Hiickel method extended

Unlike the Hiickel and extended Hiickel methods, the semi-empirical approaches that explicitly treat electron-electron interactions give rise to Fock matrix element... 

The Extended Hiickel method, for example, does not explicitly consider the effects of electron-electron repulsions but incorporates repulsions into a single-electron potential. This simplifies the solution of the Schrodinger equation and allows HyperChem to compute the potential energy as the sum of the energies for each electron. 

The Extended Hiickel method also allows the inclusion of d orbitals for third row elements (specifically. Si, P, S and Cl) in the basis set. Since there are more atomic orbitals, choosing this option results in a longer calculation. The major reason to include d orbitals is to improve the description of the molecular system. 

Note You cannot use the Extended Hiickel method or any one of the SCFmethods with the Cl option being turned on for geometry optimizations, molecular dynamics simulations or vibrational calculations, in the current version of HyperChem. 

Note You can not use the Extended Hiickel method, nor any of the other SCFmethods with the Cl option turned on, for geometry optimization or molecular dynamics simulations. 

The Extended Hiickel method neglects all electron-electron interactions. More accurate calculations are possible with HyperChem by using methods that neglect some, but not all, of the electron-electron interactions. These methods are called Neglect of Differential Overlap or NDO methods. In some parts of the calculation they neglect the effects of any overlap density between atomic orbitals. This reduces the number of electron-electron interaction integrals to calculate, which would otherwise be too time-consuming for all but the smallest molecules. 

Molecular orbital calculations for the parent vinyl cation, Cj H3, were first reported by Hoffmann (161), who used the extended Hiickel method, and more recently by Yonezawa and co-workers (162), who used a semiempirical SCF procedure. Both treated the problem of classical, 172 (R = H), versus bridged structures, 173, but the methods suffered from their inability to account satisfactorily for bond-length changes, and neither discussed the question of linear, 172a, versus bent, 172b, structures. 

The extended Hiickel method has been used in a discussion of properties and reactivity of radicals and biradicals (75). We have found it possible to correlate the basicity constants, pKbh. of radical anions with extended Hiickel data (76). 

The definition of "concepts" must be accompanied by explicit recipes for computing them is actual cases. There is no more space in theoretical chemistty for "driving forces", "effects, etc. not accompanied by specific rules for their quantification. The impact of a new "concept will be greater if the rules of quantifications are not restricted to ad hoc methods, but related to methods of general use in molecular quantum mechanics. A concept based exclusively on some specific features of a given method, e g. the extended Hiickel method, is less robust than a concurrent concept which may be quantified also using other levels of the theory. 

Let us now specialize the above equations for the special case when only the population Ur of the r-th MO changes, and the reference scheme is a simple a>-technique [10] applied to an extended-Hiickel method, which is a highly simplified form of the BMV procedure. 

Figure 1. Density of states for various Ag clusters computed for 4d-, 5 s-, and 5p-orbitals within the extended Hiickel method. (Reprinted from Ref [32], 1981, with permission from Elsevier.)...

Of the many discussions of the intrinsic properties of the Extended Hiickel method, that of Blyholder and Coulson (7a) can be specially recommended. The validity of the above mentioned cancellation of repulsions seems to be substantiated (7b). 

The electronic structures of furan, thiophene, and selenophene, their protonated complexes, and their anions have been calculated by the extended Hiickel method.6 The results of these calculations have been used to determine the influence of the heteroatom on the degree of aromaticity and electron density. 

One of the simplest approaches to comprehensive molecular orbital calculations is the extended Hiickel method. This method was developed by Roald Hoffman in the 1960s, and it was applied to hydrocarbon molecules. From the discussion presented in Chapters 2 and 3, we know that one of the first things that has to be done is to choose the atomic wave functions that will be used in the calculations. One of the most widely used types of wave functions is that known as the Slater wave functions (see Section 2.4). In the extended Hiickel method, the molecular wave functions are approximated as... 

At the opposite extreme from the ab initio SCF methods is the Wolfberg-Helmholtz approximation which Hoffmann 6> has applied extensively to organic problems under the term extended Hiickel method . While this has the advantage of requiring very little computation time, the results are so unreliable that the method is essentially useless for the calculation of potential surfaces. Not only are the errors in heats of atomization comparable with those given by ab initio SCF but they are not even the same for isomers. A good example is provided by cyclopropanone (1) which is predicted 7> to be less stable than the isomeric zwitterion 2, a result at variance with the available evidence ) concerning the... 

In the usual formulation of the extended Hiickel method, the elements of the hamiltonian matrix are computed according to a simple set of arithmetic rules, and do not depend on the molecular orbitals. In this way, there is no need for the iterations required by more sophisticated methods, and in practice the results may be obtained nowadays in a question of seconds for any reasonably sized complex. 

Figure 1. a donation interaction between metal and hydride (left), and n backdonation interaction metal and carbonyl (right) as computed by the extended Hiickel method. 

The utility of the extended Hiickel method for qualitative analysis must nevertheless not hide its limitations when quantitative results are desired. Although it can be of some utility in predicting bond and dihedral angles, it is unappropriate for the prediction of bond distances or bond energies. As a result, it cannot be applied to any reaction where bonds are made or broken,... 

The continued success of the extended Hiickel method in transition metal chemistry, where it was the method of choice until the mid 1980 s is surely related to the problems of other semiempirical methods in this area of chemistry. While methods like MOP AC [21] or AMI [22] have been extremely productive in the field of organic chemistry, they have found little success in transition metal chemistry. These methods are based in equation 2, similar to 1, but with the very significant difference that the Fock matrix F is computed from the molecular orbitals, in an iterative way, though through an approximate formula. 

The high-resolution C spectrum has also been measured, and the following values obtained chemical shift (in acetone) 62.4 ppm upheld from CSg (130.9 ppm downfield from tetramethylsilane) J (geminal) CH, 205 Hz J (vicinal) CH, 13.4 Hz. The chemical shift value is in accord with an empirical equation based on the number and position of the nitrogen atoms in several five-membered heterocyclics, and also reflects the 7T-electron density of the system as calculated by the extended Hiickel method - and by the simple MO method. spectra of v-triazole and of its 1- and 2-methyl derivative have also been obtained. ... 

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