'Towards an accurate and efficient density-functional theory for large molecules'

Density-functional theory (DFT) has emerged over the last 2 decades to become the preeminent method for ab initio computational chemistry studies in a wide variety of systems. This is surely due in large part to the extremely favourable balance between accuracy and computational cost that DFT can provide. In my talk, I discuss a contribution to the on-going development of DFT methodology with respect to both of these points. I first discuss a newly proposed hybrid exchange-correlation functional based on the long-range correction (LC) scheme, which can dramatically improve some of the failings of conventional GGA and hybrid
functionals, such as the poor description of Rydberg or charge-transfer excitation energies. The new functional improves previous LC functionals by providing a simultaneously good description of a wide range of excitation energies, reaction barrier heights, and thermochemistry. Next, I discuss our recent contributions to
linear-scaling DFT, with the introduction of two new methods for the rapid calculation of the expensive electronic Coulomb potential in large molecules, which is a traditional bottleneck for DFT calculations. Both approaches employ real-space techniques and the fast multipole method to achieve linear-scaling of CPU time. The first solves the Poisson equation in a mixed basis of Gaussian and low-order finite-element functions. The second uses a basis of high-order, adaptive, spectral
elements and avoids the Poisson equation by an efficient direct integration of the potential using a numerical low-rank representation of the Coulomb operator. Both approaches are shown to be highly effective for large-scale calculations.