Double Polarization Functions Research Articles

Accuracy of geometries: influence of basis set, exchange?correlation potential, inclusion of core electrons, and relativistic corrections

The geometries of a set of small molecules were optimized using eight different exchange–correlation (xc) potentials in a few different basis sets of Slater-type orbitals, ranging from a minimal basis (I) to a triple-zeta valence basis plus double polarization functions (VII). This enables a comparison of the accuracy of the xc potentials in a certain basis set, which can be related to the accuracies of wavefunction-based methods such as Hartree–Fock and coupled cluster. Four different checks are done on the accuracy by looking at the mean error, standard deviation, mean absolute error and maximum error. It is shown that the mean absolute error decreases with increasing basis set size, and reaches a basis set limit at basis VI. With this basis set, the mean absolute errors of the xc potentials are of the order of 0.7–1.3 pm. This is comparable to the accuracy obtained with CCSD and MP2/MP3 methods, but is still larger than the accuracy of the CCSD(T) method (0.2 pm). The best performing xc potentials are found to be Becke–Perdew, PBE and PW91, which perform as well as the hybrid B3LYP potential. In the second part of this paper, we report the optimization of the geometries of five metallocenes with the same potentials and basis sets, either in a nonrelativistic or a scalar relativistic calculation using the zeroth-order regular approximation approach. For the first-row transition-metal complexes, the relativistic corrections have a negligible effect on the optimized structures, but for ruthenocene they improve the optimized Ru–ring distance by some 1.4–2.2 pm. In the largest basis set used, the absolute mean error is again of the order of 1.0 pm. As the wavefunction-based methods either give a poor performance for metallocenes (Hartree–Fock, MP2), or the size of the system makes a treatment with accurate methods such as CCSD(T) in a reasonable basis set cumbersome, the good performance of density functional theory calculations for these molecules is very promising; even more so as density functional theory is an efficient method that can be used without problems on systems of this size, or larger.

Ethynylvinylidene

AbstractEthynylvinylidene, an energetically low‐lying isomer of diacetylene, has been studied using ab initio molecular electronic structure theory. Geometries of diacetylene, ethynylvinylidene, and the transition state between them have been optimized using the double‐ζ plus polarization (DZP) and triple‐ζ plus double polarization function (TZ2P) basis sets with the self‐consistent field (SCF), configuration interaction with single and double excitations (CISD), coupled cluster with single and double substitutions (CCSD), and CCSD with perturbatively included connected triple substitutions [CCSD(T)] methods. At the TZ2P CCSD(T) level of theory only single point energies have been determined at the TZ2P CCSD geometries. Harmonic vibrational frequencies and infrared (IR) intensities are reported for the three stationary points at the DZP SCF, TZ2P SCF, and DZP CISD levels of theory. For ethynylvinylidene, rotational constants, dipole moments, and dipole moment components along the principal axes are also given. This isomer is found to be an extremely shallow minimum on the C4H2 potential energy surface, and the classical barrier to rearrangement (to diacetylene) is vanishingly small at the highest level of theory.

Geometrical structures and vibrational frequencies of the energetically low-lying isomers of SiC3

The ground state of the SiC3 molecule is found to be a closed-shell cyclic C2v symmetry structure which can be described as a four-membered ring with a transannular (cross ring) carbon–carbon bond, r(C–C)=1.469 Å. Theoretical studies with a triple-zeta plus double-polarization function (TZ2P) basis set in conjunction with the configuration-interaction technique at the TZ2P self-consistent-field optimized geometries predict this rhomboidal structure to be 4.1 kcal/mol more stable than the linear triplet Si–C–C–C isomer. A second closed-shell rhomboidal C2v symmetry structure with carbon–silicon transannular bonding, r(Si–C)=1.880 Å, was located and characterized as a local minimum lying 4.3 kcal/mol above the ground-state rhomboidal structure at this level of theory. Higher-level theoretical methods, including contributions from triple excitations, with larger basis sets will be required to obtain a more definitive set of relative energies.