Superatom Model Research Articles

Relationship between Structural Defects and Free Electrons in Icosahedral Nanoclusters.

According to the classic superatom model, metal nanoclusters with a "magic number" of free valence electrons display high stability, manifesting as the closed-shell-dependent electronic robustness. The icosahedral nanobuilding blocks containing eight free electrons were the most common in constructing metal nanoclusters; however, the structure defect-dependent variations of the free electron count in icosahedral configurations are still far from thorough research. Here, we reported a hydride-containing [Pt2Ag15(SAdm)4(DPPOE)4H]2+ nanocluster with two largely defective Pt1Ag8 icosahedral cores. Together with previously reported complete or slightly defective icosahedra in metal nanoclusters, the largely defective Pt1Ag8 core provided important clues to reveal the evolutionary mode of structural defects and free electrons in icosahedral nanoclusters; the free electron count of icosahedron was reduced two-by-two (i.e., from 8e to 6e and then to 4e) accompanied by the structure defection. Overall, the work presented a novel Pt2Ag15 nanocluster with a largely defective core structure that enables an atomic-level understanding of the relationship between structural defects and free electrons in icosahedral nanoclusters.

Electronic structure analysis and DFT benchmarking of Rydberg-type alkali-metal-crown ether, -cryptand, and -adamanzane complexes.

Density functional theory (DFT) and electron propagator theory (EPT) calculations were performed to study ground and excited electronic structures of alkali-metal (M) coordinated 9-crown-3, 24-crown-8, [2.1.1]cryptand, o-Me2-1.1.1, and 36Adamanzane complexes. Each complex bears an expanded electron in the periphery and occupies diffuse 1p-, 1d-, 1f-type molecular orbitals (or superatomic 1P, 1D, 1F orbitals) in excited electronic states. The calculated superatomic shell model of the M(9-crown-3)2 is 1S, 1P, 1D, 1F, 2S, 2P, 2D, 1G and it is held by all other complexes up to the studied 1F level. Due to the highly diffuse nature of the electron, the ionization energies of these complexes are significantly lower (1.6-2.0 eV) and hence these complexes belong to the superalkali category. The ab initio EPT ionization energy and the excitation energies of the Li(9-crown-3)2 were used to evaluate DFT errors associated with a series of exchange correlation functionals that span multiple rungs of Jacob's ladder (i.e., GGA, meta-GGA, global GGA hybrid, meta-GGA hybrid, range-separated hybrid, double-hybrid). Among these, the best performing functional is the range-separated hybrid CAM-B3LYP and the errors are within 6% of high-level ab initio EPT results. The accuracy of CAM-B3LYP is indeed transferable to similar complexes and hence the findings are expected to accelerate the progression of studies of Rydberg-type systems.

Manipulation of single stored-photon with microwave field based on Rydberg polariton.

We demonstrate a coherent microwave manipulation of a single optical photon based on a single Rydberg excitation in an atomic ensemble. Due to the strong nonlinearities in a Rydberg blockade region, a single photon can be stored in the formation of Rydberg polariton using electromagnetically induced transparency (EIT). The manipulation of the stored single photon is performed by applying a microwave field that resonantly couples the nS1/2 and nP3/2, while the coherent readout is performed by mapping the excitation into a single photon. We achieve a single photon source with g(2)(0) = 0.29 ± 0.08 at 80S1/2 without applying microwave fields. By implementing the microwave field during the storage time and retrieval process, we show the Rabi oscillation and modulation of stored photons that can be controlled to retrieve early or late. Rapid modulation frequencies up to 50 MHz can be obtained. Our experimental observations can be well explained via numerical simulations based on an improved superatom model accounting for the dipole-dipole interactions in a Rydberg EIT medium. Our work provides a way to manipulate the stored photons by employing the microwave field, which is significant for developing quantum technologies.

