DFT studies on the influence of ligation on optical and redox properties of bimetallic [Au₄M₂] clusters

Abstract

Density functional theory based calculations have been employed to understand the lowest energy conformers of bare [Au₄M₂] and ligated [Au₄M₂(SCH₃)₆] and [Au₄M₂(PH₃)₆]²⁺ (where M = Au, Cu, Ag, Ni, Pd, Pt) clusters in the gas phase and in various implicit solvent media (water, DMSO and DCM). Computations predict that [Au₄M₂] clusters in all three charge states exist with a planar 2D-geometry, with distortion introduced by the hetero atoms. And the studies show that the ligation promotes a 2D to 3D geometrical conversion either through bridging coordination or single bond formation. The sulfur atom in the thiol ligand becomes a part of the cluster skeleton, while the PH₃ forms a passivation layer around the cluster. Moreover, the presence of sulfur in the cluster skeleton increases the chemical stability of coinage metal containing clusters, while stability decreases for d⁸ metal containing clusters. And the PH₃ passivation layer decreases the chemical stability of both coinage metal and d⁸ metal atom containing clusters. The computed redox behaviors show that the addition of an electron requires less energy compared to that needed for removal, and both occur with negligible geometrical reorganisation. The calculated blue shift in excitation energy values show a ligand to metal charge transfer in the –SCH₃ ligated cluster. However, the red shift in wavelength is observed for the –PH₃ passivated cluster, which corresponds to excitation from the HOMO to LUMO, where the orbitals have an equal contribution from the metals and ligands.

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1. Introduction

Gold clusters reveal a prosperous array of interesting electronic,^1–5 optical,^6,7chemical,⁸ and catalytic^9–15 properties, typically with a sharp size threshold that has sparked huge interest in several areas. Specifically, the studies on smaller sub-nanometer (<2 nm) gold clusters have evoked much attention due to their fascinating physical and chemical properties compared to their larger counterparts.^2,16–18 These clusters have been extensively studied for their applications in electronics, sensors, medical diagnostics and catalysis.^15,19–25 Along with monometallic gold clusters, bimetallic gold clusters (BMGC) have enthralled researchers since the additive effect of the second metallic component is found to play an important role in controlling the activity and stability.^26,27 Controlled syntheses of BMGC for particular applications turn out to be an active area of research which revealed appropriate usage of the prospective of the second metal along with gold.^27–37 Moreover, protective layer is an indispensable tool to stabilize and synthesize BMGC's evading the ones in gas phase. Ligation becomes a dominant factor,^38–41 which can vary the physical and chemical properties of clusters to a larger extent.^38,42–44 The unearthing influence of passivated layers in the BMGC open up one more dimension for progress of nanocluster chemistry.⁴⁵ Hence, comprehending the influential properties of interface between gold nanoclusters and ligand layer become a meticulous task. Numerous theoretical and experimental studies have been devoted in this concern.^41,46–55 On the theoretical side, there is an intense research effort to characterize the properties of gold clusters of various sizes, ligand shells, charge states and hydration using methods in Density Functional Theory (DFT).^{11,48,51–54,56–62} The recent crystal structure studies point that, sub-nanometre sized clusters can act as the building blocks of nanometer sized clusters.^63,64 Further, the basic building blocks can be ligated before forming the larger cluster. An example can be [Au₂₂(SR)₁₈] which is an assembly of Au₇, one [Au₆(SR)₆] and three [Au₃(SR)₄] clusters.⁶⁰ Hence, the interface chemistry of sub-nanometre sized clusters are more crucial than their larger counterparts, since it can hint even the growth mechanism of the bulkier counterpart. In this context, this work focuses on Au₆ and [Au₄M₂] clusters which have been chosen as a model in view of the following characteristics of this cluster.

(i) Au₆ is a distinctive cluster, with all the three charged states (neutral, anionic and cationic) possessing a planar triangular structure with D_3h symmetry.⁶⁵

(ii) The neutral cluster is highly stable, both chemically and physically which also exists in two-dimensional structure even up to 1100 K temperature.⁶⁵

(ii) The hexamer is exceedingly active in catalysis.^12,65

(iv) Along with neutral, both negatively and positively charged hexamer Au₆ clusters are stable up to 500–800 K temperature in its ground state geometry.⁶⁵

(v) The [Au₆(PPh₃)₆]²⁺ cluster has been synthesized and characterized.⁶⁶ And the [Au₆(SR)₆] has already been realized as a part of [Au₂₂(SR)₁₈] nanocluster.⁶⁰

(vi) The oligomer formation after –SR ligation of Au₆ and the possible application in hydration and electron affinities have been described previously.⁴²

(vii) From the report, the hexamer is predicted to bind differently with neutral triphenyl phosphine (–PPh₃) and negative thio alkyl (–SR) ligands.

