Time-frequency component of the GreenX library: minimax grids for efficient RPA and GW calculations

The central objects in many-body electronic structure theory, such as the GW method and the random-phase approximation (RPA), are defined in the complex frequency or time domain. We present here the GX-TimeFrequency component of the GreenX library, providing grids and weights for imaginary time-frequency transformations needed for Green's function based objects. The GreenX library emerged from the NOMAD Center of Excellence, whose objective is to enable accurate Green's function based electronic structure theory calculations on state-of-the-art supercomputers.

The package comprises minimax time and frequency grids and corresponding quadrature weights to numerically compute time and frequency integrals of the correlation energy as well as weights for Fourier transforms between time and frequency grids. While targeting low-scaling RPA and GW algorithms, its compact frequency grids allows one to reduce the computational prefactor in RPA implementations with conventional scaling. In addition, the time grids can be employed in Laplace-transformed direct MP2 (LT-dMP2) calculations. The GreenX source code is freely available on GitHub, and comes equipped with a build system, a comprehensive set of tests, and detailed documentation.