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American Chemical Society

10.1021/acsomega.4c02724
Article
Tube-like Gold Clusters M2@Au17q (M = W, Mo; q = 0, ±1): Structure, Electronic Property, and Optical Nonlinearity
https://orcid.org/0000-0002-1485-6569
Nhat Pham Vu †
Trang Nguyen Thi Bao ‡
https://orcid.org/0000-0003-1769-4873
Dang Minh Triet ‡
Thanh Si Nguyen §
Thao Tran Thi Ngoc ∥
Thao Pham Thi Bich ∥
https://orcid.org/0000-0002-3803-0569
Nguyen Minh Tho *⊥#
† Molecule and Materials Modeling Laboratory, Department of Chemistry, Can Tho University, Can Tho 90000, Vietnam
‡ School of Education, Can Tho University, Can Tho 90000, Vietnam
§ Institute of Environmental Science and Technology, Tra Vinh University, Tra Vinh 94000, Vietnam
∥ Department of Physics, Can Tho University, Can Tho 90000, Vietnam
⊥ Laboratory for Chemical Computation and Modeling, Institute for Computational Science and Artificial Intelligence, Van Lang University, Ho Chi Minh 70000, Vietnam
# Faculty of Applied Technology, School of Technology, Van Lang University, Ho Chi Minh 70000, Vietnam
* Email: minhtho.nguyen@vlu.edu.vn.
08 09 2024
17 09 2024
9 37 3846738476
20 03 2024
31 07 2024
30 07 2024
© 2024 The Authors. Published by American Chemical Society
2024
The Authors
https://creativecommons.org/licenses/by-nc-nd/4.0/ Permits non-commercial access and re-use, provided that author attribution and integrity are maintained; but does not permit creation of adaptations or other derivative works (https://creativecommons.org/licenses/by-nc-nd/4.0/).

Density functional theory (DFT) calculations are carried out to determine the geometries and electronic and nonlinear optical (NLO) properties of the doubly doped gold clusters in three charge states M2 @ Au17q with M = W, Mo and q = 0, ±1. At their lowest-lying equilibrium structures, the impurities that are vertically encapsulated inside a cylindrical gold framework, significantly enhance the stability and modify properties of the host. The presence of M2 units results in the formation of a tube-like ground state, which is identified for the first time for gold clusters. Having 30 itinerant electrons, the electron shell of M2@Au17– can be described as 1S21P61D102S2{1Fxz221Fyz22}1Fz32{1Fxyz21Fz(x2–y2)2}{1Fy(3x2–y2),1Fx(x2–3y2)}. The species is thus stabilized upon doping, but it is not a magic cluster. The optical transitions are shifted to the lower-energy region upon doping Mo and W atoms into Au17q. The static and dynamic NLO properties of M2@Au17q are also computed and compared to those of the pure Au19q (having the same number of atoms) and an external reference molecule, i.e., para-nitroaniline (p-NA). For hyperpolarizabilities, the doped clusters possess smaller values than those of their pure counterparts but much larger values than the p-NA. Of the doubly doped systems, the neutral M2@Au17 exhibits particularly high first and second hyperpolarizability tensors. The doped cluster units can also be used as building blocks for the design of gold-based nanowires with outstanding electronic and optical characteristics.

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pmc1 Introduction

There has been continuously growing attention in metal clusters as a deep understanding of their structure and physicochemical properties provides us with a bridge between their isolated atoms or molecules and their bulk materials. In particular, numerous experimental and theoretical studies have been devoted to gold clusters in recent times to emphasize their nonconventional properties due to the relativistic effects, and in part due to important applications in the fields of catalysis,1−3 chemical/biological sensors,4 and biomedical sciences.5 Contrary to the peculiar inertness of its bulk, gold in the nanoscale form or when finely dispersed on metal oxide surfaces typically exerts an efficient catalytic activity for many gas-phase reactions.6,7 In addition, gold nanomaterials are willing to conjugate to a variety of bimolecular systems and induce a much lower toxicity to human bodies than many other metallic elements.8 Therefore, gold nanoparticles are more and more frequently employed in medical applications such as drug delivery systems.9,10 Moreover, they possess superior optical properties as compared to other transition metals, and thus have attracted a great deal of interest in the field of biosensors and biomedical diagnostics.11−13 It can be argued that gold nanoclusters are among the most characterized atomic aggregates to date by both experimental techniques,14−17 and computational methods.18−22

Investigations into doping with foreign metals in pure gold clusters have also arisen in recent times. The presence of a doping element is expected to effectively improve the pure host properties in a more desirable fashion. A combined experimental and theoretical study using trapped ion electron diffraction, photoelectron spectroscopy, and density functional theory (DFT) confirmed the existence of highly symmetric golden cages M@Au16– (M = Fe, Co, Ni, Cu).23 It was noticeably found that although the magnetic moment of the impurity is slightly reduced, the host framework could play as a suitable accommodation to protect the magnetism of the dopant atom.24,25 Other golden cages, i.e., M@Au12 and M@Au17, with M being a transition metal, were also found to possess a high thermodynamic stability and significantly improved frontier orbital energy gaps.26−28 The effects of dopant atoms on the spectroscopic properties and reactivity of small gold clusters toward nucleophilic reagents have also been extensively reported.29−32 Besides singly doped systems, multiply metal-doped gold clusters have also attracted an increasing interest for their unexpected properties and promising applications.33−35 Recent DFT calculations combined with photoelectron spectroscopy36,37 have observed high symmetry structures and particularly thermodynamic stability of bimetallic gold clusters doped with the Nb2 unit. Such an observation is expected to open an avenue for making a new class of mixed clusters having tailor-made properties.

