Linked-atom modeling

Only recently, with the publication by Maron et al. [307], has the x-ray RDF approach to local order in PANI seen its continuation. TTiese authors present RDFs derived from synchrotron x-ray data (2 = 0.502 A) out tos=16 A ( = 47t sin0/A), where the experimental data are gradually matched with theoretical curves from a linked-atom modelling... 

Hybrid orbital methods differ from the link atom models in that no extra atoms are introduced into the system. Instead, an atom (usually a tetravalent sp carbon) at the covalent boundary is designed to have both a QM and a MM character. This is typically done by defining a set of hybrid sp orbitals on the atom, some of which are fixed and not included in the QM calculation and the remainder of which are allowed to participate. 

In an attempt to aid interpretation of the IR spectrum of MbCO we decided to model the full protein by use of a hybrid quantum mechanics/molecular mechanics approach (QM/MM), to evaluate changes in the CO stretching frequency for different protein conformations. The QM/MM method used [44] combines a first-principles description of the active center with a force-field treatment (using the CHARMM force field) of the rest of the protein. The QM-MM boundary is modeled by use of link atoms (four in the heme vinyl and propionate substituents and one on the His64 residue). Our QM region will include the CO ligand, the porphyrin, and the axial imidazole (Fig. 3.13). The vinyl and propionate porphyrin substituents were not included, because we had previously found they did not affect the properties of the Fe-ligand bonds (Section 3.3.1). It was, on the other hand, crucial to include the imidazole of the proximal His (directly bonded to the... 

To circumvent problems associated with the link atoms different approaches have been developed in which localized orbitals are added to model the bond between the QM and MM regions. Warshel and Levitt [17] were the first to suggest the use of localized orbitals in QM/MM studies. In the local self-consistent field (LSCF) method the QM/MM frontier bond is described with a strictly localized orbital, also called a frozen orbital [43]. These frozen orbitals are parameterized by use of small model molecules and are kept constant in the SCF calculation. The frozen orbitals, and the localized orbital methods in general, must be parameterized for each quantum mechanical model (i.e. energy-calculation method and basis set) to achieve reliable treatment of the boundary [34]. This restriction is partly circumvented in the generalized hybrid orbital (GHO) method [44], In this method, which is an extension of the LSCF method, the boundary MM atom is described by four hybrid orbitals. The three hybrid orbitals that would be attached to other MM atoms are fixed. The remaining hybrid orbital, which represents the bond to a QM atom, participates in the SCF calculation of the QM part. In contrast with LSCF approach the added flexibility of the optimized hybrid orbital means that no specific parameterization of this orbital is needed for each new system. 

In ball-and-stick models, balls with holes drilled at appropriate angles are used to represent the atoms, and sticks or springs are used for the bonds to link them. The resultant model is rather like the framework model, but has representations of the atoms. Models tend to look better than the framework type, but in practice tend to be bigger and less user friendly. 

The problem of linking atomic scale descriptions to continuum descriptions is also a nontrivial one. We will emphasize here that the problem cannot be solved by heroic extensions of the size of molecular dynamics simulations to millions of particles and that this is actually unnecessary. Here we will describe the use of atomic scale calculations for fixing boundary conditions for continuum descriptions in the context of the modeling of static structure (capacitance) and outer shell electron transfer. Though we believe that more can be done with these approaches, several kinds of electrochemical problems—for example, those associated with corrosion phenomena and both inorganic and biological polymers—will require approaches that take into account further intermediate mesoscopic scales. There is less progress to report here, and our discussion will be brief. 

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. 

Table 1. Values of Variable Parameters Obtained by Linked-Atom Least-Squares Refinement of Different /3-DNA Models...

Orlova, A., Galkin, V. E., Van Loock, M. S., Kim, E., Shvetsov, A., Reisler, E., and Egelman, E. H. (2001). Probing the structure of F-actin Cross-links constrain atomic models and modify actin dynamics. / Mol. Biol. 312, 95-106. 

Provided the free atom model is valid, the ratio of number of photons in the first band to the number of photons in the second band is directly related to an effective atomic number, Z, whose value can be determined using either a curve linking the theoretical points of Fig. 10 or its linear approximation. Because this procedure measures photons originating preferentially in the so-called tip region of the source spectrum, it is denoted here by the acronym HETRA - High Energy Tip Region Analysis. 

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