Finite bonds, description

Beyond the gel point, the bonds Issuing from a monomer unit can have finite or Infinite continuation. If the continuation Is finite, the Issuing subtree Is also only finite If the continuation Is Infinite, the unit Is bound via this bond to the "infinite" gel. The classification of bonds with respect to whether they have finite or Infinite continuation enables a relatively detailed statistical description of the gel structure. The probability of finite continuation of a bond Is called the extinction probability. The extinction probability Is obtained In a simple way from the distribution of units In generation g>0. This distribution Is obtained from the distribution of units In the root g-0 (for more details see Ref. 6). 

Although the adiabatic connection formula of Eq. (8) justifies a certain amount of Hartree-Fock mixing, there are situations in which a should vanish. In a spin-restricted description of the molecule Hj at infinite bond length (Sect. 4) the Hartree-Fock or A = 0 hole is equally distributed over both atoms, and is independent of the electron s position. But the hole for any finite A, however small, is entirely localized on the electron s atom, so no amount of Hartree-Fock mixing is acceptable in this case. 

The other chain atom coordinates are obtained through repeated application of a screw operator. The side groups can be defined as for finite molecules with a proper combination of bond lengths, valence and torsion angles. Finally, the crystal structure description is completed by an overall rotation 4> and three overall translations x0 y0 z (or fewer, depending on the space group). 

Another description of EPD/EPA interactions, particularly useful for strong complexes, is based on the coordinative interaction between Lewis bases or nucleophiles (as EPD) and Lewis acids or electrophiles (as EPA) [53, 58], The intermolecular bonding is seen not as a hybrid of electrostatic and charge-transfer forces, but as one of electrostatic and covalent ones. The interaction of the acceptor A with the electron pair of the donor D is a result of an overlap of the orbitals of the two molecules consequently, a finite electron density is created between the two partners according to Eq. (2-9). 

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