There is also a continuing interest in materials with pronounced nonlinear optical (NLO) responses since they were used for various optoelectronic applications including optical computing, data storage, image processing, optical switches for photonics, optical fibers, and optical signal processing.38,39 It has been well established in the recent literature that gold-containing nanoscale materials typically exhibit excellent NLO properties.40 Moreover, doping with other transition metals is also expected to significantly improve the NLO response of gold-based clusters.41 While linear and NLO properties of pure gold and singly doped clusters with another metal element have been reported,40,42 such information for the doubly doped gold clusters remains rather limited.

In this context, we report in the present paper some remarkable effects induced by the dimeric Mo2 and W2 units not only on the geometry and stability but also on the NLO response of gold clusters. Even though small, pure Aun clusters with n < 10 tend to exist as planar or quasi-planar shapes, while larger sizes up to n = 18 tend to exist as hollow cages,20,22,43 we report here, for the first time, that a triple-ring cylindrical form turns out to be the most preferred structure of the doubly doped M2@Au17q clusters with the dopant M = W, Mo in the charge states q = 0, ±1. At the equilibrium points, the tube-like geometry of the Au17 size, which is not an equilibrium structure, is significantly stabilized by the M2 dimers vertically placed inside the golden spindle-like framework. We in addition examine the electronic structures and effects of such dopant metals on the polarizability and first and second hyperpolarizability parameters that usually characterize the NLO properties. Our computed results show that doping with an M2 dimer containing a strong bond such as Mo2 or W2 can be an effective approach to enhance the stability in a tubular form and tune the NLO properties of the resulting gold nanomaterials.

2 Computational Methods

Geometry optimizations of the M2@Au170/±1 clusters are carried out through DFT calculations using the exchange-correlation functional TPSS,44 in conjunction with a scalar relativistic effective core potential (ECP) basis set, namely the cc-pVDZ-PP.45 Such a basis is widely used to model heavy metal atoms as it can significantly reduce the computational cost while still yielding reliable results for many properties of systems considered.18,45 The TPSS functional has been found to be successful in predicting the equilibrium geometry of small gold clusters.20,22 Initial geometries of doped clusters are extensively generated using both the genetic algorithm and an empirical search using the previously known structures of the sizes Au17, Au18, and Au19 as starting points. Harmonic vibrational frequencies are subsequently calculated for optimized structures to determine their nature on the potential energy surface and to generate their zero-point energies and thermal correction values. All calculations in this study are performed using the Gaussian 16 program.46

In order to examine the LO and NLO responses of studied clusters, we compute the permanent dipole moment (μ), along with polarizability (α), and first and second hyperpolarizability (β and γ) in their ground state structures. Mathematically, the μ, α, β, and γ parameters are computed by eqs 1–8.191

2

3

4

5

6

7

8

where αij, βijk, and γijkl are the tensor components of polarizability, first hyperpolarizability, and second hyperpolarizability, respectively. The origin of the permanent dipole moment computed by default is the center of mass if the chemical system is neutral; otherwise, the center of nuclear charge is used as the origin.

The energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), i.e., HOMO–LUMO energy gap (HLG), is computed by the following equation:9

This is a plausible approach, as according to the Koopmans theorem, HOMO and LUMO energies are directly related to the vertical ionization energy (vIE) and vertical electron affinity (vEA) values, respectively.47 If there is no geometry relaxation during the ionization process, the energy difference between a cation and its neutral counterpart can be approached by the HOMO energy of the latter. Similarly, by applying the Koopmans theorem, one can derive a relation of the LUMO energy to the vEA value. We can also compute the HLG values by taking the HOMO and LUMO energies from the DFT computations. However, it should be noted that the electronic structure of transition metal clusters is typically multiconfigurational due to the existence of several quasi-degenerate electronic states.48 Therefore, most of the current DFT approaches normally yield large error margins, up to dozens of kcal/mol, for energies of both HOMO and LUMO levels because they are derived from unbalanced treatment of electron correlation.49,50

