TURBOMOLE manual
v8.0

13.5 Further Recommendations

  • The direct RPA correlation energy is defined in a Kohn-Sham context without inclusion of exchange integrals and therefore the use of self-consistent KS orbitals obtained from (semi-)local functionals is recommended. HF-orbitals or KS-orbitals obtained form hybrid functionals may lead to inferior results. In case of \(\sigma\)-functionals, hybrid functionals lead to improvements, especially for main group compounds.

  • Experience has demonstrated that the difference in RPA correlation energies obtained from different (semi-)local functionals is very small (much smaller than the inherent error of the method).

  • Like MP2, RIRPA results are known to converge very slowly with increasing basis set size, in particular slowly with increasing \(l\)-quantum number of the basis set. For reliable results the use of QZVP basis sets (or higher) is recommended. For non-covalently bound systems larger basis sets (especially, with more diffuse functions) are needed.

  • It is recommended to exclude all non-valence orbitals from RIRPA calculations, as neither the TURBOMOLE standard basis sets SVP, TZVPP, and QZVPP nor the cc-pVXZ basis set families (with X=D,T,Q,5,6) are designed for correlation treatment of inner shells (for this purpose polarisation functions for the inner shells are needed). The default selection for frozen core orbitals in Define (orbitals below -3  a.u. are frozen) provides a reasonable guess. If core orbitals are included in the correlation treatment, it is recommended to use basis sets with additional tight correlation functions as e.g. the cc-pwCVXZ and cc-pCVXZ basis set families.

  • We recommend the use of auxiliary basis sets optimized for the corresponding (MO) basis sets. The auxiliary basis sets optimized for RI-MP2 and RI-CC2 are suitable for rirpa [298] correlation energy calculations.

  • Within the two-component relativistic implementation, RIRPA total energies (HF@KS + correlation) must be computed in two steps. RIRPA correlation energies can be obtained using the nohxx option, and the HF energy can then be computed separately, e.g., in ridft if the RI-J approximation is used for the Coulomb integrals. To compute the HF@KS energy, compute the KS orbitals first; then disable $dft and set $scfiterlimit 1 in the control file to perform a single SCF iteration. Finally add the total HF@KS energy from ridft to the correlation energy from the nohxx-rirpa calculation to obtain the total RIRPA energy. Note: the molecular orbitals are altered by ridft after a single-iteration, so the HF@KS energy must be computed after the RIRPA correlation energy.

  • Tight SCF ($scfconv 7) and one-electron density matrix ($denconv 1d-6) convergence criteria, large basis sets (QZVP), and large frequency grids which ensure a sensitivity measure of no more than 1d-4 should be used in combination with rpagrad for accurate results.

  • Using the frozen core approximation reduces the number of grid points required to achieve a small (\(<\) 1d-4) sensitivity measure for both the energy and gradient calculation within RIRPA.