Linked-atom description

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... 

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. 

Figure 1 Examples of lipids found commonly and used in cells, (a) DPPC (b) 1-palmitoyl-2-(1-pyrenedecanoyl)-sn-glycero-3-phosphocholine (PyrPC) (c) Palmitoyl-SM (d) Cholesterol (e) Dipalmitoylphosphatidylethanolamine (f) 1,2-di-0-palmitoyl-3-0-fi-D-galactosyl-sn-glycerol (DPGALA). Of these lipids, PyrPC is a pyrene-linked lipid probe and DPGALA is a glycolipid. The first four lipids are represented by a united-atom description, and the last two lipids are represented by a full-atom description.

It is interesting to compare the possibilities and errors of different hybrid QM/MM schemes. The careful examination and comparison of link atom and LSCF techniques was performed in Ref. [128] using the CHARMM force field [114] and the AMI method [143] as a quantum chemical procedure. In the case of the link atom procedure two options were used QQ - the link atom does not interact with the MM subsystem and HQ - link atom interacts with all MM atoms. The main conclusion of this consideration is that the LSCF and the link atom schemes are of similar quality. The error in the proton affinity determination induced by these schemes is several kcal/mol. It is noteworthy that all the schemes work rather badly in description of conformational properties of n-butane. The large charge on the MM atoms in the proximity of the QM subsystem (especially on the boundary atom) cause significant errors in the proton affinity estimates for all methods (especially, in the case of the LSCF approach where the error can be of tens of kcal/mol). This is not surprising since the stability and transferability of intrabond one- and two-electron density matrix elements Eq. (19) is broken here. It proves that the simple electrostatic model is not well appropriate for these schemes and that a detailed analysis of the... 

The MM parameters at the boundary are used similarly as they are implemented in AMBER for the link atom approach. Internal coordinate force field terms of bonds, angles, and dihedral angles are used if any MM or MMH atom is involved. Electrostatic and van der Waals (vdW) interactions are also calculated in accordance with the AMBER force field scheme [28]. Detailed description of the retained bonded and nonbonded terms, in particular the interactions with bond charges, is discussed in the following section. 

The second point that inorganic and hybrid solids have in common is their structural description. On a primary basis, their skeletons are based on the connection of polyhedral entities (considered primary building units), which can be described either in a ball-and-stick representation (often used by molecular chemists) or in terms of polyhedra (preferred by solid state scientists). The increasing complexity of the inorganic frameworks has incited researchers to simplify their representation, first in terms of connected polyhedra instead of linked atoms (Fig. 2), but even with that a further simplification was needed. The centres of the polyhedra were therefore assimilated to nodes. Their linkage defined clear figures of nets, which characterized the connectivity of the solid. This approach, initiated by Wells [52], was applied to zeolites by Smith [53] and now the structures of the latter are described using this way [54]. 

Another important polyatomic molecule is benzene, C6f I6, the parent of the aromatic compounds. In the molecular orbital description of benzene, all thirty C2s-, C2p-, and Hls-orbitals contribute to molecular orbitals spreading over all twelve atoms (six C plus six H). The orbitals in the plane of the ring (the C2s-, C2px, and ( 2/ -orbitals on each carbon atom and all six Hls-orbitals) form delocalized o-orbitals that bind the C atoms together and link the H atoms to the C atoms. The six C2pz-orbitals, which are perpendicular to the ring, contribute to six delocalized tt-orbitals that spread all the way around the ring. However, chemists... 

The location of electrons linking more than three atoms cannot be illustrated as easily. The simple, descriptive models must give way to the theoretical treatment by molecular orbital theory. With its aid, however, certain electron counting rules have been deduced for cluster compounds that set up relations between the structure and the number of valence electrons. A bridge between molecular-orbital theory and vividness is offered by the electron-localization function (cf p. 89). 

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