Role of size and shape selectivity in interaction between gold nanoclusters and imidazole: a theoretical study

Abstract

We present a theoretical study on the structure, stability, spectra and electronic properties of imidazole (Im) adsorbed on gold nanoclusters (Au_n, n = 2, 4, 6, 8, 10, and 20). These computations were performed using various density functional theories with and without inclusion of Grimme’s (D3) dispersion correction. For small clusters, we also carried out wavefunction-based ab initio (MP2 and SCS-MP2) computations for comparison. Vibrational, atoms in molecules (AIM) and natural bond orbital (NBO) analyses clearly reveal the occurrence of charge transfer (CT) through covalent (N1–Au) and noncovalent interactions that play important roles in the stability of the Im@Au_n complexes with anchor assisted H-bonds (C_α–H · Au). Therefore, gold clusters can act as H-bond acceptors with biomolecules for development of new materials and applications. Our study establishes also the ability and reliability of PBE0 and M05-2X functionals compared to B3LYP and PBE for an accurate description of covalent and noncovalent interactions between Im and gold clusters since they lead to close agreement with MP2. Finally, we show that the Au₈ cluster may be viewed as large enough to mimic the 3D gold surface.

Introduction

Gold bulk surfaces have relatively high inertness in any chemical environment. [1] Therefore, adsorption of molecules on such surfaces is difficult, whereas reactivity as well as adsorption capacity on Au_n clusters vary and depend strongly on clusters size, i.e., n. This may be connected to the possible different Au–Au coordination numbers in Au_n clusters. Particularly, inner gold Au–Au bonds are always shorter and stronger than the outer bonds [2–6]. Specifically, investigations into the interaction of biomolecules with gold nanoparticles (Au_n, n = 1–20/40 called also nanoclusters) represent a very active research topic in biological, chemical and material sciences [7–23]. These features can play important roles in various fields of application of gold complexes, such as sensors, biosensors, drug-delivery, molecular electronic devices and energy materials [7, 8, 9].

Numerous experimental and theoretical studies have been performed on the complexes formed between various sizes of selected Au_n nanoparticles and biomolecules such as DNA bases, proteins, peptides and nitrogen-based bases for biochemical applications [10–23]. For instance, nitrogen based biomolecules such as guanine (G) [10, 11], cytosine (C) [12, 13], adenine (A) [14], thymine (T) [15], uracil (U) [16], histidine (HIS) [17], cysteamine [18] and DNA base pairs (AT and GC) [19–23], with gold clusters and surfaces have attracted widespread attention. For gold clusters binding with nucleic acid base pairs (GC@Au_n and AT@Au_n, where n = 4 and 8), DFT-B3LYP calculations by Kumar et al. [14] revealed that neutral gold complexes are more stable than the corresponding anions. Using also B3LYP method, Leszczynski and co-workers [21] studied the interaction of purine base G, and the Watson-Crick GC base pair with gold nanoclusters. They reported vertical ionization energies, electron affinities and charge transfer characteristics for these complexes. These studies clearly revealed that A, G, and C adsorb at Au electrodes whereas base unit T does not, which is in line with the experimental studies by Tao et al. [24] of nucleic acid bases in interaction with the Au (111) surface. Accordingly, strong binding of the N-atom on gold surface/nanoclusters requires an unprotonated nitrogen part of the aromatic ring.

Another important issue relative to the investigation of molecules–gold nanoclusters concerns the quantification with high accuracy of various types of covalent and noncovalent interactions that may take place during chemisorption and physisorption of molecules on gold surfaces. The strength and nature of the interactions between organic adsorbate and metal substrate can be probed experimentally through, for instance, temperature-programmed desorption (TPD) and microcalorimetry measurements [25, 26]. Alternatively, theoretical approaches can be used to predict the structure, stability, bonding, binding sites and properties of these nanomaterials. In 2006, Aikens and Schatz [27] pointed out a chemical surface-enhanced Raman scattering (SERS) enhancement for pyridine linked to Au₂₀ cluster (i.e., pyridine@Au₂₀) using time dependent-density functional theory (TD-DFT) and SERS spectroscopy; however, the origins of such enhancement were not definitively established. In 2008, Iori et al. [17] treated the interaction between the HIS (Im model) side chain and the Au (111) surface using DFT-PBE. They established the existence of an unconventional H-bond (namely a C_α–H⋯Au bond) that is uncertain in DNA base pairs and a HIS model with Au (111) surface [17]. Moreover, they found that the unprotonated N1 atom of the Im moiety interacts directly with the top site of the fcc (111) hexagonal lattice [17]. In 2012, Cao and co-workers [28] found an unconventional N–H⋯Au H-bond in nucleobase–gold complexes through anion photoelectron spectroscopy and DFT calculations. Last year, experimental and theoretical reports on various phases of benzenediamine molecules with gold surface using X-ray resonant photoemission spectroscopy (RPES) revealed that ultrafast charge transfer (CT) across the metal–organic interface does not require solely covalent bonds but may occur also through noncovalent interactions [29].

