An efficient and near linear scaling pair natural orbital based local coupled cluster method

In previous publications, it was shown that an efficient local coupled cluster method with single- and double excitations can be based on the concept of pair natural orbitals (PNOs) F. Neese, A. Hansen, and D. G. Liakos, J. Chem. Phys. 131, 064103 (2009). The resulting local pair natural orbital-coupled-cluster single double (LPNO-CCSD) method has since been proven to be highly reliable and efficient. For large molecules, the number of amplitudes to be determined is reduced by a factor of 10(5)-10(6) relative to a canonical CCSD calculation on the same system with the same basis set. In the original method, the PNOs were expanded in the set of canonical virtual orbitals and single excitations were not truncated. This led to a number of fifth order scaling steps that eventually rendered the method computationally expensive for large molecules (e.g., >100 atoms). In the present work, these limitations are overcome by a complete redesign of the LPNO-CCSD method. The new method is based on the combination of the concepts of PNOs and projected atomic orbitals (PAOs). Thus, each PNO is expanded in a set of PAOs that in turn belong to a given electron pair specific domain. In this way, it is possible to fully exploit locality while maintaining the extremely high compactness of the original LPNO-CCSD wavefunction. No terms are dropped from the CCSD equations and domains are chosen conservatively. The correlation energy loss due to the domains remains below 8800 basis functions and >450 atoms. In all larger test calculations done so far, the LPNO-CCSD step took less time than the preceding Hartree-Fock calculation, provided no approximations have been introduced in the latter. Thus, based on the present development reliable CCSD calculations on large molecules with unprecedented efficiency and accuracy are realized.