Balanced basis sets

Except for very small systems it is impractical to saturate the basis set so that the absolute error in the energy is reduced below chemical accuracy, for example 1 kcal/ mol. The important point in choosing a balanced basis set is to keep the error as constant... 

Instead of a two-component equation as in the non-relativistic case, for fully relativistic calculations one has to solve a four-component equation. Conceptually, fully relativistic calculations are no more complicated than non-relativistic calculations, hut they are computationally demanding, in particular, for correlated molecular relativistic calculations. Unless taken care of at the outset, spurious solutions can occur in variational four-component relativistic calculations. In practice, this problem is handled by employing kinetically balanced basis sets. The kinetic balance relation is... 

With respect to accuracy, it is again important to employ basis sets including diffuse functions when anions are present as either reactants or products. With large well balanced basis sets, B3LYP for gas-phase energetics, and a PB SCRF solvation model, Baik and... 

There has been renewed interest in recent years in the calculation of Compton profiles and momentum expectation values. Much of the earlier work involved the use of SCF wave functions, but the results obtained using large-scale Cl wave functions have recently been published.38 It was concluded, however, that it is not necessary to go beyond the near-HF wave function in order to compute reasonable profiles, providing large, well balanced basis sets are used, a conclusion also reached by Tanner and Epstein.39... 

It is also known that geometry optimizations with too small basis sets may lead to non-realistic geometries especially if torsion angles or pyramidal structures are concerned 122>. In any case well-balanced basis sets are absolutely necessary, i.e. the quality of the basis set should be similar for all atoms. A carefully selected small GTO basis set may give reliable results for the ion-ligand interaction energies 31.125-i26> However, error compensations are at least partly responsible for this success. Therefore an improvement of the basis set may lead to less accurate results 91 >. Non-balanced small basis sets lead to large basis set superposition errors 126 l28>. This error is caused by the fact that in the calculations of the complex the wave functions... 

Weigend, R Ahhichs, R. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn design and assessment of accuracy, Phys. Chem. Chem. Phys. 2005, 7, 3297-3305. 

Balance among different basis sets is as important in the divide-and-conquer method as the basis set balance in the conventional ab initio calculations. Unbalanced basis sets will lead to nonphysical charge shifts. Take N2 molecule as an example. Putting more basis functions on one N atom than on the other will result in a nonzero dipole in this molecule. This artifact exists in both the divide-and-conquer method and the conventional methods. The experiences of balancing basis set from conventional methods can be used directly in the divide-and-conquer calculations. 

An important point put forward by the study of ammonia is the choice of a well-balanced basis set. For the calculation of effects such as barriers it is important to use a basis as saturated" as possible — or, if this cannot be achieved, at least equally well adapted to the different conformations to be considered. This requirement may be a cause of trouble, especially if the different geometrical configurations belong to different symmetry point groups. By symmetry reasons, the mixing of some atomic orbitals in a given molecular orbital may be forbidden for certain conformations and not for others. 

Other charge distributions, e.g., a finite hard sphere or a Fermi-type nuclear model, are also used. The coupling of the upper and lower components of the wavefunction via 5,p,- requires either kinetically balanced basis sets or the imposal of appropriate boundary conditions in order to avoid the so-called finite basis set disease. 

The hydrogen fluoride riddle was solved and the era of molecular Hartree-Fock computations was open. The need to have adequately large, polarized and balanced basis sets, is tantamount to require near to Hartree-Fock basis sets. The work was quickly written, submitted and printed [33] it was the first Hartree-Fock type computation for a many electron molecule with the clear message not to waste computer time and human effort with minimal basis sets. Well,... this was a rather strong message Indeed, minimal basis sets computations littered (embellished ) the computational chemistry literature for decades to follow, with the more or less acceptable excuse that computer time can be too expensive or not available. 

Fock limit. These bond angles are not particularly good at the double zeta (4-31G) level, and it appears that d-type functions in the basis set are necessary for a quantitative description of the angle in these molecules. If the limit is taken of adding only s- and p-type functions to a basis set for NH3, the predicted geometry becomes planar This illustrates the necessity of a balanced basis set. 

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