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Register a new userComplexity Reduction in Density Functional Theory Calculations of Large Systems: System Partitioning and Fragment Embedding
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With the development of low order scaling methods for performing Kohn-Sham Density Functional Theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an increase in the size of system treated comes an increase in complexity, making it challenging to analyze such large systems and determine the cause of emergent properties. To address this issue, in this paper we present a systematic complexity reduction methodology which can break down large systems into their constituent fragments, and quantify inter-fragment interactions. The methodology proposed here requires no a priori information or user interaction, allowing a single workflow to be automatically applied to any system of interest. We apply this approach to a variety of different systems, and show how it allows for the derivation of new system descriptors, the design of QM/MM partitioning schemes, and the novel application of graph metrics to molecules and materials.
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Standard flavors of density-functional theory (DFT) calculations are known to fail in describing anions, due to large self-interaction errors. The problem may be circumvented by using localized basis sets of reduced size, leaving no variational flexibility for the extra electron to delocalize. Alternatively, a recent approach exploiting DFT evaluations of total energies on electronic densities optimized at the Hartree-Fock (HF) level has been reported, showing that the self-interaction-free HF densities are able to lead to an improved description of the additional electron, returning affinities in close agreement with the experiments. Nonetheless, such an approach can fail when the HF densities are too inaccurate. Here, an alternative approach is presented, in which an embedding environment is used to stabilize the anion in a bound configuration. Similarly to the HF case, when computing total energies at the DFT level on these corrected densities, electron affinities in very good agreement with experiments can be recovered. The effect of the environment can be evaluated and removed by an extrapolation of the results to the limit of vanishing embedding. Moreover, the approach can be easily applied to DFT calculations with delocalized basis sets, e.g. plane-waves, for which alternative approaches are either not viable or more computationally demanding. The proposed extrapolation strategy can be thus applied also to extended systems, as often studied in condensed-matter physics and materials science, and we illustrate how the embedding environment can be exploited to determine the energy of an adsorbing anion - here a chloride ion on a metal surface - whose charge configuration would be incorrectly predicted by standard density functionals.
Density functional theory (DFT) provides a theoretical framework for efficient and fairly accurate calculations of the electronic structure of molecules and crystals. The main features of density functional theory are described and DFT methods are compared with wavefunction-based methods like the Hartree-Fock approach. Some recent applications of DFT to spin crossover complexes are reviewed, e.g., the calculation of Mossbauer parameters, of vibrational modes and of differences of entropy, vibrational energy, and total electronic energy between high-spin and low-spin isomers.
Given a partition of a large system into an active quantum mechanical (QM) region and its environment, we present a simple way of embedding the QM region into an effective electrostatic potential representing the environment. This potential is generated by partitioning the environment into well defined fragments, and assigning each one a set of electrostatic multipoles, which can then be used to build up the electrostatic potential. We show that, providing the fragments and the projection scheme for the multipoles are chosen properly, this leads to an effective electrostatic embedding of the active QM region which is of equal quality as a full QM calculation. We coupled our formalism to the DFT code BigDFT, which uses a minimal set of localized in-situ optimized basis functions; this property eases the fragment definition while still describing the electronic structure with great precision. Thanks to the linear scaling capabilities of BigDFT, we can compare the modeling of the electrostatic embedding with results coming from unbiased full QM calculations of the entire system. This enables a reliable and controllable setup of an effective coarse-graining approach, coupling together different levels of description, which yields a considerable reduction in the degrees of freedom and thus paves the way towards efficient QM/QM and QM/MM methods for the treatment of very large systems.
Recently a novel approach to find approximate exchange-correlation functionals in density-functional theory (DFT) was presented (U. Mordovina et. al., JCTC 15, 5209 (2019)), which relies on approximations to the interacting wave function using density-matrix embedding theory (DMET). This approximate interacting wave function is constructed by using a projection determined by an iterative procedure that makes parts of the reduced density matrix of an auxiliary system the same as the approximate interacting density matrix. If only the diagonal of both systems are connected this leads to an approximation of the interacting-to-non-interacting mapping of the Kohn-Sham approach to DFT. Yet other choices are possible and allow to connect DMET with other DFTs such as kinetic-energy DFT or reduced density-matrix functional theory. In this work we give a detailed review of the basics of the DMET procedure from a DFT perspective and show how both approaches can be used to supplement each other. We do so explicitly for the case of a one-dimensional lattice system, as this is the simplest setting where we can apply DMET and the one that was originally presented. Among others we highlight how the mappings of DFTs can be used to identify uniquely defined auxiliary systems and auxiliary projections in DMET and how to construct approximations for different DFTs using DMET inspired projections. Such alternative approximation strategies become especially important for DFTs that are based on non-linearly coupled observables such as kinetic-energy DFT, where the Kohn-Sham fields are no longer simply obtainable by functional differentiation of an energy expression, or for reduced density-matrix functional theories, where a straightforward Kohn-Sham construction is not feasible.
Iron complexes with a suitable ligand field undergo spin-crossover (SCO), which can be induced reversibly by temperature, pressure or even light. Therefore, these compounds are highly interesting candidates for optical information storage, for display devices and pressure sensors. The SCO phenomenon can be conveniently studied by spectroscopic techniques like Raman and infrared spectroscopy as well as nuclear inelastic scattering, a technique which makes use of the Mossbauer effect. This review covers new developments which have evolved during the last years like, e.g. picosecond infrared spectroscopy and thin film studies but also gives an overviewon newtechniques for the theoretical calculation of spin transition phenomena and vibrational spectroscopic data of SCO complexes.
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