EMPIRE: a highly parallel semiempirical molecular orbital program: 2: periodic boundary conditions

The increasing role of quantum chemical calculations in drug and materials design has led to a demand for methods that can describe the electronic structures of large and complex systems. Semiempirical methods based on the neglect of diatomic differential overlap (NDDO) approximation (e.g., the MNDO [1, 2], MNDO/d [3], AM1 [4], AM1* [5], and PMx [6–8] methods) are important representatives of such approaches. Many of these methods have been implemented in the massively parallel program EMPIRE [9], which makes the full quantum-mechanical treatment of systems containing 100,000 atoms or more possible. Periodic boundary conditions (PBC) enable quantum chemical programs to treat condensed-phase systems, such as proteins in a periodic water box or solids. This allows molecular materials to be studied in their Bnative^ environment, instead of comparing experimental bulk properties with gas-phase monomer calculations. For semiempirical methods, the most practical way of implementing PBC is the cycliccluster approach [10–12] in which the system is approximated by a supercell and by imposing Born–von Karman boundary conditions [13]. Using a large unit cell allows the calculation to be performed entirely in real space. This is easily affordable because of the generally low computational cost of NDDO calculations. The main advantage of this technique is that program features like the calculation of local properties [14] or excited states are directly transferable from nonperiodic calculations [15]. We have, for example, used periodic EMPIRE calculations to model amorphous carbon [16]. EMPIRE, which was especially designed for calculations on systems with very many atoms, is also suitable for use on systems with very large unit cells (e.g., disordered and amorphous systems). EMPIRE can, for example, be used in combination with a classical molecular dynamics (MD) code to perform electronic structure calculations on snapshots from an MD run on a periodic system. In the first section of this paper, we discuss the implementation of periodic boundary conditions in EMPIRE. In the second, the program performance is discussed briefly. Finally, some exemplary applications of large-scale periodic NDDO calculations are shown.