Noniterative Doubles Corrections to the Random Phase and Higher Random Phase Approximations: Singlet and Triplet Excitation Energies

Abstract

The second‐order noniterative doubles‐corrected random phase approximation (RPA) method has been extended to triplet excitation energies and the doubles‐corrected higher RPA method as well as a shifted version for calculating singlet and triplet excitation energies are presented here for the first time. A benchmark set consisting of 20 molecules with a total of 117 singlet and 71 triplet excited states has been used to test the performance of the new methods by comparison with previous results obtained with the second‐order polarization propagator approximation (SOPPA) and the third order approximate coupled cluster singles, doubles and triples model CC3. In general, the second‐order doubles corrections to RPA and HRPA significantly reduce both the mean deviation as well as the standard deviation of the errors compared to the CC3 results. The accuracy of the new methods approaches the accuracy of the SOPPA method while using only 10–60% of the calculation time. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

Benchmarking Correlated Methods for Frequency-Dependent Polarizabilities: Aromatic Molecules with the CC3, CCSD, CC2, SOPPA, SOPPA(CC2), and SOPPA(CCSD) Methods

“…12 For vertical excitation energies, on the contrary, CC2 has been shown to yield results in clearly better agreement with CC3 results than SOPPA. 24,68,69 It is then seen for the mixed methods, SOPPA(CC2) and SOPPA(CCSD), that the SOPPA results are improved by using the coupled-cluster amplitudes in the wave functions instead of the Møller−Plesset correlation coefficients, making SOPPA(CC2), with a mean deviation of 2.26 ± 0.55 au, slightly better than SOPPA and making SOPPA(CCSD) the best, with a mean deviation of 1.12 ± 0.39 au. The fact that the mean and absolute mean deviation are the same for the SOPPA, SOPPA(CC2), SOPPA(CCSD), and CC2 methods shows that all of these methods consistently overestimate the CC3 static polarizabilities.…”

Computational1H and13C NMR in structural and stereochemical studies

“…Among those are the Second-Order Polarization Propagator Approach within the second-order Møller-Plesset perturbation theory, SOPPA (MP2), Second-Order Polarization Propagator Approach in combination with the second-order approximate Coupled Cluster to second order, SOPPA (CC2), and Second-Order Polarization Propagator Approach in combination with Coupled Cluster Singles and Doubles, SOPPA (CCSD). For general references on the SOPPA-based methods for the calculation of spin-spin coupling constants, see basic publications by Stephan Sauer, [43] Enevoldsen, et al, [44] and Kjaer, et al [45,46] Sauer and his collaborators applied a variety of second-order methods and those with triple corrections for the calculation of other molecular properties like oscillator strengths and excited-state dipole moments, [47] excitation energies, [48] triplet excited states, [49] and frequency-dependent polarizabilities. [50] 2.4 | Specialized basis sets Specialized basis sets of at least triple zeta quality are recommended in most cases for the calculation of NMR parameters at either DFT or the non-empirical levels.…”

The Second-Order-Polarization-Propagator-Approximation (SOPPA) in a four-component spinor basis

“…PLEASE CITE THIS ARTICLE AS DOI:10.1063/5.0002389 (SOPPA) 5 has proven very useful, as it yields results in good agreement with experiment, while being computationally less demanding than the high-accuracy Coupled Cluster (CC) methods 6 . For larger systems of more than roughly 30 atoms or 800 basis functions, however, even SOPPA can be rather time consuming, wherefore cheaper, but also less reliable alternatives are available such as RPA 7,8 , RPA(D) [9][10][11] , HRPA 12 and HRPA(D) 9,10 . In addition to the abovementioned methods, a range of TDDFT methods are also available 13 .…”