Towards Paradigm Shifts in Electronic Structure Calculation for Large Systems: Wavelets, Fragments and Advanced Treatments of Excited States

The increasing power of massively parallel machines offers new opportunities for first principles materials simulations, providing software can be developed to effectively exploit new hardware. Density functional theory (DFT) has enjoyed widespread success for systems of up to a few hundred atoms, but is limited by the cubic scaling with the number of atoms of standard approaches. However, in recent years various linear scaling (LS) approaches have been developed, enabling simulations on tens of thousands of atoms. Since the parallel scalability is related to the number of atoms, such methods are also well suited to exploit supercomputers. One key factor influencing the accuracy and cost of DFT is the choice of basis set, where minimal, localized basis sets compete with extended, systematic basis sets. However, wavelets offer both locality and systematicity and are thus ideal for representing an adaptive local orbital basis which may be exploited for LS-DFT [1]. One may also make further approximations, e.g. dividing a system into fragments or exploiting underlying repetition of local chemical environments [2,3], where each approximation may be controlled and quantified. This ability to treat large systems with controlled precision offers the possibility of new types of materials simulations [4]. We will demonstrate the advantages of wavelets as a basis for large scale DFT calculations, as implemented in BigDFT. We will focus on the example of materials for organic LEDs, showing how our approach may be used to account for environmental and statistical effects on excited state calculations of disordered supramolecular materials [5].
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[2] Mohr et al. J. Chem. Theory Comput. 13 4079 (2017)
[3] Ratcliff et al. J. Chem. Phys. 142, 234105 (2015)
[4] Ratcliff et al. WIREs Comput. Mol. Sci. 7, e1290 (2017)
[5] Ratcliff et al. J. Chem. Theory Comput. 11, 2077 (2015)