Linked-atom solution

As already shown, conventional macromolecules (or polymers) consist of a minimum of a several hundred covalently linked atoms and have molar masses clearly above 10 g/mol. The degree of polymerization, P, and the molecular weight, M, are the most important characteristics of macromolecular substances because nearly all properties in solution and in bulk depend on them. The degree of polymerization indicates how many monomer units are linked to form the polymer chain. The molecular weight of a homopolymer is given by Eq. 1.1. 

The phase problem and the problem of arbitration. Fibrous structures are usually made up of linear polymers with helical conformations. Direct or experimental solution of the X-ray phase problem is not usually possible. However, the extensive symmetry of helical molecules means that the molecular asymmetric unit is commonly a relatively small chemical unit such as one nucleotide. It is therefore not difficult to fabricate a preliminary model (which incidently provides an approximate solution to the phase problem) and then to refine this model to provide a "best" solution. This process, however, provides no assurance that the solution is unique. Other stereochemically plausible models may have to be considered. Fortunately, the linked-atom least-squares approach provides a very good framework for objective arbitration independent refinements of competing models can provide the best models of each kind the final values of n or its components (eqn. xxiv) provide measures of the acceptability of various models these measures of relative acceptability can be compared using standard statistical tests (4) and the decision made whether or not a particular model is significantly superior to any other. 

Unfortunately QM/MM potentials are not devoid of problems. The most severe ones are probably the division of covalent bonds across the QM and MM regions and the lack of explicit polarisation of the MM approach. The first of these two difficulties has been looked at by several groups who have proposed different schemes to deal with the problem Warshel and Levitt [299] have used a single hybrid orbital on the MM atom in the QM/MM region a similar approach has been proposed subsequently by Rivail and co-workers [312, 355, 373] with their frozen orbital (or excluded orbital) in which the continuity between the two critical regions is assured by a strictly localised bond orbital (SLBO) obtained from model compounds. Another popular approach introduces link atoms [300, 310, 315] between QM and MM covalently bonded atoms to cap the valency of the QM atoms the link atoms, usually hydrogen, do not interact with the MM atoms. These are not, by any means, the only ways of dealing with this problem. However, so far it does not seem to have an obvious solution. 

For electron diffraction of the unpolymerized dimer, microscopic single crystals were obtained from a dilute hexane solution at 4 C. The structure refinement was carried out using the linked atom least-squares (LALS) program (developed by Arnott and coworkers (12) ) on 19 unique reflections. The unit cell Is... 

The presence of chemical bonds between the QM and MM regions poses a problem to the use of hybrid QM/MM methods, with different approaches taking different solutions. The particular method applied by IMQMM and derived methods, the introduction of additional link atoms to saturate the dangling bonds, will be discussed in more detail in Section 3.4 of this chapter. 

The simplest way to keep the electronic structure of the quantum subsystem as close as possible to what it would be in the entire macromolecule consists of saturating the dangling bonds with monovalent atoms called link atoms. Typically, hydrogen atoms are used. The computation now consists of a model molecule of the reactive part interacting with classical surroundings, similar to the case of solutions. This approach has been introduced by Singh and Kollman [8] and has been put in a operational form by Field et al. [9],... 

The only difference with the case of solutions arises from the treatment of the electrostatic interaction between the link atom and the classical atoms. In a first version implemented in the CHARMM package [10], this interaction was simply neglected (the QQ link). An alternative version in which the link atom interacts with all the atoms has been added (the HQ link). Due to the size of the reactive parts of... 

Slavicek P, Martinez TJ (2006) Multicentered valence electron effective potentials solution to the link atom problem for ground and excited electronic states. J Chem Phys 124 084107... 

To avoid the negative effects of dangling bonds on the quantum mechanical solution for the internal part, terminating H atoms are added. They are also called link atoms, L. The L atoms and the internal part form the cluster, C = I -f L. The energy of the total system can still be approximated by the subtraction scheme ... 

The favorable effect of a decrease in is only observed on incorporation of rigid fragments of the amine or acid type. As demonstrated above, such fragments do not prevent spontaneous transition of the copolyamide into the LC state. On the contrary, incorporation of flexible units (in the given case, m-phenylene units 1 and 7, fragments with linking atoms 2, 3, and 4) increases the flow temperatures of the solutions. 

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