Alternative Partitioning

The hypothesis that geometrical derivatives of the electric dipole moment can be used as effective charges of the atoms in a neutral diatomic molecule was initially proposed by Van Vleck. After decades of development the APT became customarily applied. In their spunky paper Lazzeretti et aV described a version of the APT approach that they claimed is probably superior to other physically based methods, and certainly more rehable on theoretical grounds than some loosely defined orbital-based approach. In their critical review of population methods they presented AIM favourably. 

Zitto et al formulated atomic populations different from those of AIM. They employed quantum-mechanical relationships involving the Atomic Polar Tensor and the related nuclear electric shielding, which provide clearcut recipes to evaluate atomic populations in molecules within the dipole acceleration formalism 

Oliferenko et al proposed a novel method to compute atomic charges. The starting data for the computation are the classical topology of a molecule and electronegativities of either constituent atoms or atomic orbitals. A comparison of the obtained charges with those produced by means of alternative computational schemes proves that the new model provides fast, convenient and reliable methods to calculate theoretically justifiable atomic charges, according to the authors. 

In their paper on the experimental determination of net atomic charge Cerofolini et al. proposed to use X-ray photoemission spectroscopy. They assert that the definition of a net charge of an atom is conceptually difficult and that as of yet no experiment has been developed to determine such a net charge. However, they are comforted by the AIM theory, which they see as giving physical meaning to an atomic charge, hence making the difficulties associated with it technical in character rather then conceptual. 

2 Electron Correlation. - Lopez-Boada et al reported on a new derivation of correlation functionals. They used AIM to compute the correlation energies for atomic fragments and simply added the values for the whole system. 

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The same approach applies to alternate partition functions the WL output is used directly in the macroscopic probability scheme. For example, in the previous grand canonical scenario, the WL simulation would yield which would be substituted directly into the macrostate probabilities as Q exp(J ) for subsequent results generation. 

However, since and -5 asymptote to the same function, one might approximate (U) = S dJ) in (3.57) so that the acceptance probability is a constant.3 The procedure allows trial swaps to be accepted with 100% probability. This general parallel processing scheme, in which the macrostate range is divided into windows and configuration swaps are permitted, is not limited to density-of-states simulations or the WL algorithm in particular. Alternate partition functions can be calculated in this way, such as from previous discussions, and the parallel implementation is also feasible for the multicanonical approach [34] and transition-matrix calculations [35],... 

An alternative partitioning, e.g. AECov = oo/(l +Soo) and AEex = UooI (1 +Soo) could also be justified because there are no physical criteria for the preference of one or the other assignment ). The only advantage of the choice in Eq. (15) is that terms of same order of overlap between individual molecular orbitals are collected. 

Pressure-driven flow in a simplified Kenics-type mixer consisting of a tube with alternating partitions. 

The next section focuses on alternative partition coefficients to P0w... 

Particular choices for p and alternative partitionings of H lead to various decouplings of the dilated electron propagator with different actualizations for A and E /71 / and in the following subsections we briefly categorize these different approaches to the construction of G(tj, E). 

Change of origin of the reference system also induces a gauge transformation and, consequently, leads to alternative partitions of tensors (93) and (99). They will be examined in some detail in Section VI. 

The direct minimization procedure has been also used by Wang and Ford (1992) in an MNDO and AMI version of the program. These authors introduce an alternative partition of the spheres defining the cavity, which still starts from the pentakisdodecahedron. The program has been used to study SnI, and Sn 2 reactions as well as tautomeric equilibria (Ford and Wang, 1992). 

The final separation of Am and Cm from RE can be done by applying the solvent extraction techniques developed in the HDEHP and TBP flow-sheets. As an alternative, partitioning techniques based on column extraction chromatography (LEVEXTREL-TBP and LEVEXTREL-HDEHP) are being experimentally studied on fully active HAW solutions. A final decision on the techniques for the actinide/RE separation will be reached at a later stage of the programme. 

Alternative partitions of the whole system into groups according to Eq. (3.5) are possible. One of them is into K shell groups and a valence shell group, which one may call the K-V separation. It is in some respects better justified than the o—n separation and has been checked by ab initio calculations of small molecules 5>6>. One drawback of the K-V separation is that the strong orthogonality condition is not automatically satisfied for symmetry reasons, as in the o—n separation. However, this does not lead to serious difficulties. 

Figure 3. Simple schematic diagram illustrating the increasing intrinsic susceptability of each subsequent polyketide intermediate toward alternative competing reactions. Our Reaction partitioning model of diversity states that evolutionary divergence of PKS product specificity results from alternative partitioning of intermediates at key mechanistic branchpoints.

Despite some good correlations with in vivo pharmacokinetics [105], log Pa/w seems to have only a limited performance in predicting brain-blood concentrations (log BB) [106— 109] or oral drug absorption [110]. The octanol-water system still has no serious rival, but alternative partition systems that might give a better description have been suggested and investigated. Notable attempts include the use of cyclohexane-water [111-113] or the use of A log P between octanol-water and cyclohexane-water [109,114,115]. 

Partitioning. - An alternative partitioning scheme of molecular density into atoms is proposed by Rico et al.119 Their minimal deformation criterion, previously proposed for the partition of the molecular density into atomic contributions, is updated and extended. The authors claim that the decomposition of the molecular density p(r) into atomic densities, p(r) = PA(r) ls intrinsically arbitrary. As a consequence the above equation has an infinite number of solutions. The relation between their method and AIM is not discussed. 

The same Mulliken-Mezey method, and the more elaborate alternative partitioning schemes serve as the basis of the ALDA (adjustable local density assembler) method and the ADMA (adjustable density matrix assembler) technique. The ALDA and ADMA methods generate geometry-adjustable electronic densities and macromolecular density matrices. The ADMA macromolecular density matrices can be computed without determining a macromolecular wave function, a feature advantageous in the macromolecular application of a variety of quantum-chemical... 

Partitioning is a means for providing isolation between components to contain and/or isolate faults. Partitioning between components may be achieved within the system architecturally by allocating unique target hardware and hardware resources to each component. Alternatively, partitioning may be achieved within the component architecture to allow multiple software or hardware items to run within the same hardware platform. Partitioning should ensure ... 

A variation of the PUREX process is being proposed by the US Department of Energy as a possible alternative partitioning scheme for the transmutation of wastes. This aqueous process called UREX, only removes uranium from spent commercial LWR fuel and leaves plutonium in the HLW stream with the other minor actinides and fission products. Nonaqueous pyroprocessing, a variation of the ANL electrorefining process, is then proposed to be used to separate both the plutonium and minor actinides so that they can be transmuted in an ADS. For further information related to potential modifications of this process for other accelerator transmutation of waste applications, see ANL-99/15 (1999). 

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