Basis sets 6-311+G

Slightly better results have been obtained, however, with the recently developed mPW and PBE functionals as can be seen from the data compiled in Table 13-5. The improvements do not exceed 2 kcal/mol though. It is interesting to note that the application of smaller (6-31+G(d)) or larger basis sets (6-311++G(3df,3pd)) does not change the picture much, in contrast to the strong influence of the basis set quality we have noted before. 

Ab-initio (nonempirical, from first principles ) methods also use the HF-SCF model but includes all electrons and uses minimal approximation. Basis sets of functions based on linear combinations of atomic orbitals (LCAO) increase in complexity from the simplest (STO-3G) to more complex (3-21G( )) to extended basis sets (6-311 + G ) for the most accurate (and most time-consuming) results. Treat systems up to 50 atoms. 

From the data provided by the systematic experimental study at standardized conditions the free energy of activation (AG exp.) was calculated from the experimental rate constant and compared to calculated AG values. Two different basis sets have been employed in the DFT calculations the split valence double- (DZ) basis set 6-31G(d) with a triple- (TZ) [44, 45] valence basis set for manganese (we will refer to this combination as basis set I (BS1)) and the triple- basis set 6-311+G(d,p), which will be denoted basis set n (BS2). The BSl-results for transition states and intermediates are shown in Table 5, a comparison of the free activation energies is shown in Figure 8 [46],... 

The interaction energy and its many-body partition for Bejv and Lii r N = 2 to 4) were calculated in by the SCF method and by the M/ller-Plesset perturbation theory up to the fourth order (MP4), in the frozen core approximation. The calculations were carried out using the triply split valence basis set [6-311+G(3df)]. 

An HF single-point calculation with a very big basis set (6-311+G(3d2f,2df,p) or 6-311+G(3d2f,2df,2p), depending on the particular CBS method)... 

For all three molecules in Table 3, the optimized bond lengths obtained using the extended basis set 6-311+G(3df,2p), labeled EBS for short, yields curiously short bond lengths in comparison with other basis sets but especially in comparison with experimental. It appears that in these and some other molecules below employing such larger basis sets may not provide one... 

Mg , and Ca (n =2, 3) clusters at the Mpller-Plesset electron correlation level (MP4) and the SCF level, using a reasonably large basis set [6-311 + G(3df)]. The 2-and 3-body decompositions of the interaction energy at the MP4 and SCF levels, the NBO population analysis and the electron density difference maps allow to elucidate the nature of bonding in alkaline-earth clusters 2001 by Academic Press. 

Our analysis is based on accurate calculations performed in Ref. [22] at the Moller-Plesset electron correlation level of the interaction energy and its many-body decomposition for Be , Mgn, and Ca (n= 2 and 3) clusters using a reasonably large basis set [6-311 + G (3df)]. All calculations were also carried out at the SCF level which allowed to study separately the SCF and electron correlation contributions and give a physical analysis of each term in the dimer and trimer energy decompositions. 

One question which has not yet been satisfactorily resolved is the ground state of the C4 molecule. The two candidates are a singlet rhombus structure and a triplet linear form. Table 10 presents relative energies of these two isomers [80], calculated by conventional ab initio and DFT methods using a large orbital basis set, 6-311+G(2df). 

In our recent work [89], the reaction of HO2 with CIO has been investigated by ab initio molecular orbital and variational transition state theory calculations. The geometric parameters of the reaction system HO2 + CIO were optimized at the B3LYP and BH HLYP levels of theory with the basis set, 6-311+G(3df,2p), which can be found in Ref. [89]. Both singlet and triplet potential energy surfaces were predicted by the G2M method, as shown in Fig. 24. 

As an application we calculated electronegativity and hardness values. For a series of 22 atoms, including cations, we obtained the following average deviations (in eV) from the "experimental" values, estimated via (11), using a large Pople type basis set (6-311++G(3df,2p) [34]... 

The polarizability of 142 molecules from the extended G2 set have been calculated using the unscreened—or uncoupled—SOS and FF approaches in combination with the HF, B3LYP, and PBE levels of approximation." The calculations, employing the same basis set [6-311+ +G(d,p)] and the same B3LYP/6-31 lG(d,p) optimized geometries have shown that, at the HF level, the SOS polarizabilities are almost always systematically underestimated with respect to the FF values whereas the opposite is found using PBE and B3LYP methods. 

Table 4 Electron Correlation Effect on Barrier Height (cm" ). Fully Relaxed Rotation. Basis Set 6-311 G(3df,2p). Geometry Optimization MP2 ...

Note that the basis sets including hydrogen-like orbitals perform better than the STO basis sets that in turn improve upon dense-core Gaussian basis sets [6-311++G(2d,p)l. 

Note that this value (calculated at with the standard TZV(2d,f) basis set of the computer program GAMESS) is suddenly much smaller than the value of 2.3 in the main text, obtained with a triple-zeta basis set (6-311++G(2d,2p) with CISD/6-311++G(2d,2p) optimised geometries)... 

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