Resonant Inelastic X-ray Scattering Amplitudes and Cross Sections in the Algebraic Diagrammatic Construction/Intermediate State Representation (ADC/ISR) Approach.

A scheme has been derived and implemented to gain computational access to the full electronic part of the Kramers-Heisenberg-Dirac (KHD) expression for resonant and nonresonant inelastic scattering amplitudes. Our implementation of this scheme is based on the complex polarization propagator in the algebraic diagrammatic construction (ADC) framework and within its intermediate state representation (ISR). The hierarchy of the second- and third-order ADC/ISR computational schemes known as ADC(2), ADC(2)-x, and ADC(3/2) is considered, and the calculated resonant inelastic X-ray scattering (RIXS) amplitudes and transition strengths for water are in excellent agreement with recent experimental data.