Optimized Structural Data at the Complete Basis Set Limit via Successive Quadratic Minimizations

Abstract

Two variants of a successive quadratic minimization method (SQM and c-SQM) are suggested to calculate the structural properties of molecular systems at the complete basis set (CBS) limit. When applied to H3 +, H2O, CH2O, SH2, and SO2, they revealed CBS/(x 1, x 2) structural parameters that significantly surpass the raw ones calculated at the x 2 basis set level. Such a performance has also been verified for the intricate case of the water dimer. Because the c-SQM method is system specific, thus showing somewhat enhanced results relative to the general SQM protocol, it can be of higher cost depending on the level of calibration used. Yet, it hardly surpasses the general quality of the results obtained with the cost-effective SQM method. Since the number of cycles required to reach convergence is relatively small, both schemes are simple to use and easily adaptable to any of the existing extrapolation schemes for the Hartree–Fock and correlation energies.

Cn, CnH and their anions: Quest for linearity with n≤8 even versus odd, and beyond

“…For comparison, calculations are additionally performed with the exact FCI method but employing the subminimal Huzinaga's MINI [74] and STO‐3G [75] basis sets. Although optimization at CBS level is possible [76], or even CBS extrapolation of the calculated energies [46, 47, 77, 78] to get values close to the best one can afford, this is deemed beyond the goal of the present work and hence not pursued. The levels of theory here employed are therefore deemed enough to explain linearity () versus nonlinearity () for the parent molecules.…”

Basis Set Extrapolation of Vibrational Frequencies

“…Equations 3 and 4 provide a recipe for estimating the basis set limiting energy at a given geometry and, by differentiation, also the corresponding gradient and Hessian. For methods where analytical gradients, and preferable also analytical Hessians, are available, it is thus possible to assess the change in geometry upon basis set extrapolation by an optimization on the extrapolated energy surface 17 and calculate the frequencies based on the extrapolated Hessian at the optimized geometry. This is necessarily an iterative procedure and thus requires a number of calculations with two different basis sets, but the geometry dependence of the Hessian is then included explicitly; this approach will be labeled Opt-xpol.…”

“…11−15 For the present purpose, we note that Hessian elements similarly can be extrapolated by eqs 3 and 4. Many molecular properties can be considered as derivatives of the energy with respect to, e.g., electric, magnetic, and geometric perturbations 16 and are expected to display a similar behavior as the energy, 17 although special tailored basis sets may be required for specific properties in order to achieve a stable convergence. 5,18 Some properties, like nuclear magnetic spin−spin coupling constants, have contributions from four different perturbation operators, and it is here less clear that extrapolations using eqs 3 or 4 are valid.…”

“…Properties based directly on the energy, as for example energy gradients with respect to atomic positions, are unproblematic, as eqs and imply that gradients can be extrapolated by the same formulas as for the energy. − For the present purpose, we note that Hessian elements similarly can be extrapolated by eqs and . Many molecular properties can be considered as derivatives of the energy with respect to, e.g., electric, magnetic, and geometric perturbations and are expected to display a similar behavior as the energy, although special tailored basis sets may be required for specific properties in order to achieve a stable convergence. , Some properties, like nuclear magnetic spin–spin coupling constants, have contributions from four different perturbation operators, and it is here less clear that extrapolations using eqs or are valid. , Nevertheless, basis set extrapolations have been used also for molecular properties. ,, …”