Basis set complete , limit

The CBS models use the known asymptotic convergence of pair natural orbital expansions to extrapolate from calculations using a finite basis set to the estimated complete basis set limit. See Appendix A for more details on this technique. 

The filled and hollow circles indicate the contributions of each successive natural orbital. The filled circles correspond to complete shells. Only these points are useful for extrapolating to the complete basis set limit. 

First consider the dipole operator (O = r). The matrix elements on rhs of eq. 17 are thus just the dipole transition moments, and the commutator becomes C = -ip. As the exact solution (complete basis set limit) to the RPA is under consideration, we may use eq. 10 to obtain... 

Dickson and Becke, 1996, use a basis set free numerical approach for obtaining their LDA dipole moments, which defines the complete basis set limit. In all other investigations basis sets of at least polarized triple-zeta quality were employed. Some of these basis sets have been designed explicitly for electric field response properties, albeit in the wave function domain. In this category belong the POL basis sets designed by Sadlej and used by many authors as well as basis sets augmented by field-induced polarization (FTP) func-... 

C-H and N-H bond dissociation energies (BDEs) of various five- and six-membered ring aromatic compounds (including 1,2,5-oxadiazole) were calculated using composite ab initio CBS-Q, G3, and G3B3 methods. It was found that all these composite ab initio methods provided very similar BDEs, despite the fact that different geometries and different procedures in the extrapolation to complete incorporation of electron correlation and complete basis set limit were used. A good quantitive structure-activity relationship (QSAR) model for the C-H BDEs of aromatic compounds... 

The slow convergence of the correlation energy with the one-electron basis set expansion has provided the motivation for several attempts to extrapolate to the complete basis set limit [6-13], Such extrapolations require a well defined sequence of basis sets and a model for the convergence of the resulting sequence of approximations to the... 

The main feature of the CBS (complete basis set) methods (e.g. CBS-Q [15] and CBS-QB3 [20]) is extrapolation to the complete basis set limit at the UMP2 level. Additional calculations [UMP4 and UQ-CISD(T) or UCCSD(T)] are performed to estimate higher-order effects. A scaled ZPVE, together with a size-consistent empirical correction and a spin-contamination correction, are added to yield the total CBS energy of the molecule. 

Equations (13) and (15) reduce to the usual MP2 correlation energy expression by substituting t — 0 and, therefore, MP2 and MP2-R12 as defined above converge to the same complete-basis-set limit, however, at vastly different rates. These... 

Because of the studies of the basis set dependence of DFT rotational strengths, the errors of many basis sets are well defined. As discussed above, TZ2P and larger basis sets (e.g. cc-pVTZ) are very good approximations to the complete basis set limit. For these basis sets, errors are negligible. Of course, for much smaller basis sets, such as 6-31G, the opposite is true. 

As already mentioned, the MOs in Eqs. (10a) and (10b) are assumed to be exact, i.e., represented at the complete basis set limit. In practice, the Kohn-Sham equations are converted into the respective self-consistent-field matrix equations in the basis, and the perturbation treatment is carried out from there. Any dependence of the basis set (GIAOs) on the perturbation (Bext in the case of shielding tensors) is in this way naturally covered. 

P. Jurecka, J. Sponer, J. Cerny, P. Hobza, Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs. Phys. Chem. Chem. Phys. 8, 1985-1993 (2006)... 

In addition to the Gaussian-n methods, there is a variety of CBS (complete basis set) methods, including CBS-Q, CBS-q, and CBS-4, which have also enjoyed some popularity among computational chemists. In these methods, special procedures are designed to estimate the complete-basis-set limit energy by extrapolation. Similar to the Gn methods, single-point calculations are also... 

The problem disappears in the complete basis set limit. Also, it does not exist for origin-less basis set, such as plane waves. For this reason the plane wave based methods are attractive for molecular dynamics simulations where the energy derivative must be evaluated many times. 

Hypoiodous acid and iodine nitrate have been investigated with coupled cluster theory and the results extrapolated to the complete basis set limit. Together with revised thermochemistry for several ancillary molecules, the enthalpy changes of working reactions yields new thermochemistry for HOI and IONO2. The latter data, employed in unimolecular rate theory, appear to be consistent with kinetic measurements on the lO -l- NO2 reaction to within the uncertainties of the kinetic analysis. 

It has been pointed out by Dunning [66] that "It is quite possible and even probably that the binding energies computed without the counterpoise correction are closer to the complete basis set limit than the uncorrected values. This situation is due to the fact that BSSE and basis set convergence error are often of opposite sign". Since it cannot be established a priori if that is the case, we have modeled the closest system to our reactant complexes with known experimental binding energy the water dimer. The experimental value for the electronic... 

Sherrill, C. D. Takatani, T. Hohenstein, E. G. An assessment of theoretical methods for nonbonded interactions comparison to complete basis set limit coupled-clusta-potential enragy curves for the benzene dimer, the methane dimer, benzene—methane, and benzene—H2S, / Phys. Chem. A 2009,113,10146-10159. 

Extrapolated to the complete basis set limit and corrected for CCSD(T). 

Morgado, C. A. Jurecka, R Svozil, D. Hobza, R Sponer, J. 1. Balance of attraction and repulsion in nucleic-acid base stacking CCSD(T)/complete-basis-set-limit calculations on uracil dimer and a comparison with the force-field description, J. Chem. Theor. Comput. 2009, 5, 1524-1544. 

Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs ... 

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