Packing schemes for Lennard-Jones clusters of 13 to 150 atoms: minima, transition states and rearrangement mechanisms

Uppenbrink, Julia; Wales, David J.

doi:10.1039/ft9918700215

Cited by 57 publications

(23 citation statements)

References 33 publications

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“…We call a cluster "Gregory-Newton" (GN) when it belongs to the set of all clusters consisting of 12 spheres kissing a central sphere. The canonical Gregory-Newton cluster is the icosahedron, which is perhaps the most common form studied in cluster chemistry and physics [2,41,65,66]. We therefore investigate this cluster type in more detail here.…”

Section: The Special Case Of a Gregory-newton Clustermentioning

confidence: 99%

From sticky-hard-sphere to Lennard-Jones-type clusters

Trombach

Hoy

Wales³

et al. 2018

Phys. Rev. E

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A relation M_{SHS→LJ} between the set of nonisomorphic sticky-hard-sphere clusters M_{SHS} and the sets of local energy minima M_{LJ} of the (m,n)-Lennard-Jones potential V_{mn}^{LJ}(r)=ɛ/n-m[mr^{-n}-nr^{-m}] is established. The number of nonisomorphic stable clusters depends strongly and nontrivially on both m and n and increases exponentially with increasing cluster size N for N≳10. While the map from M_{SHS}→M_{SHS→LJ} is noninjective and nonsurjective, the number of Lennard-Jones structures missing from the map is relatively small for cluster sizes up to N=13, and most of the missing structures correspond to energetically unfavorable minima even for fairly low (m,n). Furthermore, even the softest Lennard-Jones potential predicts that the coordination of 13 spheres around a central sphere is problematic (the Gregory-Newton problem). A more realistic extended Lennard-Jones potential chosen from coupled-cluster calculations for a rare gas dimer leads to a substantial increase in the number of nonisomorphic clusters, even though the potential curve is very similar to a (6,12)-Lennard-Jones potential.

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Section: The Special Case Of a Gregory-newton Clustermentioning

confidence: 99%

From sticky-hard-sphere to Lennard-Jones-type clusters

Trombach

Hoy

Wales³

et al. 2018

Phys. Rev. E

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“…11,[15][16][17] Morphology interconversion processes have been studied for monometallic, core-shell and vertex-decorated systems by means of transition state search algorithms, molecular dynamics or enhanced sampling techniques. [18][19][20][21][22][23][24][25][26][27][28] It has been shown that solidsolid transitions of cuboctahedral (Co) or decahedral (Dh) morphologies into icosahedral (Ih) one happens in nanoclusters, with sizes as small as 147 atoms, via cooperative screw-dislocation motions also known as diamond-square-diamond (DSD) rearrangements. 29,30 .…”

Section: Introductionmentioning

confidence: 99%

The effect of chemical ordering and lattice mismatch on structural transitions in phase segregating nanoalloys

Rossi

Baletto

2017

Phys. Chem. Chem. Phys.

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We elucidate the effect of lattice mismatch and chemical ordering on structural transitions in bimetallic nanoalloys of ∼1.5 nm. We show that collective screw dislocation motions happen in small mismatch shell@core systems while strongly mismatched ones favour incomplete outer shell rearrangements. Cooperative transitions can also become hindered when the chemical ordering breaks the geometrical symmetry. Escaping from an unfavourable morphological basin occurs first via re-arrangements of the geometry and then changes towards a better chemical pattern. We observe that the chemical re-ordering mechanisms are independent of system composition and stoichiometry but hinge on the initial and final chemical arrangements.

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“…The model process keeps connected units connected, forbids geometric overlap of units (volume exclusion) and connects randomly chosen units if geometrically permitted. Based only on such random monomer interactions and geometric constraints, akin to those in Lennard-Jones clusters and sticky hard spheres [37,38], the 3D structures self-organizing through the simple model process are consistent with those of real protein ensembles in all of the above-mentioned features simultaneously.…”

Section: Introductionmentioning

confidence: 84%

Geometric constraints in protein folding

Molkenthin

Muehle

Mey

et al. 2018

Preprint

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The intricate three-dimensional geometries of protein tertiary structures underlie protein 2 function and emerge through a folding process from one-dimensional chains of amino acids. The exact 3 spatial sequence and configuration of amino acids, the biochemical environment and the temporal sequence 4 of distinct interactions yield a complex folding process that cannot yet be easily tracked for all proteins. 5 To gain qualitative insights into the fundamental mechanisms behind the folding dynamics and generic 6 features of the folded structure, we propose a simple model of structure formation that takes into account 7 only fundamental geometric constraints and otherwise assumes randomly paired connections. We find that 8 despite its simplicity, the model results in a network ensemble consistent with key overall features of the 9 ensemble of Protein Residue Networks we obtained from more than 1000 biological protein geometries as 10 available through the Protein Data Base. Specifically, the distribution of the number of interaction neighbors 11 a unit (amino acid) has, the scaling of the structure's spatial extent with chain length, the eigenvalue spectrum 12 and the scaling of the smallest relaxation time with chain length are all consistent between model and real 13 proteins. These results indicate that geometric constraints alone may already account for a number of 14 generic features of protein tertiary structures. Author summary 27 How proteins fold constitutes one of the most persistent, broad, and exciting open research questions at the 28 intersection of biology, chemistry, and physics. Which mechanisms induce a one-dimensional sequence of 29 amino acids to form into a complex three-dimensional (3D) structure? Proteins in their active 3D structure 30 impact most of the basic processes inside cells, including gene regulation, cell metabolism, and the creation 31 of protein structures themselves. Yet, a general rule about which conditions lead to which specific 3D protein 32 structures remains unknown to date. 33 Here, we demonstrate how a simple model that takes only fundamental geometric constraints into 34 account and otherwise assumes randomly paired connections, naturally generates an ensemble of folded 35 structures that exhibits many of its coarse scale features consistent with those of protein residue networks 36 resulting from tertiary structures of biological proteins. Specifically, we tested a set of more than 1000 37 biological proteins and model structures and extracted a range of ensemble properties, including the spatial 38 extension with chain size, the distribution of the number of interacting neighbors in the folded structure, the 39 spectrum of Laplacian eigenvalues, and the distribution of the dominant non-trivial eigenvalue. We found 40 1 of 14December 21, 2018 that all of those properties are consistent between the ensemble of biological protein residue networks and 41 the networks emerging in a self-organized way from the simple model. 42 These results indicate that coarse ensembl...

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Packing schemes for Lennard-Jones clusters of 13 to 150 atoms: minima, transition states and rearrangement mechanisms

Cited by 57 publications

References 33 publications

From sticky-hard-sphere to Lennard-Jones-type clusters

From sticky-hard-sphere to Lennard-Jones-type clusters

The effect of chemical ordering and lattice mismatch on structural transitions in phase segregating nanoalloys

Geometric constraints in protein folding

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