Theory extended Hiickel

Hiickel molecular-orbital calculation, 34 227 Hiickel theory, extended, 25 2, 3 approximations, 25 6... 

Normally, the validity of the Debye—Hiickel theory extends little further than kR <1. At room temperature, this requires ionic concentrations < 0.1 mol dm-3 for univalent ions in water, 0.03moldm-3 for univalent ions in ethanol or <0.01 mol dm-3 for univalent ion in ethers. In these cases, ions may be regarded as point particles and the strong repulsive core potential ignored. Furthermore, the time taken for non-reactive ions to diffuse far enough to establish an ionic-atmosphere around an ion, which was suddenly formed in solution containing only univalent ions, is... 

Extended Hiickel theory Generalised valence bond model Hartree-Fock... 

The simplest approximation to the Schrodinger equation is an independent-electron approximation, such as the Hiickel method for Jt-electron systems, developed by E. Hiickel. Later, others, principally Roald Hoffmann of Cornell University, extended the Hiickel approximations to arbitrary systems having both n and a electrons—the Extended Hiickel Theory (EHT) approximation. This chapter describes some of the basics of molecular orbital theory with a view to later explaining the specifics of HyperChem EHT calculations. 

HyperChem currently supports one first-principle method ab initio theory), one independent-electron method (extended Hiickel theory), and eight semi-empirical SCFmethods (CNDO, INDO, MINDO/3, MNDO, AMI, PM3, ZINDO/1, and ZINDO/S). This section gives sufficient details on each method to serve as an introduction to approximate molecular orbital calculations. For further details, the original papers on each method should be consulted, as well as other research literature. References appear in the following sections. 

The off-diagonal elements of Extended Hiickel theory, (fi v) represent the effects of bonding between the atoms and are assumed to be proportional to the overlap, Sj y. An approximation for differential overlap referred to as the Mulliken approximation... 

In an early investigation (66T539) the two highest occupied and the two lowest unoccupied orbitals were calculated on the basis of an extended Hiickel theory to determine the electron transition responsible for the long wavelength UV absorption. An Ai- Bi, [Pg.197]

The pioneering calculations of Wolfsberg and Helmholtz on Mn04, Cr04 and CIO4 are usually cited as the first applications of extended Hiickel theory... 

The systematic application of extended Hiickel theory to organic molecules comes with the work of Hoffmann. 

An Extended Hiickel Theory. I Hydrocarbons Roald Hoffmann... 

Theoreticians did little to improve their case by proposing yet more complicated and obviously unreUable parameter schemes. For example, it is usual to call the C2 axis of the water molecule the z-axis. The molecule doesn t care, it must have the same energy, electric dipole moment and enthalpy of formation no matter how we label the axes. I have to tell you that some of the more esoteric versions of extended Hiickel theory did not satisfy this simple criterion. It proved possible to calculate different physical properties depending on the arbitrary choice of coordinate system. 

In analogy to extended Hiickel theory, there are also charge iterative methods for simple Hiickel theory. The equivalent of eq. (3.90) is... 

Experience shows that solutions of other electrolytes behave in a manner similar to the examples we have used. The conclusion we reach is that the Debye-Hiickel equation, even in the extended form, can be applied only at very low concentrations, especially for multivalent electrolytes. However, the behavior of the Debye-Hiickel equation as we approach the limit of zero ionic strength appears to give the correct limiting law behavior. As we have said earlier, one of the most useful applications of Debye-Hiickel theory is to... 

These arguments go hand in hand with Extended Hiickel Theory (EHT), both being based on overlap (symmetry) considerations. In fact, an EHT calculation will provide almost exactly the same results as a skilful use of the qualitative MO building scheme we have provided in this section. 

Hoffmann, R. An extended Hiickel theory. I. Hydrocarbons. J Chem Phys 1963 39 1397-412. 

As an aid in the qualitative understanding of why photocleavage occurs, it is interesting to consider the results of semiempirical extended Hiickel theory (EHT)t86) for the following model compounds<87) ... 

Bond strengths are essentially controlled by valence ionization potentials. In the well established extended Hiickel theory (EHT) products of atomic orbital overlap integrals and valence ionization potentials are used to construct the non-diagonal matrix elements which then appear in the energy eigenvalues. The data in Table 1 fit our second basic rule perfectly. 

One year later, the new model took its final name of Extended Hiickel Theory, and was cast in the concise, attractively simple form that has survived to date in a comprehensive paper on hydrocarbons, Roald Hoffmann (4) was able to show that many different properties of these compounds could be correctly calculated, thus establishing the operative validity of the method. 

This process and the related questions of the electronic structure of substituted methylenes (12), (13) were the subject of careful analysis by Extended Hiickel Theory (hence-... 

The molecular orbital methods which have been employed for such studies include extended Hiickel theory (EHT), CNDO, and ab initio LCAO-SCF. 

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