Introduction

The study of metal clusters is interesting as they provide us an opportunity to examine the size evolution of metals from the atomic to the bulk state. The properties of a material at the nanoscale can be very different from that of the bulk. As nanoclusters contain a large number of low coordinated surface atoms they readily form bonds with other species, and hence, can be very useful as catalysts. Among metal clusters, gold has been very widely investigated due to its applications in a number of fields like catalysis (Pyykkö 2004) biological diagnostics, medicine, molecular electronic devices (Cui et al. 2001; Valden et al. 1998), nanostructured materials (Whetten et al. 1996; Andres et al. 1996), optics, material science and solid-state chemistry. The properties of pristine gold clusters can be altered by doping the cluster with impurities. This tailoring of the cluster composition leads to changes in the structural, electronic, magnetic and reactivity properties, thus increasing their potential applications. The modification of cluster properties by doping can be effected in two dimensions, viz, by varying the nature and amount of the dopant. A number of studies have been carried out on doped gold clusters (Majumder et al. 2006; David et al. 2010), the most common elements used for doping being the transition metals (Li et al. 2005). There are also studies on the doping of gold clusters by s and p block elements. The electronic structure of alkali metals is similar to that of gold as both contain a single s valence electron. This makes the study of alkali-metal-doped gold clusters particularly interesting. Studies on gold aurides have revealed that the gold-alkali metal bond is highly polar with a large charge transfer from the alkali atom to the gold. Due to the high difference in electronegativity between the alkali metals and gold, alkali aurides are found to be highly stable. Among the alkali metals, the electronic structure of lithium is different as it presents an unfilled p shell (Rajesh and Majumder 2009; Heiz and Bullock 2004). In addition, lithium is the lightest element that is metallic under normal conditions. So it would be interesting to investigate how doping of a gold cluster by a lithium atom modifies its electronic properties and reactivity.

In an earlier study on the structural and electronic properties of Au n clusters (n = 2–13) using DFT (Deka and Deka 2008) we have found that the triangular Au6 cluster is highly stable. A number of isomeric Au6 clusters were considered in that study. In this paper, we examine the effect of doping Au6 clusters with a lithium atom resulting in the formation of Au5Li clusters. An exhaustive search for enhanced catalytic properties of nanoclusters by doping can be accomplished only if all isomers of the parent cluster are considered. So, we have taken a number of isomeric structures of the highly stable triangular Au6 cluster from our earlier study as candidate structures for the present investigation.

Computational details

Density functional calculations were performed to obtain full geometry optimization at the level of a generalized gradient approach via the BLYP exchange–correlation functional. This functional incorporates Becke’s exchange (Becke 1988) and Lee–Yang–Parr correlation (Lee et al. 1988). All calculations were performed using the DMol3 suite of programs (Delley 1990). Scalar relativistic effects (VPSR) (Delley 1998) were incorporated into our all electron calculations to account for gold, which is a heavy atom. Relativistic effects in gold lead to radial contraction and energetic stabilization of the s and p orbitals and a consequent radial expansion and energetic destabilization of the d and f orbitals. This leads to stronger interaction between the valence 5d and 6s orbitals thus reducing the s–d energy gap. Relativistic effects lead to shorter metal–metal bonds, and hence, more stable clusters. The planarity of gold clusters up to large system size is attributed to relativistic effects. The effects of relativity on properties like bond length, ionization potential, electron affinity, dissociation energy, etc. for Au2, AuH and Au (solid) has been listed by Pyykkö (2004) in his excellent review on gold clusters.

Self consistent field procedures were carried out with convergence criteria of 1 × 10−5 a.u. on the total energy and 1 × 10−6 a.u. on the electron density. The basis set used is of double numeric quality with polarization functions (DNP) (Delley and Ellis 1982). This basis set is comparable with the Gaussian 6-31G** basis set, but the DNP basis set is supposed to be more accurate than a Gaussian basis set of similar size. All calculations are spin restricted and the geometry optimizations have been performed without imposing any symmetry constraint.

