Systematically Convergent Correlation Consistent Basis Sets for Molecular Core−Valence Correlation Effects:  The Third-Row Atoms Gallium through Krypton

Abstract

The family of correlation consistent polarized valence basis sets has been extended in order to account for core-core and core-valence correlation effects within the third-row, main group atoms gallium through krypton. Construction of the basis sets is similar to that of the atoms boron through argon, where either the difference between core-correlated and valence-only correlation energies were calculated via configuration interaction (CISD) computations on the ground electronic states of the atoms (named cc-pCVnZ) or the sets were optimized with respect to the core-valence correlation energy and a small weight of core-core correlation energy (cc-pwCVnZ). Due to the correlation of 3d orbitals, added shells of higher angular momentum exponents compared to the valence sets are necessary to describe the core region. The pattern of added core-correlating functions is (1s1p1d1f) for double-zeta, (2s2p2d2f1g) for triple-zeta, (3s3p3d3f2g1h) for quadruple-zeta, and (4s4p4d4f3g2h1i) for quintuple-zeta. Atomic and molecular results show good convergence to the CBS limit, with the cc-pwCVnZ sets showing improved convergence compared to the cc-pCVnZ ones for molecular core-valence correlation effects. After testing the basis sets on the homonuclear diatomics Ga2-Kr2 with coupled cluster wave functions, it is concluded that a treatment of core-valence correlation effects is essential for high-accuracy ab initio investigations of third-row-containing molecules. Though the basis sets are optimal for 3s3p3d correlation, preliminary atomic and molecular results show the basis sets to be efficient with respect to 3d-only correlation, and these potentially could be used with 3d-only correlation for more qualitative studies on larger species.

Gaussian basis sets for molecular applications

“…For high-accuracy studies, it is frequently important to correlate at least an additional shell of core electrons, which requires a number of tight functions optimized for this purpose. There are two established approaches for optimizing such exponents; in the cc-pCVnZ basis sets, the exponents are optimized based on the difference between valence-only and core and valence correlation energies, [48][49][50][51] whereas in the ccpwCVnZ bases, the core-valence contribution to the correlation energy is strongly weighted over the core-core (hence the w in the basis set abbreviation). [49,50] Typically, the cc-pwCVnZ sets produce better results for small zeta, with the results from both approaches converging rapidly for larger basis sets.…”

The hyperfine structure in the rotational spectra of bromofluoromethane: Lamb-dip technique and quantum-chemical calculations

“…More precisely, the CC singles and doubles (CCSD) approximation augmented by a perturbative treatment of triple excitations (CCSD(T)) [35] has been used. The core-valence correlation consistent cc-pCVnZ bases [36,37], with n=T,Q, have been employed, and all electrons have been considered in the electron-correlation treatment. To be more specific, the CCSD(T)/cc-pCVQZ level of theory has been employed in all electric-field gradient computations, whereas the CCSD(T)/ccpCVTZ level has been adopted in the calculations of the spin-rotation interaction constants.…”

Correlation consistent basis sets for explicitly correlated wavefunctions: Pseudopotential-based basis sets for the post-d main group elements Ga–Rn

“…These sets are derived from the standard augcc-pVnZ-PP and aug-cc-pwCVnZ-PP sets, [18][19][20][21] which were constructed for use with small-core relativistic pseudopotentials of the Stuttgart-Cologne variety, 19,20,22,23 and also complement the standard all-electron correlation consistent basis sets, valence and core-valence, for these elements. [24][25][26] To accompany the new orbital basis sets of this work, new auxiliary basis sets have also been determined that are needed for density fitting of the standard 2-electron integrals (MP2FIT), as well as for the resolution of the identity of the many-electron F12 integrals (OPTRI). Preliminary versions of these sets have already been used in extensive coupled cluster benchmark calculations of several diatomic molecules containing the post-3d elements Ga-Kr, where they exhibited excellent convergence behavior to the basis set limit compared to standard basis sets in conventional calculations.…”