Cyclic Cluster Approach to Three-Dimensional Solids:  Quasi-Rrelativistic INDO Treatment

A recent implementation of the cluster crystal orbital (CCO) method for electron structure calculations of solids within the quasi-relativistic INDO treatment has been tested for a wide scale of model systems including insulators, semiconductors, metals, semimetals, and superconductors. Within the method, a sufficiently large portion of the crystal is essentially treated as a supermolecule (cluster) in which, due to imposed cyclic Born−Karman boundary conditions, all the unit cells experience the same surroundings, while all the interactions within the cluster are preserved. Hence, unwanted effects due to the cluster boundaries are removed, and transition into the complex quasi-momentum space is made possible and uniquely defined. Within the approach, the advantages of the crystal orbital method and the simple cluster model are linked simultaneously. The current implementation, based on the quasi-relativistic INDO Hamiltonian and parametrized for all elements of the periodic table, allows for very fast SCF calculation of clusters containing tens of thousands of atoms. A reasonable balance is reached between the physical model considered (sufficient scope of long-range interactions, large enough number of k-points) and the rigorousness of the method used (type of the Hamiltonian and wave functions used).