Virtual bond

As for Erep, Ect is derived from an early simplified perturbation theory due to Murrel [46], Its formulation [47,48] also takes into account the Lrj lone pairs of the electron donor molecule (denoted molecule A). Indeed, they are the most exposed in this case of interaction (see Section 6.2.3) and have, with the n orbital, the lowest ionization potentials. The acceptor molecule is represented by bond involving an hydrogen (denoted BH) mimicking the set, denoted < > bh, of virtual bond orbitals involved in the interaction. 

The average structure for the ADA-8H complex generated after energy minimization and equilibration with 20 ps of MD simulation showed considerable movement of atoms in the vicinity of the zinc ion when these residues were not constrained. Virtual bonds between zinc and the atoms that coordinate to the zinc ion were added to provide necessary atomic constraints prior to energy minimization and MD simulations. After constraints were applied, the average structure was similar to the X-ray... 

Figure 8. The mean directional correlation F(x) of virtual bond x with the initial virtual bond in the chain.25 Closed circles correspond to a calculation based on the "rigid" cellobiose map of Fig. 2 open circles refer to the relaxed cellobiose surface of Fig. 6.

V C chains with rigid moieties and virtual bonds copolymers e. g. polyesters, polyamides, and polybutadienes... 

The structure of tha polycarbonate chain Is analyzed from tha point of view of the spatial configurations. It follows that the molecule can be treated as a freely rotating chain consisting of a succession of virtual bonds (lvp) 7.0 A In length, jointed at angles (SI of ca. 112°. 

RIS theory provides a relatively simle formalism for the evaluation of the persistence vector, a, for a chain that can be represented by a repeating sequence of independent virtual bonds such as polybenzobisoxazole (PBOI and polybenzobisthiazole IPBT). The present study combines RIS theory with long molecular dynamics simulations for small fragments in order to evaluate the limiting length of a for very stiff chains. The approach can be applied to other stiff chain polymers. 

Virtual bonds are fixed at the position shown in the figure without allowing rotational freedom. 

The characteristic ratio changes from 1.3 to 2.8 with o changing from 0 to 1, when the virtual bond is used. On the other hand, when each bond of the phenylene group is taken into account individually, the two extreme values are 3.41 and 7.40. By assuming all the statistical weight factors to be unity, which corresponds to the freely-rotating chain, the characteristic ratio is 1.60 when the virtual bond is used, and 4.22 if it is not. 

The matrix required to transform from the coordinate system of virtual bond i+1 to the coordinate system of virtual bond /in the a-helix is denoted by Th. Virtual-bond vector > extends from the C atom of amino acid residue i-1 to the C of amino acid residue /. Using the dihedral angles (< >,qr - 57.4°, - 47.5°) found for helical polyil-alaninel in the solid state, Tj,1 results if the a-helix are constructed from standard peptide units, with all = - 47°, - 57.2°, Th2 results. 

Spatial Configurations of Polynucleotide Chains. I. Steric Interactions in Polyribonucleotides A Virtual Bond Model ... 

N 113 "Configurational Statistics of Polynucleotide Chains. A Single Virtual Bond Treatment"... 

A simple super or s-virtual bond scheme is developed for the treatment of tertiary or superhelical structure in polynucleotide chains. The scheme Is utilized to examine the enormous variety of tertiary structure that can be generated by regularly banding a B-DNA reference helix at the phosphodiester linkages. 

N 121 "Configuration Statistics of Polynucleotide Chains. An Updated Virtual Bond Model to... 

Virtual Bond Cellulose Pectic acid Amylose ... 

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