Ground States Of Clusters Research Articles

Density functional theory-based study on the structural, electronic and spectral properties of gas-phase PbMg n - (n = 2-12) clusters.

Gas-phase PbMg n- (n = 2-12) cluster structures were globally searched on their potential energy surfaces by means of the CALYPSO prediction software. Structural optimization and calculations of properties such as relative energy and electronic structure were then carried out by density functional theory for each size of low energy isomer. The structural, relative stability, natural charge population, natural electronic configuration and distribution of the strongest peaks of the infrared and Raman spectra of the low energy isomers of PbMg n- (n = 2-12) clusters were systematically investigated in the present work. It was shown that the PbMg7- cluster ground state isomer exhibits the highest stability, for which special electronic excitation and chemical bonding analyses were performed. It is reasonable to believe that this work enriches the structural, spectroscopic and other data of magnesium-based clusters and provides some theoretical basis for possible future experimental syntheses.

PGA: A new particle swarm optimization algorithm based on genetic operators for the global optimization of clusters.

We have developed a global optimization program named PGA based on particle swarm optimization algorithm coupled with genetic operators for the structures of atomic clusters. The effectiveness and efficiency of the PGA program can be demonstrated by efficiently obtaining the tetrahedral Au20 and double-ring tubular B20, and identifying the ground state clusters through the comparison between the simulated and the experimental photoelectron spectra (PESs). Then, the PGA was applied to search for the global minimum structures of (n = 3-30) clusters, new structures have been found for sizes n = 6, 7, 12, 14, and medium-sized 21-30 were first determined. The high consistency between the simulated spectra and the experimental ones once again demonstrates the efficiency of the PGA program. Based on the ground-state structures of these (n = 3-30) clusters, their structural evolution and electronic properties were subsequently explored. The performance on Au20, B20, , and (n = 3-30) clusters indicates the promising potential of the PGA program for exploring the global minima of other clusters. The code is available for free upon request.

Learning quantum symmetries with interactive quantum-classical variational algorithms

A symmetry of a state |ψ⟩ is a unitary operator of which |ψ⟩ is an eigenvector. When |ψ⟩ is an unknown state supplied by a black-box oracle, the state’s symmetries provide key physical insight into the quantum system; symmetries also boost many crucial quantum learning techniques. In this paper, we develop a variational hybrid quantum–classical learning scheme to systematically probe for symmetries of |ψ⟩ with no a priori assumptions about the state. This procedure can be used to learn various symmetries at the same time. In order to avoid re-learning already known symmetries, we introduce an interactive protocol with a classical deep neural net. The classical net thereby regularizes against repetitive findings and allows our algorithm to terminate empirically with all possible symmetries found. An iteration of the learning algorithm can be implemented efficiently with non-local SWAP gates; we also give a less efficient algorithm with only local operations, which may be more appropriate for current noisy quantum devices. We simulate our algorithm on representative families of states, including cluster states and ground states of Rydberg and Ising Hamiltonians. We also find that the numerical query complexity scales well for up to moderate system sizes.

A computational investigation of XnK(X = Mn, Fe, co; n = 1–8) clusters by density functional theory

The properties of XnK(X = Mn, Fe, Co; n = 1–8) clusters have been systematically investigated using quantum calculations of LANL2DZ basis sets at the PBE1PBE level. By optimizing different structural isomers, we determined the ground state structure of XnK clusters, which tends to be compact as the cluster size increases. In order to study the stability of clusters, the average binding energies, dissociation energies and second-order difference of total energies of XnK clusters are calculated. The results show that the stability of FenK clusters is comparable to that of ConK clusters, and both are higher than that of MnnK clusters. Finally, the chemical activity and magnetic properties of the clusters are discussed. The dissociation energies, second-order difference of total energies, HOMO-LUMO energy gaps, and magnetic moments of the ground-state clusters show an irregular oscillatory behavior with atomic number. Fundamental insights obtained in this study can be useful in the design of Mn-K/Fe-K/Co-K catalysts.