(viii) BMGC [Au₄M₂] has a highly stable composition and the ground state isomers possess distorted planar triangular structures like Au₆.^10,28,67,68

The alteration of passivated layers result in an evident structural evolution, which is required to be understood at the microscopic level. With this end in mind, herein we focus on the ligation of 2D Au₆ clusters and its bimetallic counterparts [Au₄M₂] where M = Ag, Cu, Ni, Pd and Pt. For ligation studies, two different ligands are chosen (i) –SCH₃ as a model for negatively charged –SR and (ii) –PH₃ as a model for neutral –PPh₃. In order to understand the electronic structure of ligated BMGC clusters systematically using DFT method, various conformers of 2D clusters are explored. The structural and electronic properties of the bare Au₆ cluster in neutral, single positive, negative charge states and the effect of an implicit solvation has also been investigated. Computed results are corroborated with available experimental and reported data. The effect of a densely packed outer layer of the passivated –SCH₃ and –PH₃ ligands with and without an implicit solvent layer on three different charge states are looked into. The energetics of ligation, spin density, chemical stability, chemical hardness, possibility of charge transfer and polarizabilities have been studied and compared. Additionally, their optical and redox properties are examined and correlated with that of a bare cluster.

This paper is organized as follows. Computational methods used are described in Section 2. The structural (in three different oxidation states), optical and redox properties of bare clusters are analysed in Section 3.1 along with their charge distribution. Section 3.2 deals with the structures of –SCH₃ passivated cluster and their polarization, optical properties and redox nature. Section 3.3 focus on the effect of monodentate –PH₃ ligand and the results are concluded in Section 4.

2. Computational methods

The use of atom centred basis functions together with pseudo potentials for the gold atoms and hybrid functionals are well established for these kind of systems.^{32,53,54,61,69}

Geometry optimizations are carried out for various conformers and clusters in various spin states using density functional theory as implemented in the Gaussian 09 suite of program⁷⁰ with the hybrid CAM-B3LYP⁷¹ functional. The LANL2DZ, RECP pseudo potential basis set for gold and 6-31+G(d) basis set for all other atoms are employed.⁵⁸ The stationary structures of the three charged states (positive, neutral and negative) of the bare Au₆ (Fig. 1) and of the ligated [Au₆(SCH₃)₆] and [Au₆(PH₃)₆]²⁺, clusters are characterized as minima on the basis of the calculation of their harmonic vibrational frequencies with the options opt = tight (10⁻⁶ hartree per bohr for the forces on atoms) and SCF = tight (10⁻⁸ hartree convergence threshold). The computed important vibrational frequencies are given in Table S1 in ESI.† The natural population analysis has been used to study the charge distribution for all optimized clusters.⁷² The implicit solvation is considered based on the Self-Consistent Reaction Field-Polarizable Continuum Model (SCRF-PCM)⁷³ with three solvents, water (ε = 80), DMSO (ε = 48) and DCM (ε = 10). Redox properties are studied by computing their ionization potential and electron affinity. The Vertical and Adiabatic Ionization Potential (AIP and VIP), Vertical and Adiabatic Electron Affinity (VEA and AEA), reorganization energies (λ_oxi and λ_red), chemical hardness, ligand Binding Energies (BE) are calculated using the equations given below,

VIP = E(N − 1)_{(cation at optimized neutral geometry)} − E(N)_{(optimized neutral)}

VEA = E(N)_{(optimized neutral)} − E(N + 1)_{(anion at optimized neutral geometry)}

AIP = E(N − 1)_{(optimized cation geometry)} − E(N)_{(optimized neutral)}

AEA = E(N)_{(optimized neutral)} − E(N + 1)_{(optimized anion geometry)}

Chemical hardness (η) = VIP − VEA

Fig. 1 Optimized structures of bare [Au₄M₂]ⁿ, where M = Au, Cu, Ag, Ni, Pd and Pt clusters in three charge states (n = 0, +1, −1). Important bond lengths (Å) for neutral (normal font), positively (italic font) and negatively charged (bold font) clusters are given.

BE = E_[Au4M2L6] − (E_[Au4M2] + E_[6L]), where E_[Au4M2L6], E_[Au4M2], E_[6L] are the total energies of neutral ligated, bare and free ligand respectively. The basis set superposition errors in binding energy values are calibrated using the Boys and Bernardi counterpoise correction method as implemented in the Gaussian 09 package at the same level of theory.⁷⁴

Reorganisation energy for reduction process, λ_red = AIP − VIP and for the oxidation process, λ_oxi = AEA − VEA.

