Dual Clusters Research Articles

Study the structure, stability and CO2 adsorption of the ScVB5 cluster

A combination of genetic algorithm and density functional theory (GA-DFT) was used to calculate the minimum structures of ScVB5 clusters. The thirteen isomers of ScVB5 cluster were investigated at the level of PBE/def2-TZVPP, TPSSh/def2-TZVPP, and TPSSh/def2-QZVP levels. The relative energies, the structural geometry, ionization energy, affinity energy of neutral isomers were reported. The ScVB5 cluster can be formed by adding atom into smaller clusters. The proposed structure of ScVB5 cluster for CO2 treatment is a pentagonal bipyramid in the Cs symmetry with vanadium atom at one of the vertices and scandium atom in the base of bipyramid. The favor position for adsorp CO2 by the ScVB5 cluster were at around of Sc and V atoms. The dual transition metal-doped boron clusters can interact with CO2 molecules stronger than pure boron clusters.

Carborane-Cluster-Wrapped Copper Cluster with Cyclodextrin-like Cavities for Chiral Recognition.

Chiral atomically precise metal clusters, known for their remarkable chiroptical properties, hold great potential for applications in chirality recognition. However, advancements in this field have been constrained by the limited exploration of host-guest chemistry, involving metal clusters. This study reports the synthesis of a chiral Cu16(C2B10H10S2)8 (denoted as Cu16@CB8, where C2B10H12S2H2 = 9,12-(HS)2-1,2-closo-carborane) cluster by an achiral carboranylthiolate ligand. The chiral R-/S-Cu16@CB8 cluster features chiral cavities reminiscent of cyclodextrins, which are surrounded by carborane clusters, yet they crystallize in a racemate. These cyclodextrin-like cavities demonstrated the specific recognition of amino acids, as indicated by the responsive output of circular dichroism and circularly polarized luminescence signals of Cu16 moieties of the Cu16@CB8 cluster. Notably, a quantitative chiroptical analysis of amino acids in a short time and a concomitant deracemization of Cu16@CB8 were achieved. Density functional tight-binding molecular dynamics simulation and noncovalent interaction analysis further unraveled the great importance of the cavities and binding sites for chiral recognition. Dipeptide, tripeptide, and polypeptide containing the corresponding amino acids (Cys, Arg, or His residues) display the same chiral recognition, showing the generality of this approach. The functional synergy of dual clusters, comprising carborane and metal clusters, is for the first time demonstrated in the Cu16@CB8 cluster, resulting in the valuable quantification of the enantiomeric excess (ee) value of amino acids. This work opens a new avenue for chirality sensors based on chiral metal clusters with unique chiroptical properties and inspires the development of carborane clusters in host-guest chemistry.

In situ illite Rb-Sr dating indicates the coevality of Carlin-type gold deposits inside and around the isolated carbonate platform in western Guangxi, China

The western Guangxi is a crucial component of the Guizhou–Yunnan–Guangxi “Golden Triangle”(hereafter referred to as the Golden Triangle) of South China. The most discovered Carlin-type gold deposits in this region are primarily situated at the periphery of isolated carbonate platforms. The ore bodies are vein-like in form controlled by faults, and the wall rock are Triassic carbonate-bearing terrigenous clastic rocks. Recently, some gold deposits have been discovered in the interior of isolated carbonate platforms. The ore bodies are primarily stratiform hosted in sedimentary unconformities. The mineralized strata span from the Cambrian to the Permian, and the host rock include sandy and muddy dolostones, as well as a combination of sandstone, mudstone, tuff, and chert. The geological and geochemical characteristics suggest that these stratiform deposits in the interior of isolated carbonate platforms share common characteristic with Carlin-type gold deposits in China and USA. However, it remains uncertain whether these deposits are products of the one mineralization system and are coeval with those vein deposits at the periphery of the isolated platforms. To address this question, we conducted geological and isotopic dating studies on the Longhuo gold deposit and the De'e gold occurrence in the interior of isolated platforms. The Longhuo stratiform gold deposit occurs along a parallel unconformity in the Carboniferous/Devonian composed of sandstone, shale, tuff, and chert. Hydrothermal illite, quartz and auriferous pyrite fill along joints and fissures, implying that illite formed during the main ore-forming stage and its age could represent the age of gold mineralization. The stratiform orebodies of De'e gold occurrence are hosted in Cambrian sandy and muddy dolostones. Gold occurs as invisible Au in zoned pyrite and arsenopyrite, with a dominant alteration assemblage of silicification, carbonate alteration, and illitization. Hydrothermal quartz, illite and dolomite often aggregate with zoned auriferous pyrite and arsenopyrite in the most intensely altered zones, suggesting that illite formed during the main ore-forming stage and its age could also represent the age of gold mineralization. Illite LA-ICP-MS Rb-Sr dating was performed on both deposits, yielding ages of 184.16 ± 3.14 Ma for the Longhuo gold deposit and 191.21 ± 6.76 Ma for the De’e gold occurrence.Previous studies have indicated that Carlin-type gold deposits in the Golden Triangle exhibits two distinct age clusters, one ranging from 184 to 235 Ma and the other from 134 to 148.4 Ma. These dual age clusters suggest the potential occurrence of two mineralization events. The obtained ∼ 190 Ma mineralization ages for the Longhuo and De'e gold deposits in this study indicate that the Carlin-type gold mineralization within the isolated platform took place during the Early Jurassic. This aligns with the early mineralization event of gold deposits along the platform's edge, implying that gold deposits inside and around the isolated carbonate platform are products of the same mineralization system, influenced by post-Indosinian extensional events. The interior of the isolated carbonate platform holds substantial exploration potential, making it a novel direction for prospecting Carlin-type gold deposits in western Guangxi.

