G basis

The second approximation in HF calculations is due to the fact that the wave function must be described by some mathematical function, which is known exactly for only a few one-electron systems. The functions used most often are linear combinations of Gaussian-type orbitals exp(—nr ), abbreviated GTO. The wave function is formed from linear combinations of atomic orbitals or, stated more correctly, from linear combinations of basis functions. Because of this approximation, most HF calculations give a computed energy greater than the Hartree-Fock limit. The exact set of basis functions used is often specified by an abbreviation, such as STO—3G or 6—311++g. Basis sets are discussed further in Chapters 10 and 28. 

The proposed proeedure are detailed next eaeh SPMD was mierowave-assisted extraeted twiee with 30 mL hexane aeetone, and irradiated with 250 W power output, until 90°C in 10 minutes, being this temperature held for another 10 minutes. Clean-up of extraet was performed by aeetonitrile-hexane partitioning eoupled by a solid-phase extraetion with a eombined eartridge of 2 g basie-alumina (deaetivated with 5% water) and 0.5 g C. ... 

Benzene will dearly illustrate this effect. Compare the first six excited states, as predicted using the 6-31G and 6-31-t-G basis sets. When setting up the route section for these jobs, include the NSfate =8 option. Although we are only looking for six... 

The main difference between the G2 models is tlie way in which tlie electron correlation beyond MP2 is estimated. The G2 method itself performs a series of MP4 and QCISD(T) calculations, G2(MP2) only does a single QCISD(T) calculation with tlie 6-311G(d,p) basis, while G2(MP2, SVP) (SVP stands for Split Valence Polarization) reduces the basis set to only 6-31 G(d). An even more pruned version, G2(MP2,SV), uses the unpolarized 6-31 G basis for the QCISD(T) part, which increases the Mean Absolute Deviation (MAD) to 2.1 kcal/mol. That it is possible to achieve such good performance with tliis small a basis set for QCISD(T) partly reflects the importance of the large basis MP2 calculation and partly the absorption of errors in the empirical correction. 

The geometry optimizations for reactions 4 and 5 were primarily carried out with the 3-21+G basis set (23). This alternative typically gives results similar to 4-31+G, but it is... 

The MCSCF and the subsequent perturbation calculations were done using a 6-31+G basis set expanded by a set of spd Rydberg functions. Exponents of this additional gaussians were 0.032 and 0.028 for the s and p shells for the oxygen atom, and 0.023 and 0.021 for the carbon atom. For the d functions, a common value of 0.015 was chosen for both heavy atoms. 

The different struetures and transitions states of interest in the neutral and negative ion reaetions are represented in Fig. 2. A first approach was done at the SCF level, using the split-valence 4-3IG basis set. In order to provide a better estimation of the energy differences implied in this reaction schemes, extensive calculations have been performed at the MP2 level of theory using the 6-311++G basis set which contains the diffuse orbitals necessary to quantitatively describe the negative ions. 

Table 2 Comparison of G, GG, and GGG sequences Relative populations, cleavage yields, and reactivities on a per-sequence and per-G basis ... 

Our data provide a ratio of 1 0.2 0.1 for reactivity at G, GG, and GGG sites on a per-G basis. These relationships are summarized in Table 2. The small difference in G vs GG vs GGG hole stability and lower reactivity of the more stable sites is, of course, precisely the combination of stability and reactivity that is required for the observation of hole transport over long distances containing multiple G and GG sites. Hole transport between two GGG sites separated by a TTGTT sequence appears to be somewhat slower than cleavage at the initially oxidized GGG site [12]. To our knowledge, the efficiency of strand cleavage in duplexes possessing more than two GGG sites has not been studied. 

Similarly, the structure of 5-nitro-2,4-dihydro-377-l,2,4-triazol-3-one (NTO) 6 has been scrutinized using molecular orbital calculations using the 6-31+G and 6-311+G basis sets. These calculations examined the various tautomers of NTO and give an insight into the molecular mechanisms involved in its explosive decomposition <1996JA8048>. 

The structures of B -Bjj cations shown in Figure 29.1 were taken from the Ref. [7], in which they were considered as the most stable structures previously reported in the literature. They were reoptimized using hybrid density functional method known in the literature as B3LYP [67-69] with the 6-311 +G basis set [70-72] as implemented in Gaussian 03 program [73]. There is no guarantee that all the considered structures here are indeed global minimum structures. 

Both syn and anti methoxy adducts were considered (Figure 4). The 6-31+G basis set was employed to give a proper description of the anions by inclusion of diffuse functions. The corresponding AEr and AGr for these... 

PM3) were used to investigate solvent effects on the alkaline hydrolysis of (149) and in the second, the effect of an ancillary water molecule on the neutral and alkaline hydrolysis mechanisms of Al-methylazetidinone (149) was smdied at the Hartree-Fock and MP2 levels using the 6-3IG and 6-31 + G basis setsJ" ... 

Three-membered ring-forming processes involving X-CH2-CH2-F or CH2-C(Y)-CH2F (X = CH2, O, or S and Y = O or S) in the gas phase have been treated by the ab initio MO method with a 6-31+G basis set." When electron correlation effects were considered, the activation (AG ) and reaction (AG°) free energies were lowered by about lOkcal mol indicating the importance of electron correlation in these reactions. The contribution of entropy of activation -TAS ) at 298 K to AG is very small the reactions are enthalpy controlled. 

Ab initio methods using the 6-31 + G basis sets have been used in a theoretical study of competing, S n2 and El reactions of NCCH2CH2CI with HO and HS in the gas phase. The antiperiplanar elimination transition state, which is favoured over those for n2 and El(gauche) reactions, is more lcB-like than that for the slower El anti) reaction of ethyl chloride. 

Unimolecular pyrolysis of the tautomers of monothioformic acid (two conformers of thiol- and two conformers of thiono-) have been studied by ab initio methods with STO-3G and 6-31 G basis sets. The barrier heights for dehydrogenation (via a four-centre transition state) and dehydrogensulfldation (via a three-centre transition state) of thiol formic acid are 67.47 and 67.09 kcalmol" respectively. Dehydration of 5-cw-HCSOH occurs via a three-centre transition state with an activation energy of 81.18 kcalmoG this is much greater than for dehydration of the s-trans form, which occurs via a four-centre transition state with a barrier of only 68.83 kcalmol" ... 

The physical characteristics of individual particles also are of environmental significance. For example, the smaller particles (diameters on the order of 1 micrometer of less) generally are most important in that they have very long atmospheric residence times (18), are least effectively controlled by pollution control devices (19), are preferentially deposited in the pulmonary regions of the lung (20,21), and may be most enriched in toxic species on a specific concentration (iig/g) basis (22-24). 

In the early calculations of IR spectra of molecules, small basis sets (e.g., STO-3G, 3-21G, or 4-31G) were used because of limitations of computational power. At present typically a basis set consists of split valence functions (double zeta) with polarization functions placed on the heavy atoms (i.e., non-hydrogens) of the molecule (the so-called DZ+P or 6-31 G basis set). Such basis sets have been... 

Comparisons with experimental results show that vertical NOF-EAs are better than those predicted by the CCSD(T) method within the 6-31++G basis set. 

According to 6-31G calculations (90JA4155), the square geometry of the N4 fragment may be stabilized in the D4h structure of tetrazete dianion with two Li+ counteranions (246) that corresponds to a minimum on the PES. Also, the planar square 67r-electron structure corresponds to a minimum on the PES, as judged from ab initio calculations with the 6-31+G basis set (90JA4155). 

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