Generally, gold interacts with N-based biomolecules through CT, van der Waals (vdWs), and hydrogen (H)-bonded interactions such as N–H⋯Au, C2–H⋯Au, and C5–H⋯Au types of interaction (see Fig. 1 for atom numbering). These unconventional types of H-bonds can be calculated by modern experimental and theoretical techniques [28]. Theoretically, quantification of CT through covalent and noncovalent interactions within organic-metal clusters can be evaluated from selection of a suitable functional. With this purpose in mind, Urban and co-workers characterized the type of metal–ligand interaction, bonding and CT properties of coinage metals and lone-pair ligands using different DFTs and CCSD (T) methods in connection with relativistic basis sets [30], and showed that the PBE0 functional is well suited to treating these kinds of complexes. At present, we use a set of exchange correlation density functionals (i.e., B3LYP, PBE, PBE0 and M05-2X) in connection with large basis sets to deduce the equilibrium structures, energetics, spectroscopy and chemical bond types (covalent, CT, vdWs) in Im@Au_n complexes, where n = 2, 4, 6, 8, 10, and 20. We first check the capability of various DFT functionals for deriving reliable data for Im@Au_n through comparison to MP2 geometries and energetics for smaller Im@Au_n (n = 2 and 4) complexes. We also considered dispersion effects via inclusion of Grimme’s corrections. Based on the evaluation, we select PBE0 and M05-2X functionals for the treatment of larger sized clusters (n = 6–20). Mainly, we show that Im@Au_n properties (both structural parameters and binding energies (BEs) converge to those of Im adsorbed on Au bulk for n ∼8 and that Im@Au_n complexes are stabilized by a strong nitrogen–gold bond together with weak anchor assisted H-bond (AAHB) interactions. Finally, we discuss the possible applications of the present findings.

Fig. 1

Optimized geometries of Im@Au₂ at B3LYP (bold), PBE (normal), PBE0 (Italic) and M05-2X (bold / italic) methods using BS1 basis set. Parenthesed distances are computed using BS2. Geometries at MP2 level are presented in red. Distances are in Ångstroms

Computational details

Difficulties in studying organic-metal cluster complexes reside in: (1) a balanced description of metal–metal and metal–hetero atoms within the complexes, (2) the correct accounting for electron correlation and dispersion that plays a crucial role in their bonding and structure, (3) the accurate description of several types of interactions that are a priori in action (e.g., covalent bonding within Im, Au–Au bond and covalent and/or non-covalent Au–Im bondings). Our approach overcomes all these difficulties, leading to accurate predictions for Im@Au_n complexes.

For the description of H, C, N atoms, we used either 6–31 + G** or aug-cc-pVTZ basis sets [31–33]. Gold atoms were described using the Los Alamos effective core potential (ECP) Lanl2DZ [34] and the associated 6-31 + G**ULanl2DZ basis set (denoted hereafter as BS1) or aug-cc-pVTZULanl2DZ basis set (denoted as BS2).

For geometry optimizations, we used GAUSSIAN 09 [35]. We considered closed-shell configuration for Im@Au_n (n = 2, 4, 6, 8, 10, and 20) complexes, which are taken in their ground singlet states. Following the investigations of Tao et al. [24], we looked for nanoclusters linking to the unprotonated nitrogen of Im since the other sites would lead to less stable isomers of Im@Au_n. The initial structures of these complexes were inspired from those of the corresponding isolated Au_n clusters as established elsewhere [36–39]. Most of them are detailed in a review by Häkkinen [5] and references therein. The Im@Au_n equilibrium geometries were then freely optimized using DFT-B3LYP, PBE, and PBE0 methods. In addition, we used the M05-2X functional. Recent reports on this kind of molecular systems proved that the M05-2X method is a priori well suited for accurate description of vdWs and dispersion interactions [40–44]. Indeed, close agreement was noted between M05-2X results and those derived using CCSD(T)/CBS on hydride ion–water clusters [45]. All optimizations were performed with Opt = tight and Int = Ultrafine keywords of GAUSSIAN 09. For some complexes, additional SCF = QC or XQC keywords were used to force convergence. Further Møller-Plesset (MP2) [46] and spin-component scaled MP2 (SCS-MP2) [47] computations were carried out for Im@Au₂ and Im@Au₄ to benchmark suitable DFT methods for the treatment of the larger Im@Au_n complexes. These computations were performed using the MOLPRO (version 2012.1) package [48]. Recent reports on H-bonded and stacked dimers have clearly established that SCS-MP2 is well suited for stacking whereas MP2 describes H-bonded dimers well [49]. To address long-range interactions, such as H-bonding and vdWs, we performed additional computations where we used Grimme’s latest version of empirical correction term (DFT-D3) [50–52]. These computations consist of single-point energy correction for geometries optimized using PBE0 and M05-2X methods.

To quantify the nature of intermolecular interactions of CT between Im and gold clusters and of the strength of AAHBs within Im@Au_n clusters, we calculated the vibrational frequencies of these clusters and performed atoms-in-molecules (AIM) analysis as implemented in the AIM 2000 package [53]. AIM is a useful tool to probe covalent and possible weakly bonded systems including vdWs complexes [54–59]. The wave function was generated from M05-2X/BS1 calculation using optimized geometry at the same level. In addition, we analyzed the CT properties between gold clusters and Im using an NBO [60] approach. NBO analysis was carried out at PBE0/BS1 level of theory. Details of the corresponding analysis and the full set of results are given in the electronic supplementary material (ESM).