Multiple magnetic transition and magnetocaloric properties in the mixed valence Eu8CuNi2.5Si42.5 type I clathrate compound

We investigated the magnetocaloric and electrical transport properties of the Eu8CuNi2.5Si42.5 clathrate compound, synthesized by an arc melting and annealing method. X-ray photoemission spectroscopy revealed a mixed valence state of Eu2+ and Eu3+. The low-field and low-temperature magnetic measurements indicated a multiple magnetic transition, from ferromagnetic near 35 K to antiferromagnetic at 25 K. Increasing the magnetic field led to the broadening of antiferromagnetic peaks and a final ferromagnetic state under high magnetic fields, indicative of spin reorientation. The transition from a ferromagnetic to an antiferromagnetic state was further corroborated by specific heat measurements. We noted spontaneous magnetization at low temperatures via magnetic hysteresis and Arrott plot analysis. The coexistence of an antiferromagnetic ground state (attributed to the Eu2+ ions) and ferromagnetic clusters (associated with the Ni2+ ions) was supported by spontaneous magnetization at low temperatures in the antiferromagnetic state. The magnetocaloric analyses revealed a high spin entropy change over a broad temperature range for Eu8CuNi2.5Si42.5, which implies its potential as a robust low-temperature magnetocaloric material, distinguished by its high refrigerant capacity.

Electronic properties and collision cross sections of AgOkHm± (k, m = 1-4) aerosol ionic clusters.

Experimental evidence shows that hydroxylated metal ions are often produced during cluster synthesis by atmospheric pressure spark ablation. In this work, we predict the ground state equilibrium structures of AgOkHm± clusters (k and m = 1-4), which are readily produced when spark ablating Ag, using the coupled cluster with singles and doubles (CCSD) method. The stabilization energy of these clusters is calculated with respect to the dissociation channel having the lowest energy, by accounting perturbative triples corrections to the CCSD method. The interatomic interactions in each of the systems have been investigated using the frontier molecular orbital (FMO), natural bond orbital (NBO) and quantum theory of atoms in molecules (QTAIM) methods. Many of the ground states of these ionic clusters are found to be stable, corroborating experimental observations. We find that clusters having singlet spin states are more stable in terms of dissociation than the clusters that have doublet or triplet spin states. Our calculations also indicate a strong affinity of the ionic and neutral Ag atom towards water and hydroxyl radicals or ions. Many 3-center, 4-electron (3c/4e) hyperbonds giving rise to more than one resonance structure are identified primarily for the anionic clusters. The QTAIM analysis shows that the O-H and O-Ag bonds in the clusters of both polarities are respectively covalent and ionic. The FMO analysis indicates that the anionic clusters are more reactive than the cationic ones. Using the cluster structures predicted by the CCSD method, we calculate the collision cross sections of the AgOkHm± family, with k and m ranging from 1 to 4, by the trajectory method. In turn, we predict the electrical mobilities of these clusters when suspended in helium at atmospheric pressure and compare them with experimental measurements.

Second response theory: a theoretical formalism for the propagation of quantum superpositions

The propagation of general electronic quantum states provides information of the interaction of molecular systems with external driving fields. These can also offer understandings regarding non-adiabatic quantum phenomena. Well established methods focus mainly on propagating a quantum system that is initially described exclusively by the ground state wavefunction. In this work, we expand a previously developed size-extensive formalism within coupled cluster theory, called second response theory, so it propagates quantum systems that are initially described by a general linear combination of different states, which can include the ground state, and show how with a special set of time-dependent cluster operators such propagations are performed. Our theory shows strong consistency with numerically exact results for the determination of quantum mechanical observables, probabilities, and coherences. We discuss unperturbed non-stationary states within second response theory and their ability to predict matrix elements that agree with those found in linear and quadratic response theories. This work also discusses an approximate regularized methodology to treat systems with potential instabilities in their ground-state cluster amplitudes, and compares such approximations with respect to reference results from standard unitary theory.

Geometries, stability and dissociation behavior of AgnCo clusters (n = 1-12): A theoretical investigation

The geometric structure, stability, dissociation channel and magnetism of AgnCo clusters (n = 1–12) have been studied using density functional theory. The results show that the Co atom tends to choose the highest coordination position. The ground state of AgnCo clusters prefers the planar motif at small sizes (n less than 4) but favors 3D structures at larger sizes (n = 5–12). The stability of clusters is not only governed by the symmetric geometry but also strongly depends on the electronic structure and the filling rule of the electron shells. The Ag9Co cluster with 18 valence electrons fully filled the electronic shell (1S21P63dCo10), which is considered as a potential superatom. The total magnetic moment of AgnCo clusters is governed by the electron localization on the Co atom. The relative stability of the clusters is determined by the average binding energy, the second-order difference energies, and the dissociation energies.

