Hiickel calculations

HyperChem performs an empirical Hiickel calculation to produce th e MO coefficien ts for a minimal basis set and th en projects th ese coefficien ts to the real basis set used in an cife calculation. Th e projected Htickel guess can be applied to rn olecular system s with an atom ic n um ber less th an or equal to 54 (Xe). 

YAcHMOP stands for yet another extended Hiickel molecular orbital package. The package has two main executables and a number of associated utilities. The bind program does molecular and crystal band structure extended Hiickel calculations. The viewkel program is used for displaying results. We tested Version 3.0 of bind and Version 2.0 of viewkel. 

In an Extended Hiickel calculation, the Aufbau population of molecular orbitals is unambiguous. The calculation method is non-iterative and the total energy is proportional to the sum of the energies of occupied orbitals. The Aufbau guarantees the lowest energy wave function. 

The second step determines the LCAO coefficients by standard methods for matrix diagonalization. In an Extended Hiickel calculation, this results in molecular orbital coefficients and orbital energies. Ab initio and NDO calculations repeat these two steps iteratively because, in addition to the integrals over atomic orbitals, the elements of the energy matrix depend upon the coefficients of the occupied orbitals. HyperChem ends the iterations when the coefficients or the computed energy no longer change the solution is then self-consistent. The method is known as Self-Consistent Field (SCF) calculation. 

Note This simple orbital interaction picture is useful for interpreting results, but neglects many aspects of a calculation, such as electron-electron interactions. These diagrams are closely related to the results from Extended Hiickel calculations. 

Projected Hiickel the initial guess at the MO coefficients is obtained from an extended Hiickel calculation ... 

In this example, the HOMO is plotted one Angstrom above the plane of the molecule. Since it is of n symmetry, it has a node in the plane of the molecule. It shows the site of electrophilic attack at the carbon adjacent to the oxygen atom. This is also the experimentally observed site. The orbital comes from an Extended Hiickel calculation of an MM-t optimized geometry. 

The principal semi-empirical schemes usually involve one of two approaches. The first uses an effective one-electron Hamiltonian, where the Hamiltonian matrix elements are given empirical or semi-empirical values to try to correlate the results of calculations with experiment, but no specified and clear mathematical derivation of the explicit form of this one-electron Hamiltonian is available beyond that given above. The extended Hiickel calculations are of this type. 

Simple Hiickel calculations on benzene, in contrast, place all the n electrons in bonding MOs. The 7t-electron energy of benzene is calculated by summing the energies of the six 71 electrons, which is 6a -F 8/S, lower by 2/S than the value of 6a -F 6/S for three isolated double bonds. Thus, the HMO method predicts a special stabilization for benzene. 

Both HMO calculations and more elaborate MO methods can be applied to the issue of the position of electrophilic substitution in aromatic molecules. The most direct approach is to calculate the localization energy. This is the energy difference between the aromatic molecule and the n-complex intermediate. In simple Hiickel calculations, the localization energy is just the difference between the energy calculated for the initial n system and that remaining after two electrons and the carbon atom at the site of substitution have been removed from the conjugated system ... 

Since the diagonal elements depend only on the nature of the atom (i.e. the nuclear charge), this means that for example all carbon atoms have the same ability to attract electrons. After having performed a Hiickel calculation, the actual number of electrons associated with atom A, / a, can be calculated according to eq. (3.90) (see section 9.1, eqs. (9.5) and (9.4)). 

Previous extended Hiickel calculations on the bis(trifluoromethyl) derivative 6 show the favored isomer to be 6b, while the CNDO/2 method favors 6a [75JCS(P2)559]. More recent ab initio calculations for different R substituents show that electron-releasing substituents favor the ring-opened dithione (6b), whereas electron-withdrawing substituents favor the cyclic structure (6a) (80JA6687). These conclusions are supported by electron diffraction (ED) (76JA899) and photoelectron (PE) spectral data... 