Selecting dual atomic clusters supported on two-dimensional biphenylene with significantly optimized capability to reduce carbon monoxide

Four dual-atomic clusters supported on two-dimensional biphenylene were identified from 28 TM2@BPN candidates, which can surpass the activity benchmarks for metals and achieve efficient CORR.

The Role of Late Presenters in HIV-1 Transmission Clusters in Europe.

Investigating the role of late presenters (LPs) in HIV-1 transmission is important, as they can contribute to the onward spread of HIV-1 virus before diagnosis, when they are not aware of their HIV status. To characterize individuals living with HIV-1 followed up in Europe infected with subtypes A, B, and G and to compare transmission clusters (TC) in LP vs. non-late presenter (NLP) populations. Information from a convenience sample of 2679 individuals living with HIV-1 was collected from the EuResist Integrated Database between 2008 and 2019. Maximum likelihood (ML) phylogenies were constructed using FastTree. Transmission clusters were identified using Cluster Picker. Statistical analyses were performed using R. 2437 (91.0%) sequences were from subtype B, 168 (6.3%) from subtype A, and 74 (2.8%) from subtype G. The median age was 39 y/o (IQR: 31.0-47.0) and 85.2% of individuals were males. The main transmission route was via homosexual (MSM) contact (60.1%) and 85.0% originated from Western Europe. In total, 54.7% of individuals were classified as LPs and 41.7% of individuals were inside TCs. In subtype A, individuals in TCs were more frequently males and natives with a recent infection. For subtype B, individuals in TCs were more frequently individuals with MSM transmission route and with a recent infection. For subtype G, individuals in TCs were those with a recent infection. When analyzing cluster size, we found that LPs more frequently belonged to small clusters (<8 individuals), particularly dual clusters (2 individuals). LP individuals are more present either outside or in small clusters, indicating a limited role of late presentation to HIV-1 transmission.

The proneural factors Ascl1a and Ascl1b contribute to the terminal differentiation of dopaminergic GABAergic dual transmitter neurons in zebrafish

The proneural factor Ascl1 is involved in several steps of neurogenesis, from neural progenitor maintenance to initiation of terminal differentiation and neuronal subtype specification. In neural progenitor cells, Ascl1 initiates the cell-cycle exit of progenitors, and contributes to their differentiation into mainly GABAergic neurons. Several catecholaminergic neuron groups in the forebrain of zebrafish use GABA as co-transmitter, but a potential role of the two paralogues Ascl1a and Ascl1b in their neurogenesis is not understood. Here, we show that ascl1a, ascl1b double mutant embryos develop a significantly reduced number of neurons in all GABAergic and catecholaminergic dual transmitter neuron anatomical clusters in the fore- and hindbrain, while glutamatergic catecholaminergic clusters develop normally. However, none of the affected catecholaminergic cell clusters are lost completely, suggesting an impairment in progenitor pools, or a requirement of Ascl1a/b for differentiation of a subset of neurons in each cluster. Early progenitors which are dlx2a+, fezf2 + or emx2 + are not reduced whereas late progenitors and differentiating neurons marked by the expression of dlx5a, isl1 and arxa are severely reduced in ascl1a, ascl1b double mutant embryos. This suggests that Ascl1a and Ascl1b play only a minor or no role in the maintenance of their progenitor pools, but rather contribute to the initiation of terminal differentiation of GABAergic catecholaminergic neurons.