Results and discussion

Figures 1, 2, 3, 4, 5 and 6 display the optimized structures of Im@Au_n (n = 2, 4, 6, 8, 10, and 20). All represent equilibrium structures, all with positive frequencies. The main geometrical parameters computed at DFT-B3LYP, PBE, PBE0 and M05-2X are given, in connection with the BS1 basis set for comparison. The calculated binding energies (BEs) are listed in Tables 1 and 2. For the Im moiety adsorbed on Au_n clusters, similar equilibrium geometries were found. For Im@Au_n (n = 2, 4), we present also those deduced using the larger BS2 basis set. Moreover, further computations at the MP2/BS1 and MP2/BS2 levels were also carried out for these two complexes. The respective MP2 and SCS-MP2 BEs are provided in Table 1.

Fig. 2

Optimized geometries of Im@Au₄ at B3LYP (bold), PBE (normal), PBE0 (italic) and M05-2X (bold / italic) methods using BS1 basis set. Distances in parenthesis were computed using BS2. Distances in Ångstroms

Fig. 3

Optimized geometries of Im@Au₆ at B3LYP (bold), PBE (normal), PBE0 (italic) and M05-2X (bold / italic) methods using BS1 level. Distances are in Ångstroms

Fig. 4

Optimized geometries of Im@Au₈ at B3LYP (bold), PBE (normal), PBE0 (italic) and M05-2X (bold / italic) methods using BS1 basis set. Distances are in Ångstroms

Fig. 5

Optimized geometries of Im@Au₁₀ at B3LYP (bold), PBE (normal), PBE0 (italic) and M05-2X (bold / italic) methods using BS1 basis set. Distances are in Ångstroms

Fig. 6

Optimized geometries of Im@Au₂₀ at B3LYP (bold), PBE (normal), PBE0 (italic) and M05-2X (bold / italic) methods using BS1 basis set. Distances are in Ångstroms. Upper panel Front view, lower panel top view

Table 1 Calculated basis set superposition error (BSSE)-corrected binding energies (BEs, in kJ mol⁻¹) for Im–Au_n (n = 2 and 4) clusters computed using B3LYP, PBE, PBE0 and M05-2X DFTs with and without inclusion of D3 correction. BEs deduced using MP2 and SCS-MP2 methods are also listed. BS1 and BS2 refer to 6-31 + G**ULanl2DZ and aVTZULanl2DZ and the associated basis sets, respectively

Table 2 Calculated BSSE corrected binding energies (BEs, in kJ mol⁻¹) of Im@Au_n clusters computed using PBE0 and M05-2X and BS1 and BS2 basis sets along with DFT + D3 values

Equilibrium geometries of Im@Au_n clusters and bonding

Im@Au₂

At all levels of theory, we found a planar Im@Au₂ stable complex (Fig. 1). This is due to the non-disturbing environment from the gold side (i.e., linear) with perfect orbital interaction between N1 and Au atoms (Fig. S1 in ESM). DFT Au-N1 equilibrium distances are 2.149 (2.117), 2.110 (2.077), 2.116 (2.0847) and 2.146 (2.124) Å and the Au–Au equilibrium distances are 2.568 (2.565), 2.550 (2.545), 2.541 (2.538) and 2.550 (2.546) Å, using the BS1 (BS2) basis set (Fig. 1). Therefore, BS2 leads to slightly shorter equilibrium distances (differences are less than 0.03 Å). MP2 predicts equilibrium distances within the same range as DFT methods. Earlier reports on G@Au₂ complex optimized at B3LYP/BS1 derived Au–N and Au–Au distances of 2.162 Å and 2.569 Å, respectively [10]. These results are in close agreement with ours at the same level of theory. For both G@Au₂ and Im@Au₂ complexes, the Au–Au distance is slightly longer than its value in the isolated Au₂ dimer. For CH and NH distances in Im, all electronic structure methods lead to sensitively the same equilibrium distances (Fig. 1). Generally, M05-2X predicts shorter distances than the other DFTs but close to MP2 data and hence predicts stronger interactions between N1⋯Au in Im@Au_n complexes.

Im@Au₄

For Au₄, a Y-shape, a rhombic and a trans-chain structure are known (see for instance Ref. [5]). For nanoclusters of Au₄ with Im, we found three different stable planar conformations: Im@Au_4a, Im@Au_4b, and Im@Au_4c (Fig. 2). Im@Au_4c is obtained by linking Im to rhombic Au₄. Im@Au_4a and Im@Au_4b result from attaching Im to the Au₄ Y-structure, which is no longer symmetrical due to the unsymmetrical nature of Im and, in particular, because of the establishment of the H-bonded interaction (C–H⋯Au) with the neighboring gold atoms (dashed lines in Fig. 2). Similarly, the more stable symmetrical tetrahedral (T_d) shape of isolated Au₄ within the Im@Au₄ cluster converts into Im@Au_4a during the optimizations (all methods). The creation of this H-bonded interaction may be related to the relatively acidic nature of the C₂-carbon atom in Im. Such H-bonds were already noted for the G@Au₂ complex and are known as anchor assisted H-bonds (AAHB) [10]. These H-bonds and weakly bound interactions were confirmed by AIM topography analysis. For illustration, Fig. 7 presents the ρ(r_c) and ∇²ρ(r_c) values, with the bond critical points (BCP), the ring critical points (RCP) and the cage critical points (CCP) pointed out. The corresponding NBO analyses and discussions can be found in the ESM.

