Tuning the electronic properties of hexanuclear cobalt sulfide superatoms via ligand substitution

Theory of acoustic polarons in the two-dimensional SSH model applied to the layered superatomic semiconductor Re6Se8Cl2

Layered superatomic semiconductors, whose building blocks are atomically precise molecular clusters, exhibit interesting electronic and vibrational properties. In recent work [Tulyagankhodjaev et al., Science 382, 438 (2023)], transient reflection microscopy revealed quasi-ballistic exciton dynamics in Re6Se8Cl2, which was attributed to the formation of polarons due to coupling with acoustic phonons. Here, we characterize the electronic, excitonic, and phononic properties with periodic density functional theory. We further parameterize a polaron Hamiltonian with nonlocal (Su-Schrieffer-Heeger) coupling to an acoustic phonon to study the polaron ground state binding energy and dispersion relation with variational wavefunctions. We calculate a polaron binding energy of about 10 meV at room temperature, and the maximum group velocity of our polaron dispersion relation is 1.5 km/s, which is similar to the experimentally observed exciton transport velocity.

Electron and Spin Delocalization in [Co6 Se8 (PEt3 )6 ]0/+1 Superatoms

Molecular clusters can function as nanoscale atoms/superatoms, assembling into superatomic solids, a new class of solid-state materials with designable properties through modifications on superatoms. To explore possibilities on diversifying building blocks, here we thoroughly studied one representative superatom, Co6 Se8 (PEt3 )6 . We probed its structural, electronic, and magnetic properties and revealed its detailed electronic structure as valence electrons delocalize over inorganic [Co6 Se8 ] core while ligands function as an insulated shell. 59 Co SSNMR measurements on the core and 31 P, 13 C on the ligands show that the neutral Co6 Se8 (PEt3 )6 is diamagnetic and symmetric, with all ligands magnetically equivalent. Quantum computations cross-validate NMR results and reveal degenerate delocalized HOMO orbitals, indicating aromaticity. Ligand substitution keeps the inorganic core nearly intact. After losing one electron, the unpaired electron in [Co6 Se8 (PEt3 )6 ]+1 is delocalized, causing paramagnetism and a delocalized electron spin. Notably, this feature of electron/spin delocalization over a large cluster is attractive for special single-electron devices.

Converting CO2 to formic acid by tuning quantum states in metal chalcogenide clusters

The catalytic conversion of CO₂ into valuable chemicals is an effective strategy for reducing its adverse impact on the environment. In this work, the formation of formic acid via CO₂ hydrogenation on bare and ligated Ti₆Se₈ clusters is investigated with gradient-corrected density functional theory. It is shown that attaching suitable ligands (i.e., PMe₃, CO) to a metal-chalcogenide cluster transforms it into an effective donor/acceptor enabling it to serve as an efficient catalyst. Furthermore, by controlling the ratio of the attached donor/acceptor ligands, it is possible to predictably alter the barrier heights of the CO₂ hydrogenation reaction and, thereby, the rate of CO₂ conversion. Our calculation further reveals that by using this strategy, the barrier heights of CO₂ hydrogenation can be reduced to ~0.12 eV or possibly even lower, providing unique opportunities to control the reaction rates by using different combinations of donor/acceptor ligands.

Rational Design of Bimetallic Metal Chalcogenide Clusters for CO2 Dissociation

Thermochemical dissociation of CO₂ on pure, ligated, and mixed transition metal (W, Cu) chalcogenide clusters are investigated using the first-principles gradient-corrected density functional approach. It is shown that although the pure and ligated metal chalcogenide clusters exhibit significantly high barriers for CO₂ dissociation, the computed barriers for the mixed clusters are relatively lower. The lowest barrier is obtained for the Cu₃W₃Se₈ cluster, which shows a dramatically reduced barrier height of only 0.41 eV. Detailed analysis reveals that the substitution of W by Cu sites leads to a charge transfer from Cu to W sites, resulting in locally active W sites. The lowering of the CO₂ dissociation barriers can be attributed to the facile transfer of charge from the locally active W sites and also due to the alteration of the binding energy of CO₂ to the charged W sites. Our studies provide an alternate strategy to design novel thermochemical catalysts for CO₂ adsorption and subsequent dissociation.