Prediction of Cu4Zn4 aggregates based on superatom network model

Recently, the tetrahedral Cu4Zn4 cluster composed of superimposed Cu4 and Zn4 was reported, which can be used as a building block for assembling Cu5Zn8-type structures. Here, we confirm that tetrahedral structures of (Cu4Zn4)4+, (Cu4Zn4)(C5H5)4, (Cu4Zn4)Cl4 and (Cu4Zn4)(SH)4 clusters are highly stable on the potential energy surfaces, and their metallic cores conform to the superatom model despite different ligand effects. The molecular dynamics simulations also show that the constructed clusters still possess good thermal stability at 500 K. Based on the superatomic characteristics of these clusters, two Cu4Zn4 aggregates are predicted, and configurations and electronic properties of them are analyzed in detail. The molecular orbitals and density of states show the tetrahedral Cu4Zn4 building blocks maintain superatom properties in extended brass structures. Hence, we give an effective strategy for assembling new brasses.

Correlated collective excitation and quantum entanglement between two Rydberg superatoms in steady state

<sec>Owing to the unique physical characteristics of Rydberg atoms, which play an important role in quantum information and quantum computation, the theoretical and applied research of Rydberg atoms have become the hot spots of scientific research in recent years. With the large polarizability of Rydberg atoms, even a small electric field could cause a considerable electric dipole moment, resulting in a strong dipole-dipole interaction between Rydberg atoms. The multiple excitations of the Rydberg states are strongly inhibited because of the strong dipole interaction between atoms within a mesoscopic interaction (blockade) region. We call this phenomenon the dipole blockade effect. The dipole blockade effect makes it possible to build single-photon quantum devices, implement quantum gates, generate quantum entanglement, and simulate many-body quantum problems, etc.</sec><sec>A Rydberg atomic ensemble in the same blockade region can be regarded as a superatom. In the same way, if these atoms trapped in two optical dipole traps, each sub-ensemble can be considered as a sub-superatom which is closely related to the superatom. According to the fact that two Rydberg sub-superatoms can be strongly correlated due to sharing no more than one excited Rydberg atom, we study correlated collective excitation and quantum entanglement between two Rydberg sub-superatoms in a steady state. With the superatom model, the problem of exponentially increasing system size with the number of atoms can be circumvented to a certain extent in studying many-body physics. By solving the two-body Lindblad’s master equation accurately, we obtain the analytical expressions for the collective excitation probabilities of the two sub-superatoms, and the concurrence measuring the bipartite entanglement between them. Our results show that they are all sensitive to the number of atoms in each Rydberg superatom: the bigger (including more atoms) the Rydberg superatom, the higher the collective Rydberg excitation probability is. And that the maximally entangled state can only be obtained with two equal-sized Rydberg superatoms. When this condition is fulfilled, the mesoscopic entanglement can be generated by adding the number of atoms in each Rydberg superatom. This may provide an attractive platform for studying the quantum-classical correspondence and have potential promising applications in quantum information processing.</sec>

Dynamical Collective Excitations and Entanglement of Two Strongly Correlated Rydberg Superatoms

Based on the dipole blockade effect and with the aid of the superatom (SA) model, we propose a scheme to investigate the correlated evolution of two Rydberg sub-superatoms (SSAs), formed by two spatially separated atomic Rydberg sub-ensembles but in the same blockade region. Starting from the pure separable states, we investigate the in-phase or anti-phase correlated dynamics and explore how two Rydberg SSAs entangle with each other mediated by a single Rydberg excitation. Starting from the entangled states, we discuss the robustness of the system against decoherence induced by the dephasing rate. Our results show that both the correlated evolution of two Rydberg SSAs and their collective-state entanglement are usually sensitive to the number of each Rydberg SSA. This allows us to coherently manipulate the Rydberg ensemble over long distances from the single-quantum level to the mesoscopic level by changing the number of atoms. Furthermore, the method for dividing an SA into two SSAs and obtaining their spin operators without any approximation can be readily generalized to the case of many SSAs. It may have potential promising applications in quantum information processing and provide an attractive platform to study the quantum-classical correspondence, many-body physics and so on.

