CWCMatrixModel(property, species_friction, species_env; maxorder=2, maxdeg=5, rcut=5.0, n_rep=1,
               partner_in_env=true, ...)

Column-wise coupled friction model (onsite + spherical offsite). partner_in_env=true (default) pools the bond partner into the offsite bond environment (see SphericalCutoff), which makes evaluating all offsite blocks of a centre cost about one onsite evaluation; false selects the original partner-excluded environment.

CWCMatrixModel(property, species_friction, species_env, evalcenter::EvaluationCenter;
               rcut_on, rcut_off, maxorder_on, maxdeg_on, ..._on/_off, bond_weight)

Backward-compatible CWC constructor with a positional evalcenter and separate onsite/offsite hyperparameters (mirrors the pre-ET interface).

PWCMatrixModel(property, species_friction, species_env;
    maxorder=2, maxdeg=5, rcut=5.0, n_rep=1, partner_in_env=true, ...)

Pairwise-coupled (offsite) friction model with a spherical pair environment. partner_in_env=true (default) pools the bond partner into the bond environment (see SphericalCutoff), which makes the evaluation of all pair blocks of a centre cost about one onsite evaluation; false selects the original partner-excluded environment.

PWCMatrixModel(property, species_friction, species_env, cutoff::EllipsoidCutoff; ...)

Pairwise-coupled offsite model with an ellipsoidal (bond-centred) environment.

PWCMatrixModel(property, species_friction, species_env, cutoff::SnowManCutoff; ...)

Pairwise-coupled offsite model on both bond ends' atom-centred environments (two overlapping spheres, one per bond end): with B_ij = basis(sphere_i, bond i→j), the block of pair (i,j) is c₊·(B_ij + B_ji) + c₋·(B_ij - B_ji) for the default SnowManCutoff(rcut) (:general; non-symmetric Γ_ij blocks, twice the parameters), and c·(B_ij ± B_ji) for SnowManCutoff(rcut, :symmetric) / :antisymmetric. See SnowManCutoff. cutoff.rcut is the per-centre radius. Accepts the same selection/radial keywords as the other PWCMatrixModel methods.

OnsiteOnlyMatrixModel(property, species_friction, species_env;
    maxorder=2, maxdeg=5, rcut=5.0, n_rep=1, ...)

Block-diagonal friction model (onsite only).

SphericalCutoff(rcut; partner_in_env = true)

Spherical pair-environment cutoff for the atom-centred offsite model: the bond environment of a pair (i,j) is the set of neighbours of atom i within rcut, with j itself the bond partner. (Cf. ACEfrictionCore SphericalCutoff.)

partner_in_env selects whether the bond partner j is also pooled into the environment features of the bond (i,j):

• true (default): the environment is all of N_i (including j). The environment features are then shared by all bonds of the centre and, since every bond basis function contains exactly one bond factor, the blocks factorise as Σ_ij = T_i · φ(r_ij) with a per-centre tensor T_i and cheap per-bond one-particle features φ. This makes the pair blocks of a centre cost about as much as a single onsite (energy-like) evaluation.
• false: the environment is N_i \ {j} (all other neighbours of i), the original convention. Every bond of a centre then has a different environment, so evaluating the pair blocks costs one many-body evaluation per bond.

The two settings are different bases (spanning the same function space), so a model must be evaluated with the setting it was fitted with; the setting is serialized, and models saved before the option existed load as false. On H/Cu reference data the two fit equally well. They coincide exactly when the partner's species is excluded from the environment factors, and for the antisymmetric SnowManCutoff at maxorder = 2.

EllipsoidCutoff(rcutbond, rcutenv, zcutenv)

Bond-centred ellipsoidal cutoff: bonds with |rij| <= rcutbond; environment atoms within the ellipsoid (z/zcutenv)^2 + (r/rcutenv)^2 <= 1 around the bond midpoint (z along the bond, r perpendicular).

SnowManCutoff(rcut, symmetry = :general; partner_in_env = true)

Atom-centred pair-environment cutoff combining both bond ends: the diffusion block of a pair (i,j) evaluates the ACE basis on the spherical environment of i (with j the bond partner) and on the spherical environment of j (with i the bond partner) — two overlapping spheres, one per bond end (the "snowman"). Writing B_ij = basis(sphere_i, bond i→j), the combination is selected by symmetry:

:general        Σ_ij = c₊ · (B_ij + B_ji) + c₋ · (B_ij - B_ji)     (default)
:symmetric      Σ_ij = c · (B_ij + B_ji)                             Σ_ji =  Σ_ij
:antisymmetric  Σ_ij = c · (B_ij - B_ji)                             Σ_ji = -Σ_ij

With :symmetric / :antisymmetric both ends share the coefficients, so every off-diagonal friction block Γ_ij = Σ_ij Σ_jiᵀ = ±Σ_ij Σ_ijᵀ is a symmetric 3×3 matrix. :general has independent coefficients for the symmetric and the antisymmetric combination (twice as many parameters: the basis is the stacked [B_ij + B_ji; B_ij - B_ji], coefficients [c₊; c₋]), so Σ_ji ≠ ±Σ_ij and Γ_ij is in general not symmetric (Γ itself stays symmetric positive semi-definite). It contains the other two as the restrictions c₋ = 0 (:symmetric) and c₊ = 0 (:antisymmetric).

symmetry is carried as a (Symbol-valued) type parameter SnowManCutoff{T, S} so the assembly dispatches on it. rcut is the per-centre spherical radius (same convention as SphericalCutoff). The keyword partner_in_env (default true) has the same meaning as for SphericalCutoff: with true the bond partner is pooled into each sphere's environment, which lets the per-centre evaluation be shared across all bonds.

Models saved before the symmetry tag was serialized load as :symmetric.