A-Potential model

B. Solvolysis of Phosphoric Acid Derivatives.—Interest continues in neighbouring-group participation in the solvolysis of phosphate esters. As a potential model compound for investigating the mechanism of ribo-nuclease action, the phenyl hydrogen phosphate ester of c/j-3,4-tetrahydro-furandiol (24) has been the subject of a detailed study. Above (and probably also below) pH 4 hydrolysis gives solely the cyclic phosphate (25)... 

In the course of studies on the physicochemical properties of natural polymers in aqueous solution, attention has been drawn to pectic acid, i.e. poly (a-D)galacturonic acid as a potential model of a rigid polysaccharide. 

Fretland, D.J., Widomski, D.L., Anglin, C.P., Levin, S. and Gagjnella, T.S. (1990). Colonic inflammation in the rodent induced by phorbol-12-myristate-13-acetate a potential model of inflammatory bowel disease, effect of SC-41930. Gastroenterology 98, A449. 

The presence of an (applied) potential at the aqueous/metal interface can, in addition, result in significant differences in the reaction thermodynamics, mechanisms, and structural topologies compared with those found in the absence of a potential. Modeling the potential has been a challenge, since most of today s ab initio methods treat chemical systems in a canonical form whereby the number of electrons are held constant, rather than in the grand canonical form whereby the potential is held constant. Recent advances have been made by mimicking the electrochemical model... 

Gregoire, L., Munkarah, A., Rabah, R., Morris, R. T., Lancaster, W. D. (1998). Organotypic culture of human ovarian surface epithelial cells a potential model for ovarian carcinogenesis. In vitro Cell Dev-An 34(8), 636-639. 

The M. truncatula tagged lines will provide a valuable resource of materials to screen for traits of agronomic interest. While many of these traits are intriguing, we have neither the time nor established screens to perform the evaluation. Other groups with interests primarily in soybean have expressed interest in our mutant populations. These groups view M. truncatula as a potential model system for the study of legume secondary metabolite/nutraceutical pathways, a niche that Arabidopsis cannot fill in some instances. 

An interesting oxycarbonyl cluster has been isolated in the reaction of 0s04 with CO under pressure. This was an intermediate in the preparation of the Os3(CO)i2. The X-ray analysis has established this as a cubane structure, with an oxygen bridging the four faces of the osmium tetrahedron. The Os-Os distance is 3.20 A and implies no bonding between the osmium centers. This molecule is of obvious interest as a potential model in the studies of carbon monoxide interaction with metal oxides and also metal surfaces, when the formation of metal oxides occurs (200). 

Stephens, R. D., Remote Sensing Data and a Potential Model of Vehicle Exhaust Emissions, J. Air Waste Manage. Assoc., 44, 1284-1292 (1994). 

Hope et al. (116) presented a combined volumetric sorption and theoretical study of the sorption of Kr in silicalite. The theoretical calculation was based on a potential model related to that of Sanders et al. (117), which includes electrostatic terms and a simple bond-bending formalism for the portion of the framework (120 atoms) that is allowed to relax during the simulations. In contrast to the potential developed by Sanders et al., these calculations employed hard, unpolarizable oxygen ions. Polarizability was, however, included in the description of the Kr atoms. Intermolecular potential terms accounting for the interaction of Kr atoms with the zeolite oxygen atoms were derived from fitting experimental results characterizing the interatomic potentials of rare gas mixtures. In contrast to the situation for hydrocarbons, there are few direct empirical data to aid parameterization, but the use of Ne-Kr potentials is reasonable, because Ne is isoelectronic with O2-. 

Pollmacher T, Holsboer, F. Sleep-wake disturbances in HIV-infected patients a potential model of the interactions between sleep and the immune system. Sleep Res Soc Bull 1996 2 37 12. 

The A-potential model multiwalled doped fullerene onions 19... 