The excited state calculations were performed with and without implicit water PCM model using Time-Dependent Density Functional Theory (TDDFT) at the same level, which has been widely used.^75–80 The excited state energies and the transition orbitals have been calculated using Complete Active Space Self Consistent Field method⁸¹ with 12 electrons and 10-orbitals active space at the same level of theory in order to validate the TDDFT methods.

3. Results and discussions

3.1. Bare Au₄M₂ clusters where (M = Au, Ag, Cu, Ni, Pd and Pt)

For bare Au₆ clusters, a D_3h symmetry structure is predicted to be the stable, lowest energy geometry in all three charge states. The computed structural parameters such as Au–Au distance (2.68 Å) and Au–Au–Au angles (64.2°) are comparable with the reported values (Table S2 in ESI†).^2,3,51 Natural charge analyses show two type of atoms in the neutral Au₆ clusters (i) electron rich edge atoms (ii) electron deficient centre atoms, which is the characteristic of a D_3h symmetry. As a result, both oxidation and reduction influence the charge localization in distinctive manner by preserving the D_3h symmetry, which has been shown in the spin density plot (Fig. 2). The dominant spin density at the edge atom after the addition of an electron proves that there is an accumulation of charge at that point ([Au₆]⁻ in Fig. 2). In contradiction, removal of an electron occurs to a larger extent at the centre atoms evading edge atoms ([Au₆]⁺ in Fig. 2). As observed for other clusters which are variously sized, negatively charged clusters are highly stable with a larger HOMO–LUMO gap in comparison to its neutral and positively charged counterparts. Calculated HOMO–LUMO gap, ionization potential, electron affinity and chemical hardness go in hand with the reported parameters,⁶⁷ which validates the method adopted here (Table 1).

Fig. 2 Spin density plots of various [Au₄M₂]ⁿ, where M = Au, Cu, Ag, Pd and Pt clusters in a single positive and negative charged states (densities are plotted with isocontour value: 0.002 Å⁻³).

Table 1 Computed redox properties of [Au₄M₂]ⁿ, where M = Au, Cu, Ag, Ni, Pd and Pt clusters in three charge states (n = 0 or +1 or −1) using CAM-B3LYP functional. Calculated AIP, AEA, VIP, VEA, η (chemical hardness) and λ_red (reorganization energy for reduction) and λ_oxi (reorganization energy for oxidation) are given (eV). Reported values are given in italics^10,28,67,68

Clusters	AIP	AEA	VIP	VEA	η	λoxi	λred
Au6	8.43	1.91	8.60	1.82	6.78	0.17	0.09
	8.46		8.83	2.39	6.44
Au4Cu2	8.46	1.87	8.53	1.73	6.80	0.07	0.14
			8.68	2.21	6.47
Au4Ag2	8.33	1.82	8.57	1.67	6.90	0.24	0.15
			8.99	2.18
Au4Ni2	6.70	3.09	7.68	3.14	4.54	0.98	0.05
Au4Pd2	7.44	2.04	7.69	3.73	2.94	0.25	1.69
Au4Pt2	7.68	3.21	8.51	3.15	5.36	0.83	0.06
			7.35	2.72

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Subsequently, [Au₄M₂] stoichiometric mishmash has been chosen to study BMGC. Among the various compositions, [Au₄M₂] has been reported as more stable.^23,28,67 Hence, this work focuses on a [Au₄M₂] BMGC composition of Cu, Ag, Ni, Pd and Pt with gold, which are known for their good catalytic and biological activities.^{32,33,41,82–88} As conveyed, all BMGC clusters with [Au₄M₂] composition exist in triangular 2D planar structure, where the hetero atom lies in the inner triangle.^10,28,67,68 Similarly, as reported, the computed energies for various spin states neutral structures show that, Au₆, [Au₄Cu₂], [Au₄Ag₂], [Au₄Pd₂] and [Au₄Pt₂] are highly stable with closed shell electronic configuration, while [Au₄Ni₂] is stable in open shell configuration (with two unpaired electrons).^67,68 Related to [Au₆] cluster, the presence of hetero metal atom distorts the geometry and reduces the symmetry. The amount of distortion is proportional to the size of the hetero metal atom. Breadth and height have been calculated for the triangular geometries (Table S2 in ESI†) to know the amount of distortion beginning from Au₆ cluster with a D_3h symmetry. The following illustrates an increase in deviation in the order, Au₆ < [Au₄Ag₂] < [Au₄Pt₂] ≈ [Au₄Pd₂] < [Au₄Cu₂] ≈ [Au₄Ni₂]. Further, the presence of hetero atom changes the bond distances and angles which are corroborated with available experimental values (Table S2 in ESI†). Analogous to Au₆ cluster, doped clusters are chemically stable with a larger HOMO–LUMO gap and chemical hardness values. Compared to the d⁸ metal doped cluster, the coinage metals give larger HOMO–LUMO gap and hardness values, which indicate their enhanced chemical stability. Among d⁸ metal series, [Au₄Pd₂] exhibits with a higher chemical stability in comparison to [Au₄Pt₂] and [Au₄Ni₂] which is predicted to be due to be its preference towards completely filled electronic configuration [5s⁰4d¹⁰].⁸⁹

