Atomic trimer

For v < E, the trimer can be formed in the state v. In this case is imaginary and the function 10.63 describes an outgoing wave of the light atom moving away from the trimer. The choice of the sign in Equation 10.64 ensures that there is no incoming flux in the atom-trimer channel. 

H. Koppel and R. Meiswinkel, Point-Charge Model for Vibronic Coupling Constants of Metal Atom Trimers , Z. Phys. D 32, 153 (1994). 

The three-body contribution may also be modelled using a term of the form i ( AB,tAc,J Bc) = i A,B,c exp(-Q AB)exp(-/i Ac)exp(-7 Bc) where K, a, j3 and 7 are constants describing the interaction between the atoms A, B and C. Such a functional form has been used in simulations of ion-water systems, where polarisation alone does not exactly model configurations when there are two water molecules close to an ion [Lybrand and Kollman 1985]. The three-body exchange repulsion term is thus only calculated for ion-water-water trimers when the species are close together. 

The first phosphazene polymers containing carbon (79), sulfur (80,81), and even metal atoms (82) in the backbone have been reported. These were all prepared by the ring-opening polymerization of partially or fully chloro-substituted (or fluoro-substituted) trimers containing one hetero atom substituting for a ring-phosphoms atom in a cyclotriphosphazene-type ring. 

AEyl chloride reacts with sodamide in Hquid ammonia to produce benzene when sodamide is in excess, hexadiene dimer is the principal product, with some trimer and tetramer (C24, six double bonds). AEylation at carbon atoms alpha to polar groups is used in the preparation of a-aEyl-substituted ketones and nittiles. Preparation of P-diketone derivatives, methionic acid derivatives, and malonic ester, cyanoacetic ester, and P-keto-ester derivatives, etc, involving substitution on an alpha carbon between two polar carbonyl groups, is particularly facEe. 

Orthorhombic HBO2 consists of trimeric units B303(0H)3 which are linked into layers by H bonding (Fig. 6.26) all the B atoms are 3-coordinate. Monoclinic HBO2 is built of chains of composition [B304(0H)(H20)] in which some of the B atoms are now 4-coordinate, whereas cubic HBO2 has a framework structure of tetrahedral BO4 groups some of which are H bonded. The increase in CN of B is paralleled by an increase in density and mp. 

LCo(H20)6] ion, and bidentate /V-donor ligands such as cn, bipy and phen form octahedral cationic complexes [Co(L-L)3] , which are much more stable to oxidation than is the hexaammine [Co(NH3)6l . Acac yields the orange [Co(acac)2(H20)2] which has the tram octahedral structure and can be dehydrated to [Co(acac)2l which attains octahedral coordination by forming the tetrameric species shown in Fig. 26.3. This is comparable with the trimeric [Ni(acac>2]3 (p. 1157), like which it shows evidence of weak ferromagnetic interactions at very low temperatures. fCo(edta)(H20)] is ostensibly analogous to the 7-coordinate Mn and complexes with the same stoichiometry, but in fact the cobalt is only 6-coordinate, 1 of the oxygen atoms of the cdta being too far away from the cobalt (272 compared to 223 pm for the other edta donor atoms) to be considered as coordinated. 

Second, as their size increases, these adislands can be limited by two kinds of close-packed atomic rows corresponding to two different types of microfacets (001) for type A and (HI) for type B. In the above mentioned experiments, Wang and Ehrlich have shown that triangular Ir trimers with type B borders are energetically favoured. 

Here, we address the more general question of the relative stability of monomers, dimers and triangular trimers on the (111) surface of FCC transition metals of the same chemical species as a function of the d band filling Nd. All possible atomic configurations of the systems are considered monomers and dimers at sites N and F, triangles with A and B borders at sites N and F (Fig. 4). The d band-filling includes the range of stability of the FCC phase (Nd > 7.5e /atom). The densities of states are obtained from... 

Figure 4. Possible atomic configurations for monomers, dimers and triangular trimers on (111) FCC surfaces at normal (N) and fault (F) sites. Trimers of type A have their center above an atom in the surface layer, for type B the center is at an adsorption site...

Figure 5. Diagram giving the relative stability of the various atomic configurations shown in Fig. 4 as a function of the d band-filling Nj- From the second to the fifth line relative stability of the F and N sites for the monomer, dimer, A trimer and B trimer. On the sixth and seventh lines relative stability of A and B triangles at N and F sites. The relative stability of HCP and FCC bulk phases is given for comparison in the first line.

In a very recent study, it has been demonstrated116 that zinc 5,15-bis(3,5-di-tert-butylphenyl)-porphyrin (13) without any activating halogen atoms at the chromophore can be directly linked in a very simple oxidative coupling reaction with silver(I) hexafluorophosphate to a mixture of porphyrin dimers, trimers and tetramers. The separation of the product mixture was achieved by gel-permeation chromatography based on the molecular weights of the oligomers. The dimer when re-exposed to the same reaction conditions yielded 25% of the tetramer.116... 

The structures of PMs are trimeric, consisting of three molecules of PS and two molecules of methylamine that are condensed together (Table 9.5). In the structures of PMs, however, the bonds created by the condensation lack adjacent hydrogen atoms, making the connectivity assignment in 1H-NMR studies virtually impossible (see the 9-membered rings in Fig. 9.11). To circumvent this problem, a model compound of panal, K-l, having 13C-labeles at the C12 and C13 positions, has been synthesized at Kishi s laboratory (Harvard University) to make a model compound of PM (Stojanovic, 1995). 

We have already shown how simultaneous codeposition of two metals in inert-gas matrices can lead to the formation of mixed-metal dimers. As in the case of silver, it was found that irradiation into the atomic absorptions of Cr or Mo results in formation of their respective dimers and trimers (114). In addition to this, however, irradiation into the atomic resonances of the two metals in the presence of each other results (114) in formation of the mixed-metal species CrMo, CrjMo, and CrMo2. It would seem that selective irradiation into the 300-400-nm bands of atomic Cr or Mo excites the 3d 4p, 3dMs 4p , or 4d 5p, ... 

When chromium atoms were cocondensed at 77 K with 1,7-cyclodeca-diyne (38), complexation was not observed however, an organic trimer of the starting material was formed. Standard, organic characterization-techniques showed that this trimer is the one depicted, rather... 

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