Molecular orbital methods extended Huckel method

Several different molecular orbital methods have been used in SAR investigations. These include simple Huckel theory, HT,(38) extended Huckel theory, EHT,(39) CND0,( ) NDD0,(41) MINDO/3,(42) and PCILO,(43)... 

Hiickel and extended Huckel methods are termed semi-empirical because they rely on experimental data for the quantification of parameters. There are other semi-empirical methods, such as CNDO, MINDO, INDO, in which experimental data are still used, but more care is taken in evaluating the Htj. These methods are self-consistent field procedures based on 3 SCF. They are discussed in various works on molecular orbital theory.4... 

At first we would like to recall a few important conclusions from earlier studies. The electronic structure of the reactant CpML has been discussed by Hofmann and Padmanabhan [22] for various ligands L and M = Co, Rh, and Ir with the extended Huckel method. As shown in Fig. 5, the valence molecular orbitals are m, ma", n -I- l)a, (w -I- l)a", and (n + 2)a orbitals under Cj symmetry. One sees that the m and rm" orbitals are mainly d x yy and orbitals stabilized by interaction with the ir orbitals on L. At somewhat higher energy is the occupied metal-based d orbital, (n + l)a , with a weak M-L antibonding a interaction. The metal-based (m + l)fl" (dj,j) and (n -H 2)a (d y) orbitals are highest in energy, destabilized by interaction with occupied tt orbitals on the Cp ring. In addition, the (n -I- 2)a orbital destabilized by interaction with the a orbital on L. Thus, it... 

Hiickel theory is clearly limited, in part because it is restricted to tt systems. The extended Huckel method is a molecular orbital theory that takes account of all the valence electrons in the molecule [Hoffmann 1963]. It is largely associated with R Hoffmann, who received the Nobel Prize for his contributions The equation to be solved is FC = SCE, with the... 

Within the Extended-Huckel method the bond energy is equal to the difference between the sum of the occupied molecular orbitals in the complex and the sum of the occupied molecular orbitals in the fragments. This follows from Eq.(2.31) when the change in intra-atomic electron-electron repulsion is ignored. This is the last assumption involved in the Extended-Huckel method ... 

In the extended Huckel method [44], molecular orbitals are expanded in a minimum basis set. 

In recent years the fundamental ideas of Huckel molecular orbital theory, the Huckel rule, and other aspects of aromaticity have been extended to polyhedral three-dimensional inorganic structures regarded as aromatic like the two-dimensional aromatic hydrocarbons. Such an extension of Huckel molecular orbital theory requires recognition of its topological foundations so that they can be applied to three-dimensional structures as well as two-dimensional structures. In this connection graph theoretical methods can be used to demonstrate the close analogy between the delocalized bonding in two-dimensional planar aromatic systems such as benzene and that in three-dimensional deltahedral boranes, and carboranes. Related ideas can be shown to be applicable for metal carbonyl clusters, bare post-transition metal clusters, and polyoxometallates. ... 

The primary reason for interest in extended Huckel today is because the method is general enough to use for all the elements in the periodic table. This is not an extremely accurate or sophisticated method however, it is still used for inorganic modeling due to the scarcity of full periodic table methods with reasonable CPU time requirements. Another current use is for computing band structures, which are extremely computation-intensive calculations. Because of this, extended Huckel is often the method of choice for band structure calculations. It is also a very convenient way to view orbital symmetry. It is known to be fairly poor at predicting molecular geometries. 

Other approximate, more empirical methods are the extended Huckel 31> and hybrid-based Hiickel 32. 3> approaches. In these methods the electron repulsion is not taken into account explicitly. These are extensions of the early Huckel molecular orbitals 4> which have successfully been used in the n electron system of planar molecules. On account of the simplest feature of calculation, the Hiickel method has made possible the first quantum mechanical interpretation of the classical electronic theory of organic chemistry and has given a reasonable explanation for the chemical reactivity of sizable conjugated molecules. 

Methods based on simulated Ab initio Molecular Orbital technique (SAMO) or cm the application of Linear Combination of Localized Orbitals have been proposed. The a priori advantages are a negligible cost (typically of the order of magnitude of an extended Huckel calculation) and the ab initio character of the approach. They suffer however from a rather tedious generation of a high number of matrix elements and it is still impossible to... 

Polymer Conformation and Crystallinity. Beyond the stereoregularity and tacticity, the geometrical conformation of the polymer chain in the solid material could influence its electronic structure, through a modification of its valence band molecular orbitals. Indeed, a few years ago, very characteristic band structures were calculated for T, G, TG, and TGTG polyethylenes ( ). More recently. Extended Huckel crystal orbital calculations showed that for isotactic polypropylene, a zig-zag planar or a helical conformation resulted in significant changes in the theoretical valence band spectra, supporting the idea that conformation effects could be detected experimentally by the XPS method ( ). 

A wide range of theoretical methods has been applied to the study of the structure of small metal clusters. The extremes are represented on the one hand by semi-empirical molecular orbital (Extended Huckel) (8 ) and valence bond methods (Diatomics-In-Molecules) ( ) and on the other hand by rigorous initio calculations with large basis sets and extensive configuration interaction (Cl) (10). A number of approaches lying between these two extremes have been employed Including the X-a method (11), approximate molecular orbital methods such as CNDO (12) and PRDDO (13) and Hartree-Fock initio molecular orbital theory with moderate Cl. 

By far, the theoretical approaches that experimental inorganic chemists are most familiar with and in fact nse to solve questions qnickly and qnalitatively are the simple Huckel method and Hoffinann s extended Hiickel theory. These approaches are nsed in concert with the application of symmetry principles in the bnUding of syimnetry adapted linear combinations (SALCs) or gronp orbitals. The ab initio and other SCF procednres ontlined above prodnce MOs that are treated by gronp theory as well, bnt that type of rigor is not usually necessary to achieve good qnahtative pictures of the character aud relative orderiugs of the molecular orbitals. 

The molecular structure entry is performed by sketching the compounds on a graphics terminal, and then storing them as connection tables. The geometries are optimized using adapt s molecular mechanics routine, MM2 [4], the semiempirical molecular orbital program (MOPAC) [5], or a newly developed extended Huckel method [6]. 

Molecular-orbital theory has taken many forms and has been dealt with by many approximations. In 1963 Hoffmann S presented a formalism which he referred to as extended Hiickel (EH). In the 1930 s, however, this formalism would simply have been called molecular-orbital, since it is a straightforward application of molecular-orbital (MO) theory, using a one-electron Hamiltonian. Hoffmann referred to it as extended Hiickel because it did not limit itself to 7r-electron systems and was able to deal with saturated molecules by including all overlap integrals. In these respects it did extend the usual, or simple Huckel, method, which was customarily applied to 7T-electrons, and assumed complete tt — a separability. 

EHMO extended Huckel molecular orbital (quantum chemical method)... 

In 1976 Leban et used this approach to study the interaction of a platinum electrode with several particles, among them the water molecule and halide ions. The cluster used was taken to be a model of the Pt( 111) surface and contained only five platinum atoms. In this work the iterative extended Huckel molecular orbital (lEHT) method was used. The stability of the adsorption of the water molecule and of the ions was tested by computing the charge transfer to the cluster and the total energy of the system for various positions of the adsorbate on the surface. 

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