syminfo_to_matrix_list {cry}

Operators of a specific space group in matrix form

Description

Returns 3\times 3 matrices and 3\times 1 vectors corresponding to point group operations, group translations and cell centring of a given space group.

Usage

syminfo_to_matrix_list(SG)

Arguments

SG

A character string. The extended Hermann-Mauguin symbol (e.g. 'P 1 1 21')

Details

A crystallographic space group consists of a series of transformations on a point (x_f,y_f,z_f) in space that are mathematically implemented as the product of a 3\times 3 point-group matrix and the point fractional coordinates, (x_f,y_f,z_f), followed by a sum with a 3\times 1 translation vector. The complete set of points thus produced can be cloned into a new and shifted set translated of an amount represented by a 3\times 1 centring vector.

Value

mat_ops_list A named list consisting of 3 lists. The first list, PG, contains 3\times 3 point group matrices; the second list, T, contains the same number of 3\times 1 translation vectors. The first matrix is always the identity matrix, the first translation vector is always the null vector. The third list, C, consists of centering vectors; the first centering vector is always the null vector. To summarize, the output looks like the following:

[[ [[I,M2,M3,...,Mn]] , [[O,V2,V3,...,Vn]] , [[O,C2,C3,...,Cm]] ]] where: I = identity 3X3 matrix 0 = null 3X1 vector M2,M3,...,Mn = point group 3X3 matrices V2,V3,...,Cn = translation 3X1 vectors C2,C3,...,Cm = centering 3X1 vectors

Examples

# Symmetry operators for space group number 4, P 1 21 1
SG <- "P 1 21 1"
mat_ops <- syminfo_to_matrix_list(SG)
print(mat_ops)