Cluster assembled materials are solids in which clusters serve as the building blocks. These materials allow the integration of multiple length scales into a hierarchical material.  Since the properties of clusters change with size, composition,  and oxidation state, and the emergent behaviors depend on the their architecture, cluster assemblies form materials with tunable properties.  These materials serve as links between the predictable size-invariant properties of solids and the evolution in properties observed at the subnanometer scale where every atom and every electron count. The materials retain many of the characteristics of the original building blocks. Cluster motifs coupled by linkers offer unusual properties because they combine intra-cluster, inter-cluster, and linker-cluster interactions, unavailable in atomic solids.   The fundamental question is, what controls the properties once the clusters are incorporated into an extended nanoscale material? 

    Cluster-assembled materials combine the nanoscale size and composition-dependent properties of clusters and embed them in potentially functional materials.  To understand the emergent properties as the clusters are assembled into hierarchical materials, we have synthesized 23 cluster-assembled materials composed of As₇^3--based motifs and different countercations, and measured their band gap energies.  The results reveal that the band gap energy can be varied from 1.09 eV to 2.21 eV. First principles electronic structure studies have been carried out to identify the physical mechanisms, which enable control of the band gap edges of the cluster assemblies. 

   To probe the origins of the variation in the band gap energies, we examined the nature of the frontier orbitals in isolated A₃As₇ clusters.  The HOMO and LUMO charge densities are plotted below.  The HOMO is composed of contributions from the As atoms, and the LUMO is localized on the alkali metal cations.  Further, the LUMO of the material is derived from the absolute position of the HOMO of the neutral alkali metal atom.  This close correlation is seen below, which shows the energies of the HOMOs of the alkali metal atoms and the calculated band gap energy of the pure Zintl materials.  These were obtained by calculating the band structures of optimized A₃As₇ and A₃As₁₁ assemblies for various alkali atoms in the observed orthorhombic and monoclinic structures of Cs₃As₇ and Cs₃As₁₁.  The experimental and theoretical band gap energy for [K-Crypt]₃[As₁₁] are also included.  The HOMO of the free neutral atom is lowest for lithium and increases as the size of the atom increases, except for the cryptated potassium, in which the lone pair on the polyether greatly destabilizes the HOMO.  Mixing of the states is evident in solids containing multiple countercations, as replacing a single Cs atom with cryptated K ions results in an increase of Ebg from 1.1 to 2.1 eV.  The nature of the countercation is the dominant factor to controls the band gap energy in these assemblies.

    The HOMO-LUMO gap of the isolated [As₇]^3- cluster is 1.80 eV, however the band gap energy of the 2D sheets of [As₇]^3- linked by Cs and Rb and separated by K-Crypt are consistently larger ranging from 1.97 to 2.08 eV.  Changing the assembly from a 0D to a 2D architecture is generally expected to decrease the band gap energy through increased band broadening due to larger coordination, however we observe an increase in band gap energy.30  To understand this phenomenon, we extended our search to the [Au₂(As₇)₂]^4- composite cluster in which we synthesized multiple counterion directed architectures of  have the same basic building [As₇Au₂As₇]^4-, but changing the cation results in 0D and 2D  architectures.  The experimental band gap energy of the 0D compound is found to be 1.69 eV and is in good agreement with the theoretically calculated value of 1.68 eV. We also synthesized structures that are 2D layers formed by interactions of Rb and Cs cations with [Au₂(As₇)₂]^4-, while cryptated alkali cations separate these layers.  The band gap energies of the 2D compounds are found to be 1.87, 1.97, and 1.98 eV, respectively, and are in good agreement with the theoretically calculated values.  The band gap energies for all of the 2D assemblies are larger than the band gap energy of the 0D assembly, whose band gap energy is expected to be the upper limit.  
How does varying the architecture of the assembly increase the band gap energy to a larger value than that of an isolated cluster motif?  

    Our hypothesis is that the counterions connected to the clusters generate an internal electric field that alters the band gap energy through modulating orbitals at the band edge in a manner analogous to crystal field theory.  To demonstrate this, we calculated the electronic structure for an isolated [Au₂(As₇)₂]^4- cluster with four point charges, z, placed at the same positions as Cs in the solid.  The point charges were varied from 0.0 to +1.0e, and the HOMO-LUMO gap and electronic spectrum was monitored.  The HOMO-LUMO gaps increased by 0.34 eV when varying the point charge from 0 to +0.5e for the gold-linked clusters and then to decrease with higher fields.  We found that the increase in the HOMO-LUMO gap is caused by stabilization of the HOMO with increasing field, while the LUMO states show little change until z = +0.6e.  Further, increased electric fields reduce the gap as the As-Au mixed states are strongly stabilized to become the LUMO at high field.  Similar electric-field-dependent behavior is observed for [As₇]^3- clusters, however the gap increases monotonically up to 2.98 eV with increasing electric field (Figure 5b).  We confirmed this by examining the local electrostatic environment of our cluster models in Figure 5c with the associated HOMO plotted as an isosurface.  Figure 5c shows the electrostatic potential of [(Au₂)(As₇)₂]^4- and Cs₄[(Au₂)(As₇)₂] as the electric field corresponds to the gradient of the electrostatic potential; a red to blue sequence indicates a stronger electric field.  In [(Au₂)(As₇)₂]^4-, the electrostatic potential falls off gradually from the isolated cluster because no adjacent counterions are present to generate internal electric fields.  In contrast, for the case of Cs₄[(Au₂)(As₇)₂], there is a large electric field generated by the Cs counterions, precisely along the path of the HOMO orbital.  The band gap energy variation also depends on the precise location of the electric field generated by the counterion and by the charge density of the states near the Fermi energy, so it may not always result in an increase of the band gap energy.  These results show that the band gap energies of the 2D ionic solids increase due to the generation of internal electric fields by the adjacent counterions.