Systematic construction of basis subsets of higher angular momentum functions in electron correlation energy calculations

Abstract

High-precision many-body perturbation theory calculations are reported for the ground state of the neon atom within the algebraic approximation, i.e. by using a finite basis set expansion. The second-order many-body perturbation theory correlation energy component is calculated using an even-tempered universal basis set sequence of Gaussian-type functions of increasing angular quantum number. The basis subsets for each symmetry are systematically truncated so as to attempt to maintain an accuracy of ~1 µHartree. The resulting energy components are compared with other recent results, including those obtained by employing correlation-consistent basis sets and the recent finite-element study by Flores and Kolb. A sub-µHartree level of accuracy was achieved for the E2( = 1) energy component.

Convergence of partial-wave expansions for energies, scattering amplitudes and positron annihilation rates

“…There are a number of basis sets that replace the continuum by a discrete set of states which is effectively complete. Some common examples are Laguerre, B-spline and Gaussian bases (see, e.g., Bray and Stelbovics 1992, Sapirstein and Johnson 1996, Moncrieff and Wilson 1999. However, there is still a question of convergence with respect to the angular momentum of the single-particle orbitals included.…”

Additivity of the Correlation Energy in Some 3D Organic Molecules

“…Thus the influence of the polarization functions was estimated in small molecules yielding the energy increments for characteristic bonds, which were subsequently transferred to larger molecules in order to obtain approximate estimates of the HF limits and MP2 energies. In the next paper Cremer , showed that it was possible to partition MP2 correlation energy in small molecules into contributions related to inner-core electrons, lone electron pairs, and coupled bond electrons. These contributions proved useful in estimating the unknown MP2 energies in large molecules and their enthalpies of formation.…”

New benchmarks for the second‐order correlation energies of Ne and Ar through the finite element MP2 method

“…This outcome could be due to the limitations of the Gaussian basis sets, and perhaps also to the difficulty of dealing with large STO basis sets in the MP2‐R12 method. Using large Gaussian basis sets in combination with the traditional MP2 method, as has been done by Moncrieff and Wilson 13 is not a very successful strategy for the purpose of μEh accuracy as it is acknowledged by those authors, due to the to the limitations of GTOs in the description of high PWs. However, we find it remarkable that their value is coincident with the FEM‐MP2 result up to 0.1 mE h without explicit correlations; the agreement is probably because of their careful angular extrapolation and selection of the basis set.…”

“…The development of more efficient explicitly correlated methods of the R12 1–7 or Gaussian geminal type (GG)8–12 and of more complete basis sets 13, 14 has created a demand for more accurate benchmarks of the correlation energies. For instance, quite recently Patowski et al 11 have computed the (second‐order Møller–Plesset) MP2 correlation energy of He with 10 significant digits using a 600‐term GG expansion and a 24‐term SCF orbital, improving the 7‐digits value of Bukowski et al 15 The MP2 correlation energy of Be has been computed with about five significant digits by Dahle et al 12 and by Bukowski et al 16.…”