The Massively Parallel Quantum Chemistry (MPQC) program is a 30-year-old project that enables facile development of electronic structure methods for molecules for efficient deployment to massively parallel computing architectures. Here, we describe the historical evolution of MPQC’s design into its latest (fourth) version, the capabilities and modular architecture of today’s MPQC, and how MPQC facilitates rapid composition of new methods as well as its state-of-the-art performance on a variety of commodity and high-end distributed-memory computer platforms.

Simplifications or modifications of coupled cluster methods such as the CCSD (coupled cluster singles and doubles) model often perform better than the original method in providing the total energy, equilibrium geometries, and harmonic vibration frequencies for the ground state. Three such methods that have been recently proposed include 2CC, parameterized CCSD generalizations, and distinguishable cluster singles and doubles (DCSD) approach. In this paper, we lay the theoretical foundation needed to treat excited states via the equation of motion (EOM) approach using these ground state CC methods. As these ground state approximations to CCSD share its property of being exact for two-electron systems, so will their excited state extensions. These methods are tested for two complementary benchmark sets of excited states for a wide range of organic molecules with focus on singlet and triplet excited states of both valence and Rydberg nature. We also test these methods for doubly excited states, taking CH as an example to test their performance at equilibrium and stretched bond geometries. Finally, we assess if any of these methods perform consistently better than EOM CCSD.

Approximation of a tensor network by approximating (e.g., factorizing) one or more of its constituent tensors can be improved by canceling the leading-order error due to the constituents’ approximation. The utility of such robust approximation is demonstrated for robust canonical polyadic (CP) approximation of a (density-fitting) factorized two-particle Coulomb interaction tensor. The resulting algebraic (grid-free) approximation for the Coulomb tensor, closely related to the factorization appearing in pseudospectral and tensor hypercontraction approaches, is efficient and accurate, with significantly reduced rank compared to the naive (nonrobust) approximation. Application of the robust approximation to the particle–particle ladder term in the coupled-cluster singles and doubles reduces the size complexity from O (N 6) to O (N 5) with robustness ensuring negligible errors in chemically relevant energy differences using CP ranks approximately equal to the size of the density-fitting basis.

The Distinguishable Cluster (DC) approximation to the coupled cluster (CC) doubles, proposed by Kats and Manby [J. Chem. Phys. 139, 021102 (2013)], can semiquantitatively describe multiple bond dissociation (which is traditionally considered a paradigm of strongly correlated electronic structure methods based on the multideterminant approach) without leaving the single-reference coupled cluster framework. DC is just one of many internally corrected (CC) methods that improve on the parent CC method by approximation. To build on the success of the DC methods, it is important to probe whether they can be systematically improved. To answer this question, we considered a set of methods in the distinguishable cluster family, culminating in the DC singles, doubles, and triples (DCSDT), a DC modification of the parent CC singles, doubles, and triples that maintains exactness for 3-electron systems. Inclusion of the complete treatment of triples leads to systematic improvement over the DCSD for equilibrium correlation energy estimates. However, this improvement is not matched by enhanced accuracy for multiple bond breaking processes.