Basis set customization

Chapter 10 represented a wave function as a linear combination of Gaussian basis functions. Today, there are so many basis sets available that many researchers will never need to modify a basis set. However, there are occasionally times when it is desirable to extend an existing basis set in order to obtain more accurate results. The savvy researcher also needs to be able to understand the older literature, in which basis sets were customized routinely. 

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There have been many more basis sets developed, but the list above enumerates the most widely used ones. Some of these sets were the work of many different authors and later improved. This sometimes results in different programs using the same name for two slightly different sets. It is also possible to combine basis sets or modify them, wliich can result in either poor or excellent results, depending on how expertly it is done. How to customize basis sets is discussed in Chapter 28. 

It will be noticed that continuous basis sets, with improper Dirao delta functions as scalar products, do not strictly belong to Hilbert space as defined in Section 8.3, where the basis is specifically required by postulate to be denumerably infinite. The nondenumerably infinite sets g> or j actually span what is known as Banach spaces,5 but we shall here conform to the custom among theoretical physicists to oall them Hilbert spaces. 

Biphenyl, terphenyl, and their alkyl or hydrogenated derivatives generally serve markets where price and performance, rather than composition, is the customer s primary concern. Performance standards for heat-transfer appHcations are usually set by the fluid suppHer. The biphenyl—diphenyl oxide eutectic (26.5% biphenyl, 73.5% DPO) represents a special case. This composition has become a widely recogni2ed standard vapor-phase heat-transfer medium. It is sold throughout the world under various trademarks. In the United States, Dow (Dowtherm A) and Monsanto (Therminol VP-1) are the primary suppHers. Alkylated biphenyls and partially hydrogenated terphenyls serving the dielectric and carbonless copy paper dye solvent markets likewise are sold primarily on the basis of price and performance characteristics jointly agreed on by producer and user. 

These SPI tables can also be used as the basis for establishing standards for molded products between the designer, molder, and customer. Users will find that two separate sets of values are represented. Commercial values represent common production tolerances that can be achieved at the most economical level. Fine values represent closer tolerances that can be held, but at a greater cost. The selection of one or the other will depend on the application under consideration and the economics involved. 

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