Efficient calculation of X-ray absorption spectra using Chebyshev-Slepian filter diagonalisation

The efficient, yet accurate, simulation of X-ray absorption spectra represents a significant challenge for ab initio electronic structure methods. Conventional approaches involve the explicit calculation of all core-excited states spanning the energy range of interest, even though only a small number of these states will contribute appreciably to the spectrum. We here report a different approach, based on a time-independent Chebyshev filter diagonalization scheme, which allows for the X-ray absorption spectrum to be computed without the explicit calculation of the core-excited eigenstates. Furthermore, in a subsequent postprocessing calculation, selected peaks may be analyzed via the calculation of natural transition orbitals, if desired. The scheme presented here is based on a refinement of the time-independent Chebyshev filter diagonalization approach. Previous formulations of this method have been characterized by a requirement for significant "user input" via the (sometimes unintuitive) tuning of various numerical parameters. To circumvent this, we introduce a new class of filters based on discrete prolate spheroidal sequences. We demonstrate that the resulting method, which we term Chebyshev-Slepian filter diagonalization, makes filter diagonalization essentially a black-box procedure. The Chebyshev-Slepian filter diagonalization method is implemented at the second-order algebraic diagrammatic construction level of theory and validated through the calculation of the X-ray absorption spectra of trifluoroacetonitrile and 1,4-benzoquinone.