Tropical F$F$‐polynomials and general presentations

AbstractWe introduce the tropical ‐polynomial of a quiver representation . We study its interplay with the general presentation for any finite‐dimensional basic algebra. We give an interpretation of evaluating at a weight vector. As a consequence, we give a presentation of the Newton polytope of . We study the dual fan and 1‐skeleton of . We propose an algorithm to determine the generic Newton polytopes, and show that it works for path algebras. As an application, we give a representation‐theoretic interpretation of Fock–Goncharov's duality pairing. We give an explicit construction of dual clusters, which consists of real Schur representations. We specialize the above general results to the cluster‐finite algebras and the preprojective algebras of Dynkin type.

Cobalt dual-atom clusters with strong chemiluminescent response for analyzing pathogenic bacteria by using cell wall bind domain as recognizer

As new type of catalysts, dual or multiple atomic clusters have displayed extremely high atom utilization rate and superior catalytic activity. In the present work, a metal binuclear atom pair with unique cobalt coordination environment of Co2-O8 were prepared on the supports of MOFs MIL-53(Al), and named as Co dual-atom clusters (CoDACs). Fascinatingly, CoDACs with desirable water dispersibility display very high catalytic efficiency for redox-based chemiluminescent (CL) reaction by generating abundant reactive oxygen species. The catalysts boosted the CL signal of luminol-H2O2 system for 1192 times as their concentration were 1.0 μg mL-1, thus can be applied as superior CL probes for tracing biorecognition events. To verify their application potential, CoDACs were used to establish a CL method for analyzing methicillin-resistant Staphylococcus aureus (MRSA) strains by adopting cell wall bind domain of bacteriophage P108 as a recognizer. The method displays a dynamic range of 6.1 × 102 - 6.1 × 107 CFU mL-1 and a detection limit of 220 CFU mL-1. The results for analysis of MRSA in biological, drug and food samples manifest their reliability for real application. To our best knowledge, it is the first study focusing on DACs as efficient catalysts for CL reaction.

Plasma-Assisted Dinitrogen Activation via Dual Platinum Cluster Catalysis: A Strategy for Ammonia Synthesis under Mild Conditions

Plasma-Assisted Dinitrogen Activation via Dual Platinum Cluster Catalysis: A Strategy for Ammonia Synthesis under Mild Conditions

Understanding the Activity and Stability of Single-Atom Catalysts for the ORR in Anion Exchange Membrane Fuel Cell(AEMFCs)

To be considered the ultimate power source for transportation systems and portable devices, anion exchange membrane fuel cells (AEMFCs) need to overcome significant cost barriers1,2. For this, the U.S. Department of Energy (DOE) recently has set some challenging activity targets for AEMFCs; this includes the near-term target PGM loading is 0.2 mg/cm2 for 2021–2023, and by 2024 the total loading should be limited to ⩽ 0.125 mg/cm2.This final milestone is the first step in enabling a shift to completely platinum group metal (PGM)-free membrane electrode assemblies (MEAs) by 20303. Unfortunately, today’s high performing4 and long-life5,6 MEAs all rely on a high loading of PGM in both the anode and the cathode, resulting in a total PGM loading of ~1 mgPGM/cm2.To reduce the PGM loading in AEMFCs, it is important to transition to very low PGM electrodes, and eventually to catalysts that are PGM-free but do not contain bulk transition metals that passivate or dissolve in the electrolyte. One approach that can be used in both cases is to create atomically-dispersed ORR catalysts. On the PGM side, single atom catalysts (or even dual atom clusters) have the potential to drastically lower the PGM loading and cost while maximizing utilization7. The rational design of electrocatalyst, either through modification of commercial catalysts or entirely new structures, is very important to reach low loading high activity electrocatalusts for fuel cells.8–10. On the non-PGM side, the most common catalyst moiety has been single atoms of Fe in N4-funcitonal groups in carbon, or Fe-N-C. Though there have been Fe-N-C catlaysts that have shown good activity and durability in ex-situ tests, these materials are yet to be transitioned successfully to MEAs that can compete with their PGM-containing counterparts.In this study, two approaches will be discussed. The first synthesizes a high densities of atomically dispersed single-atom Pt catalysts, which were prepared in-house by a simple, and scalable synthesis method of chelate fixation (CheFi). These materials have been physically characterized using a wide array of techniques including x-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), high-resolution Cs aberration-corrected scanning transmission electron microscopy (STEM). The catalysts were also tested for their ORR activity and their in-situ behavior in operating AEMFCs. In addition to their performance data, these catalysts yielded interesting mechanistic insight that will be discussed. The second approach was to investigate the effect of structure on the behavior of Fe-N-C catalysts. In this part of the work, it was demonstrated that single atoms are indeed the most active and important componenes. It is also shown that the physical properties of the carbon structure (porosity and graphitization) play a role in determining not only the ORR activity, but also the ability to translate that activity to highly performing AEMFCs. In fact, it will be shown that it is possible to create AEMFCs with a PGM-free cathode that are able to achieve a peak power density > 2.0 W/cm2 and a kinetic current at 0.9 V (iR-free) of 100 mA/cm2. These cells are also able to out-perform and out-live their PEMFC counterparts.

