The 6-31G basis

The SCF, SCVB, full valence tv, and full valence tt + S results of using a 6-3IG basis on benzene are given in Table 15.6. The geometry used is that of the minimum SCF energy of the basis. In this case the SCVB energy is lower by 0.4 eV than the full valence it energy. This is principally due to the 3d polarization orbitals present in the SCVB orbital, but absent in the valence calculation. The SCVB orbital is 

Nevertheless, there is a diflhculty with the interpretation in the last paragraph. There has developed over the years a considerable literature on this question, with many opinions on both sides. Shaik etal. have written articles on this subject[62,63]. Sueh a situation frequently indicates the existence of ambiguities in the definition, and that eertainly applies to this case. We may describe the situation according to our current terms. 

The size of the ring is seen to be a compromise between attraction due to the 7t system and repulsion due to the core. Again, the sizes of the second derivatives add to give a stable minimum. If we assume that the system behaves harmonically, the derivatives in the last column imply that the ring C—C bond distances are about 0.0204 bohr (0.0108 A) longer than the value used for the first row of the table, which are the SCF minimum distances. 

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So far, the only polarized basis set we ve used is 6-31G(d). Its name indicates that it is the 6-31G basis set with d functions added to heavy atoms. This basis set is becoming very common for calculations involving up to medium-sized systems. This basis set is also known as 6-31G. Another popular polarized basis set is 6-31G(d,p), also known as 6-31G, which adds p functions to hydrogen atoms in addition to the d functions on heavy atoms. 

The values in red are within O.OlA of the experimental value. Using the 6-31G basis set, including diffuse functions on the hydrogen atom, improves the result over that obtained with diffuse functions only on the fluorine atom, although the best result with this basis set is obtained with no diffuse functions at all. 

Determine the effect of basis set on the predicted chemical shifts for benzene. Compute the NMR properties for both compounds at the B3LYP/6-31G(d) geometries we computed previously. Use the HF method for your NMR calculations, with whatever form(s) of the 6-31G basis set you deem appropriate. Compare your results to those of the HF/6-311+G(2d,p) job we ran in the earlier exercise. How does the basis set effect the accuracy of the computed chemical shift for benzene ... 

Note that functions 1 through 9 form the heart of the 6-31G basis set three sets of functions formed from six, three and one primitive gaussian. 

These calculations have been conducted on the basis of RHF optimized geometries, considering the 6-31G basis set for the n-alkane compounds (11), and the 6-31G basis set for the polyacene series (12). In both cases, the basis set contention has been checked by comparison with more thorough investigations on small compounds, such as ADC[3] calculations (11a) on n-butane based on the 6-31IG, 6-31G and 6-31G basis, or the MRSDCI ionization spectrum of ethylene as obtained by Murray and Davidson (33) using a 196-CGTO basis set. 

For most molecules studied, modest Hartree-Fock calculations yield remarkably accurate barriers that allow confident prediction of the lowest energy conformer in the S0 and D0 states. The simplest level of theory that predicts barriers in good agreement with experiment is HF/6-31G for the closed-shell S0 state (Hartree-Fock theory) and UHF/6-31G for the open-shell D0 state (unrestricted Hartree-Fock theory). The 6-31G basis set has double-zeta quality, with split valence plus d-type polarization on heavy atoms. This is quite modest by current standards. Nevertheless, such calculations reproduce experimental barrier heights within 10%. 

In order to gather more information about this problem, it was deemed worthwhile to follow the energetics of the alkylation reaction of water by methyl-, ethyl-, and fluo-roethyldiazonium ions. The main goal of these calculations was to establish whether transition-state calculations can provide information about hard versus soft electrophilic character of these species.12 Computations at Hartree-Fock and MP2 level were performed using the 6-31G basis set. It was found that both at the Hartree-Fock level and when correlation energy affects were included, the ethyl and fluoroethyl species do not show the presence of a transition state, while the methyl species show a small transition state. It was concluded that transition state computations cannot shed light on the characters of these species. 

Another study16 investigates the effect of benzene ring fusion on the reactivity of 1,2-Oxathietane. Ab initio calculations were performed using the 3-21G and the 6-31G basis sets, at Hartree-Fock and MP2 calculational levels. It was found that the allowed (8s + 2s) cycloreversion is unfavorable energetically. A subsequent experimental and theoretical study17 favors biradical intermediates in the valence tautomerism of benzoxathiete to monothio-o-benzoquinone. 

The basis set used for calculations were the STO-3G, the 3-21G, and the 6-31G basis sets, as implemented by the Gaussian-88 computer program. The energies of interaction were computed by using the supermolecule approach where the sum of the energies of the subsystems are substracted from the energy of the complex. All the species were geometry optimized. 

The molecules were subjected to complete geometry optimization via ab initio calculations, using the 6-31G basis set. The energies of the molecules, as well as the net atomic charges, were calculated. 

The Hartree-Fock calculations used the 6-31G basis set as implemented by the Gaussian-86 computer program.55 Protonated and unprotonated species were calculated and the proton affinities were obtained as the difference between the energy of the protonated species and the energy of the unprotonated ones. In addition, 6-31G calculations of the energy, using the 6-31G obtained geometry were performed. 

The possible mechanisms of inhibition of flavin by (—)-deprenyl, as an irreversible acetylenic inhibitor, were studied by ab initio methods with the 6-31G basis set using simplified model compounds, 3-formyl-2-imino-l-hydroxypyrazine, and propargylamine. The formation of two energetically stable cyclic adducts, the 0,N adduct 286 and a C,N adduct, was shown <1999THA147>. 

Restricted Hartree-Fock calculations of the suprafacial addition of ethylene to l,4-dithioniabicyclo[2.2.0]hexane with the 6-31G basis failed to locate the transition state for this process. Synchronous suprafacial addition should... 

As shown in Table 6, the addition of p-type polarization functions to hydrogen atoms in the 6-31G basis has little effect on the calculated data. 

O Ferrall-Jencks diagram and ab initio calculations with the 6-31G basis set. It is concluded that the transition state is slightly iilcB-like for (27) and more symmetrical for (28). 

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