EHT calculation

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. 

When one considers data available, such as energies, charges and bond orders, the following statements can be obtained from the simple potential energy surface shown in Fig. 2 (see part 2.3.2). The corresponding data from EHT calculations 16) for the two points represented by (O) are shown in Table 6. 

The overlap populations for the ground and various excited states of methyl cyclopropyl ketone are shown in Figure 4.6. Only for the A —> it excited state would the EHT calculations suggest that cyclopropyl (/3) cleavage (C3-C4) should be important. While this has not been experimentally confirmed, it should be subjected to test with the proper compound. 

The electronic structure of carboxylate complexes with the lantern -type structure was studied [58] using EHT calculations (Fig. 10, Table 5). 

Fig. 11. Results of EHT calculations of technetium trigonal-prismatic clusters...

The above-reported data lead to the conclusion that the HOMO in [Tc6(/j-Br)6Br6]Br2] 3- is the a i-MO composed mainly of 5s(5p,)- and 4dz2-AO s of technetium and having 2bonding character with respect to short M-M bonds. In other words, the EHT calculations [106,107,113] overestimate the interaction of <5 - and n -MO s of dimers in the horizontal directions and underestimate the participation of 5s- and 5pz-AO s in the formation of M-M bonds [15,142],... 

Figure 10. Indicated are the HOMO and LUMO orbital energies obtained form EHT calculations for a variety of reactants. In the center are estimated orbital energies for a canonical metal cluster.

Fig.6b plots the variation of the energy along a purely a-approach and along the mini-mum-energy approach a considerable barrier is found for the former. The qualitative predictions of orbital symmetry match exactly the outcome of EHT calculations. 

Such species should be highly reactive towards acids and bases, since they have high-lying occupied and low-lying unoccupied levels due to strain, which makes them good acceptors and donors of electrons. To test this, EHT calculations were done for the approach of BH3 and NH3 to [4] (22) ... 

Even if full potential energy surfaces are not calculated, simple EHT calculations, skilfully coupled with orbital symmetry considerations, can provide insight into complex reactivity problems. This is well exemplified by Hoffmann and Stohrer s analysis of substituent effects on the Cope rearrangement (28). 

Orbital symmetry arguments and EHT calculations have also provided a way of discriminating between axial and apical substitution in the above mentioned case of pentacoordinate phosphorus. This analysis leads the way to more complex problems of coordination around transition metal atoms. 

Analogous considerations apply for tetracoordinate fragments M(CO)4. Fig. 30 shows some of the possible conformations of these fragments. As before, the directional orbitals that develop for particular values of the angle 6 (refer to Fig. 30) allow prediction of possible interaction with donors or of dimerization. Also, the level shifts for variation of 6 in both cases can be calculated, as well as for the squashing mode rearrangement of a tetrahedral into a square-planar coordination. The qualitative confomiational preferences implied by these patterns have been checked, as for the pentacoordinate case, by comprehensive EHT calculations for all dn systems of all conceivable symmetries. 

One of the most promising tools in the study of the nature and structure of adsorbed molecules is photoelectron spectroscopy (40), and results from such experiments can be compared with EHT calculations. As an example, the experimental and calculated spectra of ethylene on Ni(l 11) are compared in Fig. 40. In the calculations, the model surface consisted of a Ni atom surrounded by six nearest neighbours in the surface plane and three in the plane below. The molecular plane of ethylene was taken to be parallel to the surface. 

Orbital interaction diagram and EHT calculations show that the 1,2 intramolecular shift of hydrogen is symmetry disfavored [10]. In presence of a transition metal fragment to which the alkyne coordinates, the activation energy is considerably lower. This has been attributed to the tendency of H to shift as a proton rather than as a hydride. 

EHT calculations of, 34 173 hydrogen exchange and, 33 104-116 ionic and nonionic types, 33 122 monohydride and dihydride sites, 33 120-122... 

The dimension of the secular determinant for a given molecule depends on the choice of basis set. EHT adopts two critical conventions. First, all core electrons are ignored. It is assumed that core electrons are sufficiently invariant to differing chemical environments that changes in their orbitals as a function of environment are of no chemical consequence, energetic or otherwise. All modern semiempirical methodologies make this approximation. In EHT calculations, if an atom has occupied d orbitals, typically the highest occupied level of d orbitals is considered to contribute to the set of valence orbitals. 

Table 10 EHT Calculated Carbonyl ir-Bond Orders (Pco) and IR Stretching Frequencies (78ijciA)64)...

SCHEME 12. Isodesmic reactions based on cyclobutyl derivatives 49-52. Reaction energies from MINDO/3 (first entry) and EHT calculations (second entry) in kcal mol173... 

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