Customizing a Basis Set

Likewise, a basis set can be improved by uncontracting some of the outer basis function primitives (individual GTO orbitals). This will always lower the total energy slightly. It will improve the accuracy of chemical predictions if the primitives being uncontracted are those describing the wave function in the middle of a chemical bond. The distance from the nucleus at which a basis function has the most significant effect on the wave function is the distance at which there is a peak in the radial distribution function for that GTO primitive. The formula for a normalized radial GTO primitive in atomic units is 

a primitive with an exponent of 0.2 best describes the wave function at a distance of 0.79 Bohrs. 

Note that the answers have been rounded to three significant digits. Since the even-tempered formula is only an approximation, this does not introduce any significant additional error. 

Although the even tempered function scheme is fairly reasonable far from the nucleus, each function added is slightly further from the energy-optimized value. Generally, two or three additional functions at the most will be added to a basis set. Beyond this point, it is most elficient to switch to a different, larger basis. 

A different scheme must be used for determining polarization functions and very diffuse functions (Rydberg functions). It is reasonable to use functions from another basis set for the same element. Another option is to use functions that will depict the electron density distribution at the desired distance from the nucleus as described above. 

---

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. 

In terms of mass customization, a product platform provides the technical basis for catering to customization, managing variety, and leveraging existing capabilities. Essentially, the product platform captures and utilizes reusability underlying product families and serves as a repertoire of knowledge bases for different products. It also prevents variant product proliferation for the same set of customer requirements. TTie formulation of product platform involves inputs from design concepts. 

The general modeling approach just outlined, is appropriate for an MTS environment where finished products are being allocated. In an ATO, CTO or MTO setting, the resources allocated are raw materials or components, not finished products. Forecasts are commonly made on a product model or product family basis. However, the product model or product family does not have a predefined BoM. Rather the specific materials used are determined by the specific configuration chosen by the customer. An approach based on feature sets is described by Ervolina and Dietrich (2001). A feature set, which corresponds to a particular customer product configuration option, maps to a set of required materials. Associated with the product forecasts, are a set of ratios that relate product family quantities to features. Specifically, let F be a set of features and rf i the fraction of product family ithat demands feature /. In this setting, since features map to material requirements, we replace bij with which is defined as the material j quantity associated with feature /. Constraint (11.4) can now be replaced with ... 

The preliminary hazard list and the customer requirements form the basis for the Functional Hazard Assessment (FHA). While considering the required functionality and the respective system enviromnent the FHA shall answer the question How safe does the system need to be The analysis performed during the FHA provides the safety objectives and a first set of system safety requirements which are necessary in order to fulfil the safety goals and to prevent the identified hazards from occurring. The system requirements are amended by the system safety requirements. Doing this in the early project phase assures that the safety requirements are appropriately considered in the system design. 

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. 

---