,13) with single atom Pt replacements was used as an input structure for all calculations. The Au24Pt(SR)18 results are obtained with a neutral charge state to match experiment. Scalar relativistic effects were included by utilizing the zeroth-order regular approximation (ZORA). 55,56 All calculations were completed at the BP86/DZ level of theory. BP86 is a generalized gradient approximation (GGA) exchange-correlation functional, 57,58 and DZ refers to a double-zeta basis set. Additional calculations are performed at the BP86/TZP level of theory for benchmark purposes, where TZP is a triple-zeta polarized basis set. The structure was optimized in the gas phase for all calculations, and the energy and gradient convergence criteria were tightened to 1x10 -4 Hartree and 1x10 -3 Hartree respectively for geometric accuracy. All calculations had a tightened SCF convergence requirement of 1x10 -8 . The theoretical absorption spectrum was calculated with linear response time-dependent density-functional theory (TDDFT), 59 where the vertical excitation energies were convolved with a gaussian fit with a fullwidth half-maximum (FWHM) of 0.15 eV. TDDFT analytical excited state gradients 60 were used to optimize the S1-S21 states for R=H and R=C3H7 using the same convergence criteria and level of theory as the ground state. All pictures of the molecular orbitals were created with the ADF graphical user interface (GUI) and presented with a contour value of 0.015.
A. Geometric Structure Au24Pt(SR)18 has the same general shape as [Au25(SR)18] 1-and is composed of a 13 atom 'icosahedron' core with 6 Au2S3 motifs that protect the core by forming rigid V-shaped S-Au-S-Au-S staples that are further protected by organic ligands. It has been shown that the Pt dopant prefers the center position in the core of the nanocluster. 27,35,37,45 This paper additionally supports the conclusion that the Pt dopant prefers the center of the core; energies at the BP86/DZ and BP86/TZP levels of theory are provided in table S1 for various isomers with R=C3H7. For simplicity, the term 'icosahedron' refers to the general shape of the core, even though the core of Au24Pt(SR)18 is not made up of 20 equivalent equilateral triangles but more of a flattened triangle base, as seen by figure S1. This breaking of spherical symmetry creates a distorted oblate ellipsoid 61 and is a direct result of the Jahn-Teller effect, which occurs because the P orbitals are not completely filled. 62 The core distortion from the dopant is more prominent with the larger ligand, and in fact, this geometric change between ligands can be qualitatively observed in pictures (figure 1). The optimized ground state (S0) structures in both clusters experience an elongation of two specific Au core -Pt center bonds that have an average distance of 2.850 Å in Au24Pt(SH)18 and 2.940 Å in Au24Pt(C3H7)18. With the larger C3H7 ligand these two bonds are ~0.11 Å larger than the rest of the Au core -Pt center bonds, whereas in Au24Pt(SH)18, the elongated bonds are only 0.03 Å larger than the rest of the Au center -Pt bonds. Despite the almost identical average Au-S-C angle of 103.7° for [Au25(SC3H7)18] 1-and Au24Pt(SC3H7)18 at the BP86/DZ level of theory, the orientation of the propyl groups changes in one S-Au-S staple. To be more specific, in the lowest energy isomer of [Au25(SC3H7)18] 1-, the propyl groups attach to the Au2S3 staples in alternating cis/trans configurations, exhibited in figure S2. 63 In Au24Pt(SC3H7)18, one of the Au2S6 staples has a trans/trans orientation rather than a cis/trans orientation. As a consequence of this change, the propyl groups attached to two nearby staples create gauche/gauche/anti and gauche/anti/anti configurations, which is quite different from the all-anti configuration that is present in the propyl groups of the [Au25(SC3H7)18] 1-cluster. This shows that not only does the Pt atom distort the core, but also the shell of the nanocluster, the attachment of the propyl groups to the shell, and the configurations of the propyl groups themselves. In 2019, it was found that the interaction between phenyl groups in the TBBT ligand leads to a higher symmetry as compared to the PET ligand. 35 The work demonstrated that with that higher symmetry ligand (TBBT), the metal core shrinks. This same relationship is seen between hydrogen and propyl groups as the Pt center-Au core and Au core-Au core bonds both shrink ~0.03 Å with the more symmetric ligand (R=H). Despite the difference in electronic structure, the average bond distances in Au24Pt(SH)18 and [Au25(SR)18] 1- are very similar, differing less than 0.006 Å in the core/shell as seen in table 1. Au24Pt(SC3H7)18, on the other hand, differs quite a bit more compared to [Au25(SR)18] 1-: ~0.03 Å in the core and ~0.02 Å in the Au-S and S-S bonds. While the Jahn-Teller effects are still present in Au24Pt(SH)18, the symmetry distortion is more exaggerated with the larger ligand.
