Hitting the Trifecta: How to Simultaneously Push the Limits of Schrödinger Solution with Respect to System Size, Convergence Accuracy, and Number of Computed States

Methods for solving the Schrödinger equation without approximation are in high demand but are notoriously computationally expensive. In practical terms, there are just three primary factors that currently limit what can be achieved: 1) system size/dimensionality; 2) energy level excitation; and 3) numerical convergence accuracy. Broadly speaking, current methods can deliver on any two of these three goals, but achieving all three at once remains an enormous challenge. In this paper, we shall demonstrate how to “hit the trifecta” in the context of molecular vibrational spectroscopy calculations. In particular, we compute the lowest 1000 vibrational states for the six-atom acetonitrile molecule (CH₃CN), to a numerical convergence of accuracy 10^–2 cm^–1 or better. These calculations encompass all vibrational states throughout most of the dynamically relevant range (i.e., up to ∼4250 cm^–1 above the ground state), computed in full quantum dimensionality (12 dimensions), to near spectroscopic accuracy. To our knowledge, no such vibrational spectroscopy calculation has ever previously been performed.