High-Spin Superatom Stabilized by Dual Subshell Filling

Quantum confinement in small symmetric clusters leads to the bunching of electronic states into closely packed shells, enabling the classification of clusters with well-defined valences as superatoms. Like atoms, superatomic clusters with filled shells exhibit enhanced electronic stability. Here, we show that octahedral transition-metal chalcogenide clusters can achieve filled shell electronic configurations when they have 100 valence electrons in 50 orbitals or 114 valence electrons in 57 orbitals. While these stable clusters are intrinsically diamagnetic, we use our understanding of their electronic structures to theoretically predict that a cluster with 107 valence electrons would uniquely combine high stability and high-spin magnetic moment, attained by filling a majority subshell of 57 electrons and a minority subshell of 50 electrons. We experimentally demonstrate this predicted stability, high-spin magnetic moment (S = 7/2), and fully delocalized electronic structure in a new cluster, [NEt₄]₅[Fe₆S₈(CN)₆]. This work presents the first computational and experimental demonstration of the importance of dual subshell filling in transition-metal chalcogenide clusters.

Interfacial magnetism in a fused superatomic cluster [Co6Se8(PEt3)5]2

An isolated Co₆Se₈(PEt₃)₆ cluster is non-magnetic; however, we find that a magnetic unit can be formed by fusing two Co₆Se₈(PEt₃)₅ superatoms into a [Co₆Se₈(PEt₃)₅]₂ dimer. Theoretical studies indicate that the dumbbell-shaped [Co₆Se₈(PEt₃)₅]₂ dimer has a spin moment of 2μ_B, and the spin density is primarily localized at the interfacial Co-sites where two clusters are fused into a dimer. The dimer has a low ionization energy of 4.17 eV, allowing the dimer to donate charge to C₇₀ during the formation of a cluster assembled material, as seen in recent experiments by Nuckolls and co-workers. The donation of charge causes the dimer's magnetic moment to drop from 2μ_B to 1μ_B. We hypothesize that adding electrons to the dimer, such as doping impurities to the crystal lattice, may enhance the magnetic moment by neutralizing the charged cluster. This reveals a strategy for stabilizing magnetic moments in ligated cluster assemblies.

The superatomic state beyond conventional magic numbers: Ligated metal chalcogenide superatoms

The field of cluster science is drawing increasing attention due to the strong size and composition-dependent properties of clusters and the exciting prospect of clusters serving as the building blocks for materials with tailored properties. However, identifying a unifying central paradigm that provides a framework for classifying and understanding the diverse behaviors is an outstanding challenge. One such central paradigm is the superatom concept that was developed for metallic and ligand-protected metallic clusters. The periodic electronic and geometric closed shells in clusters result in their properties being based on the stability they gain when they achieve closed shells. This stabilization results in the clusters having a well-defined valence, allowing them to be classified as superatoms-thus extending the Periodic Table to a third dimension. This Perspective focuses on extending the superatomic concept to ligated metal-chalcogen clusters that have recently been synthesized in solutions and form assemblies with counterions that have wide-ranging applications. Here, we illustrate that the periodic patterns emerge in the electronic structure of ligated metal-chalcogenide clusters. The stabilization gained by the closing of their electronic shells allows for the prediction of their redox properties. Further investigations reveal how the selection of ligands may control the redox properties of the superatoms. These ligated clusters may serve as chemical dopants for two-dimensional semiconductors to control their transport characteristics. Superatomic molecules of multiple metal-chalcogen superatoms allow for the formation of nano-p-n junctions ideal for directed transport and photon harvesting. This Perspective outlines future developments, including the synthesis of magnetic superatoms.

Self-interaction-corrected Kohn-Sham effective potentials using the density-consistent effective potential method

Density functional theory (DFT) and beyond-DFT methods are often used in combination with photoelectron spectroscopy to obtain physical insights into the electronic structure of molecules and solids. The Kohn-Sham eigenvalues are not electron removal energies except for the highest occupied orbital. The eigenvalues of the highest occupied molecular orbitals often underestimate the electron removal or ionization energies due to the self-interaction (SI) errors in approximate density functionals. In this work, we adapt and implement the density-consistent effective potential method of Kohut, Ryabinkin, and Staroverov [J. Chem. Phys. 140, 18A535 (2014)] to obtain SI-corrected local effective potentials from the SI-corrected Fermi-Löwdin orbitals and density in the Fermi-Löwdin orbital self-interaction correction scheme. The implementation is used to obtain the density of states (photoelectron spectra) and HOMO-LUMO gaps for a set of molecules and polyacenes. Good agreement with experimental values is obtained compared to a range of SI uncorrected density functional approximations.

