Density Functional Theory for Large Molecular Systems and Application to Metcars

摘要

During the grant period, we developed a major improvement in the calculation ofthe Coulomb term appearing in ab initio electronic structure methods based on Gaussian orbitals. Our efficient implementation of the Gaussian very Fast Multipole Method (GvFMM) combines speed, accuracy, and linear scaling properties. The method is clearly superior to state-or-the-art analytic integration techniques of Gaussian functions. Our benchmarks on graphitic sheets containing more than 400 atoms and 3,500 basis functions showed that the GvFMM dramatically reduces the computational requirements of the Coulomb problem. We implemented analytic first and second ho derivatives of the energy with respect to nuclear displacements using our GvFMM method for the efficient calculation of forces and frequencies in large molecules. We developed and implemented a linear scaling exchange correlation quadrature which dramatically speeds up another of the computational bottlenecks of state-of-the-art DFT programs. The combination of fast quadratures and GvFNM yielded substantial improvements in the calculation of harmonic frequencies. In order to obtain linear scaling with the Hartree-Fock method, we developed and implemented a linear scaling method termed 'near-field exchange' for exact exchange calculations of large molecules.