Domain orbits

Figure C3.6.7 Cubic (jir = 0) and linear (r = 0) nullclines for tire FitzHugh-Nagumo equation, (a) The excitable domain showing trajectories resulting from sub- and super-tlireshold excitations, (b) The oscillatory domain showing limit cycle orbits small inner limit cycle close to Hopf point large outer limit cycle far from Hopf point.

The direction of the alignment of magnetic moments within a magnetic domain is related to the axes of the crystal lattice by crystalline electric fields and spin-orbit interaction of transition-metal t5 -ions (24). The dependency is given by the magnetocrystalline anisotropy energy expression for a cubic lattice (33) ... 

Comparison of the Domain and Orbital Models of Multiple Bonds... 

Figure 8.7 Diborane, BaH. (a) Contour map of pb in the plane of the terminal hydrogens, (b) Contour map of pb in the plane of the bridging hydrogens, (c) Calculated geometry, (d) Experimental geometry. (e) Interatomic H-H distances, (f) Ionic model, (g) Resonance structures, (h) Protonated doublebond model, (i) VSEPR domain model showing the two three-center, two-electron bridging domains, (j) Hybrid orbital model.

Several methods have been used for analyzing the electron density in more detail than we have done in this paper. These methods are based on different functions of the electron density and also the kinetic energy of the electrons but they are beyond the scope of this article. They include the Laplacian of the electron density ( L = - V2p) (Bader, 1990 Popelier, 2000), the electron localization function ELF (Becke Edgecombe, 1990), and the localized orbital locator LOL (Schinder Becke, 2000). These methods could usefully be presented in advanced undergraduate quantum chemistry courses and at the graduate level. They provide further understanding of the physical basis of the VSEPR model, and give a more quantitative picture of electron pair domains. 

One way of getting rid of distortions and basis set dependence could be that one switches to the formalism developed by Bader [12] according to which the three-dimensional physical space can be partitioned into domains belonging to individual atoms (called atomic basins). In the definition of bond order and valence indices according to this scheme, the summation over atomic orbitals will be replaced by integration over atomic domains [13]. This topological scheme can be called physical space analysis. Table 22.3 shows some examples of bond order indices obtained with this method. Experience shows that the bond order indices obtained via Hilbert space and physical space analysis are reasonably close, and also that the basis set dependence is not removed by the physical space analysis. 

Hartree-Fock energy 227 Hartree-Fock molecular orbitals 224 Hartree-Fock theory 229 helical domains 94 heroin 81... 

Fig. 12. Schematic views of bis-histidyl ferri-, ferro-, and CO-ferro-heme-hemopexin. Unlike myoglobin with one open distal site, heme bound to hemopexin is coordinated to two strong field ligands, either of which a priori may be displaced by CO. This may well produce coupled changes in protein conformation like the Perutz mechanism for 02-binding by hemoglobin (143). The environment of heme bound to hemopexin and to the N-domain may be influenced by changes in the interactions of porphyrin-ring orbitals with those of aromatic residues in the heme binding site upon reduction and subsequent CO binding.

In a well known practical but approximate method to solve the GS problem, known as the Hartree-Fock (HF) approximation (see e.g. [10]), the domain of variational functions P in Eq. (9) is narrowed to those that are a single Slater determinant (D) 9 d, constructed out of orthonormal spin orbitals tj/iix) ... 

---