Feasibility and Scaling of 3D Grid Methods for Molecular Bound and Continuum States

We investigate the feasibility and scaling of fully three-dimensional grid-based time-dependent Schrödinger equation solvers for molecular bound and continuum dynamics. Using DVR and FEDVR discretizations, we benchmark atomic and diatomic systems to establish accuracy for bound-state energies, potential energy surfaces, and photoelectron angular distributions relevant to strong-field and attosecond experiments.

We analyze convergence with respect to grid resolution, simulation volume, and time step, and characterize computational scaling toward multi-center molecular geometries. We introduce interpolating multi-center grid techniques and demonstrate their performance for molecular bound and continuum states.

Our results quantify the practical limits of grid-based molecular continuum simulations and identify regimes where such approaches can complement or outperform basis-set and scattering methods, providing a pathway toward ab initio simulations of strong-field molecular ionization and ultrafast electron dynamics.