In this section, the two simple models mentioned in the Introduction, the A-potential model and the 5-potential model, both of which are based on the listed simplifications, are reviewed. 

In the A-potential model, the C cage is modeled by a spherical, short-range, attractive potential V (r) of inner radius Rn, thickness A, and depth f/° ... 

In the framework of the A-potential model, combined with the frozen-cage approximation, the problem is solved simply. Namely, HF wavefunctions and energies of the encaged atom, solutions of the extended to encaged atoms Hartree-Fock equations (2), must be substituted into corresponding formulae for the photoionization of an nl subshell of the free atom, Equations (18)-(26), thereby turning them into formulae for the encaged atom (to be marked with superscript " A") rrni(o>) —> a A(co), Pni(fi>) Yni o>) - and 8ni((o) - 8 A(co). This accounts... 

Following the previous discussion, the following notations are maintained in this section calculated results obtained within the A-potential model at the frozen-cage approximation level are marked as a A, P A, y A and 8 A to distinguish them from the results of the 5-potential model, a s, f) s, y s and 8 s, respectively. 

Figure 4 RPAE calculated results for the Xe 4d photoionization cross section of free Xe, o 4dee, as well as of Xe C6o calculated in the framework of both the 5-potential model, a s [37] and A-potential model, a4 A [33], Also shown, for comparison, are calculated data [33], marked ct4 5a, obtained for the 4d photoionization cross section of Xe Cgo with an artificially reduced thickness of the Cgg cage from A = 1.9 au to A = 0.5 au, deepened potential depth, UgQ = 25.9 eV, and changed inner radius Rc = 6.389 au, in order to simulate the 5-potential model but keep the binding strength of the cage potential unchanged (see the main text body).

Figure 6 Nondipole asymmetry parameter xis(e) as a function of the photoelectron energy s for the Ne Is photoionization from e Cgo calculated [36] in two different approximations 1, the 5-potential model. 2, 3 and 4, the A-potential model with the following values for Rgq, f/gQ and A (all in au) ...

As an illustration, calculated data [36] for the Ne Is, 2s and 2p photoelectron angular asymmetry parameters from Ne C60, both in the 5- and A-potential models, are depicted in Figures 6-8. Note, the dipole parameter /3ns = 2,... 

Figure 7 Nondipole asymmetry parameter Y2s(s) for the Ne 2s photoionization from Ne Cgo calculated [36] in the 5-potential model (line 1) and the A-potential model (lines 2,3, and 4) with the same choice of R,n, A, and f/g0 as in Figure 6.

Figure 9 The A-potential model calculated results [28] for the Is photoionization of free Ne, as well as that of Ne from neutral Ne C6o (z = 0) and from the Ne C 0 anion with z = -1, -2, -3, and -5 (dotted line), as indicated.

Figure 18 Calculated [33] RPAE results for the Xe 5s photoionization cross section of Xe Cgo obtained in the A-potential model at the frozen-cage approximation level. (a) o 1" A iro), complete RPAE calculation accounting for interchannel coupling between photoionization transitions from the Xe 4d10, 5s2 and 5p6 subshells (b) 5 A ( >), the same as in (a) but with the 4d - f, p transitions being replaced by those of free Xe, for comparison purposes (c) o AA(

Figure 20 HF and RPAE calculated data for the Ca 4s photoionization cross section of free Ca, cr 12, and encaged Ca, calculated at the frozen-cage, [20] and dynamical-cage, a A [64] approximation levels in the framework of the A-potential model. HF-L and HF-V stands forthe HF calculation of the photoionization cross section in the length or velocity form, respectively. In RPAE [55] the length and velocity forms are equivalent.

To demonstrate the phenomenon, HF calculated results [20] for the ground-state 4s orbital as well as for the excited 3d, 4d and 5d orbitals (resulting due to 3p rid transitions) of free Ca and Ca in Ca C60 are depicted in Figure 25. The calculations for the encaged Ca atom were performed in the framework of the A-potential model. 

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