The presence of hetero atom facilitates partial charge transfer from gold, which is evident from the computed positive natural charge at the hetero atom and negative charge at the gold atom. The amount of charge gained or lost is directly proportional to the electronegativity of the dopant (Cu, Ag, Ni, Pd and Pt) atoms. Among, various hetero-metals, Cu donates more charge to gold. Moreover, the structural distortions generate new charge type atoms in BMGC clusters. Doping with Ag, Ni and Pt, results in three charge type of atoms in [Au₄Ag₂], [Au₄Ni₂] and [Au₄Pt₂] clusters, which are type (1) three corner Au atoms at the outer triangle, type (2) two hetero atoms at the inner triangle and type (3) one gold atom at the inner triangle. Nevertheless, the presence of Cu and Pd atoms in the [Au₄Cu₂] and [Au₄Pd₂] clusters distort the structure to a larger extent and as a result, gold atom in the outer triangle gets polarized to an extra direction and gives four charge types atoms. Type (1) two corner Au atoms at the outer triangle, type (2) two hetero atoms at the inner triangle, type (3) one central gold atom at the inner triangle and type (4) one gold atom in the outer triangle at the edge (Table 2). Interestingly, the types of atoms remain intact even after addition or removal of an electron from the cluster.

Table 2 Computed natural charge values (e), of various [Au₄M₂]ⁿ, M = Au, Cu, Ag, Ni, Pd and Pt clusters in three charge states (n = 0 or +1 or −1) using CAM-B3LYP functional^a

[Au4M2]^n clusters	Charge states	Natural charge of different types of atoms in the clusters
		Type 1	Type 2	Type 3	Type 4
a Types' 1 and 4 corresponds to atoms in outer triangle. Similarly, types' 2 and 3 in inner triangle.
M = Au	+1	0.26	0.02	—	—
	0	0.05	−0.05	—	—
	−1	−0.23	−0.11	—	—
M = Cu	+1	0.35	0.18	−0.10	−0.03
	0	0.12	0.02	−0.11	−0.03
	−1	−0.30	0.07	−0.26	—
M = Ag	+1	0.16	0.26	−0.09	—
	0	−0.05	0.22	−0.16	—
	−1	−0.33	0.16	−0.32	—
M = Ni	+1	0.26	0.13	−0.04	—
	0	0.01	0.04	−0.05	—
	−1	−0.18	−0.14	−0.15	—
M = Pd	+1	0.27	0.13	−0.08	0.22
	0	0.10	0.01	−0.12	−0.08
	−1	−0.17	−0.13	−0.17	—
M = Pt	+1	0.31	0.02	0.04	—
	0	−0.12	0.18	−0.06	—
	−1	−0.08	−0.36	−0.02	—

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In both charge states (positive and negative), all BMGC clusters are holding most stable configuration with a single unpaired electron. In [Au₄Ag₂] and [Au₄Cu₂], the removal of electron withdraws it from hetero atoms to the maximum extent and the added electron charge accumulates at the gold atom, which is apparent in spin density plot (Fig. 2). However, in d⁸ metal doped BMGC clusters, both removal and addition of electron occurs at the hetero metallic (Ni, Pd and Pt) centre, where the contribution of gold atoms are minimal (Fig. 2). This is due to a substantial vacancy in the valance-shell of d⁸ metals.

Complimenting Au₆ clusters, BMGC clusters have higher ionization potential and lower electron affinity values. The difference between VIP/VEA and AIP/AEA energies are very less, indicating the minimal structural relaxation after addition or removal of electron. This has been reflected in computed reorganization energies (Table 1). Further, in order to make it more realistic with experimental measurement, the standard redox potential (SRP) values are calculated with reference to the Standard Hydrogen Electrode (SHE) using Born–Haber cycle (details are given in ESI†).^90,91

