Htickel method, extended

The next example for this rule may be the heterolytic addition of chlorine to the C=C bond. Fig. 4.3b indicates the partial valence-inactive population 60> of the 2pz AO of the /9-carbon in LU, calculated by the extended Htickel method. It is seen that this quantity, (c )2, largely increases according to the approach of the chlorine cation to the carbon atom at which the addition is to take place, so that the reactivity of the /9-position towards the second chlorine atom (anionic species) grows. Also Fig. 4.3a shows the decrease of the LU energy in the direction of the reaction path which has already been mentioned above. 

In the Htickel or extended Htickel methods no explicit reference is made to electron-electron interactions although such contributions are absorbed into the V potential, and... 

Hoffmann introduced the so-called extended Htickel method. He found that a value for K= 1.75 gave optimal results when using Slater-type orbitals as a basis (and for calculating the S j,v)- The diagonal hjj elements are given, as in the conventional Htickel method, in terms of valence-state IP s and EA s. Cusachs later proposed a variant of this parameterization of the off-diagonal elements ... 

The extended Htickel method, developed by Hoffmann, has the following characteristics ... 

Another fairly new method, using the electrostatic molecular potential, will not be discussed here since it is the subject of another contribution to this volume 50>. I will now consider methods that have had the widest application in the theoretical study of chemical reactivity, in order of increasing complexity a) molecular mechanics b) extended Htickel method c), d) empirical self-consistent field methods such as CNDO and MINDO e) the simplest ab initio approach f) the different S.C.F. methods, possibly including configuration interaction g) valence bond methods, and h) the dynamical approach, including the calculation of trajectories 61>. 

What are the similarities and the differences between the basis set of the extended Htickel method and the ab initio STO-3G basis set ... 

In the simple and extended Htickel 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. (Hint look at the expression for the Fock matrix elements in terms of the density matrix.)... 

Phenylantimony(III) diiodide forms an unusual complex, 160, in which four PhSbl2 molecules are self-assembled around a central ion via primary (Sb-I 2.8 A) and secondary (Sb - - I 3.6 A) bonds. The complex was analyzed theoretically, by the extended Htickel method, as a [l2Sb(/z-I)]4 cyclic matrix, incorporating a central I" as host [401]. 

Previous extended Htickel 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... 

The main advantage of the extended Htickel theory is that only atomic ionization potentials are required, and it is easily parameterized to the whole periodic table. Extended Htickel theory can be used for large systems involving transition metals, where it often is the only possible computational model. The very approximate method of extended Htickel theory makes it unsuitable for geometry optimizations without... 

Pure atomic orbitals Extended Htickel theory 40,50) Iterative extended Hiickel theories80 81 82) Quasi SCF diagonal element method85) Kinetic-energy Hiickel theory 58) Zero-differential overlap approximation 61,69) Standard SCF method73 74 75 76,77,78) SCF group function method 83) Random-phase... 

The approach to the parameters of the ligand field is not restricted to the DFT method. The procedure in The LFDFT- an attempt to revive LFT can instead be combined with any method for electronic structure, supposing that it is able to yield (after some averaging) reasonable LF orbitals and effective LF matrix elements. Thus DFT failed badly for rare earths [32, 88, 89]. For that purpose we applied a spectroscopically adjusted extended Htickel model [90]. Alternatively, one can proceed beyond LFT and take average natural atomic orbitals resulting from an average multi-configurational procedure, such as SORCI, and calculate all matrix elements of both one- and two-electron operators. 

List the strengths and weaknesses of ab initio calculations compared to molecnlar mechanics and extended Htickel calculations. State the molecular features that can be calculated by each method. 

A formalized analysis of the EFG was also employed by Bagin et al. (1980) their model effectively explained the large quadrupole splitting that is associated with octahedral Fe, again using vacancies as part of their model. More recently, an elegant paper by Aldridge et al. (1986) used molecular orbital methods to model the electronic structure of biotite. They showed that iterative extended Htickel theory calculations of... 

We assume here that the total electronic energy is equal to the sum of the individual electronic energies. This relationship, which has the advantage of being simple, is obtained when the electronic Hamiltonian is written as a sum of monoelectronic Hamiltonians, as in the Htickel and extended Hiickel methods. This approximate formula has, of course, limited application, but it is acceptable for a qualitative analysis of orbital interactions. Further details may be found in Structure ectronique des molecules, by Y. jean and F. Volatron, Volume 2, Chapter 13, Dunod,... 

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