Implementation of parallel and divide and conquer algorithms in DeFT (LCGTO-DF).

Abstract

The program DeFT is an implementation of Density Functional Theory (DFT). The formalism that is used in this program is the linear combination of gaussian-type-orbitals (LCGTO). In this approach, there exists a method for the variational fitting of the density. Exchange-correlation is fitted on a numerical grid. It is these fitting procedures that reduce the formal scaling of LCGTO-DF to N$\sp3$ from N$\sp4$. The contribution to the total energy from the Coulomb repulsion integrals and the exchange correlation integrals causes the current bottleneck of DFT calculations. The parallelization of the three-centered two electron integrals should lead to improved efficiency. The use of the PVM communication package gives a way to a relatively simple means for transforming serial to parallel code. An advantage of using PVM is that it is portable to a large variety of architectures. This allows PVM to act as a harness between clusters of workstations. The parallel implementation of DeFT is discussed. A divide-and-conquer implementation of LCGTO-DF is incorporated in DeFT. The use of Yang's density and density matrix formulations are incorporated into this scheme. The former is used for the fitting of the XC potential while the latter is used for the fitting of the charge density. This type of algorithm should achieve linear scaling for very large systems. Test calculations with the glycine heptapeptide demonstrate the errors to be expected from the introduction of the DAC approach. The use of buffer spaces is also examined in order to reduce the errors introduced by the DAC algorithm.