Intrinsic states

Surface states can be divided into those that are intrinsic to a well ordered crystal surface with two-dimensional periodicity, and those that are extrinsic [25]. Intrinsic states include those that are associated with relaxation and reconstruction. Note, however, that even in a bulk-tenuinated surface, the outemiost atoms are in a different electronic enviromuent than the substrate atoms, which can also lead to intrinsic surface states. Extrinsic surface states are associated with imperfections in the perfect order of the surface region. Extrinsic states can also be fomied by an adsorbate, as discussed below. 

Figure 14. Tunneling to the alternative state at energy can be accompanied by a distortion of the domain boundary and thus populating the ripplon states. All transitions exemplified by solid lines involve tunneling between the intrinsic states and are coupled linearly to the lattice distortion and contribute the strongest to the phonon scattering. The vertical transitions, denoted by the dashed lines, are coupled to the higher order strain (see Appendix A) and contribute only to Rayleigh-type scattering, which is much lower in strength than that due to the resonant transitions.

The E-state indices are atomic descriptors composed of an intrinsic state value I and a perturbation AI that measures the interactions with all other atoms in a molecule. The Kier-Hall electronegativity is the starting point in the definition of the intrinsic state of an atom, which encodes its potential for electronic interactions and its connectivity with adjacent atoms. The intrinsic state of an atom i is [19, 21] ... 

The second contribution to the E-state index comes from the interactions between an atom i and all other atoms in the molecular graph. The perturbation on the intrinsic state value / of atom i due to another atomj depends on the difference between the corresponding intrinsic state values, (f- /,), and on the graph distance between atoms i andj. The overall perturbation on the intrinsic state value I of atom i is ... 

Finally, the E-state index S of atom i is the sum of the intrinsic state and of the perturbation term ... 

Another extension of the E-state descriptors describes the bond parameters derived from intrinsic states. Bond E-state indices are based on intrinsic values that are the geometric mean of the atom intrinsic value [20] ... 

The situation for three-dimensional problems is similar to that discussed in Section 7.15. One begins by constructing the ground state. The coordinate is now a vector, a, and the intrinsic state is... 

The intrinsic state (7.126) describes the ground state of a diatomic molecule. The orientation of the axis of the molecule in space can be chosen arbitrarily. It is convenient to choose it along the z direction (Figure 7.3). The coherent state (7.126) depends then only on the magnitude of a, and can be written as... 

Sidebar 10.3 outlines the useful analogy to normal-mode analysis of molecular vibrations, where the null modes correspond to overall translations or rotations of the coordinate system that lead to spurious alterations of coordinate values, but no real internal changes of interatomic distances. For this reason, the internal metric M( of (10.29) is the starting point for analyzing intrinsic state-related (as opposed to size-related) aspects of a given physical system of interest. 

As an application of this method let us choose as fermion generating functions the intrinsic states... 

The electrotopological state (E-state) indices are a group of atom level descriptors that are calculated for each atom (such as >C<, >N-, =0) or hydride group (such as -CH3, >NH, UOH) in the molecule. For simplicity, these groups are all termed atoms (Rose et al., 2002). The E-state index for an atom i in a molecule, S(i), is composed of an intrinsic state, I, plus the sum of perturbations, IM. from all other atoms in the molecule ... 

The intrinsic state and the perturbation term are calculated as follows ... 

The term Ed, stands for charging contributions. This term is absent in spectra of samples exhibiting a finite density of states at the Eermi level. For all practical purposes this is correct for aU true metals and for many semiconductors with intrinsic states near zero binding energy. Many systems relevant in catalysis do, however, not fulfill this condition (all non-black samples, glasses, porous materials, supports) or even worse, are composites of metallic and non-metaUic systems, giving rise to mixed metalhc-insulating behavior of their surface under PES. Such... 

The above case refers to the semiconductor in its intrinsic state with very low carrier concentrations under ambient conditions. The Fermi level, in this case lies approximately in the middle of the energy band-gap (Figure 4a). This simply reflects the fact that the probability of electron occupancy is very high in VB and very low in CB and does not imply an occupiable energy level at itself... 

P. Ao, D. Galas, L. Hood, X. Zhu, Cancer as robust intrinsic state of endogenous molecular-cellular network shaped by evolution. Med. Hypotheses. 70(3), 678-684 (2008)... 

The intrinsic state of an atom can be simply thought of as the ratio of k and lone pair electrons to the count of the a bonds in the molecular graph for the considered atom. Therefore, the intrinsic state reflects the possible partitioning of non-o electrons influence along the paths starting from the considered atom the less partitioning of the electron influence, the more available are the valence electrons for intermolecular interactions. From the intrinsic state the -> Q polarity index was derived. 

The perturbation Ay = /, - Ij of the ith intrinsic state by the jth atom can be viewed as an electronegative gradient whose sign gives the direction of influence of surrounding atom intrinsic states. 

From the definition of intrinsic states and field effects, it can be seen that large positive values of E-states S relate to atoms of high electronegativity and/or terminal atoms or atoms that lie on the mantle of the molecule small or negative E-state values correspond to atoms possessing only o electrons and/or buried in the interior of the molecule or close to higher electronegative atoms. Therefore, the E-state index is a measure of the electronic accessibility of an atom and can be interpreted as a probability of interaetion with another molecule. However, the index cannot be considered a pure electronic descriptor it is, in fact, a descriptor of atom polarity and steric accessibility. 

Another approach [Kier and Hall, 1999] is to apply the -state definition to each vertex of the molecular graph where the hydrogens of polar groups (-OH, -NH, -COOH, etc.) are explicitly considered as independent vertices. In this case, the intrinsic state of polar hydrogens will be ... 

---