Gold nanostructures have attracted considerable attention owing to their unique electronic and optical properties, as well as their great potential for medical applications [1–3]. Today, gold nanostructures are also promising for their possible applications in photothermal therapy, radiotherapy and cancer cell imaging because of their good biocompatibility [4–6]. However, a disadvantage of photothermal therapy is that the optical absorption of gold nanoparticles, well known surface plasmon resonance (SPR), is always located in the visible light region, which limits the wider application of photothermal therapy in vivo. To utilize the high optical transmission of biotissue, it is necessary to enhance the near-infrared (NIR) optical absorption. In recent years, several groups have developed the gold nanorod, nanocage and core/shell structure, which are recognized as the promising materials for photothermal therapy [1,7,8]. However, the increasing size would obviously reduce the permeability of tumor tissue, which is disadvantageous to photothermal therapy.

Small gold clusters of typically 1–2 nm are proposed as alternative materials. Sun et al. have shown that the Au–SiO₂ clusters can induce the unusual optical transition, and the optical absorption can be modulated to the NIR. This is also confirmed by the recent photothermal therapy and drug delivery experiment [9]. However, the gold clusters are structurally unstable and have ambiguous electronic structure. The procedure of designing gold clusters with NIR optical absorption is influenced obviously, because of the long time controversy, by the structure of gold clusters. Recently, the obvious progressing has been achieved by density functional theory (DFT) theory calculations and optical spectra experiments [10,11]. The common view is that gold clusters prefer the two dimension structure in the range of Au₄–Au₁₃, while the Au₁₄–Au₂₀ show the cage-like three dimension structure [12]. The more complex cage-like Au₃₂–Au₃₈ clusters have been predicted, although the experimental result may always be contradicted. The optical absorption of Au₂–Au₁₃, Au₁₉, and Au₂₀ have been calculated by time-dependent density functional theory (TDDFT), while the optical transition of Au₃₂ is also focused due to its more stable structure. Notably, the tetrahedral Au₂₀ cluster shows a band gap of ∼1.818 eV, and shows slight NIR absorption [13,14].

Doping Au clusters by other metals provides an available route to modulate electronic and optical properties [15]. It has been demonstrated that metal atoms, such as Zn and Cu, used to dope Au clusters can modify both their structural stability and optical properties due to the delocalizing s and d electronic configurations [16]. Bonacic-Koutecky et al. studied the structure and electronic properties of bimetallic Ag_MAu_N (3 < (M + N) < 5) clusters with DFT calculations [17]. For these clusters, the charge transferred from Ag to Au plays a dominant role in the structure of the bimetallic clusters. The Au–Ag bond is preferred to the Au–Au or Ag–Ag bond [18]. In addition, the metal-doped Au clusters may modulate the HOMO−LUMO gap [19,20]. Thus, we are interested in whether AuAg cluster has tunable optical absorption properties.

Here, we studied electronic structure and optical properties of Ag-doped Au₂₀ clusters. The paper is organized as follows. Section 2 presents and discusses the results of our calculations. First, we investigated the structural properties by analyzing the binding energy. Then we calculated the electronic structures, because the optical properties depend on both the interband and intraband transitions, which are determined by electronic states. Finally, we analyzed the optical transition in different configurations. Section 3 describes the basic ingredients and details of computational methods we applied. Section 4 concludes and summarizes our findings.

The calculations are based on density functional theory (DFT) using a plane-wave pseudopotential method [28]. We use the generalized gradient approximation (GGA) in the scheme of Perdew-Burke-Ernzerhof (PBE) to describe the exchange-correlation functional [29]. Norm-conserving pseudopotential is used to describe the electron-ion interaction. In this code, the plane wave functions of valence electrons are expanded in a plane wave basis set, and the use of norm-conserving pseudopotential allows a plane wave energy cutoff. Only plane waves with smaller kinetic energies are used in the expansion. Reciprocal-space integration over the Brillouin zone is approximated through careful sampling at a finite number of k-points using a Monkhorst-Pack mesh [30]. In the present system, full electron calculation for the Au_20−nAg_n clusters is computationally rather expensive, so it is better to introduce effective core potentials for the Au and Ag atoms to describe the inner-core electrons. Under this approximation, the 5d¹⁰6s¹ outermost valence electrons of the Au atom and 3d¹⁰4s² outermost valence electrons of the Ag atom are described. It is well known that the interaction of a photon with the electrons in the system can be described in terms of time-dependent perturbations of the ground-state electronic states. Optical transitions between occupied and unoccupied states are caused by the electric field of the photon. The spectra from the excited states can be described as a joint density of states between the valence and conduction band. The momentum matrix elements, which are used to calculate the ɛ₂(ω), are calculated between occupied and unoccupied states which are given by the eigen vectors obtained as solution of the corresponding Schrödinger equation. Evaluating these matrix elements, one uses the corresponding eigen functions of each of the occupied and unoccupied states [22,28,31]: (2) ɛ 2 ( ℏ ω ) = 2 e 2 π Ω ɛ 0 ∑ k , v , c | ψ k c | u · r | ψ k v 〉 | 2 δ ( E k c − E k v − ℏ ω )where Ω is the volume of the elementary cell, v and c represent the valence and conduction bands, respectively, k represents the k point, ω is the frequency of the incident light, and u is the vector defining the polarization of the electric field of the incident light, which is averaged over all spatial directions in the polycrystalline case. The real part of dielectric function ɛ₁(ω) can be evaluated from the imaginary part ɛ₂(ω) by the famous Kramer-Kronig relationship.

The calculations are performed at 20 × 20 Å supercell, which contains 20 neutral Au atoms. These models of gold clusters refer to the previous work, which has shown that the best structural stability and average distance between Au-Au bonding is about 2.73 Å [21]. The substitutional method has been taken into account in this paper, and Ag atoms are used to substitute Au atoms in vertex site. In this way, the Au_20−nAg_n clusters are built. In order to weaken the interaction with Ag–Ag, the separation distance should be as far as possible. We choose the energy cutoff to be 720 eV, and the Brillouin-zone sampling mesh parameters for the k-point set are 2 × 2 × 2 for Au_20−nAg_n clusters. The charge densities are converged to 2 × 10⁻⁶ eV/atom in the self-consistent calculation. And then, the Au_20−nAg_n clusters are optimized with lattice constants and the positions of substitutional atoms. In the optimization process, the energy change, maximum force, maximum stress and maximum displacement tolerances are set as 2 × 10⁻⁵ eV/atom, 0.05 eV/Å, 0.1 GPa, and 0.002 Å, respectively.

In summary, a first-principles study has been performed to evaluate the electronic and optical properties of Au_20−nAg_n clusters in different configurations. The Au_20−nAg_n clusters show better binding energy and structural stability than the Au₂₀ cluster. The increasing Ag concentration can induce the HOMO-LUMO gap variation. Subsequently, the optical transition between HOMO-LUMO has shifted to the low energy range with the increasing Ag concentration. Tunable optical transition has been observed, and was shown to decrease from 2.51 to 2.01 eV with the increase of Ag atoms. Our results clearly show that Ag incorporation can modulate the optical properties of Au₂₀ clusters.