3 Results and Discussion

3.1 Equilibrium Structures

Local minima detected for the anions M2@Au17– (M = Mo, W) at the TPSS/cc-pVDZ-PP level are displayed in Figure 1, while their Cartesian coordinates are given in Table S1 of Supporting Information. At the equilibrium point, the lowest-lying clusters tend to exist as spindle-like structures, i.e., Mo·1 and W·1 in Figure 1, composing of three five-membered Au rings Au15 encapsulated with the M2 unit inside along the axis. The next stable isomer Mo·2 located for Mo2@Au17– is computed to be ∼15 kcal/mol higher in energy. The remaining structure Mo·3 is even much less stable as it is lying about 25 kcal/mol above Mo·1. Comparable structural arrangements are also obtained for Au17W2q species. While the energy difference between W·1 and W·2 conformations is around 15 kcal/mol, the third isomer W·3 is predicted to be less stable than W·1 by 25 kcal/mol. Overall, these results indicate that for the first time a gold cluster is obviously found to be favored in the tube-like form M·1. Numerous studies have been devoted to gold clusters functionalized with organic ligands, and the formation of either cylindrical or anisotropic structures has been found for several ligand-protected gold clusters such as Au22(dppo)6,51 and M2Au36(SR)24 (M = Au, Pd, Pt).52 However, the detection of such a structural motif with the dimer M2 encapsulated inside the Au17 tubular shell is of importance, as this is the first discovery in gas-phase gold clusters of such a form, which is rather popular in other classes of atomic clusters.

Figure 1 Some low-lying isomers of M2@Au17– (M = W, Mo) clusters along with the symmetry point group and relative energy with respect to the most stable form M·1. Relative energies given kcal/mol in parentheses are obtained from TPSS/cc-pVDZ-PP + ZPE computations.

Removal of one electron from the anions M2@Au17– to form the neutral M2@Au15 is accompanied by a minor structural modification. Both neutral Mo2@Au17 and W2@Au17 clusters still adopt a tubular motif similar to that of M·1 as their global minima. However, owing to an open-shell electronic structure, they tend to undergo a Jahn–Teller distortion, giving rise to a lower symmetry structure, instead of a regular pentagonal D5h spindle-like structure as in the corresponding anions. Indeed, the ground state structure of M2@Au17 now has a symmetry of Cs and a doublet 2A″ electronic state. The second most stable isomers M·2 are computed to be less stable than M·1 by ∼9 and ∼12 kcal/mol for Mo2@Au17– and W2@Au17–, respectively.

Similarly, the cations M2@Au17+ also prefer to exist as a lower symmetry configuration (C2v), which are derived from a slightly structural relaxation of the regular pentagonal D5h spindle. However, while W2@Au17+ prefers a low spin electronic ground state (1A1), the triplet 3B1 state is predicted to be the lowest-lying energy for Mo2 @ Au17+. The singlet 1A1 state of Mo·1 is the first excited state for Mo2@Au17+ with a minor energy gap of ∼1 kcal/mol above the 3B1 state (TPSS value). Such a tiny energy gap suggests a quasi-degeneracy of these two electronic states. The remaining isomers M·2 and M·3 (Figure 1) are also located as local minima on the potential energy surface of both Mo2@Au17+ and W2@Au17+. Their symmetry, electronic states, and relative energies corresponding to the most stable form M·1 are given in Table 1.

Table 1 Symmetry Point Group, Electronic State, and Relative Energy (RE, kcal/mol) of Low-Lying States Obtained for Au17M20/±1 Clusters at the TPSS/cc-pVDZ-PP + ZPE Level

isomer	M2@Au17–	M2@Au17	M2@Au17+	
symmetry	state	RE	symmetry	state	RE	symmetry	state	RE	
Mo·1	D5h	1A1′	0.0	Cs	2A″	0.0	C2v	3B1	0.0	
Mo·2	Cs	1A′	14.5	Cs	2A′	8.9	Cs	1A′	3.6	
Mo·3	Cs	1A′	25.1	Cs	2A′	21.1	Cs	1A1	12.7	
W·1	D5h	1A1′	0.0	Cs	2A″	0.0	C2v	1A1	0.0	
W·2	Cs	1A′	14.8	Cs	2A′	12.0	Cs	1A′	4.4	
W·3	Cs	1A′	24.7	Cs	2A′	20.6	C1	1A	10.4	

The M–M bond lengths in the M·1 equilibrium structures are computed to be 2.54 and 2.65 Å for Mo2@Au17– and W2@Au17–, respectively, that are longer than the corresponding M–M distances of 1.94 and 2.02 Å in isolated Mo2 and W2 dimers. Our computed bond length of 1.941 Å obtained for Mo2 is comparable to the corresponding experimental value of 1.938 Å,21 while that of 2.017 Å of W2 is also quite close to the previous CCSD(T) value of 2.020 Å.53 The Mo–Mo bond distances in Mo2@Au17 and Mo2@Au17+ are computed to be about 2.50 and 2.47 Å, respectively, which are slightly shorter than the value of 2.54 Å in Mo2@Au17–. Similarly, the W–W bond length of 2.58 Å in the cation W2@Au17+ is also shorter than the corresponding values of 2.61 and 2.65 Å in W2@Au17 and W2@Au17–, respectively. Overall, the M–M distances are decreased in the order M2@Au17– > M2@Au17 > M2@Au17+. In other words, electron detachment tends to strengthen the M–M bonding interaction.