Ground States of Heisenberg Spin Clusters from a Cluster-Based Projected Hartree–Fock Approach

Recent work on approximating ground states of Heisenberg spin clusters by projected Hartree–Fock theory (PHF) is extended to a cluster-based ansatz (cPHF). Whereas PHF variationally optimizes a site–spin product state for the restoration of spin- and point-group symmetry, cPHF groups sites into discrete clusters and uses a cluster-product state as the broken-symmetry reference. Intracluster correlation is thus already included at the mean-field level, and intercluster correlation is introduced through symmetry projection. Variants of cPHF differing in the broken and restored symmetries are evaluated for ground states and singlet-triplet gaps of antiferromagnetic spin rings for various cluster sizes, where cPHF in general affords a significant improvement over ordinary PHF, although the division into clusters lowers the cyclical symmetry. In contrast, certain two- or three-dimensional spin arrangements permit cluster groupings compatible with the full spatial symmetry. We accordingly demonstrate that cPHF yields approximate ground states with correct spin- and point-group quantum numbers for honeycomb lattice fragments and symmetric polyhedra.

Phosphine-Stabilized Hidden Ground States in Gold Clusters Investigated via a Aun(PH3)m Database.

Nanoclusters are promising materials for catalysis and sensing due to their large surface areas and unique electronic structures which can be tailored through composition, geometry, and chemistry. However, relationships correlating synthesis parameters directly to outcomes are limited. While previous computational studies have mapped the potential energy surface of specific systems of bare nanoclusters by generating and calculating the energies of reasonable structures, it is known that environmental ions and ligands crucially impact the final shape and size. In this work, phosphine-stabilized gold is considered as a test system and DFT calculations are performed for clusters with and without ligands, producing a database containing >10000 structures for Aun(PH3)m (n ≤ 12). We find that the ligation of phosphines affects the thermodynamic stability, bonding, and electronic structure of Au nanoclusters, specifically such that "hidden" ground state cluster geometries are stabilized that are dynamically unstable in the pure gold system. Further, the addition of phosphine introduces steric effects that induce a transition from planar to nonplanar structures at 4-5 Au atoms rather than up to 13-14 Au atoms, as previously predicted for bare clusters. This work highlights the importance of considering the ligand environment in the prediction of nanocluster morphology and functionality, which adds complexity as well as a rich opportunity for tunability.

Theoretical study of Ga-doped magnesium mineral based on the atomic cluster level: Gas-phase GaMgn- (n = 2–12) DFT investigation

Ga-doped magnesium mineral based on the atomic cluster level, gas-phase GaMgn- (n = 2–12), were studied utilizing CALYPSO together with density functional theory. Tetrahedral-like and pyramidal-like structures are found to be “seeds” for GaMgn- (n = 2–12) clusters growth. Relative stability calculations indicate that GaMg8- cluster possesses the most robust stability. The natural charge population and natural electron configuration of each atom of each ground state cluster were studied, and their chemical bond properties were also investigated by ELF. Finally, the infrared, Raman and UV–vis spectra of GaMg8- cluster and its excited state properties were specially studied by NTO analysis.

Rapid 3D roll-up of gas-phase planar gold clusters and affinity and alienation for Mg and Ge: A theoretical study of MgGeAun (n=1–12) clusters

SummaryA cluster is a special matter level above a single atom and between macroscopic and microscopic matter, and it is an important bridge to understanding the relationship between the structure and function of matter. Here, we perform a comprehensive theoretical study of 2D planar Aun (n = 1–12) clusters doped with both magnesium and germanium. Two interesting results are found, namely the rapid 3D "roll-up" structural growth of the GeMgAun (n = 1–12) cluster ground state isomers, and the relative "alienation" of the different sizes of the Aun (n = 1–12) cluster framework towards the Ge atom, and the relative "affinity" towards the Mg atom. This study will not only enrich the data on gold-based clusters but will also provide a simple and clear theoretical guide for the 3D structuring of planar clusters, i.e. the doping of different classes of "affinition" and "alienatation" atoms.

