Basis Function Specs

Description

Basis function specifications control the type and order of basis functions that CASM generates.

Project files

This format is used for the following standard CASM project files:

• The basis_function_specs attribute of bspecs.json

JSON Attributes List

Basis Function Specs attributes:

Name	Description	Format
dof_specs	DoF-particular specifications	dict
dofs	DoFs to include in the basis set	array of string
global_max_poly_order	Global maximum polynomial order (global)	int
orbit_branch_max_poly_order	Orbit branch specific maximum polynomial order	dict
param_pack_type	Automatic differentation option	string

occ DoF specifications:

Name	Description	Format
site_basis_functions	Occupation site basis function choice	string or array

<flavor>magspin DoF specifications:

Name	Description	Format
max_poly_order	Site basis function maximum polynomial order	int

JSON Attributes Description

• dof_specs: dict (required for some dofs)

  Provides DoF-particular specifications for constructing basis functions. Not all DoF types require their own specifications. The options are:

  For “occ”: (required if occupation dof included)

  • site_basis_functions: string or array (required)

    Must be one of:

    • “chebychev”: For basis functions generated about the random alloy.
    • “occupation”: For basis functions generated about the ordered alloy defined by the first occupant listed for every sublattice in the prim.

    • An array specifying sublat compositions, for “composition” basis functions generated about an average composition speficified for each sublattice.

      Example sublattice composition specification, for a prim with four sublattices and two allowed occupants (“A” and “B”) on each sublattice:

      [
        { // composition on sublattices 0 and 1, as listed
        in prim
          "sublat_indices": [0, 1],
          "composition": {"A": 0.25, "B": 0.75}
        },
        { // composition on sublattices 2 and 3, as listed
        in prim
          "sublat_indices": [2, 3],
          "composition": {"A": 0.75, "B": 0.25}
        }
      ]
      

  For <flavor>magspin: (optional if <flavor>magspin dof included)

  • max_poly_order: int (optional, default=-1)

    Specifies the maximum polynomial order for site basis functions.

• dofs: array of string (optional, default= all prim DoF)

  An array of string of dof type names that should be used to construct basis functions. The default value is all DoF types included in the prim.

• global_max_poly_order: int (optional, default=-1)

  See orbit_branch_max_poly_order documentation.

• orbit_branch_max_poly_order: dict (optional, default={})

  By default, for a given cluster orbit, polynomials of order up to the cluster size are created. Higher order polynomials can be requested either on a per-orbit-branch or global basis. The most specific level specified is used. Orbit branches are specified using the string value of the cluster size as a key.

  Example:

  "orbit_branch_max_poly_order": {
      "4": 7    // use maximum polynomial order == 7,
                // for orbits of cluster size == 4
  },
  "global_max_poly_order": 3, // use max(3, cluster size),
  ...                         // for all other orbits
  

• param_pack_type: string (optional, default=”default”)

  Controls the implementation used for evaluating the cluster expansion basis functions. Options are “default” or “diff”, which enables fadbad automatic differentiating.

Examples

Example 1) “occupation” site basis functions for “occ” DoF

{
  "dof_specs": {
    "occ": {
      "site_basis_functions" : "occupation"
    }
  }
}

Example 2) “chebychev” site basis functions for “occ” DoF, global maximum polynomial order of 5

"global_max_poly_order": 5,
"dof_specs": {
  "occ": {
    "site_basis_functions" : "chebychev"
  }
}