Recent quantum chemical calculations combined with far-IR multiple photon dissociation (FIR-MPD) spectroscopy confirmed that the neutral Au17 favors a star-like form,22 whereas a hollow cage54 and an amorphous form55 are located for Au17– and Au17+, respectively. On the contrary, while the cation Au19+ tends to exist as a hollow cage (cf. Figure S1 of Supporting Information), its neutral and anionic states are likely to exist as a truncated pyramid.56 It is clearly seen for small gold clusters up to Au20 that the cylinder-like shape is not even a local minimum on the energy potential surface, and removing or adding an electron typically leads to a substantial tune on their structures. With the presence of dimer M2, the cylindrical conformation turns out to be the most preferred structure of M2@Au17q species. Moreover, unlike the pure systems, the doped counterparts undergo a minor structural modification upon electron removal or addition.

3.2 Effects of Dopants on the Stability of Gold Clusters

The stability of clusters is usually evaluated via the binding energy per atom (BE) and the detachment energy (DE). As shown in Table 2, both Au– and Au are much more difficult to detach electron than the M– and M dopant, respectively. Therefore, the BE values of M2 @ Au170/±1 are calculated by the following eqs 10–12:10

11

12

Table 2 Electron Affinity (EA) and Ionization Energy (IE) of Elements, Clusters, and Dimers in Gas Phasea

 	Au	W	Mo	Au17	W2	Mo2	
EA (eV)	2.31	0.82	0.75	3.72	0.90	0.67	
IE (eV)	9.22	7.98	7.09	6.55	6.61	7.53	
a Experimental values for Au, W, and Mo are taken from NIST Database,57 while those of Au17, W2, and Mo2 are computed at the TPSS/cc-pVDZ-PP + ZPE level.

Moreover, we find that the pure Au17 cluster also has lower IE and higher EA values than the dimer M2, indicating that it is more difficult for the latter to attach or detach an electron than for the former. Therefore, the DE values of M2@Au170/±1 species are computed as follows (eqs 13–15):13

14

15

The computed BE and DE values of M2@Au170/±1 are presented in Table 3, which also comprises, for the purpose of comparison, those of the closed size Au190/±1 and the well-known magic cluster Au20.58 Geometries of pure gold clusters are collected from recent reports,55,59,60 and then reoptimized using the TPSS functional with the cc-pVDZ-PP basis set.

Table 3 Binding Energy per Atom (BE), Dissociation Energy (DE), Vertical Electron Affinity (vEA), Vertical Ionization Energy (vIE), and HOMO–LUMO Gap (HLG) of Clusters Considereda

species	BE	DE	vEA	vIE	HLG	
(kcal/mol)	(eV)	
Mo2@Au17–	62.1	182.5	–0.69	3.02	3.71	
Mo2@Au17	60.8	199.7	2.94	6.20	3.26	
Mo2@Au17+	62.2	209.2	6.11	9.46	3.36	
W2@Au17–	65.8	237.7	–0.57	3.03	3.60	
W2@Au17	64.5	254.9	2.93	6.14	3.20	
W2@Au17+	67.0	265.2	6.08	9.42	3.34	
Au19–	55.5	77.9	–0.25	3.53	3.78	
Au19	53.6	83.1	3.47	6.50	3.04	
Au19+	56.6	76.7	5.86	10.22	4.36	
Au20	54.7	87.8	2.51	7.08	4.57	
a Data are collected at the TPSS/cc-pVDZ-PP + ZPE level (kcal/mol).

As shown in Table 3, the doped M2@Au170/±1 clusters generally have much higher BE and DE values than the pure Aun systems. The predicted BEs are around 61 and 65 kcal/mol for Mo2@Au17 and W2@Au17, respectively, that are considerably greater than the corresponding values of 54 for Au19 and 55 kcal/mol for Au20. In addition, the W2 dimer is found to induce a stronger influence than the Mo2. The BE values in the range of 64–67 kcal/mol for W2@Au170/±1 are quite larger than those of Mo2@Au170/±1, being varying from 61 to 62 kcal/mol (Table 3). Likewise, the DE values are predicted to be in the range of 182–209 kcal/mol for Mo2@Au170/±1, as compared to the values of 77–88 kcal/mol for pure gold clusters. The BE between W2 and Au170/±1 of 238–265 kcal/mol also indicates a highly effective guest–host interaction. Previously, the BE between Nb2 and Au6 in the highly stable supermolecule Nb2@Au6 was predicted to be ∼200 kcal/mol.37 The higher stability of M2@Au17q as compared to their pure gold counterparts can be understood as a consequence of the fact that an amount of electron has effectively been transferred from the shell to the core. Computed results on the NBO charge distribution of M2@Au17q, which are summarized in Table S3 of Supporting Information, reveal that the gold atoms are losing electrons while the dopants are acting as electron acceptors. For example, both Mo and W atoms in the neutral M·1 bear a negative charge of −3.5 and −3.4 electrons, respectively.

