Total extended Huckel energy

The distances found between platinum centers in these molecules have been correlated with the resonating valence bond theory of metals introduced by Pauling. The experimentally characterized partially oxidized one-dimensional platinum complexes fit a correlation of bond number vs. metal-metal distances, and evidence is presented that Pt—Pt bond formation in the one-dimensional chains is resonance stabilized to produce equivalent Pt—Pt distances.297 The band structure of the Pt(CN)2- chain has also been studied by the extended Huckel method. From the band structure and the density of states it is possible to derive an expression for the total energy per unit cell as a function of partial oxidation of the polymer. The equilibrium Pt-Pt separation estimated from this calculation decreases to less than 3 A for a loss of 0.3 electrons per platinum.298... 

Brintzinger and Bartell (6) later reported results of extended HUckel calculations that seem to support these intuitive ideas of Vol pin and his associates. Calculations of the variation in the total energy of (7j-C5H5)2Ti with respect to o>, the angle between the planes of the CSHS rings, indicate that titanocene (1) is most stable in the bent configuration with to = 30-... 

Based on the extended Huckel theory, the total electronic energy of a singlet state molecule ( ) is expressed like... 

In 1976 Leban et used this approach to study the interaction of a platinum electrode with several particles, among them the water molecule and halide ions. The cluster used was taken to be a model of the Pt( 111) surface and contained only five platinum atoms. In this work the iterative extended Huckel molecular orbital (lEHT) method was used. The stability of the adsorption of the water molecule and of the ions was tested by computing the charge transfer to the cluster and the total energy of the system for various positions of the adsorbate on the surface. 

Equation (2.37a) shows explicitly the change in the potential in orbital t due to the presence of another electron with opposite spin. The last term in Eq.(2.37b) is due to the presence of the exchange integral in which results in this specific form according to Hartree-Fock theory. The first three terms of Ffj are similar in form to that derived with the Extended-Huckel method. The contribution to the total energy due to the changed electron distributions becomes ... 

As we will see a little later, Eq.(2.52b) has the same form as the total energy in the Extended-Huckel approximation, when 5 is assumed to be small. However, one... 

Thermodynamic arguments cannot be used to derive the reaction path of dissociating CO. We will show below that the minimum-energy reaction path is that path which leads to maximum electron population of the bond weakening CO 2t orbitals. Dissociation can be studied by means of the AS ED method, introduced by Anderson I and discussed in section (2.2). In order to predict equilibrium distances and dissociation paths, the total bond strength has to be considered to be the sum of a repulsive and an attractive part. In the ASED method the attractive path of the chemical bond strength is computed with the aid of the Extended-Huckel method. Anderson has developed empirical expressions for the repulsive part of the chemical band. If used with care, they yield remarkably useful results. 

Extended Huckel theory is well-known for its flexibility and the ease with which its results lend themselves to chemical interpretation, no matter whether the objects of study are molecules or solids, and a plethora of chemical (bonding) information has been deduced from it, at least qualitatively, and in many cases semiquantitatively. EH theory, however, is not at all made for total-energy calculations or structure optimizations because the electronic potential is too primitive to yield acceptable molecular geometries the latter weakness may be cured, though [114]. 

Expression (31) for the free energy arising from charge interactions is an exact expression so that, together with Fq as defined previously, it completely defines the total free energy of the system considered here. In the present state of theory an exact evaluation of F according to (31) is out of question however for the same reasons that cannot be calculated immediately. Therefore a more approximate approach is used analogously to the Debye-Huckel treatment of ordinary ionic solutions. This approach, which we shall call the extended Poisson-Boltzmann approach, will be discussed in the next section. 

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