Crystal symmetries of plane-wave-like functions I. The symmorphic space groups

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Abstract
A set of tables of coefficients for forming linear combinations of plane waves, both without and with spin, symmetrized with respect to all the necessary sub-groups of all 73 symmorphic space groups, is presented here. A symmetry analysis of all the Brillouin zone symmetry points of these 73 space groups is also included and serves as an index to the coefficient tables. A discussion of the method of calculation is included as well as a review of the theory which underlies the desirability of symmetrized functions, and the theory of the projection operator, by which these coefficients were calculated. Section 4, a guide to the use of the tables, may be read independently of the rest.