Toward Controlling the Electronic Structures of Chemically Modified Superatoms of Gold and Silver

Atomically precise gold/silver clusters protected by organic ligands L, [(Au/Ag)_x L_y ]^z , have gained increasing interest as building units of functional materials because of their novel photophysical and physicochemical properties. The properties of [(Au/Ag)_x L_y ]^z are intimately associated with the quantized electronic structures of the metallic cores, which can be viewed as superatoms from the analogy of naked Au/Ag clusters. Thus, establishment of the correlation between the geometric and electronic structures of the superatomic cores is crucial for rational design and improvement of the properties of [(Au/Ag)_x L_y ]^z . This review article aims to provide a qualitative understanding on how the electronic structures of [(Au/Ag)_x L_y ]^z are affected by geometric structures of the superatomic cores with a focus on three factors: size, shape, and composition, on the basis of single-crystal X-ray diffraction data. The knowledge accumulated here will constitute a basis for the development of ligand-protected Au/Ag clusters as new artificial elements on a nanometer scale.

Structural order enhances charge carrier transport in self-assembled Au-nanoclusters

The collective properties of self-assembled nanoparticles with long-range order bear immense potential for customized electronic materials by design. However, to mitigate the shortcoming of the finite-size distribution of nanoparticles and thus, the inherent energetic disorder within assemblies, atomically precise nanoclusters are the most promising building blocks. We report an easy and broadly applicable method for the controlled self-assembly of atomically precise Au₃₂(ⁿBu₃P)₁₂Cl₈ nanoclusters into micro-crystals. This enables the determination of emergent optoelectronic properties which resulted from long-range order in such assemblies. Compared to the same nanoclusters in glassy, polycrystalline ensembles, we find a 100-fold increase in the electric conductivity and charge carrier mobility as well as additional optical transitions. We show that these effects are due to a vanishing energetic disorder and a drastically reduced activation energy to charge transport in the highly ordered assemblies. This first correlation of structure and electronic properties by comparing glassy and crystalline self-assembled superstructures of atomically precise gold nanoclusters paves the way towards functional materials with novel collective optoelectronic properties.

Mapping the Electronic Structure of the Uranium(VI) Dinitride Molecule, UN2

A combined anion photoelectron spectroscopic and relativistic coupled-cluster computational study of the electronic structure of the UN₂ molecule is presented. Because the photoelectron spectrum of the uranium dinitride negative ion, UN₂^-, directly reflects the electronic structure of neutral UN₂, we have measured and relied upon the photoelectron spectrum of the UN₂^- anion as a means of mapping the electronic structure of neutral UN₂. In addition to the electron affinity of the UN₂ ground state, energy levels of the UN₂ excited states were well characterized by the close interplay between the experiment and high-level theory. We found that both electron attachment and electronic excitation significantly bend the UN₂ molecule and elongate its U≡N bond. Implications for the activation of UN₂ are discussed.

A ligand-induced homojunction between aluminum-based superatomic clusters

A superatomic molecule formed by joining two metallic clusters linked by an organometallic bridge can behave like a semiconductor and the addition of ligands can induce a significant energy level shift across an inter-cluster homojunction. This shift is induced by the N-ethyl-2-pyrrolidone ligands, and the placement of the ligands strongly affects the direction of the dipole moment, including the case where the dipole moment is parallel to the cluster interface. This computational study provides an alternative strategy for constructing nanometer-scale electronic interfaces between clusters mimicking semiconductor motifs. The semiconducting features in the PAl12 clusters emerge from the grouping of the quantum states in a confined nearly free electron gas that creates a substantial energy gap. An organometallic Ge(CH3)2(CH2)2 bridge links the clusters while maintaining the cluster's electronic shell structure. The amount of level shifting between the bridged clusters can be changed by controlling the number of ligands. Attaching multiple ligands can result in a broken gap energy alignment in which the HOMO level of one cluster is aligned with the LUMO level of the other bridged cluster. Furthermore, the singly ligated bridged superatomic molecule is found to exhibit promising features to separate the electron-hole pairs for photovoltaic applications.

Superatomic molecules with internal electric fields for light harvesting

Traditional p-n junctions used for photovoltaics require an interface where a light induced electron-hole pair is separated by an electric field. Developing alternative strategies for forming strong internal electric fields for electron-hole pair separation offers the possibility for better performance. We demonstrate that fusing two superatomic clusters with donor/acceptor ligands on opposite sides of the cluster leads to such a strong internal electric field. In two fused metal-chalcogenide Re₆S₈Cl₂(L)₄ clusters with donor PMe₃ ligands and acceptor CO ligands on the opposite sides of the fused clusters, the electronic levels undergo shifts analogous to band bending in traditional p-n junctions. The fused cluster has a large dipole moment, and an optical spectrum that strongly absorbs excitation above the HOMO-LUMO gap of the fused clusters, but is optically very weak for the lowest energy excitation that can lead to electron-hole pair recombination. This is because the electron is localized on the CO portion of the fused cluster, while the electron-hole pair is localized on the PMe₃ side of the cluster. It is shown that the electronic states localized on each side of the cluster can be aligned/misaligned by applying a voltage in different directions, offering diode like characteristics.