Speeding up real-space based first-principles methods for excited-states properties using interpolative separable density fitting

Density fitting methods are a class of algorithms that provide low-rank approximations for products of orbital pairs. However, most of its applications in first-principles codes are based on localized basis sets. A recently proposed interpolative separable density fitting (ISDF) method does not rely on predefined auxiliary basis and is formulated in real space representation. We employ the ISDF method to significantly reduce the cost of linear response time-dependent density functional theory (LR-TDDFT) and GW calculations. In our implementation, we exploit the symmetry property of a system to effectively reduce the number of auxiliary basis and thus the computational cost. Our benchmarks show the cost for constructing auxiliary basis and interpolation coefficients are negligible compared to the total computational cost. Compared to a conventional “brutal-force” approach, the cost for evaluating all kernel matrix elements in LR-TDDFT and GW calculations is reduced by up to three orders of magnitude. The accuracy of our implementation is benchmarked with the GW100 set.