Extended-Hiickel calculations have been carried out [185] for systems such as IrCl4(NO)2-, based on a slightly distorted square pyramid of C4v symmetry (crystallographically studied 5-coordinate systems do not have a planar base but exhibit this slight distortion). Figure 2.104 shows how the... 

Extended Hiickel calculations have been carried out on the 1-cyclopropylvinyl cation 156 (122). These results show that the most favorable conformation for this ion is the linear bisected structure 156a. However, Hanack et al. (166b), by means of a modified CNDO technique, calculate the most stable geometry of the intermediate ion resulting from homopropargyl participation to be a bridged cyclobutenyl cation rather than 156a. 

Extended Hiickel calculations are performed with a nonorthogonalized AO basis set therefore, the spin densities are to be evaluated by gross atomic populations and not simply by squares of expansion coefficients. 

Another type of interaction is the association of radical ions with the parent compounds. Recently (118), a theoretical study was reported on the interaction of butadiene ions with butadiene. Assuming a sandwich structure for the complex, the potential curve based on an extended Hiickel calculation for two approaching butadienes (B + B) revealed only repulsion, as expected, while the curves for B + and B + B" interactions exhibit shallow minima (.068 and. 048 eV) at an interplanar distance of about 3.4 A. From CNDO/2 calculations, adopting the parameter set of Wiberg (161), the dimer cation radical, BJ, appears to be. 132 eV more stable than the separate B and B species, whereas the separate B and B species are favored by. 116eV over the dimer anion radical, BJ. This finding is consistent with experimental results formation of the dimer cation radical was proved in a convincing manner (162) while the attempts to detect the dimer anion radical have been unsuccessful. With other hydrocarbons, the reported formation of benzene dimer anion radical (163) represents an exceptional case, while the dimeric cation radical was observed... 

Table 4.2. The positional parallelism between (c ° )2 and of hydrogens in 2-chlorobutane by the extended Hiickel calculation...

In the simple LCAO treatment in which the AO overlap is neglected, the density concept is rather clear-cut. An ambiguity arises in the case of inclusion of overlap. The extended Hiickel calculation is one of the cases. The electron density is usually called "population 70>. An analysis has been made with respect to the composition of population 71>. The population of the rth AO, qr is defined by... 

The energy change, AE, due to a new "bond" arising between two 2pn AO s of a conjugated hydrocarbon, r and s, is simply represented by the Hiickel calculation as... 

Very recently Botrel et al. (166) have put forward an Extended Hiickel calculation for ferrocene in which the orbital sequencealg [Pg.134]

AuCN has a similar structure to AgCN and likewise dissolves in excess cyanide to form Au(CN)2 this is important in the extraction of gold. It has been characterized as various salts (Tl, K, Bu4N, Cs) with Au-C 1.964A (Bu4N salt [91]). The thallium salt has short Au-Au (3.10A) and Au-Tl (3.50 A) interactions extended-Hiickel calculations indicate the importance of relativistic effects in these covalent interactions. Isocyanides form stable complexes ... 

Describe how you would carry out a Hiickel calculation for the HFH+ ion. What would you expect to find the most stable structure to be ... 

One example of a — Hg- linked TTF dimer has been reported [106]. Linear coordination is expected for the mercury atom. Extended Hiickel calculations indicate that the mercury orbitals are essentially not involved in the HOMOs, and thus the two TTF redox groups can be regarded as being completely isolated from each other. The voltammograms confirm these expectations in that both TTF... 

The orbital coefficients obtained from Hiickel calculations predict the terminal position to be the most reactive one, while the AMI model predicts the Cl and C3 positions to be competitive. In polyenes, this is true for the addition of nucleophilic as well as electrophilic radicals, as HOMO and LUMO coefficients are basically identical. Both theoretical methods agree, however, in predicting the Cl position to be considerably more reactive as compared to the C2 position. It must be remembered in this context that FMO-based reactivity predictions are only relevant in kinetically controlled reactions. Under thermodynamic control, the most stable adduct will be formed which, for the case of polyenyl radicals, will most likely be the radical obtained by addition to the C1 position. 

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