All clusters are introduced in three implicit solvent environments with varying range of dielectric constants, ε = 10, ε = 48 and ε = 80, to study the effect of polarization of environment towards the stability. The presence of an electrostatic media does not change the conformer structure, electronic properties and charge distribution. However, it is found to stabilize the clusters further. The extent of stability attained is directly proportional to the dielectric constant value. As reported in the Table S3 in ESI,† bare Au₆ clusters get influenced in the dielectric media more compared to [Au₄M₂]. This is due to the comparatively larger charge delocalization (HOMO and LUMO plots in Fig. S1 of ESI†) in the metal doped clusters. Negatively charged clusters are found to be more stable than its counterparts as expected. Since all the solvents behave similarly, the SRP values are computed using water dielectric media and are given in Table S7 in ESI.† The calculated higher SRP values (1–1.4 V) for coinage metal containing BMGCs show that reduction is more promising in these clusters compared to the d⁸ doped BMGC clusters (0.1–0.5 V). Similarly, the [Au₄Ni₂], [Au₄Pd₂], [Au₄Pt₂] clusters can be oxidised with less potential compared to Au₆, [Au₄Cu₂], [Au₄Ag₂].

The excitation studies show a single peak at ∼350 nm for coinage metal containing clusters Au₆, [Au₄Cu₂], [Au₄Ag₂] and the presence of d⁸ group elements in clusters like [Au₄Ni₂], [Au₄Pd₂], [Au₄Pt₂] which red shift the band by 100–150 nm respectively from Au₆ (Table 3).

Table 3 Computed transitions and excitation wavelength (nm) for bare [Au₄M₂], ligated [Au₄M₂(SCH₃)₆] and [Au₄M₂(PH₃)₆]²⁺ clusters (M = Au, Cu, Ag, Ni, Pd and Pt) in TDDFT/CASSCF methods. Percentage contribution of each transition is given in brackets (H – HOMO, L – LUMO). The corresponding molecular orbital pictures is given in Fig. S1–S3 in ESI

Clusters	Transitions (nm)
	[Au4M2]	[Au4M2(SCH3)6]	[Au4M2(PH3)6]^2+
M = Au	H−1 → L+2 (47%), H → L (43%), 365/320	H−1 → L (47%), H → L (47%), 240/233	H → L+1 (67%), H → L (70%), 391/364
M = Cu	H−2 → L (50%), H → L (60%), 375/350	H−1 → L+1 (40%), H → L (39%), 238/213	H → L+1 (65%), H → L (68%), 391/398
M = Ag	H−1 → L (55%), H → L (60%), 362/318	H−3 → L+2 (30%), H → L+2 (34%), 234/209	H → L+1 (66%), H → L (70%), 381/386
M = Ni	H−4 → L (47%), H → L+1 (66%), 428/585	H → L (46%), H → L+1 (53%), 411/585	H−3 → L+1 (60%), H−1 → L+1 (68%), 528/647
M = Pd	H−2 → L (45%), H−1 → L (52%), 611/677	H−1 → L (33%), H → L (63%), 584/623	H−1 → L (53%), H → L (58%), 675/721
M = Pt	H−7 → L (56%), H → L+1 (59%), 501/521	H−7 → L+1 (41%), H → L (49%), 456/471	H → L+1 (66%), H → L (69%), 572/693

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3.2. Ligated [Au₄M₂(SCH₃)₆] clusters where (M = Au, Ag, Cu, Ni, Pd and Pt)

The –SR ligand has been widely used as a passivated or protecting layer in densely packed sub-nanometer clusters.^51,61,92,93 And the –SR passivated sub-nanometer cluster has likewise become a building block for heavier clusters.⁶⁰ The –SR group is modelled as –SCH₃ in this work (Fig. 3). In Au₆ cluster, the –SCH₃ group acts as bridging ligand with M–M distance 3.3 to 3.7 Å and forms a chair type or open book conformations.

Fig. 3 Optimized structures of ligated neutral [Au₄M₂(SCH₃)₆] clusters using CAM-B3LYP functional.

In neutral [Au₆(SCH₃)₆], [Au₄Cu₂(SCH₃)₆] and [Au₄Ag₂(SCH₃)₆] (Fig. 4), chair and open book shape conformers exist within 1 kcal mol⁻¹ energy difference, which shows the possibility of existence of two conformers. The computed structural parameters are given in Table S4 in ESI.†

Fig. 4 Two conformers, chair (a–c) and open book (d–f) of stable ligated [Au₆(SCH₃)₆], [Au₄Cu₂(SCH₃)₆] and [Au₄Ag₂(SCH₃)₆] clusters are calculated using CAM-B3LYP functional.

