Normal-state pairing

In other cases, discussed below, the lowest electron-pair-bond structure and the lowest ionic-bond structure do not have the same multiplicity, so that (when the interaction of electron spin and orbital motion is neglected) these two states cannot be combined, and a knowledge of the multiplicity of the normal state of the molecule or complex ion permits a definite statement as to the bond type to be made. 

The curves for HC1, HBr and HI do not cross, in the main because the ionic radii of Cl-, Br and I are much larger than that of F-. Accordingly the normal states of these molecules are essentially of the electron-pair bond type, and the formulas H Cl , H Br , and H I maybe used as giving a reasonably accurate picture of the state of the molecules. This conclusion had been reached before on the basis of other arguments, especially the tendency of fluorine alone of the halogens to form hydrogen bonds. 

Just as intriguing are the studies on the exo-compounds. Two sets of data are available, those having a low v due of 1 12 and the higher result of Humski, Malojcic, Borcic and Sunko, T20. The former value can be rationalized with a non-classical transition state in the A-B process but does not seem to require it. The larger value appears to be consistent with the presence of a normal ion-pair like transition state (B-C) involving the classical ion and is difficult to rationalize with the presence of a bridged ion. 

The heavier nonmetals may be expected to make some use of the less stable orbitals of the outermost shell (3d for P, S, Cl 4d for As, Se, Br etc-), as is indicated by the existence of compounds such as PCI and SFe, in which the central atom forms more bonds than permitted by the use of orbitals occupied by electron pairs in the adjacent noble gas. In our earlier discussion of the structure of PCI it was pointed out that a rough quantum-mechanical treatment leads to the conclusion that the structure in which the phosphorus atom forms five covalent bonds, with use of one 3d orbital in addition to the 3 and three 3d orbitals, makes a significant contribution to the normal state of the molecule (about 8 percent). 

Similar excited states have been observed for diatomic molecules of the alkali metals. They may be interpreted as involving a molecule-ion, such as Li, with a one-electron bond, plus a loosely-bound outer electron. The internuclear distances are about 0.3 A greater than for the corresponding normal states 2 2.94 A lor Lij (2.672 A for Lit), 3.41 A for Na (3.079 A for Nat), and 4.24 A for K (3.923 A for Kt). The values of the bond energies for the one-electron bonds, as indicated by the vibrational levels, are about 60 percent of those for the corresponding electron-pair bonds. 

All members of the set must have the same number of paired or unpaired electrons. For the normal state of benzene, the six it electrons have... 

The normal state of the HC1 molecule is a Z state because there is no net projection of / vectors, that is the it electrons are all paired both as to spins and as to orbital angular momenta. When a n electron is raised to a higher quantum state the Pauli Principle may be obeyed even if spins are unpaired or the directions of the / vectors are changed. Thus one may have both singlet and triplet states as well as , 17, A states. 

This quantity has been computed and is shown in Figure 10 and seems to provide a good description of the experimental data up to Tc. In order to describe the susceptibility above Tc other singlet excitations not at heart related to the superconductivity can be invoked. Therefore we are in accord with Loram etal [26] whose view is that the normal state spin gap is not essentially related to the superconducting pairing. However such excitations in the normal state are yet to be included in our theory but our conjecture is that this will not alter... 

The term was first used by Van Vleck who explained it thus, referring to carbon in CH4 ...the spins of the four electrons belonging to sp3 were assumed paired with those of the four atoms attached by the carbon. Such a condition of the carbon atom we may conveniently call its valence state. He then showed a calculation which led to the conclusion that The valence state of C has about 7 or 8 more volts of intra-atomic energy than the normal state. This is the energy required to make the C atom acquire a chemically active condition... [1]. Mulliken defines it saying [it is] a certain hypothetical state of interaction of the electrons of an atomic electron configuration and A valence state is an atom state chosen so as to have as nearly as possible the same condition of interaction of the atom s electrons with one another as when the atom is part of a molecule. [2]. 

Figure 1. Low temperature (25 K) ARPES data of optimally doped Bi2Sr2CaC208+5high temperature superconductors with oxygen isotope l60 (panels a) and 180 (panels b). These maps are normalized so that the intensity of each EDC goes from 0 to 1 (see text for details). The panels are labeled with a cut number, i.e. angle offset from the nodal cut. Inset of panel c shows the cut numbers. In panel c, isotope dependence of a few selected EDC s are shown for cut 6. The top pair corresponds to k=kF, i.e. momentum value on the normal state Fermi surface, shown as a curve in the inset.

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