These large geometric changes between the parent and the doped cluster originate from the breaking of spherical symmetry of the superatomic orbitals. As illustrated through the molecular orbital (MO) diagram in figure S4, the HOMO and HOMO-1 MOs are essentially degenerate in Au24Pt(SH)18, only differing by 0.03 eV. The larger symmetry distortion in Au24Pt(SC3H7)18 results in a larger splitting of the HOMO and HOMO-1 MOs, which have a difference in energy of 0.11 eV. The empty superatomic P MO differs significantly in energy from the two other P MOs that are occupied. Au24Pt(SR)18 clusters have a completely different electronic structure than [Au25(SR)18] 1-because of this difference in P superatomic MO occupation. This results in much smaller HOMO (H) -LUMO (L) gaps of 0.37 eV and 0.42 eV for Au24Pt(SR)18 with R=H and R=C3H7, respectively, compared to a H-L gap of 1.11 eV in [Au25(SC3H7)18] 1-. Images of the first six frontier MOs for the Pt-doped systems (H-2 through L+2) can be seen in figure S5.
In the literature, the energy of the main peak for Au24Pt(SR)18 clusters has ranged from 2.07 -2.12 eV, [33][34][35]64 with two other optical features of note: one broad band in the IR range, and one high energy shoulder on the edge of the UV spectrum. These three spectral features are similar to those seen in [Au25(SR)18] q clusters (q = -1,0,+1), where the anionic cluster has a high energy shoulder around 403 nm (3.08 eV), a peak at 450 nm (2.76 eV) and a broad peak around 680 nm (1.81 eV). 62 When the cluster starts to lose electrons, i.e. goes from the anionic to cationic cluster, and hence goes from a fully filled P shell to an empty P shell, the shoulder has slightly higher energy at 3.15 eV, the main peak redshifts to about 2.58 eV, and the broad band blue-shifts to ~1.88 eV. 29 Similar optical shifts are also seen with the Pt atom as Au24Pt(SR)18 clusters have an experimental high energy shoulder at 400 nm (3.10 eV) that slightly blueshifts compared to [Au25(SR)18] 1-, and the main peak is redshifted to 2.10 eV. 36,61 At the BP86/DZ level of theory, the spectral shape between the experimental absorption spectrum and theory matches almost identically as seen in figure S6. Depending on the ligand, the high energy shoulder is around 420 or 450 nm (2.76 or 2.95 eV), the main peak is around 550-590 nm (2.1-2.25 eV) and the broad peak at the lower energy park of the spectrum is in the 700-900 nm range (1.37-1.77 eV).
The low energy peak attributed to the band from 770-870 nm is a combination of two dominant excitations for each nanocluster. The two strongest transitions in this energy range lie at 1.62 eV and 1.66 eV for R=H (table 2), which are S20 and S21 for this system (table S2). The two strongest transitions for R=C3H7, are a little more split, with excitation energies of 1.43 and 1.54 eV (table 2), which are S14 and S17 for this system. For both ligands, the lower energy peak arises as a result of an excitation between an occupied superatomic P MO (H or H-1) to one of the two lowest energy superatomic D virtual MOs (L+1 or L+2). In the propyl ligand, an additional transition from a MO with large d-atomic orbital contributions from the gold atoms (H-13) transitions into the empty P LUMO which starts to mix with the P→D transition. This mixing is only present with the larger ligand. In general, the propyl system exhibits more mixing and splitting, which is likely due to its greater geometrical distortion from an idealized icosahedral core.
The dominant peak observed in the spectrum, corresponding to the ~600 nm experimental peak, is very different between the two ligands (figure 2). For the propyl ligand, there is one dominant excitation at 2.17 eV that makes up the peak with mixed P→D and d→P character, whereas for hydrogen, there are several excitations around 2.20 eV that make up the peak. The excitation with the largest oscillator strength lies at 2.30 eV and is made up of a dominant P→D transition. To observe the differences from the Pt dopant, the absorption energies for S1-S21 were calculated at the BP86/DZ level of theory, along with the type of transitions responsible for each excitation (table S2). Only the first 21 states were analyzed in detail; however, the first 1500 excitations were calculated to create the full theoretical spectrum (figure S6). It is worth noting that the first two excitations, S1 and S2, for Au24Pt(SR)18 originate from dipole-forbidden transitions (P→P). These transitions are present in the theoretical spectrum at 0.42 eV and 0.45 eV or 0.47 eV and 0.59 eV for the hydrogen and propyl groups, respectively. In comparison, [Au25(SC3H7)18] 1-has three vertical excitations that make up the first peak, and all of these excitations arise from P→D transitions. The excitation with the largest oscillator strength is at 1.36 eV, which is a slightly lower absorption energy than the first peak with the Pt dopant. Other density functional theory (DFT) studies resulted in an absorption energy of 1.32 eV for [Au25(SC3H7)18] 1-at the same level of theory, which matches well with our work. 63 Table 2. Absorption details of the vertical excitation energies that make up the dominant peaks in the absorption spectrum (figure 2) at the BP86/DZ level of theory in Au24Pt(SR)18 for R = H and R = C3H7.
