Surface tensor model

Recently, the surface tensor model has been used together with the dielectric continuum model to calculate the orientational order parameters of solutes in nematic solvents [8,9,27], Figure 2.32 shows the theoretical results for anthracene and anthraquinone in nematic solvents with different dielectric anisotropy. Considering only the surface tensor contribution, positive Szz and Sxx and negative are obtained, with Szz > Sxx > Syy. This corresponds to what could be expected on the basis of the molecular shape the long axis (z) is preferentially aligned with the director, and the normal to the... 

It is often argued that it is the shape anisotropy which is largely responsible for liquid crystal formation. Two methods have been proposed to introduce this view into the calculation of the interaction tensor for each conformer. In one it is assumed that the tensor is proportional to the moment of inertia tensor which is readily calculated from a knowledge of the molecular geometry [75]. However, it is found that this paramet-rization results in too great a dependence of the N-I transition temperature on the molecular length [76]. This observation was partly responsible for the development of the surface tensor model [77]. In this the interaction tensor is defined in irreducible form as... 

Using [MoeClg] as an example, apply Stone s surface tensor harmonic model to the species [Ta6Cli2]. To what extent does the topological equivalent orbital model facilitate the application ... 

In what follows the Kirchhoff-Love model of the shell is used. We identify the mid-surface with the domain in R . However, the curvatures of the shell are assumed to be small but nonzero. For such a configuration, following (Vol mir, 1972), we introduce the components of the strain tensor for the mid-surface,... 

Subsequently, Mitchell s group in Vancouver, by means of a tensor-LEED study17 of the Cu (110)-(2 x 3)N surface structure, supported a reconstruction model in which the topmost layer is described as a pseudo-(100)-c(2 x 2)N overlayer with metal corrugation of about 0.52 A in the reconstructed layer. Each nitrogen adatom is almost coplanar with the local plane formed by the four neighbouring copper atoms. Of the four N atoms present in the unit mesh, three are also bonded to Cu atoms in the layer below and therefore are five coordinate. 

An inference of fundamental importance follows from Eqs. (2.3.9) and (2.3.11) When long axes of nonpolar molecules deviate from the surface-normal direction slightly enough, their azimuthal orientational behavior is accounted for by much the same Hamiltonian as that for a two-dimensional dipole system. Indeed, at sin<9 1 the main nonlocal contribution to Eq. (2.3.9) is provided by a term quadratic in which contains the interaction tensor V 2 (r) of much the same structure as dipole-dipole interaction tensor 2B3 > 0, B4 < 0, only differing in values 2B3 and B4. For dipole-dipole interactions, 2B3 = D = flic (p is the dipole moment) and B4 = -3D, whereas, e.g., purely quadrupole-quadrupole interactions are characterized by 2B3 = 3U, B4 = - SU (see Table 2.2). Evidently, it is for this reason that the dipole model applied to the system CO/NaCl(100), with rather small values 0(6 25°), provided an adequate picture for the ground-state orientational structure.81 A contradiction arose only in the estimation of the temperature Tc of the observed orientational phase transition For the experimental value Tc = 25 K to be reproduced, the dipole moment should have been set n = 1.3D, which is ten times as large as the corresponding value n in a gas phase. Section 2.4 will be devoted to a detailed consideration of orientational states and excitation spectra of a model system on a square lattice described by relations (2.3.9)-(2.3.11). 

More advanced mathematical aspects of the graph-theoretical models for aromaticity are given in other references [36, 48, 49]. Some alternative methods, beyond the scope of this chapter, for the study of aromaticity in deltahedral molecules include tensor surface harmonic theory [51-53] and the topological solutions of non-linear field theory related to the Skyrmions of nuclear physics [54]. 

Molecular dynamic studies used in the interpretation of experiments, such as collision processes, require reliable potential energy surfaces (PES) of polyatomic molecules. Ab initio calculations are often not able to provide such PES, at least not for the whole range of nuclear configurations. On the other hand, these surfaces can be constructed to sufficiently good accuracy with semi-empirical models built from carefully chosen diatomic quantities. The electric dipole polarizability tensor is one of the crucial parameters for the construction of such potential energy curves (PEC) or surfaces [23-25]. The dependence of static dipole properties on the internuclear distance in diatomic molecules can be predicted from semi-empirical models [25,26]. However, the results of ab initio calculations for selected values of the internuclear distance are still needed in order to test and justify the reliability of the models. Actually, this work was initiated by F. Pirani, who pointed out the need for ab initio curves of the static dipole polarizability of diatomic molecules for a wide range of internuclear distances. 

The second component of the model then relates fluid flow to local stresses at the surface, giving a stress tensor... 

The usually accepted approach is to adopt an ionic model for the superoxide ion on the surface. In this model, an electron is transferred from the surface to the oxygen to form 02, and there is an electrostatic interaction between the cation at the adsorption site and the superoxide ion. A calculation of the g tensor based on this model (Section 111,A,1) accounts for nearly all the data from adsorbed 02 and is consistent with the evidence that the spin density on both oxygen nuclei is the same (Section III,A,2). However, there are examples of oxygen adsorbed on the surface where the g values do not fit the predictions of the ionic model (Section IV,E) and also a few cases where the spin density on the two oxygen nuclei is found to be different. In these situations it seems likely that a covalent model in which a a bond is formed between the cation and the adsorbed oxygen, is more relevant. 

Chuvylkin et al. (54) have used this approach to discuss EPR signals arising from weak R02 surface complexes in a number of systems where the g tensor does not fit the pattern expected [Eq. (6) and Fig. 3] from the ionic model. This is not discussed quantitatively, but they conclude that the appearance of covalently bonded oxygen is impossible without a favorable orientation of appropriate electronic orbitals. A similar covalent bonding approach has been considered theoretically for the chemisorption of oxygen on silicon surfaces (55). Examples of weakly bonded oxygen are given in Section IV,E. 

The discussion of the hyperfine tensor has indicated clearly that the analysis of the hyperfine pattern has been very valuable in developing an understanding of the adsorbed oxygen ion. On balance, in the oxide systems it would seem preferable to use the term superoxide rather than peroxide or peroxy for 02. Overall, the picture is largely consistent with an ionic model for 02 on surfaces. 

The bonding in gold cluster molecules has been interpreted using free electron models based on Stone s tensor surface harmonic theory [48, 49]. High similarity has... 

Ab initio calculations of 29Si and 13C NMR chemical shielding tensors have been used as an aid in the interpretation of experimental results aimed at elucidating the role of alkoxyalkylsilanes as external electron donors in Ziegler-Natta catalysis of propene. The results support a model in which dialkoxydialkylsilanes are loosely attached to two adjacent magnesium ions on the surface of magnesium chloride, but trialkoxyalkylsilanes are attached primarily by only one magnesium ion. 

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