The average binding energy per atom is computed from:

$$ E_{\text{b}} = \left[ { 5E({\text{Au}}_{ 1} ) \, + \, E({\text{Li}}_{ 1} ) - E({\text{Au}}_{ 5} {\text{Li}})} \right]/{6} $$

where E(Au5Li) is the energy of the Au5Li cluster.

Chemical hardness is used as a parameter to determine the reactivity of a system. In density functional theory, hardness (η) of an electronic system is defined as the second derivative of energy (E) with respect to the number of electrons (N) at constant external potential, \( v(\vec{r}) \) (Fukui 1982).

$$ {\eta = \frac{ 1}{ 2}\left( {\frac{{\partial^{ 2} E}}{{\partial N^{ 2} }}} \right)_{{v(\vec{r})}} = \frac{ 1}{ 2}\left( {\frac{\partial \mu }{\partial N}} \right)_{{v(\vec{r})}} } $$

where μ is the chemical potential of the system.

Global hardness, η can be approximated as

$$ \eta = \frac{\text{LUMO - HOMO}}{ 2} $$

Fukui function \( f(\vec{r}) \), as defined by Parr and Yang (Parr and Yang 1984; Yang et al. 1984), is a mixed second derivative of energy of the system with respect to the number of electrons N and constant potential \( v(\vec{r}) \):

$$ f(\vec{r}) = \left( {\frac{{\partial^{2} E}}{{\partial N\partial v(\vec{r})}}} \right) = \left[ {\frac{\delta \mu }{{\delta v(\vec{r})}}} \right]_{N} = \left( {\frac{{\partial \rho (\vec{r})}}{\partial N}} \right)_{{v(\vec{r})}} $$

where \( \rho \left( {\vec{r}} \right) \) represents the electron density at position \( \vec{r} \) of the chemical species.

Fukui function expresses the sensitivity of the chemical potential of a system to an external perturbation. Higher the value of Fukui function at a particular site, more is its reactivity. The condensed Fukui function for an atom k in a molecule having N electrons can be obtained from the finite difference approximation as:

$$ f_{k}^{ + } = [q_{k} (N + 1) - q_{k} (N)]\quad {\text{for nucleophilic attack}} $$

and

$$ f_{k}^{ - } = [q_{k} (N) - q_{k} (N - 1)]\quad {\text{for electrophilic attack}} $$

where \( q_{k} (N),\;q_{k} (N + 1) \) and \( q_{k} (N - 1) \) are electronic populations on the particular atom k of the molecule with N, N + 1 and N − 1 electrons, respectively. The ‘relative electrophilicity’ and ‘relative nucleophilicity’ values for the particular atom can be obtained from the ratio of Fukui functions \( f_{k}^{ + } /f_{k}^{ - } \) and \( f_{k}^{ - } /f_{k}^{ + } \), respectively.

A large number of Au6 isomeric clusters were used as candidate structures. One atom of the pristine gold cluster was replaced by a lithium atom and then the geometry was fully optimized. This replacement by a lithium atom was done for each unique atom of the cluster. Vibrational frequency calculations were then carried out at the optimized geometry to verify that the obtained structures are global minima on the potential energy surface. The Fukui functions were calculated on the basis of Hirshfeld population analysis.

Results and discussion

We started with eight isomeric structures of the Au6 cluster and doped each unique atom of each structure by a lithium atom. These isomeric structures are shown in Fig. 1. These clusters have been arranged in the order of increasing energy. The minimum energy structure is triangular. These structures have been taken from our earlier work on the structural and electronic properties of stable Au n (n = 2–13) clusters (Deka and Deka 2008). Substitution of a gold atom by a lithium atom resulted in ten stable structures of the Au5Li cluster. The other geometries either did not converge or exhibited negative frequencies. The optimized geometries are shown in Fig. 2.

