General time-dependent configuration-interaction singles. I. Molecular case

We present a grid-based implementation of the time-dependent configuration-interaction singles method suitable for computing strong-field ionization small gas-phase molecules. After outlining general equations motion used in our treatment this method, we example calculations helium, lithium hydride, water, and ethylene that demonstrate utility implementation. The following companion paper specializes to case spherical symmetry, which is applied various atoms.