A reduced-complexity variant of equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) method is formulated in terms of state-averaged excited-state pair natural orbitals (PNO) designed to describe manifolds of excited states. State-averaged excited-state PNOs for the target manifold are determined by averaging CIS­(D) pair densities over the model manifold. The performance of the PNO-EOM-CCSD approach has been tested with the help of a distributed-memory parallel canonical EOM-CCSD implementation within the Massively Parallel Quantum Chemistry program that allows treatment of systems with 50+ atoms using realistic basis sets with 1000+ functions. The use of state-averaged PNOs offers several potential advantages relative to the recently proposed state-specific PNOs: our approach is robust with respect to root flipping and state degeneracies, it is more economical when computing large manifolds of states, and it simplifies evaluation of transition-specific observables such as dipole moments. With the PNO truncation threshold of 10–7, the errors in excitation energies are on average below 0.02 eV for the first six singlet states of 28 organic molecules included in the standard test set of Thiel and co-workers (J. Chem. Phys. 2008, 128, 134110) with 50–70 state-averaged PNOs per pair.

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.

We present the coupled-cluster singles and doubles method formulated in terms of truncated pair natural orbitals (PNO) that are optimized to minimize the effect of truncation. Compared to the standard ground-state PNO coupled-cluster approaches, in which truncated PNOs derived from first-order Møller-Plesset (MP1) amplitudes are used to compress the CC wave operator, the iteratively optimized PNOs ("iPNOs") offer moderate improvement for small PNO ranks but rapidly increase their effectiveness for large PNO ranks. The error introduced by PNO truncation in the CCSD energy is reduced by orders of magnitude in the asymptotic regime, with an insignificant increase in PNO ranks. The effect of PNO optimization is particularly effective when combined with Neese's perturbative correction for the PNO incompleteness of the CCSD energy. The use of the perturbative correction in combination with the PNO optimization procedure seems to produce the most precise approximation to the canonical CCSD energies for small and large PNO ranks. For the standard benchmark set of noncovalent binding energies, remarkable improvements with respect to the standard PNO approach range from a factor of 3 with PNO truncation threshold τ = 10 (with the maximum PNO truncation error in the binding energy of only 0.1 kcal/mol) to more than 2 orders of magnitude with τ = 10.

We describe a robust method for determining Pipek–Mezey (PM) Wannier functions (WF), recently introduced by Jónsson et al. (J. Chem. Theor. Chem. 2017, 13, 460), which provide some formal advantages over the more common Boys (also known as maximally-localized) Wannier functions. The Broyden–Fletcher–Goldfarb–Shanno-based PMWF solver is demonstrated to yield dramatically faster convergence compared to the alternatives (steepest ascent and conjugate gradient) in a variety of one-, two-, and three-dimensional solids (including some with vanishing gaps) and can be used to obtain Wannier functions robustly in supercells with thousands of atoms. Evaluation of the PM functional and its gradient in periodic linear combination of atomic orbital representation used a particularly simple definition of atomic charges obtained by Moore–Penrose pseudoinverse projection onto the minimal atomic orbital basis. An automated “canonicalize phase then randomize” method for generating the initial guess for WFs contributes significantly to the robustness of the solver.

We describe a robust method for determining Pipek-Mezey (PM) Wannier functions (WF), which provide some formal advantages over the more common Boys (also known as maximally-localized) Wannier functions. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) based PMWF solver is demonstrated to yield dramatically faster convergence compared to the alternatives (steepest ascent and conjugate gradient) in a variety of 1-, 2-, and 3-dimensional solids (including some with vanishing gaps), and can be used to obtain Wannier functions robustly in supercells with thousands of atoms. Evaluation of the PM functional and its gradient in periodic LCAO representation used a particularly simple definition of atomic charges obtained by Moore-Penrose pseudoinverse projection onto the minimal atomic orbital basis. An automated "Canonicalize Phase then Randomize" (CPR) method for generating the initial guess for WFs contributes significantly to the robustness of the solver.