Optimized Pair Natural Orbitals for the Coupled Cluster Methods

Abstract

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.

Basis set truncation corrections for improved frozen natural orbital CCSD(T) energies

“…Several functional forms have been proposed including modified second-order Hylleraas-functionals [23][24][25] and other ones that utilize the overlap of the CC wave functions expanded in the full and the active virtual spaces [26,27]. The benefits of using CCSD amplitudes instead of MP1 amplitudes to define the retained virtual subspace have also been explored [28].…”

“…Besides the cost-reduction of conventional CC methods, various types of NOs are widely used to speed up local CC approaches. These include the pair natural orbitals (PNOs) [13][14][15]28] and local natural orbitals (LNOs) [48], which are pair-and orbital-specific NOs, respectively, evaluated from density matrix fragments.…”

From NWChem to NWChemEx: Evolving with the Computational Chemistry Landscape

“…414 Recently it was shown that by iterative optimization of PNOs in coupled-cluster methods the PNO truncation error can be greatly reduced. 225 Similarly, PNOs can be computed purely numerically. 415 The…”

“…[222][223][224] Pilot implementation of pair natural orbital CC methods for ground-and excited-states have also been demonstrated. 223,225 7 Solvers…”

Reduced‐scaling coupled cluster response theory: Challenges and opportunities

“…Due to their pioneering work, the LPNO and the DLPNO methods have been used successfully to study ground state properties of molecular systems previously unreachable by canonical correlated methods, such as a recent application to crambin containing 644 atoms . Recent work to improve the construction of ground‐state PNOs promises to expand the applicability of these methods even further …”