Charges centroid

Figure 10.1 Adsorption of an adsorbate onto a substrate. The charge necessary to form the adsorptive bond comes from the charge centroid of the adsorbate...

Now, to return to the orange stain, formed on the surface of a pan by adsorption of capsaicin from a solution (the curry). Such organic dyes are usually unsaturated (see the structure I above), and often comprise an aromatic moiety. The capsaicin, therefore, has a high electron density on its surface. During the formation of the adsorption bond, it is common for this electron cloud to interact with atoms of metal on the surface of the pan. Electron density flows from the dye molecule via the surface atoms to the conduction band of the bulk metal. The arrows on Figure 10.4 represent the direction of flow as electron density moves from the charge centroid of the dye, through the surface atoms on the substrate, and thence into the bulk of the conductive substrate. 

A centroid is the location of a physicochemical phenomenon or effect or quantity. A charge centroid, therefore, represents the part of a molecule or ion having the highest charge density. 

Figure 10.4 Schematic representation of a dye molecule adsorbing on a substrate. The large arrow indicates the movement of charge from the charge centroid to form an adsorptive bond. Notice the way charge delocalizes, once it enters the substrate...

The description of a and tt charge centroids in unsaturated systems, and their role in energy calculations, evaluated by means of the function F/ i, Eq. (10.35)... 

We should note here that the bond length versus charge-transfer relationship in TCNQ molecules has been established by Flandrois and Chasseau [72] from x-ray data and is thus valid for x-ray data only. In fact, x-rays and neutrons provide atom positions which generally do not coincide. The former radiation measures the charge centroid location, while the latter measures the nuclear position. As a consequence, a different parametri-zation must be used for neutron data [36]. 

The localized character of the geminals can be displayed by introducing the concepts of charge centroids [22] and charge ellipsoids [23, 24] of the geminal one-electron densities. By using these localization measures, we can classify the geminals as core electron pairs, lone pairs and bond pairs [25]. 

Fig. 1. Intersection between the xy-plane and the charge ellipsoids of the localized orbitals of the neon dimer. Relative interatomic distance twice as large as on figure. Charge centroids are marked with a cross and nuclear positions with a dot. The numbering of the ellipsoids is utilized in Table 3.

Fig. 12. Electronic properties of the formyl radical, (a) Charge centroid distribution, (b) Spin density.

Note that a distinction is made between electrostatic and polarization energies. Thus the electrostatic term, Ue e, here refers to an interaction between monomer charge distributions as if they were infinitely separated (i.e., t/°le). A perturbative method is used to obtain polarization as a separate entity. The electrostatic and polarization contributions are expressed in terms of multipole expansions of the classical coulomb and induction energies. Electrostatic interactions are computed using a distributed multipole expansion up to and including octupoles at atom centers and bond midpoints. The polarization term is calculated from analytic dipole polarizability tensors for each localized molecular orbital (LMO) in the valence shell centered at the LMO charge centroid. These terms are derived from quantum calculations on the... 

The experimental ground-state geometry [138] was used with the molecule in the xy plane. ANO basis functions contracted as C,N/ Asl>pld, H/2sl/ , were used, supplemented with Islpld Rydberg functions in the cation charge centroid. The study of the electronic spectrum of imidazole involved tt— t7, 7t, and Rydberg states (in the gas... 

When adsorption is present and the effects of a compact layer are included as well, it has been shown (Macdonald et al. [1980]) that in the [0, 0, °o] case the (U -> 0 expression for the total differential capacitance is more complicated than just Crs and Ca in parallel. One needs first to separate Cc into two series parts so Cc = C -H Cf, where C is the capacitance between the electrode and the charge centroids of the adsorbed ions (at the inner Helmholtz plane), and is that from this plane to the outer Helmholtz plane, where the diffuse layer of charge begins. Then one obtains the circuit of Figure 2.2.9, which reduces to the above result for... 

One of the first attempts of use molecular orbitals for a multipole expansion of the MEP was by Cohan [175]. The MO charge centroids were selected as expansion centres and the formal expression of this segmental expansion were compared with those of the conventional one-centre multipole expansion. As a test case, Cohan selected H2, and so the paper is simply indicative of a possible alternative to the multipole expansion strategy, being in the specific case the canonical MO coincident with the LO, and its charge centre coincident with the molecular centre of masses. 

A similar study at the MP (4th order) basis set level by different researchers finds I and IX to be the stable structures (IX, a nonplanar double-bridged structure is similar to IV) the latter is less stable than the former by 2.3 kcal/mol [3]. Yet another study treats the system similarly and identifies the charge centroids for the species. The bridge hydrogen atoms are shown to be appropriately considered as protonated double bonds. Structural parameters for XI are calculated, in this study, to be r(B-B)=1.601, r(B-H)=1.22 and 1.178 A <(Ht-B-B)=105.9 [4]. An ab initio determination of the B-B coupling constant for B2H4 gives values of 77.61 and 64.91 Hz, when the coupled-Hartree-Fock (CHF) and equations-of-motion (EOM) methods, respectively, are used. For J(B,H), values of 122.99 and 104.51 Hz are similarly obtained [5]. 

Seggem H (1981b) Detection of siuface and bulk traps. J Appl Phys 52 4086-4089 Seggem H, West J, Kubli R (1984) Determination of charge centroids in two-side metallized electrets. Rev Sci Instr 55(6) 964-967... 

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