Accelerating Core-Level GW Calculations by Combining the Contour Deformation Approach with the Analytic Continuation of W

In recent years, the GW method has emergedasa reliable tool for computing core-level binding energies. The contourdeformation (CD) technique has been established as an efficient, scalable,and numerically stable approach to compute the GW self-energy for deep core excitations. However, core-level GW calculations with CD face the challenge of higher scalingwith respect to system size N compared to the conventionalquartic scaling in valence-state algorithms. In this work, we presentthe CD-WAC method [CD with W analytic continuation(AC)], which reduces the scaling of CD applied to the inner shellsfrom O(N-5) to O(N-4) by employing an AC of thescreened Coulomb interaction W. Our proposed methodretains the numerical accuracy of CD for the computationally challengingdeep core case, yielding mean absolute errors <5 meV for well-establishedbenchmark sets, such as CORE65, for single-shot GW calculations. More extensive testing for different GW flavors proves the reliability of the method. We have confirmedthe theoretical scaling by performing scaling experiments on largeacene chains and amorphous carbon clusters, achieving speedups ofup to 10x for structures of only 116 atoms. This improvementin computational efficiency paves the way for more accurate and efficientcore-level GW calculations on larger and more complexsystems.