Table 3 also includes the HOMO–LUMO energy gap (HLG), a parameter often used to evaluate the kinetic stability and electronic transitions of chemical systems. It is clearly seen that the doped M2@Au170/±1 clusters overall have smaller HLGs than their pure gold counterparts. The HLG values are computed to be 3.7 eV (86 kcal/mol) for Mo2@Au17– and 3.6 eV (83 kcal/mol) for W2@Au17–, which are markedly lower than a corresponding value of 4.6 eV (106 kcal/mol) predicted for the magic tetrahedron Au20.

3.3 Gold-Based Nanowires from M2@Au17

The search for new nanomaterials with tailor-made electronic and optical properties for relevant applications has become a fundamental challenge for many scientists in chemistry, physics, and nanoscience over the last decades. One of the most promising approaches to creating novel materials is using size-specific clusters as building units.61 In this context, a legitimate question is whether the tubular M2@Au17 clusters can be used as a starting unit for the synthesis of gold nanowires. To tackle this query, we now examine the possibility of forming the dimers M4@Au33 based on the following reactions 16 and 17:16

17

The structures of the M4@Au33 dimers are displayed in Figure 2. They are generated by placing one M2@Au16 block on top of the other connected together by an Au atom playing as a linker. Full vibrational calculations are performed, and both optimized structures are confirmed as real minima with all positive vibrational frequencies.

Figure 2 Optimized structures of dimers M4@Au33 (TPSS/cc-pVDZ-PP).

As shown in Figure 2, each dimer M4@Au33 is formed by assembling two M2@Au16 units along the main axis of the pentagonal antiprism. The building blocks are connected to each other by five-membered Au rings and an Au atom. The shared Au–Au (dAu–Au) bond lengths in M4@Au33 are around 2.95 and 2.98 Å for M = Mo and W, respectively, which are somewhat longer than the dM–Au distances of 2.66 Å between the assembled units. In Mo4@Au33, the dMo–Mo distance is 2.37 Å, as compared to 2.50 Å in Mo2@Au17. Similarly, the dW–W length of 2.49 Å in W4@Au33 is also quite shorter than a corresponding value of 2.61 Å in W2@Au17.

The thermodynamic stability of M4@Au33 nanowires are analyzed via the BE, the DE, and assembling energies (AE), which are defined by eqs 18–21:18

19

20

21

Computed results in Table 4 point out that the BEs of M4@Au33 are ∼4 kcal/mol larger than those of M2@Au17. Indeed, these values of M4@Au33 are predicted to be 63 and 67 kcal/mol for M = Mo and W, respectively, as compared to 61 kcal/mol for Mo2@Au17 and 65 kcal/mol for W2@Au15.

Table 4 BE, DE, and AE Values (kcal/mol) for M4@Au33 Systems (TPSS/cc-pVDZ-PP + ZPE)

dimer	BE	DE	AE1	AE2	monomer	BE	DE	
Mo4@Au33	63.2	245.5	–29.0	–92.9	Mo2@Au17	60.8	199.7	
W4@Au33	66.8	296.1	–19.7	–86.5	W2@Au17	64.5	254.9	

For detachment energies, a similar tendency is also observed, but the difference is much more significant (Table 4). Moreover, calculations on the AE with respect to different channels indicate that forming the dimers M4@Au33 from M2@Au17 and M2@Au16 is more energetically favorable than that from two M2@Au17 units. The AE releasing computed by eq 21 are larger than those computed by (20) up to 60 kcal/mol.

3.4 Electronic Structures and Absorption Spectra

The electronic structures and stability patterns of metal clusters have typically been analyzed by the electron shell model. In terms of the phenomenological shell model (PSM),62 the clusters having a number of valence electrons corresponding to the electronic shells of 1S, 1P, 1D, 2S, 1F, 2P, 1G, and so on tend to exist as a spherical shape and should be particularly stable. For systems not having enough valence electrons to fulfill such electronic shells, either an oblate or a prolate structure is likely to be more preferred, and the energy ordering of the shell orbitals should be tuned. In particular, frontier orbitals that are degenerate in energy should split into various levels to remove the degeneracy and lower the total energy.

Let us analyze the electron shell of the anions Au17M2– which has 30 valence electrons, including six electrons from each dopant and one electron from each Au atom. This shell could be formed with an unbalanced electron configuration, i.e., [1S2 1P6 1D10 2S2 1F10], if their equilibrium structures were spherical. As a result of the Jahn–Teller effect, spindle-like structures having D5h symmetry are reached to lower the energy of frontier orbitals.

