All-electron molecular tunnel ionization based on the weak-field asymptotic theory in the integral representation

Tunnel ionization (TI) underlies many important ultrafast processes, such as high-harmonic generation and strong-field ionization. Among the existing theories for TI, many-electron weak-field asymptotic theory (ME-WFAT) is by design capable of accurately treating many-electron effects in TI. An earlier version of ME-WFAT relied on an accurate representation of the asymptotic tail of the orbitals, which hindered its implementation in Gaussian-basis-set-based quantum chemistry programs. In this work, we reformulate ME-WFAT in the integral representation, which makes the quality of the asymptotic tail much less critical, hence greatly facilitating its implementation in standard quantum chemistry packages. The integral reformulation introduced here is therefore much more robust when applied to molecules with arbitrary geometry. We present several case studies, among which is the CO molecule where some earlier theories disagree with experiments. Here we find that ME-WFAT produces the largest ionization probability when the field points from C to O, as experiments suggest. An attractive feature of ME-WFAT is that it can be used with various types of multielectron methods whether of density functional [I. S.Wahyutama et al., Phys. Rev. A 106, 052211 (2022)] or multiconfiguration types, this in turn facilitates tunnel ionization calculation in systems exhibiting a strong multireference character.