Coarse-Grained DFT
Mauricio Ponga (Caltech), Michael Ortiz (Caltech), Kaushik Bhattacharya (California Institute of Technology)
From Atomistics to Reality: Spanning Scales in Simulations and Experiments Symposium A
Tue 4:20 - 5:40
CIT 165
Crystal defects play a critical role in the determination of mechanical properties of materials. The study of defects at realistic concentrations is difficult due to the connection between the chemistry of the core and the long-range elastic decay. Methods based on Density Functional (DFT) are one of the best computational tools to simulate the chemical effects of defects. However, due to the large number of degrees of freedom and the cubic scaling with the number of atoms of traditional DFT based methods, the study of crystals defects is restricted to unrealistic concentrations of defect. In addition, the orthogonality requirement of wave-functions makes the coarse graining representation difficult. It is for these reasons that in this work we apply a recently developed formulation of Suraynarayana et al. that seamlessly coarse-grains DFT by recourse to controlled numerical approximations without the introduction of new or spurious physics. The method, called Coarse-Grained Density Functional (CG-DFT), is based on the Linear Scaling Spectral Gauss Quadrature (LSSGQ) method which proposes a reformulation of the traditional DFT equations. One of the main advantages of the LSSGQ method is that eliminates the need to explicitly compute wave-functions by using integral representations of the electronic quantities over the spectrum of the linear Hamiltonian operator, resulting in linear scaling with number of atoms. Additionally, the evaluation of these integrals can be performed using spectral Gaussian quadrature rules, where the nodes and weights are computed independently for each point in the domain. This property allows us to apply a systematic coarse graining description of the LSSGQ method using the Quasi-Continuum (QC) framework and reduce the total number of degrees of freedom of the system. In this work the fundamental equations of the coarse graining description and also preliminary results using the CG-DFT method will be presented.