The taskfarming in CRYSTAL, as implemented as part of this dCSE project, requires the number of taskfarms to be an exact divisor of the number of processors. That is, an equal number of processors are used for each task. It is possible a more sophisticated division of the processors may be desirable. In addition, the round robin implementation may need to be improved if load balancing for the taskfarms proves to be a bottleneck.

The current implementation of D&C in CRYSTAL does not include long range Coulombic interactions. This could be corrected by performing a multipole expansion of the charge distribution and embedding the cluster subsystems in a field created by static multipoles. An Ewald summation could be used to correctly represent the long range electrostatic potential of the periodic system. The machinery for much of this work exists in the CRYSTAL code base, time constraints meant that it was not possible to apply these to this algorithm during this project.

For periodic covalently bonded systems, e.g. silicon, the D&C algorithm requires modification to prevent the division of the system into subsystems causing undercoordinated terminal atoms. Simply terminating the subsystem at a defined halo radius leads to unphysical ``dangling bonds.'' which cause the subsystem's electronic structure to differ significantly from the global system, the subsystems are unphysically spin polarised. The ``dangling bonds'' can be capped, usually with hydrogen, however a method to add these hydrogen atoms automatically has not been implemented yet. It is also unknown how the presence of capping hydrogen affects the convergence of the D&C algorithm with respect to the size of the halo region. This procedure, of predicting the location of hydrogen atoms in covalent systems, is similar to problems encountered when determining the crystal structure of biological systems by X-ray crystallography. It may be possible to apply similar heuristic approaches to locating hydrogen atoms to cap the clusters used in the D&C algorithm.

Further work is required to make the D&C algorithm generally useful, currently only weakly interacting systems such as molecular crystals can be studied using this method. However, there are several examples of ab initio studies of molecular crystals in the literature, e.g. [15,16]. So even with these limitations this algorithm may be a useful alternative to the traditional Hamiltonian matrix diagonalisation approach for certain systems.

Daniel R. Jones 2011-12-06