With growing demand for time-domain simulations of correlated many-body
systems, the development of efficient and stable integration schemes for the
time-dependent Schr\"odinger equation is of keen interest in modern electronic
structure theory. In the present work, we present two novel approaches for the
formation of the quantum propagator for time-dependent equation-of-motion
coupled cluster theory (TD-EOM-CC) based on the Chebyshev and Arnoldi
expansions of the complex, non-hermitian matrix exponential, respectively. The
proposed algorithms are compared with the short-iterative Lanczos method of
Cooper, et al [J. Phys. Chem. A. 2021 125, 5438-5447], the fourth-order
Runge-Kutta method (RK4), and exact dynamics for a set of small but challenging
test problems. For each of the cases studied, both of the proposed integration
schemes demonstrate superior accuracy and efficiency relative to the reference
simulations.Comment: 28 pages, 4 figure