Fig. 7

Molecular graphs of Im@Au_n complexes at M05-2X/BS1 geometries. Black ρ(r_c) values, red ∇²ρ(r_c) values. These values are shown near to the bond paths corresponding to Au⋯N, C₂–H⋯Au, and C₅–H⋯Au interactions. Red dots Bond critical points (BCP), yellow dots ring critical points (RCP), green dots cage critical points (CCP)

Similar to Im@Au₂, the N1 atom of the Im moiety coordinates directly with an Au atom with a computed Au–N1 distance of ∼2.1 using either DFT/BS1 or DFT/BS2. The intra Im distances are similar to those given in Fig. 1 for Im@Au₂. All DFT methods predict Au–Au distances ranging from ∼2.6 to 2.7 Å, which are slightly longer than those found for Im@Au₂. We compute AAHB distances in the order of 3.6 and 4.2 Å using B3LYP that reduce by 0.2–0.6 Å using either PBE0 or M05-2X. Figure 2 shows that AAHB distances are distinctly shorter in Im@Au_4a than in Im@Au_4b,4c. This is in line with the larger BE computed for Im@Au_4a (Table 1). Generally, the M05-2X functional provides shorter C₂–H Au H-bonds than the other DFTs. M05-2X and PBE0 account for weak interactions at both BS1 and BS2 levels while B3LYP does not. The reliability of these functionals may affect the energetics of these complexes (see next section). Small changes are observed only in the Au–N1 distance with PBE and PBE0 methods. Moreover, M05-2X and PBE0 always predict shorter NH–Au distances (at AAHB) and hence stronger interactions within both moieties of the Im@Au₄ complexes. Moreover, close agreement is found with MP2 results (Table 1). Accordingly, PBE0/BS1 and M05-2X/BS1 levels are suited to the treatment of larger n complexes.

Im@Au₆

DFT and ab initio [MP2/CCSD(T)] computations [61] showed that the Au₆ hexamer presents three stable forms of D_3h, C_5v and D_4h symmetries. These were used as starting points to link with Im. Figure 3 displays the optimized geometries of Im@Au₆ isomers using DFT and BS1. Three isomers were found (Im@Au_6a, Im@Au_6b and Im@Au_6c) where Im forms a complex with the Au₆ cluster with an unprotonated nitrogen. Im@Au_6a consists of a planar Au₆ cluster bonding to Im, which is located in the perpendicular plane of the Au₆ plane, whereas both Au₆ and Im belong to the same plane in Im@Au_6b and Im@Au_6c isomers. Figure S1 in the ESM shows that there is a favorable interaction between the orbitals of N1 and the Au adatom for these configurations. A further charge transfer stabilization through covalent and noncovalent bonds may take place also. Indeed, Im@Au_6a and Im@Au_6b present an adatom type of interaction that is characterized by a unique Au–N1 bond, whereas the Im@Au_6c isomer form is stabilized by three different types of interactions consisting of an Au⋯N1 bond and two H-bonded (C–H⋯Au) weak noncovalent interactions as those described above for Im@Au₄. The Au–N1 distance was computed to be ∼2.2 to 2.3 Å. Even though other possible conformations were searched, optimizations led solely to Im@Au_6a, Im@Au_6b and Im@Au_6c clusters forms. This is due to orbital overlapping and additional types of noncovalent interactions within these clusters that favor these three conformations. Note that Im@Au_6b converts into Im@Au_6a at PBE0/BS1 and M05-2X/BS1 levels.

Im@Au₈

The three most stable forms of Au₈ are of D_4h, C_2v and T_d symmetries [62]. When Im interacts with Au₈, six isomers are found: Im@Au_8a, Im@Au_8b, Im@Au_8c, Im@Au_8d, Im@Au_8e and Im@Au_8f (Fig. 4). In Im@Au_8a,8b,8e,8f, the gold octamer is a planar star-/wheel-like molecule with Im either in the gold atom plane or orthogonal to it. In Im@Au_8c and Im@Au_8d, Im is connected to 3D Au₈ either as an adatom or to the surface of the cluster. For the Au₈ cluster, Hansen et al. [62] recently predicted a similar non-planar structure, which has the lowest energy isomer using CCSD(T). Im@Au_8a, Im@Au_8b, Im@Au_8c and Im@Au_8e clusters present relatively short Au⋯N distances (of ∼2.2 Å) whereas a slightly longer Au⋯N distance (of ∼2.3 Å) is computed for Im@Au_8d and Im@Au_8f. The latter can be considered as models for Im adsorbed on an Au(111) surface [63]. It is interesting to discuss the Im@Au_8f geometry obtained from the M05-2X method. For instance, this cluster shows a structure that is tilted slightly towards gold surface whereas other methods (B3LYP, PBE and PBE0) predict Im exactly perpendicular to the surface. Based on our geometrical data, hybrid meta functionals are well suited to the accurate description of covalent and dispersive interactions. No obvious H-bonded interaction (C–H⋯Au) is visible for Im@Au₈. Surprisingly, the PBE method leads to a relatively shorter Au⋯N distance (2.257 Å) compared to the other DFT methods.

