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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. This builds upon earlier by Cooper, et al. [J. Phys. Chem. A, 2021 125, 5438-5447] which presented a similar TD-EOM-CC integration scheme based on the short-iterative Lanczos (SIL) method. The proposed algorithms are compared with SIL, the fourth-order Runge-Kutta method (RK4), and exact dynamics for a set of small test problems. For each of cases studied, both of the proposed integration schemes demonstrate superior accuracy and efficiency than the reference simulations., Comment: 23 pages, 3 figures

One-electron reduced density matrices (1RDMs) from equation-of-motion (EOM) coupled-cluster with single and double excitations (CCSD) calculations are analyzed to assess their N-representability ({\em i.e.}, whether they are derivable from an physical N-electron state). We identify EOM-CCSD stationary states whose 1RDMs violate either ensemble-state N-representability conditions or pure-state conditions known as generalized Pauli constraints (GPCs). As such, these 1RDMs do not correspond to any physical N-electron state. Unphysical states are also encountered in the course of time-dependent EOM-CC simulations; when an external field drives transitions between a pair of stationary states with pure-state N-representable 1RDMs, the 1RDM of the time-dependent state can violate ensemble-state conditions. These observations point to potential challenges in interpreting the results of time-dependent EOM-CCSD simulations.

Simulations of laser-induced electron dynamics in a molecular system are performed using time-dependent (TD) equation-of-motion (EOM) coupled-cluster (CC) theory. The target system has been chosen to highlight potential shortcomings of truncated TD-EOM-CC methods [represented in this work by TD-EOM-CC with single and double excitations (TD-EOM-CCSD)], where unphysical spectroscopic features can emerge. Specifically, we explore driven resonant electronic excitations in magnesium fluoride in the proximity of an avoided crossing. Near the avoided crossing, the CCSD similarity-transformed Hamiltonian is defective, meaning that it has complex eigenvalues, and oscillator strengths may take on negative values. When an external field is applied to drive transitions to states exhibiting these traits, unphysical dynamics are observed. For example, the stationary states that make up the time-dependent state acquire populations that can be negative, exceed one, or even be complex-valued.

p$^\dagger$q is a C++ accelerated Python library designed to generate equations for many-body quantum chemistry methods and to realize proof-of-concept implementations of these equations for rapid prototyping. Central to this library is a simple interface to define strings of second-quantized creation and annihilation operators and to bring these strings to normal order with respect to either the true vacuum state or the Fermi vacuum. Tensor contractions over fully-contracted strings can then be evaluated using standard Python functions ({\em e.g.}, \np's einsum). Given one- and two-electron integrals these features allow for the rapid implementation and assessment of a wide array of many-body quantum chemistry methods.

The Chronus Quantum (ChronusQ) software package is an open source (under the GNU General Public License v2) software infrastructure which targets the solution of challenging problems that arise in ab initio electronic structure theory. Special emphasis is placed on the consistent treatment of time dependence and spin in the electronic wave function, as well as the inclusion of relativistic effects in said treatments. In addition, ChronusQ provides support for the inclusion of uniform finite magnetic fields as external perturbations through the use of gauge-including atomic orbitals (GIAO). ChronusQ is a parallel electronic structure code written in modern C++ which utilizes both message passing (MPI) and shared memory (OpenMP) parallelism. In addition to the examination of the current state of code base itself, a discussion regarding ongoing developments and developer contributions will also be provided., Comment: 43 pages, 2 figures

Analytic energy gradients are presented for a variational two-electron reduced-density-matrix-driven complete active space self-consistent field (v2RDM-CASSCF) procedure that employs the density-fitting (DF) approximation to the two-electron repulsion integrals. The DF approximation significantly reduces the computational cost of v2RDM-CASSCF gradient evaluation, in terms of both the number of floating-point operations and memory requirements, enabling geometry optimizations on much larger chemical systems than could previously be considered at the this level of theory [E. Maradzike et al., J. Chem. Theory Comput., 2017, 13, 4113-4122]. The efficacy of v2RDM-CASSCF for computing equilibrium geometries and harmonic vibrational frequencies is assessed using a set of 25 small closed- and open-shell molecules. Equilibrium bond lengths from v2RDM-CASSCF differ from those obtained from configuration-interaction-driven CASSCF (CI-CASSCF) by 0.62 pm and 0.05 pm, depending on whether the optimal reduced-density matrices from v2RDM-CASSCF satisfy two-particle N-representability conditions (PQG) or PQG plus partial three-particle conditions (PQG+T2), respectively. Harmonic vibrational frequencies, which are obtained by finite differences of v2RDM-CASSCF analytic energy gradients, similarly demonstrate that quantitative agreement between v2RDM- and CI-CASSCF requires the consideration of partial three-particle N-representability conditions. Lastly, optimized geometries are obtained for the lowest-energy singlet and triplet states of the linear polyacene series up to dodecacene (C50H28), in which case the active space is comprised of 50 electrons in 50 orbitals. The v2RDM-CASSCF singlet-triplet energy gap extrapolated to an infinitely-long linear acene molecule is found to be 7.8 kcal/mol

Complete active space self-consistent field (CASSCF) computations can be realized at polynomial cost via the variational optimization of the active-space two-electron reduced-density matrix (2-RDM). Like conventional approaches to CASSCF, variational 2-RDM (v2RDM)-driven CASSCF captures nondynamical electron correlation in the active space, but it lacks a description of the remaining dynamical correlation effects. Such effects can be modeled through a combination of v2RDM-CASSCF and on-top pair-density functional theory (PDFT). The resulting v2RDM-CASSCF-PDFT approach provides a computationally inexpensive framework for describing both static and dynamical correlation effects in multiconfigurational and strongly correlated systems. On-top pair-density functionals can be derived from familiar Kohn-Sham exchange-correlation (XC) density functionals through the translation of the v2RDM-CASSCF reference densities [Li Manni et al., J. Chem. Theory Comput. 10, 3669-3680 (2014)]. Translated and fully-translated on-top PDFT versions of several common XC functionals are applied to the potential energy curves of N2, H2O, and CN-, as well as to the singlet/triplet energy splittings in the linear polyacene series. Using v2RDM-CASSCF-PDFT and the translated PBE functional, the singlet/triplet energy splitting of an infinitely-long acene molecule is estimated to be 4.87 kcal/mol.