Theoretical prediction for growth behavior and electronic properties of monoanionic Ru2Gen− (n = 3–20) clusters

We present a detailed theoretical study on the structural and electronic properties of monoanionic Ru2Gen− (n = 3–20) clusters using comprehensive genetic algorithm combined with density functional theory (CGA-DFT). It is shown that the geometrical growth patterns of the ground state Ru2Gen− clusters are polyhedral pyramidal structures with n ≤ 9 and gradually to form pentagonal prism-based structures with two endohedral Ru atoms from 10 ≤ n ≤ 15, then the structures evolve into a oblate cage-like configuration with two Ru atoms in center from cluster sizes n ≥ 16. In general, one extra electron will influence the geometric structures of Ru2Gen clusters to compare with their neutral ones we have studied. Based on the obtained ground state structures, we find that the clusters of Ru2Ge10−, Ru2Ge12− and Ru2Ge14− have relatively higher structural and chemical stability in which Ru2Ge14− is more prominent through the analysis of binding energy, second order of energy difference and highest occupied and lowest unoccupied molecular orbital (HOMO-LUMO) gap. Furthermore, we analyzed natural charge, natural electronic configuration, the frontier molecular orbitals and orbital composition to verify the clusters of Ru2Gen− with n = 10, 12, 14 and 16 have relatively higher chemical stability owning to the less contribution of Ru-d orbitals. In addition, the clusters of Ru2Ge3−, Ru2Ge4−, Ru2Ge6−, Ru2Ge10− and Ru2Ge16− have magnetic moment of 3 μB, while others are 1 μB. And also the vertical detachment energy (VDE) and adiabatic detachment energy (ADE) for all ground state clusters are computed to support future experiment.

Insights into the electronic structure and stability of TiMgn (n = 1–12) clusters: Validation of electron counting rule

The present study reports the investigation of the electronic structure and stability of TiMgn (n = 1–12) nanoclusters in the framework of the linear combination of atomic orbital density functional theory (DFT) together with a spin-polarized generalized gradient approximation (GGA). We have calculated different thermodynamic and chemical parameters, such as binding energy (BE), embedding energy (EE), fragmentation energy (FE), HOMO-LUMO gap, vertical ionization potential (VIP), vertical electron affinity (VEA), etc. during the growth process of the cluster to understand their stability. From the study, the TiMg8 cluster comes out to be the most stable cluster. Further, the positive charge (Mulliken charge) on the Ti in TiMg8 cluster indicates that the Mg8-cage behaves as an electron acceptor during hybridization with the Ti. The absence of any reactive site (obtained from NBO), minimum Mg-Ti bond length, and negative NICS in TiMg8 ground state cluster support it as a globally stable cluster. Low ELF index value revealing the non-reactivity of the TiMg8 cluster. Finally, orbital analysis shows that TiMg8 clusters follow closed-cell electronic orbital sequence 1S21P61D102S2 and satisfy the 20-electron counting rule. IR and Raman spectrum calculations are also presented to understand the vibrational nature of the clusters.

Ground states of Heisenberg spin clusters from projected Hartree-Fock theory

We apply the projected Hartree-Fock theory (PHF) for approximating ground states of Heisenberg spin clusters. Spin-rotational, point-group, and complex-conjugation symmetry are variationally restored from a broken-symmetry mean-field reference, where the latter corresponds to a product of local spin states. A fermionic formulation of the Heisenberg model furnishes a conceptual connection to PHF applications in quantum chemistry and detailed equations for a self-consistent field optimization of the reference state are provided. Different PHF variants are benchmarked for ground-state energies and spin-pair correlation functions of antiferromagnetic spin rings and three different polyhedra, with various values of the local spin-quantum number $s$. Although PHF is not suitable to study the thermodynamic limit (where it reduces to the conventional HF results), the low computational cost and the compact wave-function representation make PHF a promising complement to existing approaches for ground states of finite spin clusters, particularly for large local spin $s$ and a moderately large number of sites $N$. The present work may also motivate future explorations of more accurate post-PHF methods for Heisenberg spin clusters.

A Comparison of Structure, Stability of Neutral and Cationic Vanadium-doped Germanium Clusters GenV0/+ (n = 2 - 8) by using Density Function Theorym clusters GenV0/+ (n = 2 - 8) by using density function theory

The geometries, stabilities and electronic properties of vanadium-doped germanium clusters GenV0/+ (n=2-8) were systematically investigated by using density functional theory (DFT) at the PBE level and the 6-311+G(d) basis set. The results show that the geometries of lowest-energy structures of the cationic clusters are only significant different from those of the neutral at n = 6 or 7. The ground state of neutral clusters is a doublet, except Ge2V which is a quartet while that of cationic clusters is a triplet, except Ge8V+, which is a singlet. The average binding energy values generally increase with increasing cluster size. The results from average binding energies showed that it is more stable for the cationic than neutral clusters at the same size. Furthermore, the calculated values of fragmentation energy, second-order energy difference, HOMO-LUMO gap and adiabatic ionization potential suggest that the neutral clusters possess higher stability when n = 2, 5, 8 and the cations are more stable when n = 2, 3, 5 and 6.

