Growth

Configurational-bias regrowth of chain ends

A Monte Carlo move that samples chain conformations of a built, typed cell. It picks a chain, one of its free ends and one to a few of the rotatable backbone bonds nearest that end, and regrows the end bond by bond from the inside out: at each bond k torsion angles are drawn uniformly on the circle, each weighted by the Boltzmann factor of the energy of the atoms it places, and one is chosen by its weight. The old end is retraced the same way (its own torsion counted as one of the trials) and the new end is accepted with probability min(1, W_new/W_old). Trial energies are the assigned force field's: van der Waals (shifted to zero at the cut-off, 1-4 pairs scaled), damped shifted force electrostatics and the torsion terms about each regrown bond, class II cross terms included. Bond lengths, angles, impropers and every stereo configuration are untouched; ring, double, aromatic and carbonyl C–N/C–O bonds are held.

Siepmann & Frenkel 1992; Rosenbluth & Rosenbluth 1955

When to use it

After growth and a first minimisation, before dynamics: it relaxes chain-end conformations and local packing far faster than MD at the same temperature. It does not move chain interiors (double-bridging and end-bridging moves would) and does not change the density.

Source

core/src/cbmc.cpp (cbmc_regrow)

Tested by

Cbmc.ButaneTorsionsFollowBoltzmann (trans population equals the grid-integrated Boltzmann one), Cbmc.MeltKeepsGeometryAndCountsEnergy (energy change equals the Evaluator's to 1e-6; bond lengths kept to 1e-9 Å)

Departure from the reference

uniform torsion trials at fixed bond lengths and angles (the rigid-geometry ensemble, no Fixman term); electrostatics by damped shifted force, not Ewald

References

1. Siepmann, J. I., Frenkel, D., "Configurational bias Monte Carlo: a new sampling scheme for flexible chains", Mol. Phys. 75, 59–70 (1992). doi:10.1080/00268979200100061
2. Rosenbluth, M. N., Rosenbluth, A. W., "Monte Carlo calculation of the average extension of molecular chains", J. Chem. Phys. 23, 356–359 (1955). doi:10.1063/1.1741967

Functional groups on nanotubes, sheets and fillers

Groups grafted covalently onto a filler: the sidewalls, ends and edges of carbon and boron nitride nanotubes and sheets (and any sp² framework), or the atoms chosen. A group is a preset (hydroxyl, carboxyl, amine, methyl, fluoro, phenyl, nitrophenyl, amide, ester, hydroxymethyl, vinyl, thiol, aminopropyl, octadecylamide, PEG) or a SMILES with one attachment point. The sites follow a pattern: at random, every site at a spacing, a band along the axis, a helix round a tube, the tube's rim or the flake's edge hydrogens, or the selected atoms; only the elements named (e.g. boron of h-BN). A sidewall group sits on its site's outward normal — the normal of the three bonds, turned away from the filler's centre (outside a tube, on top of a sheet; inside or below, or both at random, on request); sites stay at least the spacing apart.

When to use it

Functionalised CNT, graphene and BN fillers for polymer and rubber composites: build the filler, graft the groups, relax (the grafted sp² atoms pyramidalise), then embed it in the matrix or compare adsorbates on it with the Adsorption locator.

Source

core/src/functionalize.cpp (functionalize)

Tested by

Functionalize.TubeSidewallOutsideAndInside, SheetSidesSpacingAndElements, EndsAndHelix

Departure from the reference

the grafted atoms keep their sp² places until relaxed; no two neighbouring sites are grafted (by the spacing)

Chain growth by trial placement

Chains grow unit by unit inside the periodic cell. Each step places the next backbone atom and its substituents from internal coordinates (NeRF), tries many torsions (trans and gauche with jitter, ring rotations) and keeps the roomiest: the trial whose worst distance to any atom already in the cell, minus its contact limit, is largest. A poor step backs up a few units; a chain that cannot continue restarts elsewhere.

CAPS's own scheme

When to use it

Building amorphous cells, films on surfaces and blends at a chosen density. Measure chain dimensions only after equilibration.

