Basis-set dependency

Since taking simply ionic or van der Waals radii is too crude an approximation, one often rises basis-set-dependent ab initio atomic radii and constnicts the cavity from a set of intersecting spheres centred on the atoms [18, 19], An alternative approach, which is comparatively easy to implement, consists of rising an electrical eqnipotential surface to define the solnte-solvent interface shape [20],... 

The Lowdin population analysis scheme was created to circumvent some of the unreasonable orbital populations predicted by the Mulliken scheme, which it does. It is different in that the atomic orbitals are first transformed into an orthogonal set, and the molecular orbital coefficients are transformed to give the representation of the wave function in this new basis. This is less often used since it requires more computational work to complete the orthogonalization and has been incorporated into fewer software packages. The results are still basis-set-dependent. 

This results in a population analysis scheme that is less basis set dependent than the Mulliken scheme. Flowever, basis set effects are still readily apparent. This is also a popular technique because it is available in many software packages and researchers find it convenient to use a method that classifies the type of orbital. 

A much less basis set dependent method is to analyze the total electron density. This is called the atoms in molecules (AIM) method. It is designed to examine the small effects due to bonding in the primarily featureless electron density. This is done by examining the gradient and Laplacian of electron density. AIM analysis incorporates a number of graphic analysis techniques as well as population analysis. The population analysis will be discussed here and the graphic techniques in the next chapter. 

Basis set dependence is important. The results in Table 16.1 were obtained for HF-LCAO calculations on pyridine. In each case, the geometry was optimized As a general rule, ab initio HF-LCAO calculations with small basis sets tend to underestimate the dipole moment, whilst extended basis sets overestimate it A treatment of electron correlation usually brings better agreement with experiment. 

This will again be basis set dependent, but not nearly as sensitive as atomic charges. 

Table 8-1. Basis set dependence of SVWN-optimized C-C/C-H bond lengths [A].

Table 13-3. Basis set dependence of activation (AEa) and reaction energies (AEr) computed using the B3LYP functional for the concerted gas-phase cycloaddition of ethylene to trans-butadiene [kcal/mol]. All calculations include zero-point vibrational contributions evaluated at the B3LYP/6-311+G(d,p) level.

Hertwig, R. H., Koch, W., 1995, On the Accuracy of Density Functionals and Their Basis Set Dependence An Extensive Study on the Main Group Element Homonuclear Diatomic Molecules Li2 to Br2 , J. Comput. Chem, 16, 576. 

Scheiner, A. C., Baker, J., Andzelm, J. W., 1997, Molecular Energies and Properties from Density Functional Theory Exploring Basis Set Dependence of Kohn-Sham Equation Using Several Density Functionals , J. Comput. 

H20, CH3OH-. . H20, CN-. . HzO, HCC-. . H20, HCOCT. . H20. The DFT(B3LYP) and the DFT(BLYP) results were in a fair agreement with the MP2 results. The root mean square deviation of the DFT and the MP2 complexation enthalpies amounted to 0.7 and 1.1 kcal/mol, for B3LYP and BLYP, respectively. From the basis set dependence of the DFT results, it was concluded that the nonlocal DFT calculations require diffuse atomic functions. 

One way of getting rid of distortions and basis set dependence could be that one switches to the formalism developed by Bader [12] according to which the three-dimensional physical space can be partitioned into domains belonging to individual atoms (called atomic basins). In the definition of bond order and valence indices according to this scheme, the summation over atomic orbitals will be replaced by integration over atomic domains [13]. This topological scheme can be called physical space analysis. Table 22.3 shows some examples of bond order indices obtained with this method. Experience shows that the bond order indices obtained via Hilbert space and physical space analysis are reasonably close, and also that the basis set dependence is not removed by the physical space analysis. 

Table 1.5 The basis-set dependence of the AE of the CO molecule (kJ/mol). The calculations have been carried out at the all-electron CCSD(T) level at the geometry optimized in the cc-pCVQZ basis [25],...

The basis-set dependence and correlation correction for the -values were first studied by using the idealized face-to-face interaction between two methyl radicals. The interaction was found to be always antiferromagnetic, and the APUMP2 4-3IG procedure was found to be best for semiquanti-tative evaluation the APUHF STO-3G method was still acceptable for qualitative discussion of larger systems (Yamaguchi et al., 1989a). 

The relative energies apparently exhibit a rather weak basis set dependence the equilibrium between the N- and p-protonated forms is driven by electron correlation, while the ortho-para equilibrium is apparently quite well reproduced even at the HartreeFock level. We may safely argue that the Wlc results are converged with respect to the basis set. 

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