SC method

Naplitali-Sandholm SC Method This method employs the equilibrium-stage model of Figs. 13-48 and 13-49 but reduces the number of vari les by 2N so that only N(2C + 1) equations in a hke number of unknowns must be solved. In place of Vj, Lj, Xij, and iji j, component flow rates are used according to their definitions ... 

Use the Naphtali-Sandholm SC method to compute stage temperatures and interstage vapor and liquid flow rates and compositions for the rehoiled-stripper specifications shown in Fig. 13-53. The specified hottoms rate is equivalent to removing most of the nCs and nCe and some of the nC in the hottoms. 

In the purely non-adiabatic limit the phase (5.52) coincides with that calculated in [203] and for very long flights (rt b,v" v) or high energies (.E e) it reduces to what can be obtained from the approximation of rectilinear trajectories. However, there is no need for these simplifications. The SCS method enables us to account for the adiabaticity of collisions and consider the curvature of the particle trajectories. The only demerit is that this curvature is not subjected to anisotropic interaction and is not affected by transitions in the rotational spectrum of the molecule. 

Figure 3.8 Schematic representation of solid grinding (SC) method.

Other props Sc methods of prepn of the dinitro derivs are given in the Refs Refs 1) Beil 14, 210, (470) 2) Beil 14,... 

N-fiAetbyl-etbylenediamine [called N-Methyl-athylendiamin or Methyl-(2-amino-athyl)-amin In Ger] CH3.NH.CH2.CH2.NH2 liq, bp 115-117° forms numerous salts, such as the Cu perchlorate, [Cu(C3HioN2)2](C10ij)2, blue-violet crysts, defglr on heating (Ref 3) Other props Sc methods of prepn are given in the Refs... 

Other props Sc methods of prepn are found in Refs... 

Thus, the Coulson—Fischer representation keeps the simplicity of the covalent picture while treating the covalent—ionic balance by embedding the effect of the ionic terms in a variational way, through the delocalization tails. The Coulson—Fischer idea was subsequently generalized to polyatomic molecules and gave rise to the GVB and SC methods, which were mentioned in Chapter 1 and will be discussed later. 

The GVB and SC methods provide wave functions that are, of course, much more compact than the corresponding valence—CASSCF one (e.g., only 14 spin-coupling modes for methane with the SC method, and a single one with the GVB method). Owing to this difference in size, the GVB and SC methods cannot be expected to include the totality of the nondynamical correlation, even if these two methods treat well, by definition, the left—right correlation for each bond of the molecule. Physically, this is because the various local ionic... 

Despite these restrictions, the GVB and SC methods generally provide energies that are much closer in quality to CASSCF than to Hartree Fock (19), and wave functions that are close to the CASSCF wave function having the same number of electrons and orbitals in the active space. This property has been used to devise a fast method to get approximate SC wave functions. 

The GVB and SC methods take care of the left-right correlation for each bond of a polyatomic molecule. However, these methods do not include the totality of the "non-dynamical" correlation since the various local ionic situations are not interconnected with these methods. For example, the two ionic situations 1 and 2 below are expected to have different weights, 2 being more important than 1,... 

The SC method describes an AT-electron molecule through a set of N singly occupied SC orbitals ()>, which are completely free to overlap with one another. The coupling of the spins is described by a linear combination of the full space of f" spin eigenfunctions v>, where SJ1 are the usual spin quantum numbers, and... 

SEPARATION BY EXTERNAL FIELDS (Sc METHODS) ELECTROPHORESIS AND SEDIMENTATION... 

A partial compilation of field types is shown in Table 8.1. Some static (Sc) methods (or phenomena) associated with such fields are shown. (Processes like photophoresis—based on radiation pressure—hardly deserve to be called methods because the separation power is so weak that no useful methodology exists. However, natural photophoresis fractionated the gases forming our primitive earth as described in Chapter 1.) For completeness, some non-Sc (largely based on flow) separation systems utilizing these fields are shown in the final column of the table. 

In the following pages we describe several practical Sc techniques. We then evaluate the potential magnitude of N and ne for these systems. This evaluation will provide a rough comparison between the Sc methods and will show their strength relative to chromatography, where N is a well-known measure of separation efficiency. 

Sedimentation in an ultracentrifuge is a powerful means for separating biological particles and large macromolecules. Sedimentation is the only static field (Sc) method other than electrophoresis (in all of its various forms) commonly used for multicomponent separations. 

STEADY-STATE VARIANTS OF Sc METHODS ISOELECTRIC FOCUSING AND ISOPYCNIC SEDIMENTATION... 

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