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# Explicitly correlated local coupled‐cluster methods using pair natural orbitals

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Recently developed explicitly correlated local coupled‐cluster methods [PNO‐LCCSD(T)‐F12] are reviewed. Extensive benchmarks for reaction energies and intermolecular interaction energies are presented, in which the convergence of the results with respect to all local approximations is studied. The explicit correlation treatment (F12) is shown to be essential to minimize basis set incompleteness errors, as well as errors caused by domain approximations. Generally, the errors of relative energies due to local approximations can be reduced to below 1 kcal/mol. The methods are well parallelized, and using small computer clusters with 100–200 computing cores, calculations for systems with 100–200 atoms using augmented triple‐ζ basis sets can be carried out within a few hours of elapsed time. Recommendations are made on how such calculations should be carried out, how the accuracy can be tested, and which computational resources are required. This article is categorized under: Electronic Structure Theory> Ab Initio Electronic Structure Methods Software> Quantum Chemistry
Speedup for the PNO‐LCCSD(T)‐F12 calculation of the Auamin molecule relative to 60 CPU cores on three nodes. The cc‐pVTZ‐F12 basis set and default parameters were used
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PNO‐LMP2 and PNO‐LMP2‐F12 interaction energies of the stacked benzene dimer as a function of IEXT (left panel, REXT = (2 × IEXT + 1) a0 implied) and (right panel). Pair approximations and domain approximations other than the PAO truncation (left panel) or the PNO truncation (right panel) were not applied in these calculations
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(T) Contribution to the reaction energy of the Isomer4 reaction as the function of TNO thresholds. The black line shows the (T0) contribution as a function of , and the red line shows the (T) contribution as a function of while keeping = 10−9
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PNO‐LCCSD‐F12 reaction energies of the Isomer4 reaction as a function of the threshold Tcutpairs. Pairs with LMP2 energies below this threshold are either neglected or approximated by LMP2‐F12, SCS‐LMP2‐F12, or by our close and weak pair approximations. In the latter case, Tclose = Tcutpairs, Tweak = Tclose/10. Domain corrections and the contributions from distant or very distant pairs are not included
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LMP2 pair energies of the Isomer4 reactant as a function of the orbital distance Rij. The red line corresponds to R−6 decay. Each point corresponds to one pair ij
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Reaction energy as a function of the PNO domain threshold for the Auamin reaction using the cc‐pVTZ‐F12 basis set. The solid lines represent the results after the MP2(‐F12) domain correction (using  = 10−9 and  = 0.997), and the dashed lines represent the uncorrected coupled‐cluster results
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Reaction energies of the Isomer4 reaction as a function of IEXT. The cc‐pVTZ‐F12 basis set and default settings for other parameters were used
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Benchmark systems for testing the PNO‐LCCSD(T)‐F12 method
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Number of PNOs per pair as a function of the orbital distance Rij for the Isomer4 reactant (c.f. Figure ) using the cc‐pVTZ‐F12 basis set. Each point corresponds to one pair ij
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