In [Au₄Ni₂(SCH₃)₆], [Au₄Pd₂(SCH₃)₆] and [Au₄Pt₂(SCH₃)₆] clusters, the d⁸ metals prefer four coordination environment with a tetrahedral geometry (Fig. 3), while Au atoms in these clusters prefer different coordination. Each Ni, Pd and Pt atoms are found to interact with a minimum of three –SCH₃ groups and one metal atom. Moreover, a strong bond between hetero atoms have been observed (two Ni, Pd and Pt atoms) and the bond strength increases from Ni to Pt (Table S4 in ESI†). As a result, regular open book and chair patterns are lost in these three clusters. Note that, the [Au₄Ni₂(SCH₃)₆] cluster exist lowest energy configuration with two unpaired electrons as observed for bare [Au₄Ni₂] cluster. However, in all the BMGC clusters, –SCH₃ becomes a part of the interior cluster (bridging ligand) and is not found to act as a capping layer.

The positive natural charge at S atom provide evidence for ligand to metal charge transfer in all clusters (Table S5 in ESI†). Moreover, the variation in the extent of charge transfer banks on the dopant metals (Cu, Ag, Ni, Pd and Pt). As observed in the bare, negatively charged state is more stable than any other charge states of ligated clusters (Table 4). The computed negative binding energies indicate an increase in stability after the ligation. Amidst all, [Au₄Pd₂(SCH₃)₆] holds highest negative binding energy. Binding energies (Table 4) are found to increase in the following order for hexa metal clusters,

[Au₄Pt₂(SCH₃)₆] < [Au₄Ni₂(SCH₃)₆] < [Au₄Ag₂(SCH₃)₆] < [Au₄Cu₂(SCH₃)₆] < [Au₆(SCH₃)₆] < [Au₄Pd₂(SCH₃)₆].

Table 4 Computed redox properties of ligated [Au₄M₂(SCH₃)₆], M = Au, Cu, Ag, Ni, Pd and Pt clusters using CAM-B3LYP functional. Calculated AIP, AEA, VIP, VEA, η, BE with counterpoise correction and λ_red, λ_oxi are given in (eV)

Clusters [Au4M2(SCH3)6]	AIP	AEA	VIP	VEA	η	BE	λoxi	λred
M = Au	9.10	0.16	8.58	0.50	8.08	−27.44	0.52	0.16
M = Cu	9.76	0.22	10.14	1.69	8.45	−27.43	0.38	1.47
M = Ag	9.10	0.29	8.54	0.07	8.47	−25.77	0.56	0.36
M = Ni	9.10	1.92	7.35	2.72	4.63	−24.93	1.75	0.80
M = Pd	6.49	2.30	6.62	1.87	4.75	−28.36	0.13	0.43
M = Pt	7.61	4.19	7.70	3.26	4.44	−23.78	0.09	0.93

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Moreover, the –SCH₃ ligation in [Au₆], [Au₄Cu₂], [Au₄Ag₂] clusters increases the HOMO–LUMO gap (Fig. 5) and chemical hardness values compared to bare, which shows the enhanced chemical stability and hardness of these clusters. This is due to the uniform SCH₃ binding, which leads to delocalised HOMO and LUMO (Fig. S2 in ESI†). However, in [Au₄Ni₂(SCH₃)₆], [Au₄Pd₂(SCH₃)₆], [Au₄Pt₂(SCH₃)₆] clusters, slightly decrease in HOMO–LUMO gap observed compared to bare clusters, which indicate a decrease in the chemical stability. The HOMO and LUMO pictures of these clusters clearly indicate the localisation of orbitals in different regions (Fig. S2 in ESI†) due to presence of two different coordination environments. This might be the reason for the sharp decrease in HOMO–LUMO gaps of [Au₄Ni₂(SCH₃)₆], [Au₄Pd₂(SCH₃)₆], [Au₄Pt₂(SCH₃)₆] when compared to coinage metal containing clusters.

Fig. 5 Computed HOMO–LUMO gaps of bare [Au₄M₂] and ligated [Au₄M₂(SCH₃)₆], [Au₄M₂(PH₃)₆]²⁺ clusters. HOMO–LUMO gap for [Au₄Ni₂] is calculated as the difference between β-LUMO and α-HOMO.

Moreover, the considerable charge transfer from ligand to metal is also found to tune the redox properties of the clusters. The –SCH₃ passivation in Au₆, [Au₄Cu₂], [Au₄Ag₂], increased IP and decreased EA by ≈0.70 eV while the trend is reversed in the case of [Au₄Pt₂(SCH₃)₆], [Au₄Ni₂(SCH₃)₆] and [Au₄Pd₂(SCH₃)₆]. This can be explained on the grounds of the change in bonding mode of each metal in d⁸ metal containing clusters. Related phenomenon is observed in the hardness. Nonetheless, minimal structural relaxation due to addition or removal of electron is observed in the passivated clusters as in bare (Table 4).