Im@Au₁₀

Optimized geometries of Im@Au₁₀ complexes are presented in Fig. 5. In total, five structures were computed (Im@Au_10a–e). Im@Au_10a–c clusters are planar whereas 3D structures were found for Im@Au_10d–e. Interestingly, Im@Au₁₀ clusters show a transition from 2D to 3D structures as already noted for isolated Au₁₀ [64]. For Im@Au_10a,b,c,e clusters, Im links to the Au₁₀ cluster via a unique Au–N bond in the N1 atom, whereas the N1 atom of Im forms two coordination covalent bonds with two gold atoms with equal distances (of 2.261 Å) in Im@Au_10d. For Im@Au_10a, B3LYP, PBE, and PBE0 predict a stable structure, whereas this isomer shows different geometry and converts into Im@Au_10d using the M05-2X method because of the unequal arrangement of gold atoms at the Im interaction site. Here, the excess exchange correlation functional favors geometry reorganization. The other complexes have a double ring (hexagon model) type for gold clusters (i.e., planar) but Im forms two different types of interactions. Im@Au_10b has a unique Au and N1 bond. Im@Au_10e presents a Au⋯N bond and an H-bonded interaction (C–H⋯Au). No H-bonds were found for Im@Au_10a and Im@Au_10c. For Im@Au_10d, a C–H⋯Au bond was characterized in addition to the two Au⋯N bonds already noted above, leading to a further stabilization of this isomer. Our results agree with those found for cyclometalated 6-benzylpyridines interacting with gold (III) conformers, where a short Au–N distance ranging from 2.098 to 2.105 Å was predicted using B3LYP/def2-TZVP [65]. In contrast, the calculated Au–N1 bond distances were shorter than in the Im@Au(111) surface (i.e., ≈2.3 Å) [63].

Im@Au₂₀

Through analysis of combined photoelectron spectroscopy and density functional results, Li et al. [2] proposed a highly symmetrical tetrahedral structure for Au₂₀ gold clusters. Aikens and Schatz [27] suggested two different types of cluster model: (1) a tetrahedral gold cluster similar to that proposed by Li et al. [2] and (2) a vertex model with an adatom structure. The Au₂₀ tetrahedral

Binding energies of Im@Au_n clusters

In addition to geometries, BEs of complexes are very important in validating suitable DFT methods for the accurate description of noncovalent interactions [45]. The BEs of all complexes were calculated within the supermolecule approach and corrected for basis set superposition error (BSSE) using the procedure suggested by Boys and Bernardi [72]. The counterpoise (CP) method implemented in the Gaussian package was used to carry out BSSE correction. The BEs of various complexes were calculated using the following energy expression:

$$ BE=\left({E}_{AB}-\left({E}_A+{E}_B\right)\right) $$

where E _AB is the total energy of the Im@Au_n complex at equilibrium, E _A is the energy of the Au_n gold nanocluster and E _B is the energy of Im.

In benchmark computations, we calculated the BEs of Im@Au₂ and Im@Au₄ using either BS1 or BS2 and DFT approaches. Therefore, their BSSE-corrected BEs calculated at the B3LYP, PBE, PBE0, M05-2X and MP2 (SCS-MP2) methods using BS1 and BS2 [single point (SP)] basis sets are listed in Table 1. BE enhancement was observed when the size of the basis set increases (from BS1 to BS2). Also, using B3LYP, computed BEs at BS1 and BS2(SP) energies were almost equal except for Im@Au₂. As expected, the B3LYP/BS1 method was not sufficient to predict the geometry and energies of Im and gold clusters. The same BEs at B3LYP and PBE/BS2 levels were in very good agreement with SCS-MP2 rather than MP2 values. Moreover, differences between MP2/BS2 with DFT methods were B3LYP (−19), PBE(−19), PBE0(−27) and M05-2X (−28) (all values are in kJ mol⁻¹). As established in the literature, B3LYP and PBE methods are very suitable for the description of covalent interactions. To scrutinize the ability of these functionals to describe noncovalent types of interaction, we treated Im@Au₄ clusters, which are stabilized by both (Au⋯N and C–H⋯Au) interactions. M05-2X, PBE and PBE0 methods predict BEs relatively higher than the corresponding B3LYP methods. Values using M05-2X and PBE0 are particularly close to SCS-MP2 values. From this, we conclude that use of PBE and B3LYP methods with BS2 is appropriate for covalently bonded interactions whereas noncovalent interactions need an additional exchange correlation functional (i.e., PBE0 or M05-2X). Finally, SP energies and BEs at optimized structures using either BS1 or BS2 were found to be close. Based on these benchmarks, we calculated the BEs of larger size gold clusters (n ≥6) using the BS2 basis set, where SP computations were performed at the respective optimized structure at the corresponding DFT/BS1 level.