Source

core/src/grow.cpp · core/src/polymer.cpp

Tested by

Grow and polymer tests (tests/test_polymer.cpp)

Departure from the reference

not configurational-bias Monte Carlo: trials are ranked by geometric room, not Boltzmann weights, so the grown chains are not a Rosenbluth-weighted ensemble

References

1. Parsons, J., Holmes, J. B., Rojas, J. M., Tsai, J., Strauss, C. E. M., "Practical conversion from torsion space to Cartesian space for in silico protein synthesis", J. Comput. Chem. 26, 1063–1068 (2005). doi:10.1002/jcc.20237
2. Matsumoto, M., Nishimura, T., "Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator", ACM Trans. Model. Comput. Simul. 8, 3–30 (1998). doi:10.1145/272991.272995

Thiolate ligands on metal particles

Surface atoms of a gold (silver, copper, platinum, palladium) particle are those with fewer neighbours than the bulk. Sulfur sits in three-fold hollows of three mutually neighbouring surface atoms, 2.45 Å from each (on top of an atom where the surface has no hollow), sites at least √3 times the metal's nearest-neighbour distance apart — the √3 × √3 R30° packing of thiolates on Au(111). Each ligand's chain is straightened (all anti) and points out of the surface, rolled about its axis away from the others.

packing as reviewed by Love et al. 2005

When to use it

Model a capped nanoparticle to embed or solvate; relax with a force field that has metal–sulfur terms before dynamics (no metal–S bonds are written).

Source

core/src/edit.cpp (cap_thiolates) · core/src/nano.cpp

Tested by

Nano.GoldParticleCappedWithThiolates

Departure from the reference

a geometric placement, not an equilibrated monolayer; adatom (staple) motifs of small clusters are not built

References

1. Love, J. C., Estroff, L. A., Kriebel, J. K., Nuzzo, R. G., Whitesides, G. M., "Self-assembled monolayers of thiolates on metals as a form of nanotechnology", Chem. Rev. 105, 1103–1170 (2005). doi:10.1021/cr0300789

Clusters from periodic structures

The periodicity removed: every molecule made whole and moved by lattice vectors to its image nearest a centre; molecules whose centroid (or any atom) lies within the radius are kept, the cell dropped. Radius 0 keeps them all.

c_M the centroid of the whole molecule; a network larger than the cell keeps its atoms by their own nearest images

When to use it

A finite model around a site (a crosslink, an additive, a filler contact) for quantum chemistry or a gas-phase check; a whole-molecule snapshot of a melt without the cell.

Source

core/src/lattice.cpp

Tested by

tests/test_crystal.cpp Lattice.ClusterFromAPeriodicMelt (radius 0 keeps every atom, no cell; 12 Å keeps whole chains, centroids inside, no stretched bonds)

Departure from the reference

the surface of the cluster is a vacuum surface: no embedding or boundary charges

Cleaving molecular crystals

A slab of a molecular crystal (polymer crystal, cellulose, organic solid) with each molecule placed in the layer of its centroid, whole: the surfaces are made of complete molecules and no covalent bond is broken by the cut.

molecules followed through the bonds to their images; one endless along the surface normal (a chain along it) is cut at the atomic planes, and said

When to use it

Fibre surfaces from crystal structures (cellulose Iβ, PE, PET, aramid) for fibre–rubber interfaces, with chains along the surface kept whole.

Source

core/src/crystal.cpp

Tested by

tests/test_crystal.cpp Crystal.CleaveKeepsMoleculesWhole (N₂ across the cell boundary: broken by the plain cut, whole and bonded with the option)

Departure from the reference

the slab's thickness follows the molecules, not the planes: its faces are rougher than a plane cut

Chain shape: backbone torsions

Every backbone dihedral of a chain set in turn from its first end to a repeating pattern: all-trans for the planar zig-zag, TG for a 3₁ helix, TTGG, or any list of angles. Each bond's far side turns about it; ring bonds stay.

the backbone is the longest heavy-atom path outside rings (or through them when rings are in the main chain); the side groups turn with the atoms beyond each bond

When to use it

Crystalline chain models for fibres and lamellae (PE zig-zag, helices of isotactic and syndiotactic polypropylene), extended chains for pulling or for a crystal cell from one chain.

Source

core/src/torsion.cpp

Tested by

tests/test_torsion.cpp Torsion.BackboneTorsionPatterns (decane all-trans: every dihedral 180°; TG: alternately 180° and 60°)

Departure from the reference

bond lengths and angles are kept as they are: minimise afterwards to settle them and remove clashes

Polymer brushes on surfaces

Chains grafted by one end to sites on a fibre or filler surface: a site atom near the top face with a hydrogen pointing up (a silanol's O) loses that hydrogen and the chain's head bonds in its place, leaving along it. Sites are drawn at random at least a spacing apart, at a grafting density σ; the chains grow upward with the same contact rules as any growth.

the head–site bond and the atoms within three bonds of it are bonded neighbours, not contacts; the first unit's torsions are referenced to the site's own neighbours (Si–O–C)

When to use it

Silane-coupled or polymer-grafted silica in rubber, sized fibre surfaces, brushes between a filler and the matrix: the grafted layer before the matrix is added (stack a melt on it) or relaxed on its own.