Correlated dynamics of three-body Rydberg superatoms

Owing to the long lifetime of Rydberg atom, easy to operate and easy to control the interaction between Rydberg atoms, Rydberg atom has attracted considerable attention in quantum information and quantum optics fields. Specially, the anti-blockade effect, as a physical resource, can be used to implement various tasks in quantum information processing. Based on the rigid dipole blockade, an ensemble of two-level Rydberg atoms trapped in three magneto-optical traps can be regarded as a superatom. Based on the superatom model, the in-phase and anti-phase dynamics of the three-body Rydberg superatoms are studied by adjusting the numbers of atoms, and the W state and two kinds of maximal entangled states are generated simultaneously. Our work has great potential applications in coherent manipulation and quantum information processing.The numerical simulations are performed based on the superatom model and thereby the formidable obstacle that the Hilbert space dimension grows exponentially with the particle number increasing can be completely removed. As a result, the quantum control and quantum entanglement can be achieved from the single-quanta level to the mesoscopic level.

Emergent electronic properties in Co-deposited superatomic clusters.

We report an intercluster compound based on co-deposition of the Au cluster [Au9(PPh3)8](NO3)3 and the fulleride KC60(THF). Electronic properties characteristic for a charge interaction between superatoms emerge within the solid state material [Au9(PPh3)8](NO3)3-x(C60)x, as confirmed by UV-VIS and Raman spectroscopy and I-V measurements. These emergent properties are related to the superatomic electronic states of the initial clusters. The material is characterized by Fourier-transform infrared spectroscopy, x-ray diffraction, Raman spectroscopy, and electrical measurements. Structural optimization and ab initio band structure calculations are performed with density functional theory to interpret the nature of the electronic states in the material; Bader charge calculations assigneffective oxidation states in support of the superatomic model of cluster interactions.

Superatomic nature of metal encapsulated dodecahedrane: The case of M@C20H20 (M = Li, Na, Mg+)

AbstractThe idea of designing unprecedented materials made of superatomic building blocks, motivated the present study on endohedral M@C20H20 (M = Li, Na, Mg+) species. Ground and excited electronic structures of M@C20H20 (M = Li, Na, Mg+) were analyzed by means of high‐level quantum calculations. In their ground states, one electron occupies a defuse superatomic s‐orbital that lies around the C20H20 cage. These entities populate higher angular momentum p‐, d‐, f‐, g‐superatomic orbitals in their low‐lying electronic states. The proposed superatomic Aufbau shell model for Li@C20H20 and Na@C20H20 is 1s, 1p, 1d, 2s, 1f, 2p, 2d, 1g, 2f slightly different from that of Mg@C20H20+ which is 1s, 1p, 1d, 2s, 1f, 2p, 2d, 1g, 3s, 2f, 2g, 3p. These introduced superatomic orbital series resemble the Aufbau principle of solvated electron precursors.

Toward quantitative electronic structure in small gold nanoclusters.

Ligand-protected gold nanoclusters (AuNCs) feature a dense but finite electronic structure that can be rationalized using qualitative descriptions such as the well-known superatomic model and predicted using quantum chemical calculations. However, the lack of well-resolved experimental probes of a AuNC electronic structure has made the task of evaluating the accuracy of electronic structure descriptions challenging. We compare electronic absorption spectra computed using time-dependent density functional theory to recently collected high resolution experimental spectra of Au9(PPh3)8 3+ and Au8(PPh3)7 2+ AuNCs with strikingly similar features. After applying a simple scaling correction, the computed spectrum of Au8(PPh3)7 2+ yields a suitable match, allowing us to assign low-energy metal-metal transitions in the experimental spectrum. No similar match is obtained after following the same procedure for two previously reported isomers for Au9(PPh3)8 3+, suggesting either a deficiency in the calculations or the presence of an additional isomer. Instead, we propose assignments for Au9(PPh3)8 3+ based off of similarities Au8(PPh3)7 2+. We further model these clusters using a simple particle-in-a-box analysis for an asymmetrical ellipsoidal superatomic core, which allows us to reproduce the same transitions and extract an effective core size and shape that agrees well with that expected from crystal structures. This suggests that the superatomic model, which is typically employed to explain the qualitative features of nanocluster electronic structures, remains valid even for small AuNCs with highly aspherical cores.

