Fast Time-Dependent Density Functional Theory Calculations of the X-ray Absorption Spectroscopy of Large Systems

The computational cost of calculations of K-edge X-ray absorption spectra using time-dependent density functional (TDDFT) within the Tamm-Dancoff approximation is significantly reduced through the introduction of a severe integral screening procedure that includes only integrals that involve the core s basis function of the absorbing atom(s) coupled with a reduced quality numerical quadrature for integrals associated with the exchange and correlation functionals. The memory required for the calculations is reduced through construction of the TDDFT matrix within the absorbing core orbitals excitation space and exploiting further truncation of the virtual orbital space. The resulting method, denoted fTDDFTs, leads to much faster calculations and makes the study of large systems tractable. The capability of the method is demonstrated through calculations of the X-ray absorption spectra at the carbon K-edge of chlorophyll a, C₆₀ and C₇₀.