Planar random-cluster model: fractal properties of the critical phase

This paper is studying the critical regime of the planar random-cluster model on {mathbb {Z}}^2 with cluster-weight qin [1,4). More precisely, we prove crossing estimates in quads which are uniform in their boundary conditions and depend only on their extremal lengths. They imply in particular that any fractal boundary is touched by macroscopic clusters, uniformly in its roughness or the configuration on the boundary. Additionally, they imply that any sub-sequential scaling limit of the collection of interfaces between primal and dual clusters is made of loops that are non-simple. We also obtain a number of properties of so-called arm-events: three universal critical exponents (two arms in the half-plane, three arms in the half-plane and five arms in the bulk), quasi-multiplicativity and well-separation properties (even when arms are not alternating between primal and dual), and the fact that the four-arm exponent is strictly smaller than 2. These results were previously known only for Bernoulli percolation (q = 1) and the FK-Ising model (q = 2). Finally, we prove new bounds on the one, two and four-arm exponents for qin [1,2], as well as the one-arm exponent in the half-plane. These improve the previously known bounds, even for Bernoulli percolation.

Genome mining combined metabolic shunting and OSMAC strategy of an endophytic fungus leads to the production of diverse natural products

Endophytic fungi are promising producers of bioactive small molecules. Bioinformatic analysis of the genome of an endophytic fungus Penicillium dangeardii revealed 43 biosynthetic gene clusters, exhibited its strong ability to produce numbers of secondary metabolites. However, this strain mainly produce rubratoxins alone with high yield in varied culture conditions, suggested most gene clusters are silent. Efforts for mining the cryptic gene clusters in P. dangeardii, including epigenetic regulation and one-strain-many-compounds (OSMAC) approach were failed probably due to the high yield of rubratoxins. A metabolic shunting strategy by deleting the key gene for rubratoxins biosynthesis combining with optimization of culture condition successfully activated multiple silent genes encoding for other polyketide synthases (PKSs), and led to the trace compounds detectable. As a result, a total of 23 new compounds including azaphilone monomers, dimers, trimers with unprecedented polycyclic bridged heterocycle and spiral structures, as well as siderophores were identified. Some compounds showed significant cytotoxicities, anti-inflammatory or antioxidant activities. The attractive dual PKSs gene clusters for azaphilones biosynthesis were mined by bioinformatic analysis and overexpression of a pathway specific transcription factor. Our work therefor provides an efficient approach to mine the chemical diversity of endophytic fungi.

Dual pH-triggered catalytic selective Mn clusters for cancer radiosensitization and radioprotection.

Hypoxia is known to be a common feature within many types of solid tumors, which is closely related to the limited efficacy of radiotherapy. Meanwhile, due to the non-discriminatory killing effect of both normal and cancer cells during the radiation process, traditional radiosensitizers could bring severe non-negligible side-effects to the whole body. In this work, stable and atomically precise Mn clusters which possess efficient pH-triggered catalytic selective capacity are developed rationally. Mn clusters could efficiently catalyze oxygen production in an acidic tumor microenvironment, while exhibiting strong reducibility and free radical scavenging ability in neutral circumstances. In vivo experiments show that Mn clusters are able to enhance the radiotherapy effect in the mouse model of 4T1 tumors and protect normal tissues from radiation at the same time. Thus, the present work provides a novel dual-functional strategy to enhance radiotherapy-induced tumor treatment by improving tumor oxygenation and protect normal tissues from radiation simultaneously.