On Heteronuclear Isoelectronic Alternatives to [Au13(dppe)5Cl2]3+: Electronic and Optical Properties of the 18-Electron Os@[Au12(dppe)5Cl2] Cluster from Relativistic Density Functional Theory Computations.

The development of well-defined atomically precise heteronuclear nanoclusters passivated by protecting ligands is presently a booming area, owing to the fact that doping well-known homonuclear nanostructures allows fine-tuning of their properties. Here, we explore by means of density functional theory calculations the possibility of doping the central gold atom in the classical [Au13(dppe)5Cl2]3+cluster (1) by Os. Although both [Au13(dppe)5Cl2]3+ and [Os@Au12(dppe)5Cl2] have the same total number of electrons, we show that they are not isoelectronic within the formalism of the superatom model, being respectively an 8- and an 18-electron species. It results that they exhibit similar structures but present significantly different optical behaviors (ultraviolet/visible and circular dichroism). Similar results are obtained for the Ru and Fe relatives. Emission properties indicate some redshift of the T1→S1 decay with respect to [Au13(dppe)5Cl2]3+, involving an equatorial distortion of the Au12Cl2 core in the T1 state, rather than the axial distortion afforded by 1. The sizable highest occupied molecular orbital-lowest unoccupied molecular orbital gaps found for the three doped species suggest that further experimental exploration of different stable doped species derived from the ligand-protected Au12Cl2 core should be encouraged.

Coherent control of Goos-Hänchen shift in a guided-wave surface plasmon resonance structure with Rydberg atoms

We proposed an effective and flexible scheme to achieve tunable giant Goos-Hänchen (GH) shift of reflected light in the configuration of guided-wave surface plasmon resonance with Rydberg atoms. With the super atom model of Rydberg atom due to the dipole blocking effect, we investigated the influence of Rydberg state population on GH displacement. By adjusting the external driving field on Rydberg atoms without changing the structure geometry, not only can GH shift be enhanced significantly to the magnitude of millimeter, but also the transition between positive and negative GH shift can be controlled at the same resonant angles. Furthermore, the resonant angle position of the maximum GH shift is also tunable via detuning the field. Our scheme may offer promising prospects for the optical switches and nano-sensors with high precision.

Understanding Superatomic Ag Nanohydrides.

Bulk Ag hydrides are extremely challenging to make even at very high pressures, but they may become stable as the particle size shrinks to the nanometer regime. Here, the formation and electronic structure of Ag nanohydrides are investigated from a superatomic perspective by density functional theory. It is found that as the coverage increases, adsorption energy of hydrogen atoms on Ag38 cluster to form Ag38 H2 n nanohydride (n is from 1 to 15) can be energetically favorable with respect to bare Ag38 and H2 . Furthermore, the adsorbed hydrogen atoms contribute their 1s electrons to the superatom electron count and behave as a metal instead of a ligand. The electronic structure of the silver nanohydrides follows the superatomic complex model, leading to magic or relatively more stable compositions such as Ag38 H2 , Ag38 H20 , and Ag38 H30 , which correspond to 40-electron, 58-electron, and 68-electron shell closings, respectively. Angular momentum analyses of the superatomic orbitals suggest a convoluted interaction of geometry, symmetry, and orbital splitting.

Massive dipoles across the metal-semiconductor cluster interface: towards chemically controlled rectification.

