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TYC@imperial: Potentialities of a Wavelet Formalism Towards a Reduction in the Complexity of Large Scale Electronic Structure Calculations

Dr Luigi Genovese,

Université Grenoble Alpes, Grenoble, France

Wednesday 25th October 2017
Time: 13.00pm
Venue: Lecture Room G20, Royal School of Mines, Imperial college London
Contact: Ms Hafiza Bibi
Tel: 0207594 7252

Abstract: Since a few years ago, the BigDFT software package implements a linear scaling Kohn-Sham density functional theory optimization algorithm based on Daubechies wavelets, where a minimal set of localized support functions are optimized in situ and therefore adapted to the physico-chemical properties of the system under investigation. [1]  With respect to similar approaches, the underlying use of a wavelet basis makes the approach explicitly compatible with systems in various boundary conditions, like surface geometries or systems with a net charge or polarization.  Support functions generated in this way provide a high level of sparsity of the Kohn Sham operators by preserving quasi-orthogonality of the basis.  These properties, together with the use of chemically accurate PSP enable the effective usage of linear scaling approaches, making the O(N) treatment attractive even for systems of a few tens of atoms in some cases. [2,3]  In this presentation, we fill first provide an overview of the potentialities that the wavelet formalism offers in this regard. [4]

Nonetheless, even when a DFT approach gives an accurate description of a microscopic system, it is advantageous in certain situations to consider an effective complexity reduction, allowing one to get the same level of accuracy by explicitly considering fewer degrees of freedom.  The basic principle lies in the identification of the essential moieties (i.e., 'fragments') of a system out of an atomistic description.  These fragments should then in turn be treated with an adequate methodology depending on the specific needs.  Such a procedure would allow a better understanding of the relevant mechanisms that govern the interactions among the constituents of the system, and makes possible the design and interpretation of simulations which would be unnecessarily costly if kept at the atomistic level.

We illustrate, from a general perspective, a quantitative method to identify and assess the partitioning of a large quantum-mechanical system into fragments [5].  Our approach reduces arbitrariness in the fragmentation procedure and enables the possibility of assessing quantitatively whether the corresponding fragment multipoles can be interpreted as observable quantities associated with a system moiety.  Such an approach is based on general grounds and its implementation is unrelated to the wavelet formalism. However, we show that the use of a minimal set of in situ-optimized basis functions allows at the same time a proper fragment definition and an accurate description of the electronic structure.

[1] J. Chem. Phys. 140, 204110 (2014) 

[2] Phys. Chem. Chem. Phys., 2015, 17, 31360-31370

[3] J. Chem. Theory Comput., in press. DOI: 10.1021/acs.jctc.7b00348

[4] WIREs Comput Mol Sci, 7 (2017)

[5] J. Chem. Theory Comput. 2017, 13, 4079-4088

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