PNO++: Perturbed Pair Natural Orbitals for Coupled Cluster Linear Response Theory

Abstract

Reduced-scaling methods are needed to make accurate and systematically improvable coupled cluster linear response methods for the calculation of molecular properties tractable for large molecules. In this paper, we examine the perturbed pair natural orbital-based PNO++ approach that creates an orbital space optimized for response properties derived from a lower-cost field-perturbed density matrix. We analyze truncation errors in correlation energies, dynamic polarizabilities, and specific rotations from a coupled cluster singles and doubles (CCSD) reference. We find that incorporating a fixed number of orbitals from the pair natural orbital (PNO) space into the PNO++ methoda new method presented here, the “combined PNO++” approachrecovers accuracy in the CCSD correlation energy while preserving the well-behaved convergence behavior of the PNO++ method for linear response properties.

Self-Consistent Field Calculation of Nuclear Magnetic Resonance Chemical Shielding Constants Using Gauge-Including Atomic Orbitals and Approximate Two-Electron Integrals

“…184 We should also mention here the work by Crawford and coworkers in the field of local coupled cluster linear response theory for the calculation of molecular properties, including frequency-dependent polarizabilities and specific optical rotations. [185][186][187][188] Work in the Neese group has focused on the domain-based local pair natural orbital (DLPNO) approximation and has resulted in orbital-unrelaxed first derivatives of DLPNO-CCSD, which can be used to calculate, e.g., dipole moments and HFCs. 189,190 Fully orbital-relaxed first derivatives and nuclear gradients were also implemented for the DLPNO-MP2 method, [191][192][193] and those results highlight the importance of the PNO relaxation contributions, e.g.…”

Reduced-Cost Second-Order Algebraic-Diagrammatic Construction Method for Core Excitations

“…75−77 Their efficient Laplace transform-based multistate approach was also extended to analytic energy gradient calculations. 78,79 Parallel to those efforts, promising schemes were also proposed by Haẗtig et al extending the pair natural orbital (PNO) approximation to excited-state theories, 80−82 while further PNO-based approaches were presented by Dutta and co-workers 83 and Crawford et al 84 We note that other approximations are also available to reduce the computational requirements, such as the multilevel schemes developed by Koch and co-workers. 85,86 The usage of the aforementioned approximations for core excitations is rather limited.…”

“…The first local excited-state approach was presented by Crawford et al, − while several advances were reported later by different groups. In this direction, one of the most significant results was achieved by Korona, Schütz, and their co-workers. − Their efficient Laplace transform-based multistate approach was also extended to analytic energy gradient calculations. , Parallel to those efforts, promising schemes were also proposed by Hättig et al extending the pair natural orbital (PNO) approximation to excited-state theories, − while further PNO-based approaches were presented by Dutta and co-workers and Crawford et al We note that other approximations are also available to reduce the computational requirements, such as the multilevel schemes developed by Koch and co-workers. , …”

Accurate and Efficient Prediction of Post-Hartree–Fock Polarizabilities of Condensed-Phase Systems

“…Polarizability (α) is a fundamental quantity in many disciplines, especially materials science. , It is also involved in vibrational Raman , and sum-frequency generation spectra . For small molecular to macromolecular systems in the gas phase, computation of the polarizability is routine. − For example, recent machine learning (ML)-based techniques − have been introduced to accelerate the prediction of molecular polarizability. However, for condensed-phase systems, only sporadic studies have been reported. − This is mainly because conventional density functional perturbation theory (DFPT) − suffers from efficiency limitations, and periodic post-Hartree–Fock methods are even more computationally expensive.…”