At the M05-2X/BS2 level, we computed BEs of ∼ −126, ∼ −168, ∼ −160 and ∼ −145 (in kJ mol⁻¹) for Im@Au₂, Im@Au_4a, Im@Au_4b, Im@Au_4c, respectively. Such large BEs can be explained by the strong Au–N bond created upon complexation. Moreover, isomer Im@Au_4a is more stable than the other isomers. This is due to the formation of relatively stronger unconventional (C–H⋯Au) H-bonds between gold and Im. Im@Au_4b possesses an analogous type of interaction but different C–H groups are involved in the AAHB, resulting in a reduction in BE(Im@Au_4b) reduction by ∼8 kJ mol⁻¹. Indeed, it can be found from our calculations that the acidic nature of the C₂–H Au interaction within Im@Au_4a is relatively stronger than the C₅–H⋯Au H-bond in Im@Au_4b.

Table 2 presents the BSSE-corrected BEs computed using PBE0 and M05-2X for Im@Au_n (n = 6, 8, 10 and 20). The corresponding values computed using B3LYP and PBE are listed in Table S1 of the ESM. Close examination of Table 2 reveals that adatom model isomers are more stable than the other weakly bonded models, except for Im@Au₁₀ where the 3D isomers (Im@Au_10d and Im@Au_10e) exhibit outstanding stability (BEs of ∼ −200 kJ mol⁻¹) due to the strong chemical bonds occurring there. These two Au₁₀ clusters together with Im@Au_6c, Im@Au_8d, Im@Au_8f and Im@Au_20b may mimic the Au surface model. The calculated dipole moment value of these clusters is close to zero, hence confirming that these clusters may mimic the surface environment. This is largely corroborated by a smaller Au–N distance (i.e., ≤2.3 Å) for adatom type complexes whereas Au–N distances of ∼2.3 Å are computed for surface type models.

At the M05-2X/BS2 level, the calculated BEs for Im@Au_6c, Im@Au_8d, Im@Au_8f and Im@Au_20b complexes are −57.5, −60.3, −72.9, and −53.0 kJ mol⁻¹, respectively. In particular, Au₈ surface models (Au_8d and Au_8f) have larger BEs than the other surface mimicking models. This is due to the additional AAHB (C₂–H⋯Au) interaction within Im@Au_8d at the bridge site, and to dispersion interactions within the Im@Au_8f complex. Note that the calculated M05-2X/BS2 BEs (∼ −50 kJ mol⁻¹) for surface model clusters are in close agreement with the recent PBE treatment of Im adsorbed on a gold (111) surface {Im@Au(111), BE = ∼ −42 kJ/ mol⁻¹ [63]} and an earlier PBE study [17] of HIS adsorbed on a gold (111) surface) (HIS@Au(111), BE = −45.6  mol⁻¹).

Tables 1 and 2 also present the D3 corrected PBE0 and M05-2X BEs. For Im@Au₂ and Im@Au₄, Table 1 shows that an enhancement of BEs is observed for PBE0 + D3 (ranging from −7 to–13 kJ mol⁻¹) whereas M05-2X and M05-2X + D3 lead to similar BEs (differences of ∼ −2 kJ mol⁻¹). Hence, M05-2X represents better predictions for these complexes than PBE0. These BEs are also in close agreement with the SCS-MP2 method. Similar remarks can be drawn for larger sized gold clusters interacting with Im (shown Table 2), where D3 dispersion accounts for −9 to −31 with PBE0 and −2 to −8 kJ mol⁻¹ with M05-2X, respectively. The largest deviations are for Im@Au_6c, Im@Au_8d, Im@Au_8f and Im@Au_20b, which are “surface mimicking models”. More generally, our work reveals that dispersions play an important role in the stability of Im@Au_n complexes.

AIM analysis

Bader’s AIM theory has been employed to quantify the nature of bonding between two molecules or surfaces [53–58]. Several studies have reported characterization of the nature of bonding between organic molecules and metal clusters using AIM parameters [22, 73–76]. AIM can also be used to characterize the agostic type of interaction since it provides more precise quantitative measures with which to describe them. The electron density [ρ(r_c)] and Laplacian [∇²ρ(r_c)] at the bond critical points (BCPs) of the Au N1, C₂-H Au, and C5-H · Au interactions of molecular graphs are shown in Fig. 7. The red, yellow and green dots indicate BCP, RCP (ring) and CCP (cage), respectively. In addition to ρ(r_c) and its ∇²ρ(r_c), other significant parameters such as the kinetic (G_c), potential (V_c), and total (H_c = G_c + V_c) energy density values are provided in Table 3.

