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For the selection of these domains the usual natural orbital occupation number criterion is found to be insufficient, and an additional energy criterion is used. For extended one-dimensional systems, the computational effort of the method scales nearly linearly with the number of correlated electrons, but the linear scaling regime is usually not reached in real-life applications for three-dimensional systems.
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The convergence of the results with respect to the thresholds and options that control the domain, pair, and projection approximations is extensively tested. Benchmark examples for several difficult and large cases are presented, which demonstrate that the errors of relative energies e.
Global method for electron correlation
The remaining errors are mainly caused by the finite PAO domains. The larger these are made, the more intramolecular or intermolecular basis set superposition errors are introduced, and the canonical results are approached only very slowly.
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This problem is eliminated in the explicitly correlated variant of our method PNO-LCCSD-F12 , which will be described in a separate paper, along with a larger set of benchmark calculations. Create citation alert.
A more fundamental approach to correlation | RIKEN
Buy this article in print. A relatively simple approximate ab initio method for the evaluation of correlation effects on atomic energy differences is developed.
In this method, which is a modification of the semiempirical version of Sinanoglu's non-closed-shell many-electron theory NCMET , the all-external contributions to the correlation energies are evaluated by a scheme based on the knowledge of second-order pair energies calculated for approximate closed-shell atomic systems. The present method can be applied to a much larger set of atomic systems than the semiempirical NCMET.
To test the reliability of the present approach extensive calculations are performed for energy differences involving states of the 1s 2 2s m 2p n configurations for various atomic numbers. These calculations could be to a large extent based on previously published values of both the 'charge' contributions to the energies and the relevant pair energies. The results for i term splittings within a single configuration for neutral atoms as well as positive and negative ions, ii excitation energies, iii ionisation potentials and iv electron affinities prove that the present approach can be used for reliable predictions of atomic energy differences.
Since the method is non-relativistic, some attempts have been made to account for the relativistic corrections. In all cases considered the inclusion of these corrections has further improved the agreement with the experimental results.