General contraction

A second issue is the practice of using the same set of exponents for several sets of functions, such as the 2s and 2p. These are also referred to as general contraction or more often split valence basis sets and are still in widespread use. The acronyms denoting these basis sets sometimes include the letters SP to indicate the use of the same exponents for s andp orbitals. The disadvantage of this is that the basis set may suffer in the accuracy of its description of the wave function needed for high-accuracy calculations. The advantage of this scheme is that integral evaluation can be completed more quickly. This is partly responsible for the popularity of the Pople basis sets described below. 

There are two different ways of contracting a set of primitive GTOs to a set of contracted GTOs segmented and general contraction. Segmented contraction is the... 

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. 

One popular way of obtaining general contraction coefficients is from Atomic Natural Orbitals (ANO), to be discussed in section 5.4.4. The difference between segmented and general contraction may be illustrated as shown in Figure 5.2. 

All of the above basis sets are of the segmented contraction type. Modem contracted basis sets aimed at producing very accurate wave functions often employ a general contraction scheme. The ANO and cc basis sets below are of die general contraction type. 

LI. Landers, L. C., Final Report, Aerojet-General, Contract AF 04(611)-9889 (1965). 

The new Colour Index volume Pigments and Solvent Dyes lists some 350 solvent dyes and gives their chemical structures, unlike earlier editions which named 800 dyes but included few structures. This fall in numbers is not because of any decreased use but rather the general contraction in numbers of all dyes used in the textile industry. Solvent dyes have been introduced not by attempts to synthesise new colorants but by selection and in some cases modification of known disperse dyes to meet the technical requirements. The majority of solvent dyes are azo compounds but among the blue dyes there are anthraquinones. The aqueous solubility of some of the parent sulphonated dyes has been reduced to acceptable levels by formation of their salts with heavy metals or long-chain alkylamines. 

More generally, contracting the transposed projection tensor with a force to its right (or the projection tensor with a force to its left) produces a constrained force given by the sum of the original force and the constraint force induced by it. Such constrained forces may have nonzero hard components, but, on contraction with induce velocities that do not. 

An alternative method to carrying out a segmented contraction is to use a so-called general contraction (Raffenetti 1973). In a general contraction, there is a single set of primitives that are used in all contracted basis functions, but they appear with different coefficients... 

Maintenance/repair (automotive, aircraft, furniture, general contracting, miscellaneous) (10 plants, 1976-81)... 

For heavier elements primitive basis sets are available, but their contraction is a real art, at least if segmented contractions are used. The use of general contractions is far preferable and is much easier to carry out. 

For heavy atoms the ECP s quickly become essential. The basis set size at the ECP level does not change if we go to the second or third row TM, while a generally contracted basis set for a second row TM would comprise 45 basis functions. The difference increases even more drastically for the third row TM s where in addition the 4f orbital can be included in the core in the ECP case. 

R. C. Raffenetti,. Chem. Phys., 58, 4452 (1973). General Contraction of Gaussian Atomic... 

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