PHYSICS 250.2: Computational Band Theory

Fall 1998

Projects

Pseudopotential Plane Wave Code

Oct 5: A sorted (by length) list of plane waves: Seeing stars

The problem is to "construct G-space" -- to find and to order in an array all reciprocal lattice verctors{G} whose length |G| is less than some predetermined (input) value Gmax. You are given (again, input) the direct lattice vectors R1, R2, R3, from which you calculate G1, G2, G3. Then make the computer find all G vectors less than Gmax, without missing any.

Oct 8: Further sorting the plane wave list into symmetry related "stars." The space group of a crystal is the set of all operations that transform an infinite crystal lattice into itself. The simple translation of the Bravais lattice are separate, and are taken care of by requiring that the wavefunctions have Bloch periodicity. The remaining operations are of the form {R|tR}, where R is a (proper of improper) rotation [represented by a 3x3 matrix] and tR is the associated non-primitive translation that completes the symmetry operation. If all of the tR are zero, the group is symmorphic, otherwise it is non-symmorphic. These operations will be discussed in class and are discussed in most solid state texts. The problem is to create and algorithm and code it up, to group together the RLVs into stars which transform among themselves under the point group (the set of rotations {R} in the space group.}