Axial quantum mechanical atom

The general qualitative agreement with experiment provides support for the theory that the potential barriers to internal rotation result from the interaction of adjacent hybrid bond orbitals with a small amount of / character. The magnitude of the potential barriers, about 4 per cent of the energy of the axial bond in case that there are three interacting bonds on each of the two atoms and proportionately less for a smaller number of bonds, is also reasonable. A detailed quantum-mechanical treatment of restricted rotation carried out along the lines sketched here should yield results that would permit a detailed test of the theory to be made in the meantime I believe that the above simple treatment and the extensive empirical support of the theory provide justification for it. 

In an attempt to aid interpretation of the IR spectrum of MbCO we decided to model the full protein by use of a hybrid quantum mechanics/molecular mechanics approach (QM/MM), to evaluate changes in the CO stretching frequency for different protein conformations. The QM/MM method used [44] combines a first-principles description of the active center with a force-field treatment (using the CHARMM force field) of the rest of the protein. The QM-MM boundary is modeled by use of link atoms (four in the heme vinyl and propionate substituents and one on the His64 residue). Our QM region will include the CO ligand, the porphyrin, and the axial imidazole (Fig. 3.13). The vinyl and propionate porphyrin substituents were not included, because we had previously found they did not affect the properties of the Fe-ligand bonds (Section 3.3.1). It was, on the other hand, crucial to include the imidazole of the proximal His (directly bonded to the... 

The one-electron s, p, and d orbitals frequently used to explain observed stereochemistries are a convenient but arbitrary means of decomposing the electron density into spherical harmonics. They represent nothing more than a suitable basis set for a quantum mechanical calculation. When assigned solely on the basis of the observed geometry, they convey no very profound information about the bonding processes at work. It is much simpler and more informative to say that an atom is tetrahedrally coordinated than to say that it is sp hybridized, just as it is easier to say that it forms three equatorial or two axial bonds than to say it is sp or sp hybridized, respectively. Only in the case of the electronically distorted ions discussed in Chapter 8 does an orbital description provide a meaningful rationale for the observed stereochemistry. 

The state of polarization, and hence the electrical properties, responds to changes in temperature in several ways. Within the Bom-Oppenheimer approximation, the motion of electrons and atoms can be decoupled, and the atomic motions in the crystalline solid treated as thermally activated vibrations. These atomic vibrations give rise to the thermal expansion of the lattice itself, which can be measured independendy. The electronic motions are assumed to be rapidly equilibrated in the state defined by the temperature and electric field. At lower temperatures, the quantization of vibrational states can be significant, as manifested in such properties as thermal expansion and heat capacity. In polymer crystals quantum mechanical effects can be important even at room temperature. For example, the magnitude of the negative axial thermal expansion coefficient in polyethylene is a direct result of the quantum mechanical nature of the heat capacity at room temperature." At still higher temperatures, near a phase transition, e.g., the assumption of stricdy vibrational dynamics of atoms is no... 

Van t Hoff postulated free rotation round a single bond in order to explain the lack of cis and Irons isomers in molecules of the type of di-chlorethane. In the light of the quantum mechanical theory of the chemical bond, the free rotation is explained by the axial symmetiy of the a bond between the two carbon atoms. Thus the a bond is not in itself a hindrance to free rotation, but as the rotation occurs the relative configurations of the atoms will be changed, so that the distances between the non-bonded atoms and consequently their energies of interaction will alter. 

New solutions can be generated indefinitely by new linear combinations, amounting to an endless number of axial rotations without any progress beyond the definition and rotation of the three-fold degenerate set, defined by (7) and (8). In the solid angle of 4tt the polar axis (Z) can be directed in infinitely many directions, each representing a linear combination of i/ j, ipQ and i/ i of (7) and (8). In a chemical context the bottom line is that each linear combination ( e.g. fui) defines a specific orientation of the polar axis". With this choice of axes there is no second polar axis and no other linear combination (e.g. that solves (4) in the same coordinate system. The tetrahedral carbon atom remains quantum-mechanically undefined. 

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