01545 - Group Theoretical Methods and Applications to Molecules and Crystals.pdf

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This book explains the basic aspects of symmetry groups as applied to problems

in physics and chemistry using an approach pioneered and developed by the

author. The symmetry groups and their representations are worked out explicitly,

eliminating the unduly abstract nature of group theoretical methods.

The author has systematized the wealth of knowledge on symmetry groups

that has accumulated during the century since Fedrov discovered the 230 space

groups. All space groups, unitary as well as anti-unitary, are reconstructed from

the algebraic de®ning relations of the point groups. The matrix representations

are determined through the projective representations of the point groups. The

representations of the point groups are subduced by the representations of the

rotation group. The correspondence theorem on basis functions belonging to a

representation is introduced to form the general expression for the symmetry-

adapted linear combinations of equivalent basis functions with respect to a point

group. This is then applied to form molecular orbitals and symmetry coordinates

of vibration of a molecule or a crystal and the energy band eigenfunctions of the

electrons in a crystal. The book assumes only an elementary knowledge of

quantum mechanics. Numerous applications of the theorems are described to aid

understanding.

This work will be of great interest to graduate students and professionals in

solid state physics, chemistry, mathematics and geology and to those who are

interested in magnetic crystal structures.

To `Eomma'

Group Theoretical Methods

and Applications to Molecules and Crystals

SHOON K. KIM

Temple University