In the D5h-symmetric crystal-field, degenerate orbitals on the P and D shells split into two and three different subshells, respectively. On the contrary, the 1F orbitals go from a 7-fold degenerate shell in a spherical cluster to four different levels, namely {1Fy(3x2–y2), 1Fx(x2–3y2)} (e2′), {1Fxyz, 1Fz(x2–y2)} (e2″), {1Fxz2, 1Fyz2} (e1′), and 1Fz3 (a2″) orbitals. The electron shell of the M2@Au17– species with 30 itinerant electrons can be described as follows:

The {1Fy(3x2–y2),1Fx(x2–3y2)} subshell (Figure 3) now becomes unoccupied and is lying higher in energy than {1Fxz2, 1Fyz2}, 1Fz3, and {1Fxyz, 1Fz(x2–y2)}. Both HOMO and LUMO of the D5h spindle-like anions M2@Au17– are degenerate. Therefore, attachment or detachment of an electron is expected to accompany a lowering of its symmetry due to a Jahn–Teller distortion. Indeed, the removal of one electron from these structures should result in a unbalanced configuration with three electrons on the doubly degenerate e2″ orbitals, i.e., {1Fxyz, 1Fz(x2–y2)}. Such an electronic degenerate state is not stable, and each cluster tends to undergo a structural relaxation to lower its total energy. The neutral and cationic states are thus more stable in a distorted pentagonal antiprism with Cs and C2v point groups, respectively.

Figure 3 Splitting of 1F shell orbitals in the D5h cylindrical anions M2@Au17–.

For more insights into interactions between the Au17 cage and the dimer, we plot in Figure 4 the partial density of states (PDOS) for the anions M2@Au17–. The HOMO band of W2@Au17– consists of both Au17– shell and W2 core, while the LUMO mostly gives rise from the shell (cf. Figure 4). On the contrary, both the shell and the core contribute almost equally to the HOMO and LUMO bands of Mo2@Au17–. The calculated PDOS in addition shows a strong hybridization of M-d orbitals with s, p, and d orbitals of Au atoms (Figure 4).

Figure 4 Partial density of states (PDOS) of Mo2@Au17– (upper panel) and W2@Au17– (lower panel) (TPSS/cc-pVDZ-PP).

Besides, the unique optical properties of gold clusters and nanoparticles have received great attention in recent years for both basic interest and practical applications. Investigations on small, unsupported clusters as model systems under controlled conditions and without interactions with an outside environment could provide fundamental knowledge that enhances the understanding of more complex systems. Many theoretical and experimental efforts have been devoted to the optical properties of the small gold clusters. At the nanoscale size, classical or semiclassical approaches based on Maxwell’s equations for electromagnetic waves coupling with spherical metallic particles can be used to predict the surface plasmon resonance, i.e., a strong optical response giving rise from collective oscillations of valence electrons.63 However, in order to clarify the molecule-like absorption behaviors of small metal clusters, a full quantum chemical treatment for all valence electrons instead of classical models, is required.64 It is quite challenging but necessary to probe the optical response of gold clusters due to the strong relativistic effect and active participation of 5d-electrons in gold atoms. Another noteworthy finding is that the inclusion of impurity atoms is inherently accompanied by pronounced impacts on their optical properties, such as decreasing the excitation energy and increasing the dipole moment and oscillator strength.40

Using the time-dependent density functional theory (TD-DFT), the optical absorption spectra of Au190/±1 and M2@Au170/±1 systems (M = Mo, W) are simulated and presented in Figures 5 and 6. The TD-DFT calculations are carried out on the lowest-lying DFT optimized geometries. Generally, their absorption spectra are dominated by transitions in the visible region. While the absorption spectra of Au19– and Au19+ species are identified by intense peaks near 500 and 540 nm, respectively (Figure 6), that of Au19 is characterized by a much lower intensity band centered at 630 nm (Figure 5). As compared to the closed-shell systems Au19∓, neutral Au19 with an open-shell electronic structure tends to exhibit a more complicated absorption feature. The absorption spectrum of Au19 comprises several electronic transitions giving rise to a broad band in the lower-energy region (Figure 5).

Figure 5 Absorption spectra of the Au190/±1 obtained by TD-DFT computations at the TPSS/cc-pVDZ-PP level.

Figure 6 Absorption spectra for Mo2@Au170/±1 (above) and W2@Au170/±1 (below) obtained by TD-DFT computations at the TPSS/cc-pVDZ-PP level.

As indicated above, the introduction of Mo and W impurities significantly alters the structures of pure gold clusters. Due to the presence of either Mo2 or W2, the cylinder-like shapes with the dopants encapsulated inside turn out to be mostly preferred. Such structural changes should lead to a charge transfer between the host Aun framework and the dimers M2 placed inside. As a result, substitution of Mo and W for Au atoms has a huge effect on the optical responses. Indeed, our TD-DFT results show that the major transitions of M2@Au170/±1 systems are remarkably shifted to the longer wavelength region (Figure 6). For doped systems, the optical absorption bands centered below 600 nm are strongly suppressed, and the intensity is also greatly decreased. The major absorption peaks for M2@Au170/±1 are now observed in the range between 650 and 800 nm, while those of Au190/±1 are typically located below 600 nm.