An interface between a metallic cluster (MgAl12) and a semiconducting cluster (Re6Se8(PMe3)5) is shown to be marked by a massive dipole reminiscent of a dipolar layer leading to a Schottky barrier at metal-semiconductor interfaces. The metallic cluster MgAl12 with a valence electron count of 38 electrons is two electrons short of 40 electrons needed to complete its electronic shells in a superatomic model and is marked by a significant electron affinity of 2.99 eV. On the other hand, the metal-chalcogenide semiconducting cluster Re6Se8(PMe3)5, consisting of a Re6Se8 core ligated with five trimethylphosphine ligands, is highly stable in the +2 charge-state owing to its electronic shell closure, and has a low ionization energy of 3.3 eV. The composite cluster Re6Se8(PMe3)5-MgAl12 formed by combining the MgAl12 cluster through the unligated site of Re6Se8(PMe3)5 exhibits a massive dipole moment of 28.38 D resulting from a charge flow from Re6Se8(PMe3)5 to the MgAl12 cluster. The highest occupied molecular orbital (HOMO) of the composite cluster is on the MgAl12 side, which is 0.53 eV below the lowest unoccupied molecular orbital (LUMO) localized on the Re6Se8(PMe3)5 cluster, reminiscent of a Schottky barrier at metal-semiconductor interfaces. Therefore, the combination can act as a rectifier, and an application of a voltage of approximately 4.1 V via a homogeneous external electric field is needed to overcome the barrier aligning the two states: the HOMO in MgAl12 with the LUMO in Re6Se8(PMe3)5. Apart from the bias voltage, the barrier can also be reduced by attaching ligands to the metallic cluster, which provides chemical control over rectification. Finally, the fused cluster is shown to be capable of separating electron-hole pairs with minimal recombination, offering the potential for photovoltaic applications.

Theoretical Analysis of the Mackay Icosahedral Cluster Pd55 (PiPr3 )12 (μ3 -CO)20 : An Open-Shell 20-Electron Superatom.

The electronic structure of the spherical Mackay icosahedral nanosized cluster Pd55 (PiPr3 )12 (μ3 -CO)20 is analyzed by using DFT calculations. Results reveal that it can be considered as a regular superatom with a "magic" electron count of 20, characterized by a 1S2 1P6 1D10 2S2 jellium configuration. Its open shell nature is associated with partial occupation of non-jellium, 4d-type, levels located on the interior of the Pd55 kernel. This shows that the superatom model can be used to rationalize the bonding and stability of spherical ligated group 10 clusters, despite their apparent 0-electron count.

High Precision Electronic Spectroscopy of Ligand-Protected Gold Nanoclusters: Effects of Composition, Environment, and Ligand Chemistry.

Atomically precise gold nanoclusters (AuNCs) are a class of nanomaterials valued for their electronic properties and diverse structural features. While the advent of X-ray crystallography of AuNCs has revealed their geometric structures with high precision, detailed electronic structure analysis is challenged by environmental, compositional, and thermal averaging effects present in electronic spectra of typical samples. To circumvent these challenges, we have adapted mass spectrometer-based electronic absorption spectroscopy techniques to acquire high-resolution electronic spectra of atomically precisely defined nanoclusters separated from a synthetic mixture. Here we discuss recent results using this approach to link the surface chemistry of triphenylphosphine-protected AuNCs to their electronic structure and expand on key elements of the experiment and the link between these gas-phase measurements and solution-phase behavior of AuNCs. Chemically derivatized Au8(P(p-X-Ph)3)72+ and Au9(P(p-X-Ph)3)83+ clusters, where X = -H, -CH3, or -OCH3, are used to derive systematic trends in the response of the electronic spectrum to the electron-donating character of the ligand shell. We find a linear relationship between the substituent Hammett parameter σp and the transition energy between both sets of clusters' highest occupied and lowest unoccupied molecular orbitals, a transition that is localized in the metal core within the limits of the superatomic model. The similarity of the mass-selective and solution-phase UV/vis spectra of Au9(PPh3)83+ indicates that the interpretation of these experiments is transferable to the condensed phase. He and N2 environments are introduced to a series of isovalent clusters as a subtle probe of discrete environmental effects over electronic structure. Strikingly, select bands in the UV/vis spectrum respond strongly to the identity of the environment, which we interpret as a state-selective indicator of interfacially relevant electronic transitions. Physically predictable trends such as these will aid in building molecular design principles necessary for the development of novel materials based on nanoclusters.

5-Fold symmetry in superatomic scandium clusters: exploiting favourable orbital overlap to sequester spin.

