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.