Fig. 1
figure 1

Optimized geometries of Au6 clusters arranged in the order of increasing energy. The unique atoms have been marked

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Fig. 2
figure 2

Isomeric structures of Au5Li clusters arranged in the order of increasing energy. Gold atoms are numbered as 1 and Li atoms as 2. The relative energies are given in eV

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The structures have been named as S1, S2, S3, …, S10 by their relative stability, namely, S1 is the most stable structure and S10 is the least stable. Of the ten structures of the Au5Li cluster, five are found to be planar. The structures of the Au6 clusters are mostly retained on doping with a lithium atom, the two-triangle S8 structure being an exception. In case of the Au6 cluster, this structure is three-dimensional having C2h symmetry, while in case of Au5Li, it is planar. The structure S2 which is a capped square pyramid has not been found in case of the Au6 cluster. As in case of pristine Au6 cluster, the minimum energy structure of the Au5Li cluster is triangular with a small inner triangle housed inside a big outer triangle. The lithium atom occupies the mid position which forms a vertex of the inner triangle. The other stable isomer having a similar triangular structure is S4 where the lithium atom occupies the apex position forming a vertex of the outer triangle. To the best of our knowledge there has been no theoretical or experimental study on the Au5Li bimetallic cluster. So, a direct comparison of our parameters with those of other workers is not possible. As seen from Table 1, the average Au–Au distances for the various isomers of the pristine gold clusters lie in the range 2.63–2.79 Å while those for the Au5Li clusters vary between 2.45 and 2.60 Å, respectively. Another DFT study with the PW91 exchange correlation functional and a plane wave basis set (Li et al. 2006) gives average Au–Au distances varying between 2.58 and 2.82 Å for various isomers of pristine Au6 clusters. Our study reveals that bond distances for neighbouring Au–Li atom pairs are shorter than those of the Au–Au atom pairs, indicating that Li substitution leads to stronger bonds. However, our Au–Li distances are much larger compared to the AuLi dimer bond length (2.27 Å) (Leonardo et al. 2006), and hence, much weaker.

Table 1 Geometric and energetic parameters of pristine Au6 and bimetallic Au5Li clusters
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The binding energy per atom values of the different isomers of the Au5Li cluster is given in Table 1. In addition, shown in Table 1 are the binding energies per atom of the corresponding pristine Au6 clusters for comparison. The most stable triangular Au5Li cluster S1 with the lithium atom having a coordination number of 4 exhibits the highest binding energy of 1.966 eV. The binding energy per atom of the pristine triangular Au6 cluster has a value of 1.843 eV. Similar GGA calculations at the PW91PW91/6-31G* (Majumder et al. 2006) and PW91/LANL2DZ (Li et al. 2007) levels of theory reveal binding energy per atom values of 1.82 and 1.826 eV, respectively, for the minimum energy triangular Au6 cluster. Our binding energy value for triangular Au5Li cluster is higher than each of these values. Thus, lithium substitution leads to an increase in the binding energy per atom of this structure by 0.123 eV in our case. For the structure S4 where the lithium atom has a coordination number of 2, the binding energy per atom value is 1.848 eV. As can be seen from Table 1 this value is only slightly higher than that of the corresponding pure gold cluster. Thus, gain in binding energy due to lithium substitution into the minimum energy triangular Au6 cluster is more when the lithium atom has a higher coordination number. On going from the most stable S1 cluster to the least stable S10 cluster the binding energies go on decreasing. The S10 structure has a binding energy of 1.647 eV. A comparison of the binding energy values of the Au5Li and Au6 clusters reveal that in each case the binding energies increase due to lithium substitution.

