Symmetry and Group Theory for Density-Functional Methods

From the standpoint of performing quantum-mechanical calculations efficiently, describing the behavior of molecular- and cluster- based quantum devices, and effectively storing or processing quantum information, the use of symmetry or automated group theoretical methods offers significant advantages for researchers. Here we describe the development and use of an automated tool that determines the point-group symmetry of a molecule and then determines every sub-group and associated set of inequivalent atoms that describe the structure of the entire molecular system. To illustrate the utility of this tool, in conjunction with density functional theory, we present examples on developing efficient workflows for (1) the calculation of exchange-coupling parameters in inorganic molecular magnets (2) the determination of polarizabilities in the benzene molecule and (3) the calculation of infrared-active vibrations in methane.