Orbitals, atomic resonance

Anti-bonding tt orbital, 293 Atomic orbital resonance, 295 16/3-Azido- 17a-iodoandrostanes, 24 16p-Azido-17a-iodo-5a-androstan-3 -ol acetate, 28... 

Here A and B denote atoms in each of the two interacting molecules. The V operator contains all the potential energy operators from both molecules, and the (xa V xb) integral is basically a resonance type integral between two atomic orbitals, one from each molecule. The pa is the electron density on atom A, and the first term in (15.1)... 

Having just seen a resonance description of benzene, let s now look at the alternative molecular orbital description. We can construct -tt molecular orbitals for benzene just as we did for 1,3-butadiene in Section 14.1. If six p atomic orbitals combine in a cyclic manner, six benzene molecular orbitals result, as shown in Figure 15.3. The three low-energy molecular orbitals, denoted bonding combinations, and the three high-energy orbitals are antibonding. 

As pointed out in Chapter 7, the atomic orbital (valence bond) model regards benzene as a resonance hybrid of the two structures... 

In Chapter 7, we used valence bond theory to explain bonding in molecules. It accounts, at least qualitatively, for the stability of the covalent bond in terms of the overlap of atomic orbitals. By invoking hybridization, valence bond theory can account for the molecular geometries predicted by electron-pair repulsion. Where Lewis structures are inadequate, as in S02, the concept of resonance allows us to explain the observed properties. 

Y. Yano and S. Oae, 3d Orbital Resonance in the Bivalent Sulfur Atom, Mechanisms of Reactions of Sulfur Compounds, Vol. 4, Intra-Science, 1969, p. 167. 

The parameter ais the ionization energy of an electron from the p,th atomic orbital located on the Ath atom and ft is the so-called resonance integral (represented here by a simple exponential). The QB and P terms of represent corrections to the effective ionization potential due to the residual charges on the different atoms. The charges are determined by... 

As an example of the MO treatment, let us consider the case of a diatomic molecule (AB) with two electrons in the presence of a bare proton. For our specific example, we will neglect the resonance interaction between the molecule and the ion using fiAC = jiBC = 0, where C designates an atomic orbital on the proton site. 

A note on good practice The concepts of promotion, hybridization, and resonance belong to valence bond theory, not molecular orbital theory. Instead, molecular orbitals are built from all the available atomic orbitals by noting whether or not they have the right shape to overlap with one another. 

It was pointed out in my 1949 paper (5) that resonance of electron-pair bonds among the bond positions gives energy bands similar to those obtained in the usual band theory by formation of Bloch functions of the atomic orbitals. There is no incompatibility between the two descriptions, which may be described as complementary. It is accordingly to be expected that the 0.72 metallic orbital per atom would make itself clearly visible in the band-theory calculations for the metals from Co to Ge, Rh to Sn, and Pt to Pb for example, the decrease in the number of bonding electrons from 4 for gray tin to 2.56 for white tin should result from these calculations. So far as I know, however, no such interpretation of the band-theory calculations has been reported. 

In the interaction of a pair of atomic orbitals, two electrons form a bond and four electrons form no bond (Sect. 1.1). The snbstitnted carbocations are stabilized by the electron delocalization (hyperconjngation and resonance) through the interaction of the doubly occupied orbitals on the snbstitnents with the vacant p-orbital on the cation center. The exchange repulsion (Sect. 1.5) is cansed by four electrons. Now... 

The rationale behind this choice of bond integrals is that the radical stabilizing alpha effect of such radicals are explained not by the usual "resonance form" arguments, but by invoking frontier orbital interactions between the singly occupied molecular orbital of the localized carbon radical and the highest occupied molecular orbital (the non-bonding electrons atomic orbital) of the heteroatom (6). For free radicals the result of the SOMO-HOMO interaction Ts a net "one-half" pi bond (a pi bond plus a one-half... 

Schreckenbach, G., Ziegler, T., 1997b, Calculation of the g-Tensor of Electron Paramagnetic Resonance Spectroscopy Using Gauge-Including Atomic Orbitals and Density Functional Theory , J. Phys. Chem. A, 101, 3388. 

In order to reveal the mechanism of this molecular half-adder, the T(E) spectra of the molecule are presented in Fig. 26b. When perpendicular to the plane of the molecule, each NO2 contributes a very sharp resonance which does not participate in the overall conductance. When rotated by 90°, an NO2 introduces a supplementary resonance in the gap of the molecule. Due to its asymmetrical delocalization over the atomic orbitals, this resonance increase the conduction between the drive and the XOR electrode, but not between the drive and the AND electrode. This insures a 1 output for the former and a 0 for the latter. When the two NO2S are rotated, the two resonances they introduce create a deep interference between the drive and the XOR electrode. Located on the Fermi energy of the molecule, this interference leads to a low conductance state and a 0 logical output for the XOR gate. In contrast, the two resonances do not interfere destructively between the drive and the AND electrode, leading to a high conductance state and a 1 logical output. 

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