Here, we present an ab initio approach to full simulation of an attosecond molecular pump-probe experiment. Sequential molecular double ionization by the pump and probe laser pulses with controlled delay is described from first-principles with a full account of the continuum dynamics of the photoelectrons. Many-electron bound-continuum dynamics is simulated using the time-dependent (TD) molecular B-spline algebraic diagrammatic construction (ADC) method. Our calculations give a quantitative prediction about the creation of a coherent superposition of molecular ionic states in the photoionization process and simulate the probe of the ensuing attosecond dynamics by a second ionizing pulse within a single first-principles many-electron framework. We therefore demonstrate the capability to simulate and interpret the results of a prototypical molecular pump-probe experiment of interest in attoscience. As a particular example, we simulate and elucidate the interpretation of a pump-probe experiment in CO2 aimed at measuring strong field-induced hole dynamics via photoionization yields.
