EHMO methods

Molecular orbital calculations of varying sophistication have been used to try to predict the relative stabilities of the W, S, and U conformers. The earliest using the EHMO method predicted that the U conformer is the most stable (70), but MNDO (74) suggests that the W form is of lowest energy for the parent C5H7 anion. Most of these calculations relate to the gaseous ion, but similar conclusions were reached by inclusion of lithium or BeH (71-73). The merits and demerits of the calculations are discussed by Dewar et al. (74). 

Steric factors probably prohibit simultaneous rotation of the olefin and alkyne C2 units which would crowd all four metal-bound carbons into the same plane. Separate rotation of each unsaturated ligand was explored theoretically using the EHMO method. Rotation of the olefin destroys the one-to-one correspondence of metal-ligand tt interactions. Overlap of the filled dxz orbital with olefin n is turned off as the alkene rotates 90°, creating a large calculated barrier for olefin rotation (75 kcal/mol). Alkyne rotation quickly reveals an important point the absence of three-center bonds involving dir orbitals allows the alkyne to effectively define the linear combinations of dxy and dyz which serve as dn donor and dir acceptor orbitals for 7T and ttx, respectively. Thus there should be a small electronic barrier to alkyne rotation (the Huckel calculation with fixed metal... 

Qualitative MO theory (extended Hiickel molecular orbital ((EHMO) method) was employed for a rationalization of the electron density distributed over the three centers S-I-I in diiodine adducts of 4,5-ethylenedithio-l,3-dithiole-2-thione <1999IC4626>. 

For the treatment of large polyatomic systems, computational methodologies deal with a compromise between an overall description of the entire system and a more detailed handling of a properly selected part of it. This situation particularly applies to the transition metal structures that have to be drastically minimized for an adequate ob initio, local density functional, or even semiempirical calculation at a good correlation level. In contrast to this simplification of the system, the improvements of the simpler methods, which are capable of handling the system as a whole, have regained acceptability. This is the case of the EHMO method developed by Hoffman [19], which was initially used for a reasonable description of the structural and electronic properties of the systems at a frozen geometry. Improvements of this method are mainly related to the addition of the (two-body electrostatic correction) term as explained above [20,21],... 

We are only interested in the localized wave function of the electron, for example, the highest occupied molecular orbital (HOMO), of the transition state complex with the electron transferred. Hence, we may use the HOMO wave function of the transition state complex after the electron transfer, including only the nearby surface metal atoms that contribute significantly to this HOMO [40]. This wave function at the cluster is calculated using the EHMO method together with the parameters of VSIP and double-zeta orbitals given in [31] ... 

In its standard form, the EHMO method is poor at determining bond lengths but can give useful results of angular variations like barriers to rotation. For example, the EHMO calculations [89] of the rotational barriers of r)3-cyclopropenyl ligands attached to [MX2(r 5-C5R5)] (M = Mo, Ru X = Cl, Br, I R = H, CH3) (see Fig. 3) successfully predict the higher barrier of the Ru system. 

At a more qualitative level, the EHMO method continues to provide important insights into the mechanism of organometallic reactions. For example, the sites of protonation of q3-butadiene coordinated to [Mo(CO)2L] species can be successfully predicted based on a charge controlled mechanism [112] (Fig. 7). Tsipis [73] gives numerous other examples of the use of this method for studying qualitatively a whole range of organometallic reactions. 

Although several theoretical studies ab-initio and DFT) have appeared for spe-eific eases,this ehapter exploits qualitative MO theory and, in partieular, the undeniable power of the correlation diagrams, to draw the links between molecules dilferent but similar. The arguments are developed with the help of the EHMO method and of the graphie eapabilities of the package CACAO. ... 

For important contributions to the theory of the electronic structure of transition metal complexes using the EHMO method see ... 

M = Mn, Cu, Zn, Cd ) synthesized were studied by W NMR spectroscopy and it was indicated that the solid-state polyoxoanion structures of the diamagnetic Zn and Cd derivativesare preserved in solution. The charges on metal cations of the coordination sphere of polyoxometalates (POM) of V, Mo and W were calculated using the EHMO method, and obtained values were compared with the Mo and NMR chemical shifts of the corresponding nuclei as mentioned above. ... 

The calculation of the surface featured in Fig. 1.15 has been done by the simplest EHMO method. But even a more rigorous treatment [20,83] gives a similar energy sequence in the Td, C4, and D4 structures. The situation changes when all symmetry constraints (two symmetry planes and equivalence of all C—H bond lengths) are removed and a complete geometry optimization is carried out. In such a case, the structure C4, reduces its symmetry to the C2, form (see Fig. 1.16) which is associated with the true saddle point on the PES. (For a more detailed analysis of this problem see Ref. [20].)... 

Fig. 1.15. Potential energy surface for the enantiotopomerization reaction (degenerate enantiomerization) of methane as a function of the angles a and (tetrahedral compression mode). The calculations have been performed by the EHMO method [20,82] with the imposed condition of equality of all C—H bond lengths...

The extended Hiickel (EH) method is much like the simple Hiickel method in many of its assumptions and limitations. However, it is of more general applicability since it takes account of all valence electrons, o and n, and it is of more recent vintage because it can only be carried out on a practical basis with the aid of a computer. The basic methods of extended Hiickel calculations have been proposed at several times by various people. We will describe the method of Hoffmann [1], which, because of its systematic development and application, is the EHMO method in common use. 

The above example suggests that the EHMO method lowers the energy by maximizing weighted overlap populations at the expense of net AO populations. It also suggests that the EH energy should be lowered whenever a molecule is distorted in a way that enables overlap population to increase. These are useful rules of thumb, but some caution must be exercised since the existence of several different kinds of atom in a molecule leads to a more complicated relation than that in the above example. 

Results such as these have tended to restrict use of the EH method to qualitative predictions of conformation in molecules too large to be conveniently treated by more accurate methods. However, just as the simple Huckel method underwent various refinements (such as the cjo technique) to patch up certain inadequacies, so has the EH method been rehned. Such refinements have been shown to give marked improvement in numerical predictions of various properties. The EH method has been overtaken in popularity by a host of more sophisticated computational methods. (See Chapter 11.) However, it is still sometimes used as a first step in such methods as a way to produce a starting set of approximate MOs. The EHMO method also continues to be important as the computational equivalent of qualitative MO theory (Chapter 14), which continues to play an important role in theoretical treatments of inorganic and organic chemistries (as, for example, in Walsh s Rules and in Woodward-Hoffmann Rules). 

The relationship between metal carbonyl hydrides and dihydrogen complexes of metal carbonyl derivatives has been further explored.The interactions of d ML5 fragments with H2 have been studied by EHMO methods,and the structures and some reactions of n -H2 complexes of Cr, Mo, W, Fe and Co carbonyl derivatives examined.Intramolecular ligand rearrangements in [M(C0)5H] anions (M = Cr or Mo) have been investigated using variable temperature n.m.r. A twist mechanism that provides a pathway for intramolecular axial-equatorial CO exchange is favoured.The catalytic role of these... 

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