Hiickel molecular-orbital method

The U s can in the molecular orbital method (Hiickel approximation) be easily expressed in terms of Coulomb integrals a and resonance integrals which characterize the C atoms and the CC bonds.39... 

Hiickel improved his treatment of aromaticity in a second paper, through a method (referred to by Hiickel himself as method II) that still bears his name the HMO method (Hiickel s molecular orbital method) (Hiickel 1932 Pullman and Pullman 1952 Dewar 1969 Coulson, O Leary, and Mallion 1978). The end result was a quantum mechanical treatment of aromaticity, through the 4k+2 (where k = 0, 1, 2,. ..) rule as the criterion for aromaticity. The formula referred to the number of k electrons in a given organic cyclic compound, which would be classified as aromatic if the number was 2, 6, or 10. Furthermore, this explained the stability of the aromatic molecules with respect to reactions. One important result of his approach was that for aromatic and unsaturated compounds, the number of possible valence structures is not the same as the number of different states of determined energy, nor is a state of determined energy necessarily identified with a specific valence structure. 

To become familar with the algorithm for charge calculation by partial equalization of orbital electronegativity (PEOE) and by a modified Hiickel Molecular Orbital method... 

Hiickel linear combination of atomic orbitals pyridines and benzo derivatives, 2, 102 Hiickel molecular orbital method colour and constitution, 1, 342 Hugerschoff bases synthesis, 6, 475-477, 493 Humulene... 

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

The indices are all defined in terms of the Hiickel molecular orbital method. This has been described on many occasions, and need not be discussed in detail here, but a brief statement of the basic equations is a necessary foundation for later sections. The method utilizes a one-electron model in which each tt electron moves in a effective field due partly to the a-bonded framework and partly to its averaged interaction with the other tt electrons. This corresponds conceptually to the Hartree-Fock approach (Section IX) but at this level no attempt is made to define more precisely the one-electron Hamiltonian h which contains the effective field. Instead, each 7r-type molecular orbital (MO) is approxi-... 

These integrals are difficult to evaluate exactly and the Hiickel molecular orbital method centres on approximations to them. 

We will consider the application of the Hiickel molecular orbital method to the benzene molecule and we will first see what happens when we do not make use of symmetry. The benzene molecule has a framework of six carbon atoms at the comers of a hexagon and each carbon atom contributes one 7r-electron. The tt-electron MOs will be constructed from six 2pc atomic orbitals, each located at one of the carbon atoms, thus, c... 

Hiickel molecular orbital method, 205 for benzene, 206 for trivinylmethyl radical, 212. 

Over the past 20 years and, in particular since 1955, many theoretical studies of the electronic structure of pyrrole using the molecular orbital approach with varying degrees of refinement have been reported. The 7r-electronic structure of pyrrole has been extensively discussed in terms of both the simple Hiickel molecular orbital (LCAO) theory37- 41-55-65 and the more sophisticated self-consistent field molecular orbital method (SCFMO method).18- 66-77 Extended... 

A number of tautomeric forms of some fundamental purines have been studied quantum mechanically with the help of the standard, semiempirical Hiickel approximation of the molecular orbital method.57 58 Limited to ti electrons, these studies nevertheless enabled the determination of a number of electronic differences among the tautomers. Using some simplifying ideas, typical in 77-electron calculations, information has also been obtained, within the limits of this approximation, concerning the relative tendencies of the bases to undergo a given type of tautomerization, and this information has been used successfully for the prediction of the preferential mutagenic sites in the nucleic acids.50... 

The generalized free electron molecular orbital method (G-FEMO) gives a good description of the ground state properties of imidazole and yields equivalent results299 to Hiickel molecular orbital calculations. 

The Hiickel approximation of the molecular orbital method (HMO method) can be used to interpret and predict the quantities of Sections IV,B, 1-3 from the energies of the molecular orbitals.64,05 The theoretical data for the quantities of Sections IV, B, 4 and 5 are obtainable from the expansion coefficients of the molecular orbitals. 

The Hiickel method. In the Hiickel molecular orbital method the Fock matrix (see Eq. (4)) is replaced by a certain effective matrix H whose elements H j are not explicitly specified. 

---