Layer-by-layer assembled magnetic bimetallic metal-organic framework composite for global phosphopeptide enrichment

The highly selective enrichment of phosphopeptides is vital for the research of phosphorylated proteomics. Herein, a magnetic bimetallic metal-organic framework (MOF) with Zr-O and Ti-O clusters (denoted as Fe3O4@SiO2@(Zr-Ti-PTA)15) has been fabricated using a layer-by-layer assembly approach via the coordination of metal ions with carboxyl groups. The composite has large specific surface area (135.84 m2 g−1) and superparamagnetism (62.03 emu g−1). Compared with single-metal cluster MOF, the Fe3O4@SiO2@(Zr-Ti-PTA)15 showed higher binding capacity (100 mg g−1), enhanced affinity, better selectivity (nβ-casein : nBSA = 1 : 2000) and sensitivity (0.3 fmol/μL) towards phosphopeptides due to the combination of the dual metal clusters. Furthermore, the Fe3O4@SiO2@ (Zr-Ti-PTA)15 was successfully applied to extracting phosphopeptides from non-fat milk tryptic digest, and 10 mono-phosphopeptides and 22 multi-phosphopeptides were captured. As a result, 1294 phosphopeptides (476 multi-phosphopeptides and 818 mono-phosphopeptides) were selectively extracted and detected from tryptic digest of rat brain extract, indicating its great application potential in phosphorylated proteomics research.

Dual phenazine gene clusters enable diversification during biosynthesis.

Biosynthetic gene clusters (BGCs) bridging genotype and phenotype continuously evolve through gene mutations and recombinations to generate chemical diversity. Phenazine BGCs are widespread in bacteria, and the biosynthetic mechanisms of the formation of the phenazine structural core have been illuminated in the last decade. However, little is known about the complex phenazine core-modification machinery. Here, we report the diversity-oriented modifications of the phenazine core through two distinct BGCs in the entomopathogenic bacterium Xenorhabdus szentirmaii, which lives in symbiosis with nematodes. A previously unidentified aldehyde intermediate, which can be modified by multiple enzymatic and non-enzymatic reactions, is a common intermediate bridging the pathways encoded by these BGCs. Evaluation of the antibiotic activity of the resulting phenazine derivatives suggests a highly effective strategy to convert Gram-positive specific phenazines into broad-spectrum antibiotics, which might help the bacteria-nematode complex to maintain its special environmental niche.

FRSVC: Towards making support vector clustering consume less

In spite of with great advantage of discovering arbitrary shapes of clusters, support vector clustering (SVC) is frustrated by large-scale data, especially on resource limited platform. It is due to pricey storage and computation consumptions from solving dual problem and labeling clusters upon the pre-computed kernel matrix and sampling point pairs, respectively. Towards on it, we first present a dual coordinate descent method to reformulate the solver that leads to a flexible training phase carried out on any runtime platform with/without sufficient memory. Then, a novel labeling phase who does connectivity analysis between two nearest neighboring decomposed convex hulls referring to clusters is proposed, in which a new designed strategy namely sample once connected checking first tries to reduces the scope of sampling analysis. By integrating them together, a faster and reformulated SVC (FRSVC) is created with less consumption achieved according to comparative analysis of time and space complexities. Furthermore, experimental results confirm a significant improvement on flexibility of selective efficiency without losing accuracy, with which a balance can be easily reached on the basis of resources a platform equipped.

PERFORMANCE ANALYSIS OF MESSAGE PASSING INTERFACE COLLECTIVE COMMUNICATION ON INTEL XEON QUAD-CORE GIGABIT ETHERNET AND INFINIBAND CLUSTERS

The performance of MPI implementation operations still presents critical issues for high performance computing systems, particularly for more advanced processor technology. Consequently, this study concentrates on benchmarking MPI implementation on multi-core architecture by measuring the performance of Open MPI collective communication on Intel Xeon dual quad-core Gigabit Ethernet and InfiniBand clusters using SKaMPI. It focuses on well known collective communication routines such as MPI-Bcast, MPI-AlltoAll, MPI-Scatter and MPI-Gather. From the collection of results, MPI collective communication on InfiniBand clusters had distinctly better performance in terms of latency and throughput. The analysis indicates that the algorithm used for collective communication performed very well for all message sizes except for MPI-Bcast and MPI-Alltoall operation of inter-node communication. However, InfiniBand provides the lowest latency for all operations since it provides applications with an easy to use messaging service, compared to Gigabit Ethernet, which still requests the operating system for access to one of the server communication resources with the complex dance between an application and a network.