The HOMO–LUMO gap is a measure of stability of clusters. Larger the HOMO–LUMO gap, more stable is the cluster. In Table 1 we show the HOMO–LUMO gap of the optimized Au5Li clusters along with those of the corresponding pure Au6 clusters. The most stable Au5Li cluster S1 exhibits the highest HOMO–LUMO gap of 1.736 eV. The other triangular Au5Li cluster S4 has a HOMO–LUMO gap of 1.586 eV. The parent structure of both these clusters is the triangular Au6 cluster having a HOMO–LUMO gap of 1.727 eV. Thus, lithium substitution leads to increase in the LUMO–LUMO gap, the change in HOMO–LUMO gap being larger when lithium occupies the mid position. The pentagonal pyramidal structure S3 with a 5-coordinated lithium atom at the top also has a large HOMO–LUMO gap of 1.684 eV. The analogous Au6 cluster has an energy gap of 1.641 eV. It is seen that in most cases lithium substitution leads to an increase in the HOMO–LUMO gap with the octahedral structure S9 being an exception. In addition, shown in Table 1 are the values of chemical hardness of the clusters. As expected, the most stable cluster has the highest value of chemical hardness. It is seen that for most of the structures, chemical hardness increases due to lithium substitution.

To study the local reactivity at different sites within a cluster, we choose the most stable Au5Li cluster, S1 for our investigation. The Hirshfeld charges and Fukui functions for this structure are shown in Table 2. In addition, shown are analogous values of the pristine triangular Au6 cluster. As can be seen from the table, the lithium atom bears a positive charge of 0.189 q while the gold atoms are negatively charged. In case of the pure Au6 cluster, three atoms, namely, those lying at the vertices of the outer triangle carry negative charges while those forming the vertex of the inner triangle bear positive charges of equal magnitude, thus making the cluster neutral as a whole. Thus, on doping the Au6 cluster with the lithium atom, lithium donates electrons to the gold atoms becoming positively charged in the process, while the negative charge on the gold atoms increase. In addition, shown in Table 2 are the values of the Fukui functions at different sites within the cluster. For the pure Au6 cluster the atoms lying at the vertex of the outer triangle have higher values of relative electrophilicity \( f^{ + } /f^{ - } \) indicating that these atoms are prone to attack by nucleophiles like CO. The atoms forming the vertex of the inner triangle on the other hand having higher values of relative nucleophilicity \( f^{ - } /f^{ + } \) and hence are prone to attack by electrophiles like O2. On substituting the lithium atom at the mid site the outer gold atoms still remain prone to attacks by nucleophiles like CO. But in addition we have a new site which prefers a nucleophile like CO or H2O. A look at Table 2 reveals that the lithium atom has a higher value of \( f^{ + } /f^{ - } \) compared to \( f^{ - } /f^{ + } \), and hence, prefers a nucleophile like CO. In case of the pure gold cluster this site is prone to electrophilic attack. Thus, as a result of lithium substitution the number of possible sites for nucleophilic attack on the system increases.

Table 2 Hirshfeld charges, Fukui functions, relative electrophilicity and relative nucleophilicity values for unique atoms of pristine Au6 and bimetallic Au5Li clusters
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The spatial orientation of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energy levels are depicted in Fig. 3. It is seen that the HOMO is strongly delocalized with contribution from all the gold atoms of the cluster. This delocalization of the electronic wave-function leads to stabilization of the planar structure. The LUMO is found to be concentrated at the gold atoms forming the vertex of the outer triangle. So the electron accepting power of the cluster is higher at these sites. Thus, an electron-rich species like CO is most likely to be adsorbed at these sites. This further confirms the predictions regarding nucleophilic attack obtained from the Fukui function values.

Fig. 3
figure 3

Spatial orientations of the highest occupied molecular orbital and lowest unoccupied molecular orbital of the minimum energy triangular Au5Li cluster

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Summary

We have obtained the optimized geometries of ten isomeric Au5Li clusters. These structures were obtained by replacing one gold atom of pure Au6 clusters by a lithium atom. The structure and energetics of these clusters were compared with analogous structures of the pristine Au6 cluster. It is found that the structures of most of the gold clusters are retained on lithium substitution. Parameters like binding energy per atom, HOMO–LUMO gap and chemical hardness increase on doping the Au6 cluster by a lithium atom indicating that the bimetallic Au5Li clusters are more stable than their pristine Au6 counterparts. Further it is found from Fukui function values that lithium substitution leads to increase in the number of sites prone to be attacked by nucleophiles like CO. The HOMO of the minimum energy planar triangular Au5Li cluster is strongly delocalized leading to its high stability.