Table 3 Electron density parameters (in a.u.) at Au⋯N1 in Im@Au_n clusters computed at the corresponding M05-2X/BS1 equilibrium geometries. G _c Kinetic energy density, V _c potential energy density, H _c  total energy density (= G_c + V_c)

The ∇²ρ(r_c) values indicate the nature of bonding; in particular, positive and negative values of ∇²ρ(r_c) dictate noncovalent and covalent character, respectively [55]. The electronic energy density also provides the valuable information about the nature of bonding. G_c and V_c are always positive and negative, respectively, whereas H_c value depends on the relative magnitude of G_c and V_c. If the G_c value is larger than the absolute value of V_c, the H_c value is positive, thus a purely closed shell interaction is expected. Otherwise, the negative H_c indicates that the interactions correspond to some degree of covalent character. It can be found from our calculated negative values of H_c that all our Au · N1 (Im) complexes are covalent in nature.

Figure 7 shows that the ρ(r_c) values of Im@Au_n clusters range from 0.0608 to 0.0988 a.u. The strongest interaction was found for Au_4a,b complexes [ρ(r_c) values of ∼0.0966 a.u.) and the interaction at surface models such as Au_6c, Au_8d and Au_20b [ρ(r_c) values range from 0.0608 to 0.0658 a.u.]. ∇²ρ(r_c) values exhibited similar trends. The calculated values of ρ(r_c) and ∇²ρ(r_c) at the H-bonds (designated as HBCP) for all the clusters ranged from 0.0051 to 0.0092 and 0.0036 to 0.0084 a.u., respectively. These values clearly indicate the involvement of weak H-bonding interactions in the stabilization of these clusters. Close scrutiny of our AIM analysis (see Fig. 7) shows that the C₂–H Au interaction is present only in Im@Au_4a rather than the Im@Au_4b complex (here C5–H⋯Au) hence rationalizing the observed major stability of Im@Au_4a vs. Im@Au_4b. Similarly, the large BE found for Im@Au_10d (∼ −233 kJ mol⁻¹) due to the formation of double Au⋯N1 (Im) bonds (Fig. 5) is also consistent with our ρ(r_c) and ∇²ρ(r_c) values at BCPs for this complex. Generally, the calculated electron density at the BCPs correlates roughly with the strength of interaction reported by several authors [77–81].

Vibrational spectroscopy

Table 4 lists the M05-2X/6-31 + G** calculated vibrational stretching frequencies, intensities and red/blue shifts. The shifts were calculated from the asymmetric (ν_as) and symmetric (ν_ss) stretching frequencies of N–H and C–H of isolated Im. Upon formation of Im@Au_n complexes, the free N–H group in Im always red shifts whereas ν_CH frequencies are blue-shifted except Im@Au_4a. Similarly, all free N–H and H-bond N–H have red shifts. It can be observed that the red/blue shifts and intensities of C–H⋯Au (ν_C2H) are significantly higher than that of C–H⋯Au (ν_C4H) interactions. For instance, the calculated ν_NH, ν_C2H and ν_C3H frequency shifts for Im@Au_4a are −10, −43, and 23 cm⁻¹, respectively. The ν_NH shifts range from −50 to −5 cm⁻¹and the ν_C2H and ν_C4H shifts are in the ranges ±43 to 38 cm⁻¹ respectively. The largest effect is observed for the Im@Au_4a complex (−43 cm⁻¹) ν_C2H frequency. This is due to the strong AAHB interaction between C₂–H and the gold surface. Moreover, we observed a strong enhancement of the intensity of the N–H stretching bands on the complexes compared to free Im. The effects on C–H stretching band intensities were less pronounced. Complexation-induced shifts and changes in the intensity of the corresponding bands can be checked by means of vibrational spectroscopy as performed by Gruene et al. [71] for isolated small gold clusters.

Table 4 Main vibrational stretching frequencies (ν, in cm⁻¹) of isolated Im or adsorbed on Au_n (n = 2–20) clusters. We give also the band intensities (I, in km mol⁻¹) and the induced shifts (in cm⁻¹) upon complexation. Harmonic vibrational frequencies were computed at the M05-2X/BS1 level of theory and scaled further on by a factor of 0.9445 to derive the corresponding anharmonic frequencies (ν) [86]

UV–vis spectra

Recent benchmark calculations showed that the PBE0 method is accurate enough for the prediction of the optoelectronic properties [82]. Therefore, UV–vis adsorption spectra of Im@Au_n (n = 2–20) complexes along with those of the respective monomers (depicted in Fig. 8) were computed from TDDFT calculations using the PBE0 functional. It can be found from this figure that isolated Au₂ and Im exhibit bands below 250 nm, whereas Im@Au_n complexes exhibit intense peaks from 400 to 700 nm. It is interesting to note that small-sized clusters with Im have bands in both ranges with moderate intensities. Comparison of the spectra in Fig. 8 reveals a significant intensity enhancement as the gold clusters size increases. This is due to the increased efficiency of ligand-to-metal charge transfer in accordance with NBO analysis (cf. ESM)

Fig. 8

UV-vis spectra of Im, isolated Au_n clusters and Im@Au_n complexes

Systematic changes observed in the absorption spectrum and intensity with cluster size clearly reveals that Im@Au_n complexes have potential applications. Recent experimental and theoretical studies on adenine with gold in solution showed similar trends [83]. They also pointed out that, after complex formation, there is an immediate reduction in the intensity of surface plasmon absorbance and a significant red shift in the wavelength (from 525 to 717 nm). Last year, experimental studies on thiol derivatives adsorbed on gold clusters and embedded in polymers [84] showed significant visible fluorescence activity when the thiols were substituted with Im, which is in line with the present findings.