Source

core/src/interface.cpp

Tested by

tests/test_crystal.cpp Crystal.PolymerBrushOnSilanols (polyisoprene on hydroxylated quartz: one H fewer per graft, each head bonded to an O at a C–O length, every O two-coordinate, σ = N/A)

Departure from the reference

the chains start stretched from the surface as grown: equilibrate before reading the brush height

Nanotube ropes and walls of any chirality

Multi-walled tubes with each wall's own (n, m) — a periodic tube is made long enough for every wall's period, each wall stretched to the common length by at most 2 % — and ropes of identical tubes: 7, 19 or 37 in hexagonal rings, or the periodic triangular lattice of an endless rope, each tube its own molecule.

a = √3 a_CC; T the wall's period along the axis, k its whole periods in the length L; neighbouring axes D apart (g wall to wall, 3.4 Å by default); the rope lattice's cell D × D√3 with two tubes

When to use it

Carbon-nanotube bundles in rubber (aggregated filler), double- and triple-walled tubes with mixed chiralities as grown, the inter-tube gap's effect on load transfer.

Source

core/src/nano.cpp

Tested by

tests/test_nano.cpp Nano.WallChiralitiesAndRopes ((5,5)@(10,10)@(26,0): atoms per period and every atom on its wall's radius; walls too close and lengths too short refused; seven tubes as seven molecules; the lattice cell D × D√3)

Departure from the reference

the walls of a periodic mixed-chirality tube carry a small axial strain (stated); the rope's tubes are identical and in register

Point defects: vacancies and doping

A share (or a count) of one element's sites — in the whole structure or the selection — picked at random, at least a spacing apart, and either emptied (vacancies) or given another element (substitutional doping). The charge the removed atoms carried is reported.

distances by the minimum image in a periodic cell; picked in a random order (seeded), skipped when too close to one already picked

When to use it

Defective fillers (oxygen vacancies in silica or titania, missing atoms in a metal nanoparticle), doped particles (Cu in Al, Zn in a sulphide), a carbon lattice with nitrogen in it.

Source

core/src/edit.cpp

Tested by

tests/test_nano.cpp Nano.VacanciesAndDoping (an Al particle: 10 % vacancies exactly; Cu on five sites at least 5 Å apart)

Departure from the reference

no relaxation and no charge compensation: minimise afterwards and assign the charges again

Analogs from R groups

A core SMILES with numbered attachment points [*:1] … [*:9] and, for each, a list of substituents: every combination built as its own structure (the 3D embedding and clean-up as for one molecule). A substituent's first atom bonds to the core (or a leading * marks the atom that does); H leaves the core atom's own hydrogen.

each joined by a ring-closure bond across '.' (%9k), so any substituent SMILES works as written

When to use it

A family of curatives, antioxidants or coupling agents (different alkyl chains, leaving groups), plasticiser series, monomers with different side groups — built side by side and run through the same steps.

Source

core/src/smiles.cpp

Tested by

tests/test_molecule.cpp Molecule.AnalogsFromRGroups (benzene with two R groups: six analogs, each one molecule, toluene and anisic acid among them)

Departure from the reference

the substituents are joined as written: stereochemistry at the attachment is not enumerated

Layer stacks: flip, shift, shared strain

Each added layer can be turned upside down (180° about x, so its other face meets the layer below and its handedness is kept) and shifted in the plane to set its registry; the lateral mismatch can be shared by every layer instead of taken by the upper ones alone.

n_l the repeats that bring layer l nearest the cell; each layer then strained by A/(n_l a_l) − 1 (and the same along b)

When to use it

A film between two identical fibre or filler surfaces facing it with the same face; two crystals of close spacing (e.g. bilayers of 2D fillers) without putting all the strain on one; stacking registry (AB against AA).

Source

core/src/layers.cpp

Tested by

tests/test_layers.cpp Layers.AverageFlipAndShift (20 and 21 Å cells meet at 20.5 Å, ±2.5 % each; a flipped layer's top face at its bottom; a 1.5 Å shift exact)

Departure from the reference

a shared strain strains a crystal too: check its stress after relaxing