Design and testing of a synthetic biology framework for genetic engineering of Corynebacterium glutamicum

BackgroundSynthetic biology approaches can make a significant contribution to the advance of metabolic engineering by reducing the development time of recombinant organisms. However, most of synthetic biology tools have been developed for Escherichia coli. Here we provide a platform for rapid engineering of C. glutamicum, a microorganism of great industrial interest. This bacteria, used for decades for the fermentative production of amino acids, has recently been developed as a host for the production of several economically important compounds including metabolites and recombinant proteins because of its higher capacity of secretion compared to traditional bacterial hosts like E. coli. Thus, the development of modern molecular platforms may significantly contribute to establish C. glutamicum as a robust and versatile microbial factory.ResultsA plasmid based platform named pTGR was created where all the genetic components are flanked by unique restriction sites to both facilitate the evaluation of regulatory sequences and the assembly of constructs for the expression of multiple genes. The approach was validated by using reporter genes to test promoters, ribosome binding sites, and for the assembly of dual gene operons and gene clusters containing two transcriptional units. Combinatorial assembly of promoter (tac, cspB and sod) and RBS (lacZ, cspB and sod) elements with different strengths conferred clear differential gene expression of two reporter genes, eGFP and mCherry, thus allowing transcriptional “fine-tuning”of multiple genes. In addition, the platform allowed the rapid assembly of operons and genes clusters for co-expression of heterologous genes, a feature that may assist metabolic pathway engineering.ConclusionsWe anticipate that the pTGR platform will contribute to explore the potential of novel parts to regulate gene expression, and to facilitate the assembly of genetic circuits for metabolic engineering of C. glutamicum. The standardization provided by this approach may provide a means to improve the productivity of biosynthetic pathways in microbial factories for the production of novel compounds.

Percolation and criticalO(n)loop configurations

We study a percolation problem based on critical loop configurations of the O(n) loop model on the honeycomb lattice. We define dual clusters as groups of sites on the dual triangular lattice that are not separated by a loop, and investigate the bond-percolation properties of these dual clusters. The universal properties at the percolation threshold are argued to match those of Kasteleyn-Fortuin random clusters in the critical Potts model. This relation is checked numerically by means of cluster simulations of several O(n) models in the range 1<or=n<or=2. The simulation results include the percolation threshold for several values of n, as well as the universal exponents associated with bond dilution and the size distribution of the diluted clusters at the percolation threshold. Our numerical results for the exponents are in agreement with existing Coulomb-gas results for the random-cluster model, which confirms the relation between both models. We discuss the renormalization flow of the bond-dilution parameter p as a function of n, and provide an expression that accurately describes a line of unstable fixed points as a function of n, corresponding with the percolation threshold. Furthermore, the renormalization scenario indicates the existence, in a p versus n diagram, of another line of fixed points at p=1, which is stable with respect to p.

Defect motifs for spherical topologies

Putative global minima for the Thomson problem of $N$ charges on a sphere are located for selected sizes in the range $N\ensuremath{\le}4352$. For small sizes most global minima simply exhibit 12 disclinations. However, around $N=400$ extended dislocations are common, where a heptagon lies between two pentagons in the Voronoi representation. At larger sizes around $N=1000$ twinned grain boundaries are favorable and then between about $N=1000$ and 2000 ``rosette'' defects appear, containing a central pentagon surrounded by five heptagons alternating with five additional pentagons in the Voronoi representation. Structures with 12 rosettes and $I$ point group symmetry are particularly low in energy for $N=1632$ and 1902. Above $N=2000$ the lowest minima located generally contain irregular grain boundaries, sometimes with a few rosette defects. Face dual carbon clusters corresponding to ${I}_{h}$ local minima at $N=432$ and 582 are characterized as local minima for ${\text{C}}_{860}$ and ${\text{C}}_{1160}$.