The geometries and electronic structures of icosahedral A13C (A = Sc, Y; C = 0, ±1, ±2) clusters have been determined at a range of multiplicities at each cluster charge, using density functional theory methods. These clusters demonstrate a complex electronic structure which provides insight into the anomalously high magnetic moment of icosahedral group 3 clusters and further contextualises the role of transition metals and d-electrons within the superatomic model. Embedded deeply within the density of states for these clusters are typical superatom orbitals which are populated up to the 2S level. Above the 2S-state there are three states of apparent F symmetry, which are preferentially singly occupied, followed by an abundance of approximately degenerate P-, G-, D- and F-states at the Fermi energy, which are at most singly occupied. In spite of apparent angular symmetry and a nodal structure reminiscent of superatomic orbitals these states are actually formed from preferential overlap of the valence d-orbitals of the cluster atoms. This analysis was further contextualised through analysis of the Sc19 cluster, which shows a similar construction of Kohn-Sham states, but with the breaking of 5-fold symmetry along one of its Cartesian axes. Finally, this work clearly demonstrates the ability of d-electrons to give rise to superatomic orbitals is not just constrained by atomic species but also by the local environment of the atoms.

Theoretical Prediction of Optical Absorption and Emission in Thiolated Gold Clusters.

Although the photoluminescence of gold clusters has been extensively studied so far, there are still questions on the origin of the emission in these materials. In this work, we report time-dependent density functional theory calculations on the absorption and emission spectra of the well-studied Au25(SR)18- cluster, the lowest energy isomer of the Au38(SR)24 cluster, and five isomers of the Au22(SR)18 cluster. Good agreement between the calculated and measured absorption spectra, as well as with the lowest-energy emission values for these clusters, was demonstrated, verifying the accuracy of the theoretical methods employed. Our results for Au25(SR)18- explain a newly observed feature in the absorption peak, also rationalizing the optical response in terms of the superatom model. The analysis of the absorption and emission characteristics of the Au25(SR)18- and Au38(SR)24 clusters provides an estimate of the spectral regions, where fluorescence or phosphorescence is predicted to occur. Interestingly, we find that for Au22(SR)18, one of the five proposed structures could be present at a significant concentration in the sample, even though it is not the lowest in energy structure, which can be explained, in part, by solvent effects.

Point Group Symmetry Analysis of the Electronic Structure of Bare and Protected Metal Nanocrystals.

The electronic structures of a variety of experimentally identified gold and silver nanoclusters from 20 to 246 atoms, either unprotected or protected by several types of ligands, are characterized by using point group specific symmetry analysis. The delocalized electron states around the HOMO–LUMO energy gap, originating from the metal s-electrons in the cluster core, show symmetry characteristics according to the point group that describes best the atomic arrangement of the core. This indicates strong effects of the lattice structure and overall shape of the metal core to the electronic structure, which cannot be captured by the conventional analysis based on identification of spherical angular momentum shells in the “superatom” model. The symmetry analysis discussed in this paper is free from any restrictions regarding shape or structure of the metal core, and is shown to be superior to the conventional spherical harmonics analysis for any symmetry that is lower than Ih. As an immediate application, we also demonstrate that it is possible to reach considerable savings in computational time by using the symmetry information inside a conventional linear-response calculation for the optical absorption spectrum of the Ag55 cluster anion, without any loss in accuracy of the computed spectrum. Our work demonstrates an efficient way to analyze the electronic structure of nonspherical, but atomically ordered nanocrystals and ligand-protected clusters with nanocrystal metal cores, and it can be viewed as the generalization of the superatom model demonstrated for spherical shapes 10 years ago (Walter, M.; et al. Proc. Natl. Acad. Sci. U. S. A.2008, 105, 9157−916218599443).

Nonclassical storage and retrieval of a multiphoton pulse in cold Rydberg atoms

We investigate the storage and retrieval of a multiphoton probe field in cold Rydberg atoms with an effective method based on the superatom model. This probe field is found greatly attenuated in light intensity and two-photon correlation yet suffering little temporal broadening as a result of the partial dipole blockade of Rydberg excitation. In particular, the output field energy exhibits an intriguing saturation effect against the input field energy accompanied by an inhomogeneous nonclassical antibunching feature as a manifestation of the dynamic cooperative optical nonlinearity. Our numerical results are qualitatively consistent with those in a recent experiment and could be extended to pursue quantum information applications of nonclassical light fields.