In 2016, the S1 state of [Au25(SR)18] 1-was reported to be the emissive state originating from a superatomic P→D transition in the core of the nanocluster. 63 Because the S1 state arises from P→P transitions in Au24Pt(SR)18 clusters, these clusters will undergo a very different PL mechanism from the [Au25(SR)18] 1-cluster. Excited state optimization calculations on the S1 and S2 excited states of the Au24Pt(SR)18 clusters failed due to near-degeneracies with the ground state, which indicate that a conical intersection is nearby. Nonradiative relaxation occurs quickly near conical intersections, so these findings indicate that the S1 and S2 states are unlikely to yield emission with an appreciable quantum yield. This conical intersection likely occurs because the P orbitals that provided the HOMO and LUMO in the ground state can become degenerate once the nanocluster has appropriately distorted during the excited state relaxation process. To examine the PL mechanism further, higher excited state geometry optimizations were completed. Two states (S3, S19) in Au24Pt(SC3H7)18 and three states (S15, S18, S21) out of the first 21 in Au24Pt(SH)18 converged geometrically to our chosen criteria, rather than failing due to quasidegeneracies with the next lower energy excited state. Out of the five minima found for the two clusters, three of the excited states originate from d→P transitions (S3, S15, S18, S19). Some of these excited states have optimized HOMO-LUMO gaps that are less than 0.10 eV (table 3). Of note, the S15, S18 and S19 states have very small energy gaps between the optimized excited state geometries and the state below (denoted as n-1, where n is the optimized excited state). A smaller energetic gap between orbitals leads to more efficient coupling of the excited state with the ground state, promoting a nonradiative transition over the emission of a photon. 48 Thus, the system is unlikely to remain in these geometries for any significant amount of time. The Sn -Sn-1 gap is a little larger for the S3 state, at 0.28 eV. Even though we were unable to fully converge the S3 geometry when R=H, we observe a similar energy gap between S3 and S2. The separation between the S3 and the S2 state could potentially be large enough to observe emission; however, this emission is predicted to be very low in energy (< 0.51 eV) and may be outside of typical experimental windows.
The S21 state is unique, originating from a dipole allowed P→D transition with a predicted emission energy of 1.52 eV. At the optimized S21 geometry, the nanocluster has a relatively large HOMO-LUMO gap of 0.23 eV. This value is not as large as the optimized H-L gap in the S1 state of [Au25(SR)18] 1-(0.83 eV); 63 however, the energy gap could be large enough to potentially emit a photon. At the optimized S21 state, however, the S20 energy only differs by 0.002 eV from the S21 energy. As the energy difference is negligible between the two states, it is likely that a system in the S21 state would quickly cross to the S20 state. While likely not an emissive minimum, the S21 state does have a more unique electronic structure than the other excited state minima. The purely radiative lifetime of the S21 state is predicted to be 0.42 μs, which is ~45x faster than the radiative lifetime value of 19.36 μs from the S1 state in [Au25(SR)18] 1-, predicted by the Fermi-Golden rule. Geometrically, the there is no notable difference between the S0 and S21 states, as each type of bond changes less than 0.005 Å (table S3).
Overall, this work shows that all the minima found from the first 21 excited singlet states would likely exhibit nonradiative relaxation rather than the emission of a photon, and therefore, these findings indicate that there is not an emissive state for the Au24Pt(SR)18 cluster in the 600-1600 nm energy range. Transient absorption and other pump/probe experiments have been used to try and gain insights into the excited state relaxation mechanism by exciting higher energy states. These studies have concluded that excited state deactivation includes ultrafast (∼0.6 ps) relaxation within the core states, several picoseconds of core relaxation to surface states, followed by slow relaxation (>1 ns) back to the ground state. 47 Further, it was shown that the core states should not contribute to the TA signal after 30 ps. 49 The present theoretical work indicates that there are no charge transfer surface or 'trap' states between the superatomic core states, but there are no likely candidates for singlet states that would undergo radiative relaxation. The full picture of electronic relaxation in the Au24Pt(SR)18 nanocluster is not complete without a nonradiative analysis, which would require nonadiabatic calculations that are outside the scope of this work.
Heteroatom dopants have provided a new way to tune the geometric, optical and photoluminescent properties of atomically precise thiolate protected gold nanoclusters for several different applications. Known for their large catalytic ability, Au24Pt(SR)18 clusters provide a good example of how the distortion from a different superatomic electron count directly changes the properties of [Au25(SR)18] 1-. (TD)DFT calculations were performed to investigate these changes in the gas phase. Geometrically, the dopant distorts the parent cluster from an icosahedron to an ellipsoid, redshifts the absorption energy of the main peak and quenches the photoluminescence. Replacing the small hydrogen groups with a bulkier ligand, such as propyl, creates more distortion in the core/shell structure both geometrically and electronically, and redshifts the absorption energy. Higher excited state calculations suggest that there is not an emissive electronic state due to the small energy gaps between orbitals, but instead, nonradiative relaxation mechanisms are expected to dominate in the excited state dynamics mechanism. No charge-transfer or surface states are observed in this work, which suggests that the change in the superatomic P electron count in the electronic structure of the core is the primary origin for the change in photoluminescence properties observed between the doped and parent cluster.