General trends

Figure 9 displays the evolution of BEs and Au–N distances versus n for both adatom and surface model clusters at M05-2X/BS2 level. We also give the corresponding values for Im adsorbed on Au(111) surface [Im@Au(111)] [63]. This figure shows that the calculated |BEs| decrease gradually from Au₂ to the Au₂₀-mer except for Im@Au₄ clusters because of the additional unconventional H-bonds (i.e., AAHB) that stabilize such complexes further. For surface model clusters, |BEs| converge smoothly to the corresponding value for Im@Au(111). Im@Au₈, Im@Au₁₀ and Im@Au₂₀ clusters also present some common characteristics with Im adsorbed on a Au (111) surface [Im@Au(111)]. Therefore, these clusters can be considered as suitable models for investigating organic molecules interacting with the Au (111) surface at low computational cost. Moreover, the nature of the interaction at AAHB can be quantified from AIM analysis. This clearly reveals that gold can act as a potential H-bond acceptor from different environments. These important findings were confirmed by NBO and AIM analysis (see ESM) and vibrational spectra for these complexes. Recently, Aiswaryalakshmi et al. [74] studied the hydrogen bonded complexes formed between the square pyramidal Fe(CO)₅ with HX (X = F, Cl, Br). They showed that Fe can act as a strong H-bond and halogen bond acceptor [74]. Similarly, Sun and Felice [22] found that gold can act as H-bond acceptor with biomolecules (N–H⋯Au and N/O⋯Au). In addition, very recent investigations on Au_n clusters with halogen molecules revealed the covalent nature of the interaction between gold and halogen(s) within such clusters [75], whereas further stabilization is ensured by the occurrence of noncovalent interactions between gold and their complexes as in the present case.

Fig. 9

Evolution of the Au–N distances and BEs of Im@Au_n complexes vs n at M05-2X/BS2 level compared with the Im@Au(111) surface [63]

Both BEs and structures of Im@Au_n clusters clearly show that various types of noncovalent interaction stabilize these complexes. AIM analysis indicates the involvement of weak H-bonding interactions in the stabilization of these clusters in addition to the Au–N bond for which a donor-acceptor type interaction was confirmed by NBO analysis (see ESM for further details). Indeed, the donor-acceptor interactions in these clusters involve the interaction of the lone pairs of the N1 nitrogen atom [LP(1)N1] of Im and Au clusters antibonding orbitals (cf. Table S2). For Im@Au₂, the charge transfer from lone pair of N1 to the antibonding orbital of gold [BD*(1)Au –Au] is higher than the LP(1)N to LP*(1)Au interactions. Therefore, the nature of N1 and the Au1 bond is covalent. Similarly, charge transfer in Im@Au_6c and Im@Au_20b (surface models) exhibits such LP(1)N to LP*(1) Au interactions. An analogous type of charge transfer interaction is also observed in adatom models (Im@ Au_6a, Au_8a, Au_8b, Au_10a and Au_20a). Back bonding effects of gold to Im and intra molecular charge transfer in Im play crucial roles in Im@Au_n complexes. Especially, significant space through charge transfer from the LP of gold [LP*(6)Au1) to C2 and C5 atoms of Im (RY*(2)C2(5)] was observed from our surface model (Im@Au_20b). In addition, charge transfer characterization features of these complexes have also been observed from their shape in frontier molecular orbital analysis. For illustration, Figures S1 and S2 display the isosurface density (0.02 a.u) plots for the Im@Au_n complex calculated at PBE0/BS1. Both surface models Im@Au_6c, and Im@Au_20b complex HOMO orbitals are localized on the N atom of Im and the corresponding LUMO orbitals are localized mostly at gold clusters.

Conclusions

We treated Im@Au_n (n = 2, 4, 6, 8, 10, and 20) complexes using various DFT functionals and basis sets. We found that electron correlation plays a crucial role in the description of these organo-metal complexes and at interfaces. Our work establishes the capability of GGA-PBE0 and M05-2X functionals for providing accurate results for the chemisorption of small molecules on metal clusters and for physisorption, which is dominated mostly by vdWs interactions.

Upon complexation of Im with Au_n clusters, strong Au⋯N bonds occur between Au and the deprotonated nitrogen of Im as well as weak C–H⋯Au H-bond interactions [unconventional type of AAHB (C₂–H⋯Au)]. Vibrational, AIM and NBO analyses revealed the role of various types of noncovalent interactions in the stability of these complexes. On the whole, Im molecular arrangements at gold clusters depend on both covalent and dispersive interactions. Principally, surface mimicking models (such as Im@Au_6c, Im@Au_8d, Im@Au_8f and Im@Au_20b) have more of a dominant dispersion effect than the other, adatom-type, complexes. Finally, we characterized a strong bond between Im and Au_n species that may serve for self-assembled monolayers (SAMs) of organic molecules on gold instead of the well-known gold–sulfur ones for further applications of SAMs [85].