State-Averaged Pair Natural Orbitals for Excited States: A Route toward Efficient Equation of Motion Coupled-Cluster.

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, 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.