Molecular orbital methods extended Hiickel method

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. 

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. 

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

In the usual formulation of the extended Hiickel method, the elements of the hamiltonian matrix are computed according to a simple set of arithmetic rules, and do not depend on the molecular orbitals. In this way, there is no need for the iterations required by more sophisticated methods, and in practice the results may be obtained nowadays in a question of seconds for any reasonably sized complex. 

The continued success of the extended Hiickel method in transition metal chemistry, where it was the method of choice until the mid 1980 s is surely related to the problems of other semiempirical methods in this area of chemistry. While methods like MOP AC [21] or AMI [22] have been extremely productive in the field of organic chemistry, they have found little success in transition metal chemistry. These methods are based in equation 2, similar to 1, but with the very significant difference that the Fock matrix F is computed from the molecular orbitals, in an iterative way, though through an approximate formula. 

In the simple and extended Hiickel methods, the molecular orbitals are calculated and then filled from the bottom up with the available electrons. However, in ab initio calculations the occupancy of the orbitals is taken into account as they are being calculated. Explain. 

The extended Hiickel method, which is a semiempirical quantum chemistry method, is often used as a preliminary step in the DFT study of molecular orbital analysis. The acetylide-bridged organometallic dinuclear complexes 5.2 were studied by Halet et al. using the extended Hiickel method for qualitative analysis and DFT for additional electronic properties [97], The extended Hiickel analysis concluded that the main contribution of the Pt-C bond arises from ct type interactions while the n back-donation is very weak. The DFT/BP86 calculation gives a 2.371 eV HOMO-LUMO gap. The electronic communication parameter Hdb between the bis-ferrocene compound linked with platinum acetylide (5.3) was calculated to be 0.022 eV, compared with 0.025 eV obtained experimentally by Rapenne and coworkers using DFT and the extended Hiickel method [98],... 

The extended Hiickel method (EHM) 74> is the simplest empirical all valence electron molecular-orbital method available at present. 

The above QSAR method was used to solve concrete problems.Beside the extended Hiickel methods, other ones (CNDO/2, MINDO, MNDO, etc.) were also employed.Good QSAR equations have been obtained by using CNDO/2 methods to calculate electronic parameters. In particular, for a series of phenyltriazenes, using atomic charges and the energy of the lowest unoccupied molecular orbital E (LUMO) as electronic parameters, the following two-parameter regression equation for the antisarcoma activity was obtained ° ... 

Several other chemists who have won the Nobel Prize did not receive it for their computational chemistry per se, but nevertheless were extremely influential in computational chemistry. Among these scientists is Professor William N. Lipscomb, Jr., of Harvard University. He received the 1976 Prize for his work on the bonding of boron hydrides,but it was also in his laboratory where the extended Hiickel method first evolved, as well as other original molecular orbital treatments. ... 

In the extended Hiickel method, molecular orbitals are derived by solving the matrix equation ... 

The extended Hiickel method for molecular orbitals includes a treatment of all valence electrons (cr and tt), not just the tt electrons. Atomic orbitals from atoms are used to determine molecular orbital energies by defining the integrals H y and S y in a fashion similar to that just presented for the tt electrons. Although similar in principle, it requires larger matrices because all valence electrons are treated. Other concerns preclude a detailed discussion here, but other references can be consulted for details. ... 

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. 

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. 

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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