Spin density plots (Fig. 6) point out that the added electron goes to the empty d-orbital of sulphur specifically with minimal metal contribution. Similarly, the removal of electron is evidently from s or p-orbital of ligands and a metal d-orbital. Though a difference in spin density distribution is observed, it is delocalized in specific regions. As a result, implicit solvation influences uniformly effect all types of clusters. Higher dielectric constants (water) can stabilize the cluster more than solvents with lower dielectric constant (DCM) (Table S6 in ESI†). This is further reflected in their computed larger SRP values compare to bare (Table S7 in ESI†). The presence of LMCT has been further proved by computing the absorbance spectra for these clusters using TDDFT and CASSCF methods. Irrespective of metal dopants, the LMCT shifted the wavelength to lower region compared to bare. Among various dopants used, the coinage metal clusters has blue shifted the absorbance band to a larger extent (Table 3).

Fig. 6 Spin density plots of ligated [Au₄M₂(SCH₃)₆]ⁿ, where M = Au, Cu, Ag, Ni, Pd and Pt clusters in a single positive and negative charged states, (densities are plotted with isocontour value: 0.004 Å⁻³).

3.3. –PH₃ ligated [Au₄M₂(PH₃)₆]²⁺ clusters where (M = Au, Ag, Cu, Ni, Pd and Pt)

–PPh₃ is a unidentate ligand, which has been synthesized and crystallized with halogen ions and used widely for drug delivery.⁶⁶ –PPh₃ ligands were synthesized in 1 : 1 ratio, where each gold atom is bonded with one –PPh₃ ligand. As a result of passivation, the cluster gains a +2 charge, which is usually neutralized with a counter Cl⁻ ion.⁸⁰ The Cl⁻ ions present outside the –PPh₃ layer does not interact directly with gold clusters. Hence, the counter ion has been excluded in our cluster models. Moreover PPh₃ as modelled as PH₃ in this work.

Unlike –SCH₃ ligand, –PH₃ act as a capping layer without collapsing the intact nature of a metal cluster (Fig. 7). In other words, the intact metal core has been protected by a ligand layer (Table S4 in ESI†) with variation in core geometry. –PH₃ forms a single bond with all the metals. In coinage metals, inner core exist as less distorted structure while the preference of tetrahedral coordination makes the d⁸ element core more distorted. M–P bond length is found to increase in the order,

[Au₆(PH₃)₆]²⁺ < [Au₄Ag₂(PH₃)₆]²⁺ < [Au₄Pd₂(PH₃)₆]²⁺ ≈ [Au₄Ni₂(PH₃)₆]²⁺ < [Au₄Cu₂(PH₃)₆]²⁺ < [Au₄Pt₂(PH₃)₆]²⁺

Fig. 7 Optimized geometries of ligated [Au₄M₂(PH₃)₆]²⁺, M = Au, Cu, Ag, Ni, Pd and Pt clusters using CAM-B3LYP functional.

The absence of LMCT band in absorbance spectra in –PH₃ passivated clusters could be due to the different in binding mode between –SCH₃ and –PH₃ containing (Table S4 in ESI†). The computed the absorption energies (391 nm) of [Au₆(PH₃)₆]²⁺ are slightly higher than the experimentally observed π to π* transition value (242–267 nm),⁹⁴ which might be due to the absence of solvent. Consequently, ligation stabilized the cluster, which is apparent from the computed negative binding energy values. The capability for binding increased in the following order (Table 5):

[Au₄Cu₂(PH₃)₆]²⁺ < [Au₄Pd₂(PH₃)₆]²⁺ < [Au₄Ag₂(PH₃)₆]²⁺ < [Au₆(PH₃)₆]²⁺ < [Au₄Ni₂(PH₃)₆]²⁺ < [Au₄Pt₂(PH₃)₆]²⁺

Table 5 Computed redox properties of ligated [Au₄M₂(PH₃)₆]²⁺, M = Au, Cu, Ag, Ni, Pd and Pt clusters using CAM-B3LYP functional. Calculated AIP, AEA, VIP, VEA, η, BE with counterpoise correction, λ_red and λ_oxi are given in (eV)

Clusters [Au4M2(PH3)6]^2+	AIP	AEA	VIP	VEA	η	BE	λoxi	λred
M = Au	12.86	6.78	12.42	6.45	5.97	−13.14	0.44	0.33
M = Cu	12.49	6.55	12.62	6.62	6.00	−12.42	0.13	0.07
M = Ag	12.30	6.43	12.43	6.50	5.93	−12.89	0.13	0.07
M = Ni	11.83	7.59	11.96	7.60	4.36	−13.25	0.13	0.01
M = Pd	12.81	7.24	12.95	7.32	5.63	−12.62	0.14	0.08
M = Pt	12.75	6.93	12.89	7.01	5.88	−14.35	0.14	0.08

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The extent of charge transfer from –PH₃ to the metal cluster [Au₄M₂] is lower than that for –SCH₃ metal cluster [Au₄M₂], which is apparent from computed natural charges (Table S4 in ESI†). Thus, the binding efficiency of –SCH₃ is stronger than –PH₃. Additionally, the decrease in HOMO–LUMO gap (Fig. 5) and chemical hardness values prove that –PH₃ passivation decreases the chemical stability of all the clusters. Herein, d⁸ metals follow the same trend as coinage metal doped clusters.

