Efficient Algorithm for Two-Center Coulomb and Exchange Integrals of Electronic Prolate Spheroidal Orbitals

We present a fast algorithm to calculate Coulomb/exchange integrals of prolate spheroidal electronic orbitals, which are the exact solutions of the single-electron, two-center Schr\"odinger equation for diatomic molecules. Our approach employs Neumann's expansion of the Coulomb repulsion 1/|x-y|, solves the resulting integrals symbolically in closed form and subsequently performs a numeric Taylor expansion for efficiency. Thanks to the general form of the integrals, the obtained coefficients are independent of the particular wavefunctions and can thus be reused later. Key features of our algorithm include complete avoidance of numeric integration, drafting of the individual steps as fast matrix operations and high accuracy due to the exponential convergence of the expansions. Application to the diatomic molecules O2 and CO exemplifies the developed methods, which can be relevant for a quantitative understanding of chemical bonds in general.Comment: 27 pages, 9 figure

Embedded-Cluster Calculations in a Numeric Atomic Orbital Density-Functional Theory Framework

We integrate the all-electron electronic structure code FHI-aims into the general ChemShell package for solid-state embedding (QM/MM) calculations. A major undertaking in this integration is the implementation of pseudopotential functionality into FHI-aims to describe cations at the QM/MM boundary through effective core potentials and therewith prevent spurious overpolarization of the electronic density. Based on numeric atomic orbital basis sets, FHI-aims offers particularly efficient access to exact exchange and second order perturbation theory, rendering the established QM/MM setup an ideal tool for hybrid and double-hybrid level DFT calculations of solid systems. We illustrate this capability by calculating the reduction potential of Fe in the Fe-substituted ZSM-5 zeolitic framework and the reaction energy profile for (photo-)catalytic water oxidation at TiO2(110).Comment: 12 pages, 4 figure

Efficient electronic structure calculation for molecular ionization dynamics at high x-ray intensity

We present the implementation of an electronic-structure approach dedicated to ionization dynamics of molecules interacting with x-ray free-electron laser (XFEL) pulses. In our scheme, molecular orbitals for molecular core-hole states are represented by linear combination of numerical atomic orbitals that are solutions of corresponding atomic core-hole states. We demonstrate that our scheme efficiently calculates all possible multiple-hole configurations of molecules formed during XFEL pulses. The present method is suitable to investigate x-ray multiphoton multiple ionization dynamics and accompanying nuclear dynamics, providing essential information on the chemical dynamics relevant for high-intensity x-ray imaging.Comment: 28 pages, 6 figure

ELSI: A Unified Software Interface for Kohn-Sham Electronic Structure Solvers

Solving the electronic structure from a generalized or standard eigenproblem is often the bottleneck in large scale calculations based on Kohn-Sham density-functional theory. This problem must be addressed by essentially all current electronic structure codes, based on similar matrix expressions, and by high-performance computation. We here present a unified software interface, ELSI, to access different strategies that address the Kohn-Sham eigenvalue problem. Currently supported algorithms include the dense generalized eigensolver library ELPA, the orbital minimization method implemented in libOMM, and the pole expansion and selected inversion (PEXSI) approach with lower computational complexity for semilocal density functionals. The ELSI interface aims to simplify the implementation and optimal use of the different strategies, by offering (a) a unified software framework designed for the electronic structure solvers in Kohn-Sham density-functional theory; (b) reasonable default parameters for a chosen solver; (c) automatic conversion between input and internal working matrix formats, and in the future (d) recommendation of the optimal solver depending on the specific problem. Comparative benchmarks are shown for system sizes up to 11,520 atoms (172,800 basis functions) on distributed memory supercomputing architectures.Comment: 55 pages, 14 figures, 2 table

Critical analysis of fragment-orbital DFT schemes for the calculation of electronic coupling values

We present a critical analysis of the popular fragment-orbital density-functional theory (FO-DFT) scheme for the calculation of electronic coupling values. We discuss the characteristics of different possible formulations or 'flavors' of the scheme which differ by the number of electrons in the calculation of the fragments and the construction of the Hamiltonian. In addition to two previously described variants based on neutral fragments, we present a third version taking a different route to the approximate diabatic state by explicitly considering charged fragments. In applying these FO-DFT flavors to the two molecular test sets HAB7 (electron transfer) and HAB11 (hole transfer) we find that our new scheme gives improved electronic couplings for HAB7 (-6.2% decrease in mean relative signed error) and greatly improved electronic couplings for HAB11 (-15.3% decrease in mean relative signed error). A systematic investigation of the influence of exact exchange on the electronic coupling values shows that the use of hybrid functionals in FO-DFT calculations improves the electronic couplings, giving values close to or even better than more sophisticated constrained DFT calculations. Comparing the accuracy and computational cost of each variant we devise simple rules to choose the best possible flavor depending on the task. For accuracy, our new scheme with charged-fragment calculations performs best, while numerically more efficient at reasonable accuracy is the variant with neutral fragments