3.5 Optical Nonlinearity

Due to their structural diversity, gold-based clusters typically exhibit unique optical properties that are challenging but worth probing. Thus, we carry out further calculations on the dipole moment, polarizability, and first and second hyperpolarizability for the clusters in their ground state structures to examine their linear and NLO characteristics. In this section, the LC-BLYP functional is employed in conjunction with the cc-pVDZ-PP basis set. The rationale for the selection of such an approach is given below.

Typically, benchmark studies have often used para-nitroaniline (p-NA) to test the accuracy and suitability of the methods employed. Table S4 (Supporting Information) lists the calculated gas-phase dipole moment and frequency-dependent polarizability tensors of p-NA, along with the available experimental data for comparison. For the static dipole moment (μ), we find that all functionals considered are likely to overestimate the experimental value. As compared to the experimental value of μ = 2.70 a.u., either wB97XD or LC-BLYP appears to provide a more reliable result than other approaches. Moreover, based on the LC-BLYP/aDZ calculation, a β∥(−2ω, ω, ω) = 1046.9 (a.u.) at 1064 nm is obtained for p-NA, which is also in good agreement with the corresponding value of 1072 ± 44 a.u. measured in the gas phase.65 On the contrary, other functionals tend to greatly overestimate the experimental result. Overall, the LC-BLYP long-range corrected functional is found to properly reproduce the experimental μ and β values for p-NA, and it is thus selected for evaluation of NLO properties of the clusters considered.

The static and dynamic polarizabilities for M2@Au17q clusters computed with the LC-BLYP functional are listed in Table 5. Accordingly, the anions M2@Au17– have larger values of αiso than their neutral and cationic counterparts. The dynamic isotropic polarizabilities of M2@Au17q are predicted to be in the range of 547–611 a.u., which are quite lower than those predicted for the pure gold systems. Thus, the replacement of Au by Mo and W atoms decreases the polarizability of Au19q species. Furthermore, the dynamic polarizability of both M2@Au17q and Au19q typically has values higher than the static one, except for the Au19 cluster. Moreover, as compared to an external reference, these clusters have particularly large values of αiso, being from 5.75 to 7.96 times greater than p-NA. Except for the anion Au19–, all clusters considered also exhibit slightly higher values of αaniso than p-NA. The largest and smallest dynamic anisotropic polarizabilities of 257.8 and 67.8 a.u. are obtained for Mo2@Au17+ and Au19– clusters, respectively, as compared to a corresponding value of 81.2 a.u. for the p-NA molecule.

Table 5 Gas-Phase Dipole Moment (μ), Isotropic (αiso), and Anisotropic (αaniso) Polarizabilities, and First-Order (β) and Second-Order (γ) Hyperpolarizabilities in Atomic Unit (a.u.) of Au19q, M2@Au17q Clusters, and the p-NA Moleculea

q	 	Mo2 @ Au17q	W2 @ Au17q	Au19q	p-NA	
–1	0	+1	–1	0	+1	–1	0	+1	
μ	 	0.0	0.31	0.47	0.0	0.27	0.51	0.39	0.60	0.35	2.77	
α	
αiso	(0)	609.9	583.3	555.5	610.5	547.6	555.1	757.4	757.3	608.2	99.2	
 	(−ω)	636.7	608.8	585.1	635.1	586.3	581.0	804.4	747.2	638.6	101.0	
αaniso	(0)	193.3	181.8	182.8	192.8	121.9	188.0	66.0	82.0	100.7	78.2	
 	(−ω)	200.7	230.5	257.8	199.0	174.2	251.5	67.7	70.0	118.3	81.2	
β	
βtot	(0)	0.05	2187.6	1667.6	0.04	2577.1	1276.2	2983.8	8910.5	422.7	1177.9	
 	(−ω)	0.22	1100.1	1430.0	0.04	233.7	1479.5	3928.8	36942.2	526.4	1333.5	
 	(−2ω)	17.5	36.6	387.7	2.22	209.3	1574.1	28047.2	23979.4	1634.2	1755.1	
β∥	(0)	0.0	–1312.6	–1000.6	0.0	–1546.2	–765.7	–1790.3	–2930.2	–253.6	702.6	
 	(−ω)	0.0	–660.1	–858.0	0.0	–140.2	–887.7	–2357.3	–22147.1	–315.9	795.4	
 	(−2ω)	0.0	22.0	–232.6	0.0	–125.5	–944.4	–16828.3	–12357.8	–980.5	1046.9	
γ/104	
γtot	(0)	24.0	16.2	8.98	24.9	16.7	8.37	37.7	22.8	9.04	2.03	
 	(−ω)	25.9	11.0	7.78	31.5	42.6	7.76	49.4	31.8	10.1	2.33	
 	(−2ω)	21.0	81.5	13.9	30.1	23.3	27.7	42.0	32.9	15.2	3.20	
γ∥	(0)	39.6	25.5	14.3	41.7	28.1	14.2	61.3	39.2	15.6	2.55	
 	(−ω)	41.6	18.1	6.51	53.3	60.3	8.19	85.3	54.5	17.3	2.88	
 	(−2ω)	32.0	118.4	19.0	47.6	40.2	46.5	58.1	51.7	25.9	3.80	
a Dynamic (hyper) polarizabilities are computed at the fundamental wavelength of λ = 1064 nm, using the LC-BLYP functional and cc-pVDZ-PP basis set.