Chromone-methanol clusters in the electronic ground and lowest triplet state: a delicate interplay of non-covalent interactions.

Chromone offers two energetically almost equivalent docking sites for alcohol molecules, in which the hydroxyl group is hydrogen bonded to one of the free electron pairs of the carbonyl O atom. Here, the delicate balance between these two competing arrangements is studied by combining IR/R2PI and UV/IR/UV spectroscopy in a molecular beam supported by quantum-chemical calculations. Most interestingly, chromone undergoes an efficient intersystem crossing into the triplet manifold upon electronic excitation, so that the studies on aromatic molecule-solvent complexes are for the first time extended to such a cluster in a triplet state. As the lowest triplet state (T1) is of ground state character, powerful energy decomposition approaches such as symmetry-adapted perturbation theory (SAPT) and local energy decomposition using the domain-based local pair natural orbital coupled-cluster method (DLPNO-CCSD(T)/LED) are applied. From the theoretical analysis we infer for the T1 state a loss of planarity (puckering) of the 4-pyrone ring of the chromone unit, which considerably affects the interplay between different types of non-covalent interactions at the two possible binding sites.

Electrolyte clusters as hydrogen sponges: diffusion Monte Carlo simulations.

We carry out Diffusion Monte Carlo simulations of up to five hydrogen molecules aggregated with two Stockmayer clusters that solvate a single lithium ion. The first one contains six point dipole solvent particles with parameters tuned to emulate nitromethane. The second cluster is a relative large system investigated recently [G. DiEmma, S. Kalette, and E. Curotto, Chem. Phys. Lett. 2019, 725, 80-86]. In both cases we find that the aggregated hydrogen molecules perturb significantly the ground state of the host cluster and form a distorted tetrahedral cage around the Li+ ion. The fifth hydrogen molecule is absorbed by the larger Stockmayer cluster while remaining in the proximity of the solvated charge.

Growth mechanism, electronic properties and spectra of aluminum clusters

Density functional theory (DFT) and particle swarm optimization (PSO) have been applied to study the growth behavior, electronic properties and spectra of neutral, anionic and cationic aluminum clusters with 3–20 atoms. Many isomers have been obtained through a comprehensive structural search. The results indicate that the ground state structures of neutral and anionic aluminum clusters follow an identical periodic growth law. When the number of atoms is 6–11 and 13–18, Al atoms in these clusters grow around an octahedral cluster nucleus and an icosahedral cluster nucleus, respectively. For Aln+ (n ≤ 14 and n ≠ 7) clusters, the most stable structure is different from that of Aln or Aln−clusters. When n > 14, the ground state structure of Aln+ clusters is similar to that of Aln or Aln−clusters. The electronic properties of aluminum clusters have been analyzed by the averaged binding energy, second-order difference of energy, energy gap and dissociation energy. It is found that the Al7+ and Al13− clusters have very high stability and a large energy gap and can be regarded as two superatoms. The aluminum cluster with 18 or 40 valence electrons are the least likely to lose an electron. The dissociation behavior of Aln+ clusters caused by collision is reasonably explained by means of the dissociation energy. The optical absorption spectra of neutral aluminum clusters have been simulated by using the time-dependent density functional theory. The ground states of anionic aluminum clusters have been determined by comparing theoretical photoelectron spectra (PES) with experimental findings. Infrared and Raman spectra of cationic aluminum clusters have been forecasted and can assist in identifying the most stable structure in future experiments.

Bridging Polyoxometalate-Based Mn4 Cubane Clusters with Inorganic Phosphates: Structural Transformation and Magnetic Properties.

The mixed-valent tetramanganese MnIII3MnIV (Mn4) cubane clusters have been at the forefront of molecular magnetism and biomimetic catalysis research for decades. Incorporating robust polyoxometalates to Mn4 cubanes significantly improves their stability and aqueous solubility, while providing a great platform for studying their deposition onto selected surfaces during device fabrication. In this work, we discovered that the terminal carboxylate ligands in these polyoxometalate-based [MnIII3MnIVO4] magnetic clusters can be partially or completely replaced by inorganic phosphate/polyphosphate groups. This replacement leads to oligomeric aggregates of the Mn4 clusters. The magnetic data of the monomeric and oligomeric Mn4 clusters suggested that the introduction of inorganic phosphate bridges may not alter the S = 9/2 ground state of individual Mn4 clusters, although different magnetic behaviors, especially at low temperatures, were observed primarily because of intercluster interactions.