Extended Hiickel theory calculation

After the finding of a sweet taste in L-Asp-L-Phe-OMe (aspartame) by Mazur et at. (6), a number of aspartyl dipeptide esters were synthesized by several groups in order to deduce structure-taste relationships, and to obtain potent sweet peptides. In the case of the peptides, the configuration and the conformation of the molecule are important in connection with the space-filling properties. The preferred conformations of amino acids can be shown by application of the extended Hiickel theory calculation. However, projection of reasonable conformations for di- and tripeptide molecules is not easily accomplished. 

The extended Hiickel theory calculations, used in this work and discussed below, are based on the approaches of Hoffmann Although VSIP values given by Cusachs, Reynolds and Barnard were explored for use as the Coulomb integrals, the VSIP values obtained from a Hartree-Fock-Slater approximation by Herman and Skillman were consistently used in the present EHT calculations by this author. Both the geometric mean formula due to Mulliken and Cusachs formula ) were considered for the Hamiltonian construction, but the Mulliken-Wolfsberg-Helmholtz arithmetic mean formula was chosen for use. 

Fig. 20. Molecular orbital diagram for CN based upon extended Hiickel theory calculations...

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. 

HyperChem currently supports one first-principle method ab initio theory), one independent-electron method (extended Hiickel theory), and eight semi-empirical SCFmethods (CNDO, INDO, MINDO/3, MNDO, AMI, PM3, ZINDO/1, and ZINDO/S). This section gives sufficient details on each method to serve as an introduction to approximate molecular orbital calculations. For further details, the original papers on each method should be consulted, as well as other research literature. References appear in the following sections. 

In an early investigation (66T539) the two highest occupied and the two lowest unoccupied orbitals were calculated on the basis of an extended Hiickel theory to determine the electron transition responsible for the long wavelength UV absorption. An Ai- Bi, [Pg.197]

The pioneering calculations of Wolfsberg and Helmholtz on Mn04, Cr04 and CIO4 are usually cited as the first applications of extended Hiickel theory... 

Theoreticians did little to improve their case by proposing yet more complicated and obviously unreUable parameter schemes. For example, it is usual to call the C2 axis of the water molecule the z-axis. The molecule doesn t care, it must have the same energy, electric dipole moment and enthalpy of formation no matter how we label the axes. I have to tell you that some of the more esoteric versions of extended Hiickel theory did not satisfy this simple criterion. It proved possible to calculate different physical properties depending on the arbitrary choice of coordinate system. 

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. 

One year later, the new model took its final name of Extended Hiickel Theory, and was cast in the concise, attractively simple form that has survived to date in a comprehensive paper on hydrocarbons, Roald Hoffmann (4) was able to show that many different properties of these compounds could be correctly calculated, thus establishing the operative validity of the method. 

Protonation shifts, obtained from nmr spectra in deutero-chloroform and trifluoroacetic acid, for 1-methylimidazoles also suggest that the cations show amidinium type resonance, because the signal of the proton on C-2 shifts downfield much more than those of the protons on C-4 and C-5 (Barlin and Batterham, 1967). Amidinium type resonance in benzimidazoles activates the proton on C-2, which becomes susceptible to base-catalysed exchange (Elvidge et al., 1973). The effects of protonation on electron densities in the imidazole ring have been calculated by extended Hiickel theory (Adam et al., 1967). 

All electron calculations were carried out with the DFT program suite Turbomole (152,153). The clusters were treated as open-shell systems in the unrestricted Kohn-Sham framework. For the calculations we used the Becke-Perdew exchange-correlation functional dubbed BP86 (154,155) and the hybrid B3LYP functional (156,157). For BP86 we invoked the resolution-of-the-iden-tity (RI) approximation as implemented in Turbomole. For all atoms included in our models we employed Ahlrichs valence triple-C TZVP basis set with polarization functions on all atoms (158). If not noted otherwise, initial guess orbitals were obtained by extended Hiickel theory. Local spin analyses were performed with our local Turbomole version, where either Lowdin (131) or Mulliken (132) pseudo-projection operators were employed. Broken-symmetry determinants were obtained with our restrained optimization tool (136). Pictures of molecular structures were created with Pymol (159). 

The different behavior of tertiary and quaternary carbon atoms seems to be due to either the complete neglect of overlap in these calculations or to polarization effects of the carbon-nitrogen bonds, Similar results are obtained for a series of 5-halouracils by plotting the 13C NMR chemical shifs versus 7r-electron charge densities calculated by the extended Hiickel theory [756], Though for several nitrogen heterocycles a better correla-... 

We have seen three broad techniques for calculating the geometries and energies of molecules molecular mechanics (Chapter 3), ab initio methods (Chapter 5), and semiempirical methods (Chapters 4 and 6). Molecular mechanics is based on a balls-and-springs model of molecules. Ab initio methods are based on the subtler model of the quantum mechanical molecule, which we treat mathematically starting with the Schrodinger equation. Semiempirical methods, from simpler ones like the Hiickel and extended Hiickel theories (Chapter 4) to the more complex SCF semiempirical theories (Chapter 6), are also based on the Schrodinger equation, and in fact their empirical aspect comes from the desire to avoid the mathematical... 

A series of extended Hiickel theory (EHT) band calculations on crystal structures 16 and 17 have been performed <2003JA14394, 2004CM1564>. They show that the dispersion curves plotted along the stacking direction arise from the SOMOs of the radicals in the cell unit, that is, the putative half-filled conduction band of the molecular metal. Clearly, none of the materials are metallic, but the dispersion curves nonetheless provide insight into the extent of the intermolecular interaction along and perpendicular to the slipped 7t-stacks. 

It is often assumed that resonance integrals are proportional to the overlap between the atomic orbitals which formally underlie the pi Hamiltonian [58]. If these are assumed to be ordinary 2p atomic orbitals for carbon, the distance dependence of the overlap can be calculated analytically, and the distance dependence of the t parameters is often taken to be of this form, as for example in Extended Hiickel Theory [59]. But there is no need to make this assumption since the parameters in the pi Hamiltonian should more properly be thought of as rescaled effective integrals, and there is evidence that the model performs better if the t values are allowed to vary more rapidly with distance. Accordingly, we have adopted the form... 

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