Htickel model

An instructive view of the relation between the spectra of the Htickel model (U=0), the Heisenberg model (U large) and the Hubbard model is provided in Fig. 1. Those states described by the Heisenberg model are all of covalent... 

Note that only the free-electron and Htickel models predict an absorption band in the visible in agreement with observation. While the orbital calculations in Ref. 4 are poor for polymethine dyes, they are in principle a superior approach and have given excellent results for saturated hydrocarbons. Indeed unsaturated molecules like the poly-methines can be very well modeled by the semiempirical configuration interaction (CIS) method. 

The initial application of quantum mechanics to the electronic states of a perfect linear conjugated chain, as in the Htickel model discussed in Section 4.2.5 and above, led to a model of a one-dimensional semiconductor with well-defined valence and conduction bands. This labelling of the electronic states is widespread in the literature. On the other hand, when electron correlation is included, the electronic states are more localised and an exciton description is more appropriate. The disorder present in all but a few exceptional cases inevitably leads to the conclusion that the electronic states must be localised by chain defects. The extent to which the electronic states of conjugated polymers are localised, i.e. deviate from the band model, has been a matter of debate. There is a growing body of experimental and theoretical evidence, discussed in Sections 9.4.2 and 9.4.3 below, that suggests that the exciton description is closer to the truth. 

When the Debye-Htickel model was developed, an important hypothesis was made for mathematical convenience, i.e., yi, < kT. Now, using an aqueous 1 1 electrolyte solution at 25 °C as an example, reassess the validity of the hypothesis. What is the physical nature of the hypothesis (Xu)... 

For each model system developed in this book, make it a habit to write out the systems description whenever you encounter that model. Tliis includes the kinetic theory of gases, thermodynamic systems, the Born model, the Debye-Htickel model, electric circuit models of electrochemical systems, etc. 

The Debye-Htickel model considered the solvent to be a structureless medium whose only property is to reduce the interactions between ions in a vacuum by a factor given by the macroscopic relative permittivity, e. No cognisance was taken of the possibility of ion-solvent interactions, and the size of the ion was assumed to be that of the bare ion. Gurney in the 1930s introduced the concept of the co-sphere and this has proved to be a useful concept in the theory of electrolyte solutions. Many recent theories of conductance are based on the Gurney co-sphere concept (see Section 12.17). 

The approach to the parameters of the ligand field is not restricted to the DFT method. The procedure in The LFDFT- an attempt to revive LFT can instead be combined with any method for electronic structure, supposing that it is able to yield (after some averaging) reasonable LF orbitals and effective LF matrix elements. Thus DFT failed badly for rare earths [32, 88, 89]. For that purpose we applied a spectroscopically adjusted extended Htickel model [90]. Alternatively, one can proceed beyond LFT and take average natural atomic orbitals resulting from an average multi-configurational procedure, such as SORCI, and calculate all matrix elements of both one- and two-electron operators. 

According to the Htickel model proposed by Ceulemans and Fowler, the two extra n electrons of the neutral TigC are accommodated in a triply degenerate orbital with t symmetry. Such a situation is susceptible to geometric instability of the Jahn-Teller type. Rather than considering a small deformation toward the trigonal symmetry predicted from the epikemel principle to be the most stable,... 

The Htickel Model of Polyacetylene Revisited Asymptotic Analysis of Peierls Instability... 

Figure 2 shows some of the results for the calculations. We considered a ring of 204 sites and the two approximations of Fig. 1(b) and (c) for different field strengths. Since the Htickel model assumes a set of atom-centered orthonormal basis functions, the coefficients to the eigenfunctions give directly information on the number of electrons on the different atoms. From the total number of electrons, depicted in the figure, it is immediately seen that, for the largest fields, the approximation of Fig. 1(c) leads to solutions where parts of the electrons flow from one end to the other, but in the middle part of the chain the two curves seem to be very similar. There are, however, also in this case minor differences that may be important. Thus, simply... 

The connection between an EEM-like model and semi-empirical quantum mechanical models has been analyzed by Ghosh et al. [40]. The Htickel model for example was found [40,41] to anticipate the idea of taking the response kernels as reactivity indices (hardness and softness kernels and two-variable linear response function). We briefly summarize the main results. 

In the simple Htickel model the approximations are taken to the limit. Only planar conjugated systems are considered. The o-orbitals, which are symmetric with respect to a reflection in the molecular plane, are neglected. Only the Ji-electrons (antisymmetric with respect to the molecular mirror plane) are considered. The overlap matrix... 

In solvents with high dielectric constant, such as water, the solution deviates very little from ideal solutions if they are diluted enough (about 0.1 M) and can be treated using the Debye-Htickel model, as described in section 11.4. 

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