Contracted primitives

In a general contraction primitives (on a given atom) and of a given angular momentum enter all the contracted functions having that angular momentum, but with different contraction coefficients. 

The data in Figure 4.22 represent the best results for the choice that the Slater 2s exponent be varied to minimize the energy of the 2s orbital. This choice was made because, as you will find, in all the calculations possible on this spreadsheet, the main defect is the modelling of the 2s orbital, even with the best choice of Slater exponent. For the choice of best Slater 2s exponent the calculated 2s orbital energy in the basis of six contracted primitives is returned as —0.1234611 Hartree, which is some 4 kJ/mole in error from the exact value of —0.1250 Hartree. 

In Table 3, a detailed analysis of the orbital expansion coefficients is reported for the subset containing functions of x-type centred on the F nucleus. Again the functions retained in the truncated subsets are indicated by the dots. The numbers of functions in each of the subsets for Too, 6, T5, T4 and T3 are 30, 26, 24, 20 and 17. In each of the truncated sets there are more functions surviving the condition (5) than in the corresponding sets centred on the B nucleus. This reflects the higher nuclear charge in F which necessitates the retention of more contracted primitive functions. 

Contracted Primitive Contracted Primitive Contracted Primitive... 

Name Contracted primitives Functions Elements Average errors in geometries and other properties" ... 

In the 6-3IG basis, the inner shell of carbon is represented by 6 primitives and the 4 valence shell orbitals are represented by 2 contracted orbitals each consisting of 4 primitives, 3 contracted and 1 uncontracted (hence the designation 6-31). That gives... 

Another family of basis sets, commonly referred to as the Pople basis sets, are indicated by the notation 6—31G. This notation means that each core orbital is described by a single contraction of six GTO primitives and each valence shell orbital is described by two contractions, one with three primitives and the other with one primitive. These basis sets are very popular, particularly for organic molecules. Other Pople basis sets in this set are 3—21G, 4—31G, 4—22G, 6-21G, 6-31IG, and 7-41G. 

Many basis sets are just identihed by the author s surname and the number of primitive functions. Some examples of this are the Huzinaga, Dunning, and Duijneveldt basis sets. For example, D95 and D95V are basis sets created by Dunning with nine s primitives and hve p primitives. The V implies one particular contraction scheme for the valence orbitals. Another example would be a basis set listed as Duijneveldt 13s8p . 

In order to describe the number of primitives and contractions more directly, the notation (6s,5p) (ls,3p) or (6s,5p)/(ls,3p) is sometimes used. This example indicates that six s primitives and hve p primitives are contracted into one s contraction and three p contractions. Thus, this might be a description of the 6—311G basis set. However, this notation is not precise enough to tell whether the three p contractions consist of three, one, and one primitives or two, two, and one primitives. The notation (6,311) or (6,221) is used to distinguish these cases. Some authors use round parentheses ( ) to denote the number of primitives and square brackets [ ] to denote the number of contractions. 

This section gives a listing of some basis sets and some notes on when each is used. The number of primitives is listed as a simplistic measure of basis set accuracy (bigger is always slower and usually more accurate). The contraction scheme is also important since it determines the basis set flexibility. Even two basis sets with the same number of primitives and the same contraction scheme are not completely equivalent since the numerical values of the exponents and contraction coefficients determine how well the basis describes the wave function. 

MINI—i i = 1—4) These four sets have different numbers of primitives per contraction, mostly three or four. These are minimal basis sets with one contraction per orbital. Available for Li through Rn. 

MIDI—i Same primitives as the MINI basis sets with two contractions to describe the valence orbitals for greater flexibility. 

The contracted basis in Figure 28.3 is called a minimal basis set because there is one contraction per occupied orbital. The valence region, and thus chemical bonding, could be described better if an additional primitive were added to each of the valence orbitals. This is almost always done using the even-tempered method. This method comes from the observation that energy-optimized exponents tend to nearly follow an exponential pattern given by... 

For the past year Strike had been in consultation with contract labs over the making of phenylisopropyl alcohols using sulfuric acid and allylbenzenes (don t ask). The lab owners would listen patiently as Strike primitively described how and why an OH should go on the beta carbon. And without exception, the lab owners would point out to Strike that the best way to get an OH on the beta carbon would be to put a Br there first. But Strike don t wanna put a Br there first Strike would say, Strike wants the OH put on directly using sulfuric acid " The lab guys had to do what Strike said because Strike was holding all the money (...a fool and her money etc.). But out of curiosity Strike asked how they would get that Br on the beta carbon. Every one of them said it was simply a matter of using the 48% HBr in acetic acid. They even showed Strike their stock solutions (usually from Aldrich or Fisher). 

HyperChem offers an easy way to interactively add certain basis functions to a molecular system. The Extra Basis Function dialog box can be used to add an S, P, D, SP, or SPD shell to the selected atom(s). These extra basis functions are primitives with no contractions. Thus, the extra basis functions are uniquely defined by the shell type and the value of the exponent. 

The contraction exponents and coefficients of the d-type functions were optimized using five d-primitives (the first set of d-type functions) for the STO-NG basis sets and six d-primitives (the second set of d-type functions) for the split-valence basis sets. Thus, five d orbitals are recommended for the STO-NG basis sets and six d orbitals for the split-valence basis sets. 

The contracted Gaussian functions are a linear combination of the primitive Gaussian functions. That is,... 

Linear combinations of primitive gaussians like these are used to form the actual basis functions the latter are called contracted gaussians and have the form ... 

The atomic unit of wavefunction is. The dashed plot is the primitive with exponent 2.227 66, the dotted plot is the primitive with exponent 0.405 771 and the full plot is the primitive with exponent 0.109 818. The idea is that each primitive describes a part of the STO. If we combine them together using the expansion coefficients from Table 9.5, we get a very close fit to the STO, except in the vicinity of the nucleus. The full curve in Figure 9.4 is the contracted GTO, the dotted curve the STO. 

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