As the hyperpolarizabilities are proportional to the electric dipole moment, the systems without dipole moment like, Mo2@Au17– and W2@Au17–, have almost zero values of β components, implying that they do not have a pronounced NLO activity. However, their neutral and cationic counterparts show significant nonlinearity. In particular, Mo2@Au17 and W2@Au17 have a value of βtot(0) around 2188 and 2577 a.u., respectively, which are much smaller than the corresponding value of 8911 au obtained for Au19, but almost two times larger than that of the highly π-delocalized p-NA (1178 a.u.).

Overall, the β values for M2@Au17q undergo a significant reduction, compared to that of the pure gold counterparts. Such a phenomenon was also observed for AunM systems (n = 17, 19; M = Cu, Ag).66 We in addition note that, while the dynamic values for Au19q clusters follow the expected order of β(0) < β(−ω) < β(−2ω), the doped clusters only show a similar trend for W2@Au17+. Another noticeable result is the negative values of the β component in the direction of μ, i.e., the β∥ value, for both pure and doped gold clusters. This reflects a negative change of dipole moments following excitation from the ground to the excited states.67

The computed results for static and dynamic second-order hyperpolarizabilities of M2@Au17q clusters are also collected in Table 5. For Mo2@Au17q, W2@Au17q, and Au19q clusters, the static γtot(0) values are in the range of 9.0–24.0, 8.4–24.9, and 9.0–37.7 (×104 a.u.), respectively, that are much larger than the corresponding value of 2.0 × 104 a.u. obtained for p-NA. Noticeably, the anions M2@Au17– are found to have particularly large values of static second-order hyperpolarizabilities, while the β components are almost zero (Table 5). Thus, it is likely that they exhibit an excellent NLO activity related to the hyperfine structure,67 although the NLO response is rather weak in the second-order fine structure. Computed results listed in Table 5 in addition reveal that the second dynamic hyperpolarizability of both pure and doped gold clusters is typically larger than the static one, but not always following a correct order, γ(0) < γ(−ω) < γ(−2ω), as in the p-NA molecule. Moreover, the cluster in anionic states is predicted to have larger γ values, both static and dynamic, than the corresponding cation, even though the former is more symmetric and has a dipole moment lower than that of the latter.

4 Concluding Remarks

In the present theoretical study, we presented the structure, stability, and electronic and optical nonlinearity properties of the cylindrical M2@Au17q clusters that were thoroughly investigated using quantum chemical computations with the DFT and TD-DFT approaches. In contrast to the pure Aun clusters up to n = 20, a tube-like form with a dopant dimer M2 encapsulated inside an Au17 framework along the symmetry axis was found for the first time as the dominant structure of the doped M2@Au17q species. Energetic calculations for several parameters, such as the BE per atom and DE, show that the presence of Mo2 and W2 units significantly enhances the stability of the gold clusters. Their effects on the electronic structures and optical responses are also remarkable.

The absorption spectra of M2@Au17q species are characterized by major electronic transitions in the range of 650–800 nm rather than below 600 nm as in the pure clusters Au190/±1. These binary systems emerge as ideal building blocks for the formation of gold-assembled nanowires, which are connected together by the five-membered Au rings and an Au atom.

We in addition examine the NLO properties of Au17M2q clusters in comparison with those of Au190/±1 clusters and p-nitropaniline (p-NA) molecules based on the static and dynamic (hyper) polarizability tensors. The hyperpolarizabilities of clusters were found to undergo a significant reduction upon replacement of Au atoms by Mo2 and W2 units but remain much larger than those of p-NA. The neutrals M2@Au17 are expected to exert excellent optical responses as they exhibit exceptionally high values for both the first- and second-order NLO coefficients. Present results reveal that these pure and doped gold clusters are good materials to be considered for different optoelectronic features.

Data Availability Statement

Quantum chemical computations were carried out using the Gaussian 16 program. The main isomers optimized are given in the Supporting Information.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.4c02724.Ground state structures of Au19q clusters located at the TPSS/cc-pVDZ-PP level; optimized geometries and Cartesian coordinates of M2@Au17q isomers; Cartesian coordinates of the dimers M4@Au33; natural charges distributed on Mo and W atoms in M2 @ Au170/±1 clusters computed at the TPSS/cc-pVTZ-PP level; and gas-phase dipole moment and first hyperpolarizability tensors in atomic unit of p-NA (PDF)

Supplementary Material

ao4c02724_si_001.pdf

The authors declare no competing financial interest.

Acknowledgments

This research is funded by the Vietnam Ministry of Education and Training under Grant No. B2024-TCT-06.
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