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Accelerating time-dependent density functional theory and GW calculations for molecules and nanoclusters with symmetry adapted interpolative separable density fitting.

Computing integrals over orbital pairs is one of the most costly steps in many popular first-principles methods used by the quantum chemistry and condensed matter physics community. Here we employ a recently proposed interpolative separable density fitting method (ISDF) to significantly reduce the cost of steps involving orbital pairs in linear response time-dependent density functional theory and GW calculations. In our implementation, we exploit the symmetry property of a system to effectively reduce the number of interpolation points and thus the computational cost. The performance of ISDF is demonstrated with calculations on the GW100 set and silicon nanoclusters. We demonstrate the cost for constructing auxiliary basis and interpolation coefficients are negligible compared to the total cost. Compared to the conventional brute-force approach, the computation cost for evaluating all kernel matrix elements is reduced by nearly three orders of magnitude. The total cost for GW calculations can be reduced by four to eight times, depending on the system size.