As predicted, the negatively charged clusters are more stable compared to other charged clusters. Added electron is localized at the inner metal core with minimal contribution from ligand layer (Fig. 8). However, the removal of electron has a noticeable contribution from ligand layer which is lesser than the contribution from metal core. The –PH₃ ligands play a major role in determining the redox properties. The IP and EA values are found to increase during the passivation, which may be an artefact of the positive charge developed on the capping layer (Table 5). Seemingly, the presence of surrounding electrostatic media in implicit solvation method has decreased the IP and EA values predominantly. In the experimental environment, Cl⁻ ions surround the capping layer which might reduce the IP and EA further. Hence, our solvation studies propose that (Table S6 in ESI†) the presence of –PH₃ capping, reduces the IP and EA. The difference in VIP/VEA and AIP/AEA values are minimal as inspected in –SCH₃ ligated and bare cluster. As observed for IP and EA, the SRP values for these clusters are found to decrease when compared to SCH₃ ligated cluster (Table S7 in ESI†). The absorbance peaks observed are due to the excitation of electrons from HOMO to LUMO which are delocalized (Fig. S3 in ESI†) and possess equal contribution from ligand and metal. As a result the wavelength is red shifted when compared to bare. The shift is larger for d⁸ metals containing clusters than coinage metals containing clusters.

Fig. 8 Spin density plots of ligated [Au₄M₂(PH₃)₆]¹⁺ and [Au₄M₂(PH₃)₆]³⁺, M = Au, Cu, Ag, Ni, Pd and Pt clusters, (densities are plotted with isocontour value: 0.004 Å⁻³).

4. Conclusions

We have computed the lowest energy structures, redox nature, optical properties, chemical stabilities and charge population of bimetallic bare [Au₄M₂] and ligated [Au₄M₂(SCH₃)₆], [Au₄M₂(PH₃)₆]²⁺ clusters. Irrespective of the stoichiometry and ligation, the negatively charge clusters are comparatively stable than neutral and positively charged clusters. In bare form, all the clusters Au₆, [Au₄Ag₂], [Au₄Cu₂], [Au₄Ni₂], [Au₄Pd₂] and [Au₄Pt₂] invariably exist in a 2D triangular form in all three charge states. The hetero-metals are present as a part of inner ring. However, the symmetry of bimetallic cluster has been reduced by the introduction of a hetero metal atom due to gold to hetero-metal charge transfer and as a result the new charge type atoms arise. The introduction of –SCH₃ ligand made it a part of the skeleton of [Au₄M₂(SCH₃)₆] clusters while, the –PH₃ ligation remains as a passivation layer by preserving the metal core. A maximum charge flows from –SCH₃ to the metal atom than from –PH₃, which is reflected in the binding energy values. The –SCH₃ passivation increases the chemical stability of the coinage metals while it decreases for Ni, Pd, Pt containing clusters, which might be due to the d⁸ group preference towards tetrahedral coordination sphere. However, –PH₃ ligand, decreases the chemical stability of all the clusters. This shows that [Au₄Ag₂(SCH₃)₆], [Au₄Cu₂(SCH₃)₆], [Au₆(SCH₃)₆] may appropriately display catalytic activity due to their chemically inert nature. While –PH₃ protection can bring about some other applications. The calculated AIP and AEA values of ligated clusters support the above fact. The lower reorganization energy shows the possible uses of these candidates in electronic devices. Further, excitation studies show a thiol ligation blue shift the absorbance band (due to LMCT), while PH₃ ligation red shift because of HOMO and LUMO orbitals which are delocalized over metals and ligands.

Acknowledgements

We thank DST-SERB, UGC-Faculty Recharge Programme, UGC-MRP for funding. We also thank Prof. S. Balasubramanian, Chemistry and Physics of Materials Unit, JNCASR, Jakkur, Bangalore for his support.

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Footnote

† Electronic supplementary information (ESI) available: The supplementary file contains the following information (i) computed optimized structural parameters of bare and ligated bimetallic cluster (ii) redox properties in three implicit solvent media (iii) natural atomic charge distribution of ligated clusters and (iii) computed important collective vibrational frequencies of ligated clusters (iv) computed HOMO and LUMO pictures for bare and ligated clusters. See DOI: 10.1039/c6ra14886g

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