Extended Hiickel Theory EHT

This method is very fast, though ignoring electron-electron repulsion is a serious disadvantage. However, unlike NDO methods, overlap is not neglected in normalizing and evaluating the wavefunction. Furthermore, since the complex two electron integrals are not present, the method uses STOs as the basis set. 

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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. 

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. 

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. 

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

Extended Hiickel theory (EHT) was applied to study the decomposition of the five-membered metallacycle intermediate proposed by Mimoun for the epoxidation by Mo bisperoxo complexes [44, 45]. Another EHT study [40] proposed the coordination of ethene to the metal center of an MoO(02)2 complex as the first step, followed by a slipping motion of ethene toward... 

Prior to considering semiempirical methods designed on the basis of HF theory, it is instructive to revisit one-electron effective Hamiltonian methods like the Hiickel model described in Section 4.4. Such models tend to involve the most drastic approximations, but as a result their rationale is tied closely to experimental concepts and they tend to be intuitive. One such model that continues to see extensive use today is the so-called extended Hiickel theory (EHT). Recall that the key step in finding the MOs for an effective Hamiltonian is the formation of the secular determinant for the secular equation... 

A series of extended Hiickel theory (EHT) band calculations on crystal structures 16 and 17 have been performed <2003JA14394, 2004CM1564>. They show that the dispersion curves plotted along the stacking direction arise from the SOMOs of the radicals in the cell unit, that is, the putative half-filled conduction band of the molecular metal. Clearly, none of the materials are metallic, but the dispersion curves nonetheless provide insight into the extent of the intermolecular interaction along and perpendicular to the slipped 7t-stacks. 

The most widely used semiempirical quantum chemistry technique for theoretical chemisorption studies is the Extended Hiickel Theory (EHT). The method was first proposed by Hoffmann/95/ in its nonrelativistic form, and by Lohr and Pyykko/96/ and also Messmer/97/ in its relativistic form, based on the molecular orbital theory for calculating molecular electronic and geometric properties. For a cluster the molecular orbitals are expanded as linear combinations of atomic orbitals... 

Blower et al. have used extended Hiickel theory (EHT) to find an explanation for the spontaneous C-S bond cleavage in 9S3 complexes of Re and Tc with loss of ethene, while the analogous complexes of higher transition metals become more and more stable <1999JCD3759>. 

The first of these methods was developed by Hoffmann in 1963 (1) and is known as extended Hiickel theory (EHT). Briefly, the method uses Hiickel formalism however, explicit consideration of non-bonded interactions and all overlap integrals are a refinement. Slater orbitals are used, and the computations require only one parameter, the valence state ionization potential for the Coulomb integral and indirectly for the reso-... 

Hoffmann-type extended Hiickel theory (EHT) calculations have been carried out on the parent cyclopropyl radicaP. The calculations were in reasonable agreement with the ESR spectral results obtained by Fessenden and Schuler . However, the predicted a-... 

More sophisticated procedures involve taking the start MO coefficients from a semi-empirical calculation, such as Extended Hiickel Theory (EHT) or Intermediate Neglect aif Differential Overlap (TNDO) (Sections 3.12 and 3.9). The EHT method has the advantage that it is readfiy parameterized for allEIements, and irxau provide starF orbitals for systems involving elements from essentially the whole periodic table. An INDO calculation normally provides better start orbitals, but at a price. The EMDO... 

Nowadays, the success of the methods proposed by Hoffmann 50> and by Pople and Segal 51> among the chemists tends to promote the use of pure atomic orbital bases for all-valence treatments. The first method is a straightforward application of the Wolfsberg-Helmholz treatment of complexes to organic compounds and is called the Extended Hiickel Theory (EHT), because its matrix elements are parametrized in the same way as the Hiickel method with overlap for n electrons. The other method, known under the abbreviation Complete Neglect of Differential Overlap (CNDO), includes electron repulsion terms by extending to a orbitals the successful approximation of zero-differential overlap postulated for n electrons. 

Computations on biomolecules have been performed by practically all the available all-valence electrons prcedures. The simplest is the extended Hiickel theory (EHT) in the version developed by Hoffmann 2) which is an extension of the well-known Hiickel approximation for it electrons in the sense that the molecular orbitals are obtained.as the eigenvalues of an effective Hamiltonian H that is not explicit, the matrix elements of H being treated as empirical input characteristics of the atoms involved. 

Extended Hiickel Theory (EHT) uses the highest degree of approximation of any of the approaches we have already considered. The Hamiltonian operator is the least complex and the basis set of orbitals includes only pure outer atomic orbitals for each atom in the molecule. Many of the interactions that would be considered in semi-empirical MO theory are ignored in EHT. EHT calculations are the least computationally expensive of all, which means that the method is often used as a quick and dirty means of obtaining electronic information about a molecule. EHT is suitable for all elements in the periodic table, so it may be applied to organometallic chemistry. Although molecular orbital energy values and thermodynamic information about a molecule are not accessible from EHT calculations, the method does provide useful information about the shape and contour of molecular orbitals. 

Extended Hiickel Theory (EHT) Poor Determining shapes of MOs Good Low Upto 100 atoms or more... 

The most common theoretical tool used is calculation by the extended Hiickel theory (EHT). For solids these lead to a density-of-states (DOS) diagram. This is a picture of the number of energy levels per unit of energy, as a function of the energy. A high density of states at the Fermi level leads to stronger adsorption of a substrate. It may also be recalled that the DOS at the Fermi level is equal to the local softness. In DFT a high value of the softness also leads to better interaction with a substrate. 

A generalization of the Hiickel method to nonplanar systems comprised of carbon and heteroatoms is the Extended Hiickel Theory (EHT) [27 30]. It takes explicitly into account all valence electrons, i.e., Is for H and 2s,2p for C, N, O, and F. Similar to the HMO method, the Fock matrix in EHT FEHT does not contain two-electron integrals. The diagonal elements F T are obtained from experimental ionization potentials (IPs) where the Koopmans theorem [31] has been used. 

Extended Hiickel theory (EHT) calculations on oxazole suggest a significant polarization of the a framework.223 This a polarization appears to follow simple electronegativity considerations. The calculated ir polarizations are independent of, and may be opposed to, the corresponding a polarizations. A good correlation is observed between the total (calculated electron densities223 and the experimental proton chemical shifts (see Section III,G). 

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