We describe a complete set of algorithms for ab initio molecular simulations based on numerically tabulated atom-centered orbitals (NAOs) to capture a wide range of molecular and materials properties from quantum-mechanical first principles. The full algorithmic framework described here is embodied in the Fritz Haber Institute "ab initio molecular simulations" (FHI-aims) computer program package. Its comprehensive description should be relevant to any other first-principles implementation based on NAOs. The focus here is on density-functional theory (DFT) in the local and semilocal (generalized gradient) approximations, but an extension to hybrid functionals, Hartree–Fock theory, and MP2/GW electron self-energies for total energies and excited states is possible within the same underlying algorithms. An all-electron/full-potential treatment that is both computationally efficient and accurate is achieved for periodic and cluster geometries on equal footing, including relaxation and ab initio molecular dynamics. We demonstrate the construction of transferable, hierarchical basis sets, allowing the calculation to range from qualitative tight-binding like accuracy to meV-level total energy convergence with the basis set. Since all basis functions are strictly localized, the otherwise computationally dominant grid-based operations scale as O(N) with system size N. Together with a scalar-relativistic treatment, the basis sets provide access to all elements from light to heavy. Both low-communication parallelization of all real-space grid based algorithms and a ScaLapack-based, customized handling of the linear algebra for all matrix operations are possible, guaranteeing efficient scaling (CPU time and memory) up to massively parallel computer systems with thousands of CPUs

The efficient implementation of electronic structure methods is essential for first principles modeling of molecules and solids. We present here a particularly efficient common framework for methods beyond semilocal density-functional theory (DFT), including Hartree-Fock (HF), hybrid density functionals, random-phase approximation (RPA), second-order Møller-Plesset perturbation theory (MP2) and the GW method. This computational framework allows us to use compact and accurate numeric atom-centered orbitals (NAOs), popular in many implementations of semilocal DFT, as basis functions. The essence of our framework is to employ the 'resolution of identity (RI)' technique to facilitate the treatment of both the two-electron Coulomb repulsion integrals (required in all these approaches) and the linear density-response function (required for RPA and GW ). This is possible because these quantities can be expressed in terms of the products of single-particle basis functions, which can in turn be expanded in a set of auxiliary basis functions (ABFs). The construction of ABFs lies at the heart of the RI technique, and we propose here a simple prescription for constructing ABFs which can be applied regardless of whether the underlying radial functions have a specific analytical shape 2 (e.g. Gaussian) or are numerically tabulated. We demonstrate the accuracy of our RI implementation for Gaussian and NAO basis functions, as well as the convergence behavior of our NAO basis sets for the above-mentioned methods. Benchmark results are presented for the ionization energies of 50 selected atoms and molecules from the G2 ion test set obtained with the GW and MP2 selfenergy methods, and the G2-I atomization energies as well as the S22 molecular interaction energies obtained with the RPA method. 6.2. Benchmark MP2 and RPA results for the G2-I atomization energies . . . . . . 40 6.3. Benchmark MP2 and RPA binding energies for the S22 molecular set . . . . . 42 7. Conclusions and outlook 44 Acknowledgments 44 Appendix A. Matrix elements for numeric atom-centered orbitals 45 Appendix B. Ionization energies of a set of atoms and molecules 48 Appendix C. The modified Gauss-Legendre grid 48 References 50 New Journal of Physics 14 (2012) 053020 (http://www.njp.org/) 3 1. IntroductionAccurate quantum-mechanical predictions of the properties of molecules and materials (solids, surfaces, nano-structures, etc) from first principles play an important role in chemistry and condensed-matter research today. Of particular importance are computational approximations to the many-body Schrödinger or Dirac equations that are tractable and yet retain quantitatively reliable atomic-scale information about the system-if not for all possible materials and properties, then at least for a relevant subset. Density-functional theory (DFT) [1,2] is one such successful avenue. It maps the interacting many-body problem onto an effective single-particle one where the many-body complexity is hidden in the unknown exchange-correlation (XC) term, which has to be approx...

The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We report the results of a community-wide effort that compared 15 solid-state codes, using 40 different potentials or basis set types, to assess the quality of the Perdew-Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that predictions from recent codes and pseudopotentials agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Older methods, however, have less precise agreement. Our benchmark provides a framework for users and developers to document the precision of new applications and methodological improvements

DFTB+ is a versatile community developed open source software package offering fast and efficient methods for carrying out atomistic quantum mechanical simulations. By implementing various methods approximating density functional theory (DFT), such as the density functional based tight binding (DFTB) and the extended tight binding method, it enables simulations of large systems and long timescales with reasonable accuracy while being considerably faster for typical simulations than the respective ab initio methods. Based on the DFTB framework, it additionally offers approximated versions of various DFT extensions including hybrid functionals, time dependent formalism for treating excited systems, electron transport using non-equilibrium Green’s functions, and many more. DFTB+ can be used as a user-friendly standalone application in addition to being embedded into other software packages as a library or acting as a calculation-server accessed by socket communication. We give an overview of the recently developed capabilities of the DFTB+ code, demonstrating with a few use case examples, discuss the strengths and weaknesses of the various features, and also discuss on-going developments and possible future perspectives.

The heptazine-based polymer melon (also known as graphitic carbon nitride, g-C3N4) is a promising photocatalyst for hydrogen evolution. Nonetheless, attempts to improve its inherently low activity are rarely based on rational approaches because of a lack of fundamental understanding of its mechanistic operation. Here we employ molecular heptazine-based model catalysts to identify the cyanamide moiety as a photocatalytically relevant ‘defect'. We exploit this knowledge for the rational design of a carbon nitride polymer populated with cyanamide groups, yielding a material with 12 and 16 times the hydrogen evolution rate and apparent quantum efficiency (400 nm), respectively, compared with the unmodified melon. Computational modelling and material characterization suggest that this moiety improves coordination (and, in turn, charge transfer kinetics) to the platinum co-catalyst and enhances the separation of the photogenerated charge carriers. The demonstrated knowledge transfer for rational catalyst design presented here provides the conceptual framework for engineering high-performance heptazine-based photocatalysts.