Size extensive formulations applications

The CASSCF method itself is not very useful for anything else than systems with few electrons unless an effective method to treat dynamical correlation effects could be developed. The Multi-Reference Cl (MRCI) method was available but was limited due to the steep increase of the size of the Cl expansion as a function of the number of correlated electrons, the basis set, and the number of active orbitals in the reference function. The direct MRCI formulation by P. Siegbahn helped but the limits still prevented applications to larger systems with many valence electrons [20], The method is still used with some success due to recent technological developments [21], Another drawback with the MRCI approach is the lack of size-extensivity, even if methods are available that can approximately correct the energies. Multi-reference coupled-cluster methods are studied but have not yet reached a state where real applications are possible. 

This article is organized as follows in Section 22.2.1 we will first describe the formulation of the spin-free SS-MRCC theory. We wUl next present the development of the API-SSMRCC method in Section 22.2.2. In Section 22.2.3 we will discuss the aspects of size-extensivity and consistency of the API-SSMRCC method. We will discuss the spin-free formulation of SS-MRPT and SS-MRCEPA methods starting from the SS-MRCC theory in Sections 22.3 and 22.4, respectively. The IMS version of the SS-MRCC method will be covered in Section 22.5. In Section 22.6, we will present the illustrative numerical applications, along with discussions. Einally, Section 22.7 will summarize our presentation. 

Major components of the pressed powder blusher include the powder phase and binder (or oil) phase. Components of the powder phase include mineral powder fillers such as talc (a magnesium silicate), mica (a magnesium ahuninum silicate), sericite (a form of hydrated mica), and kaolin (known as China clay). Talc is the most popular of all fillers used, as it tends to be virtually transparent depending on the particle size, and it is very soft to the touch. Although mica is also used extensively as a result of its transparency and smooth texture, it often exhibits a shiny appearance with skin application and has poor compression characteristics when used in a pressed powder. Modern non-oil control formulations rarely contain kaolin, as it tends to exhibit course texture, an extremely matte appearance, and excessive oil-absorption capabilities. Dry binders are also used to allow tlie compressed powder to retain form these include metallic soaps such as zinc stearate and magnesium stearate and... 

Cyclodextrins, on the other hand, are used extensively in cosmetic and drug delivery applications (132-136). Cyclodextrins, as the name implies, are cyclic amyloses comprised of 6 (a-), 7 (P-), and 8 (y-), a-D-(l,4)-glucose monosaccharides (Fig. 30). Their small size classifies them as oligo- instead of polysaccharides, which places them somewhat outside the scope of this chapter. Nevertheless, cyclodextrins are important components in many cosmetic formulations where they function as hosts and solubilizing agents for water-sensitive or water-insoluble materials. 

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