Molecules Huckel electronic energy

Exercise 1.2. Consider a diatomic molecule that has two orbitals (A and B on the atoms A and B, respectively) and two electrons in the MOs formed by these orbitals. What is the Huckel electronic energy of this system in terms of the parameters aA, aB, and PAB1... 

Within the framework of the simple tight-binding Huckel molecular orbital (HMO) approximation (see the next paragraph) the total 7i-electron energy of a conjugated molecule is given by... 

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

The total -electron energy is one of the most important parameters of a conjugated molecule that can be obtained from the Huckel MO calculations [65]. It can be used selectively, to relate to the thermodynamic stability of conjugated structures. A parametrization scheme, based on thermodynamic data, by Hess and Schaad [66], has produced agreement with experiment to the same d ee of qumititative accuracy as the much more sophisticated SCF r-MO procedure developed by Dewar (67). In addition. Schaad and Hess [68] have shown that in many instances Bir follows linearly the total (thermodynamically measurable) energy of the conjugated molecule. The physical reasons leading to the answer as to how it Is possible that a model as simple as the Huckel model can ve not only qualitative, but sometimes also fair quantitative... 

The simple Huckel method is usually applied only to the calculation ir electron energies in conjugated organic systems. The simple method is based on the assumptirai of the separability of the electron systems in the molecule. This is a very crude approximation and works best when the energy level pattern is determined largely by the synunetry of the molecule. (See Chapter 12.)... 

Use the Huckel approximation to calculate the t-electron energies of cyclobutadiene. Hence determine the electronic ground state of cyclobutadiene. What is the delocalization energy of this molecule ... 

Using the HMO approximation, the ir-electron wave function is expressed as a linear combination of atomic orbitals (for the case in which the plane of the molecule coincides with the y-z plane of the coordinate axis), in much the same way as described previously for the generalized MO method. Minimizing the total -jT-electron energy of the molecule with respect to the coefficients (the variation method) leads to a series of equations from which the coefficients can be extracted by way of a secular determinant. The mathematical operations involved in solving the equations are not difficult. We will not describe them in detail, but will instead concentrate on the interpretation of the results of the calculations. For many systems, the Huckel MO energies and atomic coefficients have been tabulated." ... 

The simplest approximation to the delocalization energy is on the level of the Huckel method. For benzene the energy of the delocalized n electron system can be described as the sum of the orbital energies of the three doubly occupied orbitals. For the localized system, the n electron energy of three ethylene molecules is chosen. 

The orbital arrangement for pentalene shown in Fig. 2 serves to indicate how close the second excited state is to the first excited state when two more electrons are placed in the nonbonding orbital to form the dianion. The very small (E2 — E1) values for fulvalene and hepta-fulvalene are realized from the orbital arrangements shown in Fig. 4 in both molecules the two lowest excited states ( 3 and 211) have the same energy in the Huckel picture. 

The requirements necessary for the occurrence of aromatic stabilisation, and character, in cyclic polyenes appear to be (a) that the molecule should be flat (to allow of cyclic overlap of p orbitals) and (b) that all the bonding orbitals should be completely filled. This latter condition is fulfilled in cyclic systems with 4n + 2n electrons (Huckel s rule), and the arrangement that occurs by far the most commonly in aromatic compounds is when m = 1, i.e. that with 6k electrons. IOti electrons ( = 2) are present in naphthalene [12, stabilisation energy, 255 kJ (61 kcal)mol ], and 4n electrons (n = 3) in anthracene (13) and phenanthrene (14)—stabilisation energies, 352 and 380 kJ (84 and 91 kcal) mor respectively ... 

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... 

The experimental observations on the mechanism(s) of electroreduction of 2-thio-pyrimidines have been interpreted on the basis of their electronic structures as calculated with the aid of the CNDO/2 and Huckel procedures l42). The energies of LUMO (lowest unoccupied molecular orbitals), calculated for pyrimidine and its 2-oxo-and 2-thioderivatives, were compared with the reduction half-wave potentials (Table V). These show that the presence of a carbonyl or thione substituent at C2 enhances the electron acceptor properties of the molecule, which are correlated with formation of a dimer susceptible to photooxidation. 

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