Extended-Hiickel

You can use any ah initio SCT calciilalion and all Ihe semi-empiri-cal methods, except Extended Hiickel. for molecular dynamics simulations. The procedures and considerations are similar for sim u lation s using molecular mech anics m eihods (see Molecular Dynamics" on page 69). 

Extended Hiickel is the simplest and fastest senii-empirical method included m IlyperC hem, but it isalso the least accurate. It Is particularly simple in its treatment of electron-electron interactions it has no explicit treatment of these interactions, although it may include some of their effects by parameteri/.aiioii. 

Extended Hiickel theory Generalised valence bond model Hartree-Fock... 

Unlike the Hiickel and extended Hiickel methods, the semi-empirical approaches that explicitly treat electron-electron interactions give rise to Fock matrix element... 

Extended Hiickel gives a qualitative view of the valence orbitals. The formulation of extended Hiickel is such that it is only applicable to the valence orbitals. The method reproduces the correct symmetry properties for the valence orbitals. Energetics, such as band gaps, are sometimes reasonable and other times reproduce trends better than absolute values. Extended Hiickel tends to be more useful for examining orbital symmetry and energy than for predicting molecular geometries. It is the method of choice for many band structure calculations due to the very computation-intensive nature of those calculations. 

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. 

The Extended Hiickel method, for example, does not explicitly consider the effects of electron-electron repulsions but incorporates repulsions into a single-electron potential. This simplifies the solution of the Schrodinger equation and allows HyperChem to compute the potential energy as the sum of the energies for each electron. 

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. 

This method is available for all semi-empirical methods except Extended Hiickel, and for ab initio calculations. This algorithm may be used if the structure is far from a minimum. 

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

The Extended Hiickel method also allows the inclusion of d orbitals for third row elements (specifically. Si, P, S and Cl) in the basis set. Since there are more atomic orbitals, choosing this option results in a longer calculation. The major reason to include d orbitals is to improve the description of the molecular system. 

Note You cannot use the Extended Hiickel method or any one of the SCFmethods with the Cl option being turned on for geometry optimizations, molecular dynamics simulations or vibrational calculations, in the current version of HyperChem. 

Note You can not use the Extended Hiickel method, nor any of the other SCFmethods with the Cl option turned on, for geometry optimization or molecular dynamics simulations. 

The neglect of electron-electron interactions in the Extended Hiickel model has several consequences. For example, the atomic orbital binding energies are fixed and do not depend on charge density. With the more accurate NDO semi-empirical treatments, these energies are appropriately sensitive to the surrounding molecular environment. 

HyperChem cannot perform a geometry optimization or molecular dynamics simulation using Extended Hiickel. Stable molecules can collapse, with nuclei piled on top of one another, or they can dissociate into atoms. With the commonly used parameters, the water molecule is predicted to be linear. 

The Extended Hiickel method neglects all electron-electron interactions. More accurate calculations are possible with HyperChem by using methods that neglect some, but not all, of the electron-electron interactions. These methods are called Neglect of Differential Overlap or NDO methods. In some parts of the calculation they neglect the effects of any overlap density between atomic orbitals. This reduces the number of electron-electron interaction integrals to calculate, which would otherwise be too time-consuming for all but the smallest molecules. 

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. 

Normally, you would expects all 2p orbitals in a given first row atom to be identical, regardless of their occupancy. This is only true when you perform calculations using Extended Hiickel. The orbitals derived from SCE calculations depend sensitively on their occupation. Eor example, the 2px, 2py, and 2pz orbitals are not degenerate for a CNDO calculation of atomic oxygen. This is especially important when you look at d orbital splittings in transition metals. To see a clear delineation between t2u and eg levels you must use EHT, rather than other semiempirical methods. 

Apart from speed, an appealing aspect of CNDO is its simplicity. It uses fewer parameters than any other method except for Extended Hiickel and, consequently, it is easier to understand the results of modifying a 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. 

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