Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Analytical gradients.

A full implementation of analytical energy gradients for molecular and periodic systems is reported in the TURBOMOLE program package within the framework of Kohn-Sham density functional theory using Gaussian-type orbitals as basis functions. Its key component is a combination of density fitting (DF) approximation and continuous fast multipole method (CFMM) that allows for an efficient calculation of the Coulomb energy gradient. For exchange-correlation part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097) is extended to energy gradients. Computational efficiency and asymptotic O(N) scaling behavior of the implementation is demonstrated for various molecular and periodic model systems, with the largest unit cell of hematite containing 640 atoms and 19,072 basis functions. The overall computational effort of energy gradient is comparable to that of the Kohn-Sham matrix formation. © 2016 Wiley Periodicals, Inc.

Density Functional Theory for Molecular and Periodic Systems Using Density Fitting and Continuous Fast Multipole Methods.

An implementation of Kohn-Sham density functional theory within the TURBOMOLE program package with Gaussian-type orbitals (GTO) as basis functions is reported that treats molecular and periodic systems of any dimensionality on an equal footing. Its key component is a combination of density fitting/resolution of identity (DF) approximation and continuous fast multipole method (CFMM) applied for the electronic Coulomb term. This DF-CFMM scheme operates entirely in the direct space and partitions Coulomb interactions into far-field part evaluated using multipole expansions and near-field contribution calculated employing density fitting. Computational efficiency and favorable scaling behavior of our implementation approaching O(N) for the formation of Kohn-Sham matrix is demonstrated for various molecular and periodic systems including three-dimensional models with unit cells containing up to 640 atoms and 19072 GTO basis functions.

Cage-Like Nanoclusters of ZnO Probed by Time-Resolved Photoelectron Spectroscopy and Theory.

Zinc oxide nanoclusters have been predicted as promising building blocks for cluster-assembled materials with unprecedented properties. Here, for the first time these clusters are probed by time-resolved photoelectron spectroscopy and characterized in detail by density functional theory. Their validity as building blocks for cluster-assembled materials is confirmed via rigid cage-like structures facilitating three-dimensional aggregation in combination with large band gaps that are nevertheless significantly lower than any known ZnO polymorph. In addition, electron-hole pair localization in the excited state of the cluster anions combined with their structural rigidity leads to extraordinary long-lived states above the band gap virtually independent of the cluster size, defying the rule "every atom counts".