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

Abstract

A number of approaches are proposed and assessed to reduce the frozen natural orbital (FNO) truncation error of coupled-cluster singles and doubles with perturbative triples [CCSD(T)] energies. The diagrammatic energy decomposition method of Irmler and Grüneis [J. Chem. Phys. 151, 104107 (2019)] is extended to the FNO truncation correction of the particle-particle ladder (PPL) term in the case of closedand open-shell molecular systems. The approach is tested for reaction and interaction energies, as well as atomization processes, and it is found the most robust for a wider range of FNO truncation thresholds outperforming the commonly employed additive MP2 correction. We also show that the linear extrapolation (LE) of FNO-CCSD(T) energies as a function of second-order Møller-Plesset (MP2) energies provides the best correlation energies and most balanced energy differences with tighter FNO thresholds, but it lacks systematic error compensation that would be required for the better performance with looser FNO thresholds. Further insight is gained from a diagrammatic and spin-component decomposition based analysis. Moreover, orbital (pair) specific energy decompositions are utilized to introduce size-consistent variants of the promising PPL and LE FNO corrections and their analogues for (T), which are also readily applicable in the context of popular local correlation methods.

Linear-Scaling Local Natural Orbital CCSD(T) Approach for Open-Shell Systems: Algorithms, Benchmarks, and Large-Scale Applications

“…Thus, the default LNO threshold values of ε o = 10 –5 and ε v = 10 –6 are selected, which are recommended also based on our closed-shell LNO-CCSD­(T) benchmarks , as both the correlation energy and energy difference deviations are sufficiently converged (with at most 0.14% and 0.53 kcal/mol deviations, respectively, for the examples of this section). We note in passing that this value is not directly comparable to the frozen NO , or pair NO threshold settings as only the strong pair LMOs are included in our orbital specific LNO density matrices (Section. ), while the summation is not restricted for the frozen NO and even more restricted for the orbital pair specific pair NO density matrices.…”

“…This motivates the introduction of reduced-scaling approximations, such as the robust frozen natural orbital (NO) approach, , which can extend the applicability range of NO-CCSD(T) somewhat further. , Alternatively, one can also accelerate the basis set convergence via explicitly correlated (F12) CC methods, − leading to more compact atomic orbital (AO) basis set requirements. However, even our recent combination of the NO approach and an optimized F12 implementation allowed us to approach the complete basis set (CBS) limit for closed-shell species of only up to 50 atoms with an even smaller open-shell limit of about 30–35 atoms …”

Basis Set Limit CCSD(T) Energies for Extended Molecules via a Reduced-Cost Explicitly Correlated Approach

“…The weakly populated NOs are dropped, and the active space is composed of the NOs of larger occupation numbers. The error introduced by this approximation can be efficiently reduced by computing the so-called ΔMP2 correction, which is the difference of the second-order MP (MP2) energies evaluated in the full MO basis and the active space. , In addition, the FNO approximation can also be improved by more advanced correction schemes and by extrapolation techniques. ,− The FNO approach was also extended to open-shell systems, , higher-order CC methods, and excited states. ,,− Concerning larger systems, the use of FNO techniques was enabled by reduced-scaling density matrix construction algorithms. − …”

“…The error introduced by this approximation can be efficiently reduced by computing the so-called ΔMP2 correction, which is the difference of the second-order MP (MP2) energies evaluated in the full MO basis and the active space. 3 , 11 In addition, the FNO approximation can also be improved by more advanced correction schemes 14 and by extrapolation techniques. 13 , 15 − 18 The FNO approach was also extended to open-shell systems, 13 , 19 higher-order CC methods, 20 and excited states.…”

Multireference Theories of Electron Correlation Based on the Driven Similarity Renormalization Group

“…58,59 In this method, the one-particle reduced density matrix (1-RDM) of a low-level correlated wave function is diagonalized and orbitals with small natural occupation numbers are discarded for subsequent high-level electron correlation computations. Successful applications of FNO are mostly found in the CC hierarchy, [60][61][62][63][64] where 20-60% of the virtual orbitals can be removed without sacrificing the accuarcy significantly for a triple-𝜁 basis set. 60 More recently, FNO-based excited-state methods have also been formulated, including LR/EOM-CC, [65][66][67] ADC, 68,69 and 𝐺𝑊 theories.…”