Spin bond order

Multiplying the resonance integral by the quadrupled transferable spin bond order PoL = CQ- (3.14) results in the resonance energy of the m-th bond which is the only nontrivial contribution to the molecular energy at this (FAFO) level of approximate treatment of the MINDO/3 Hamiltonian using the SLG trial wave function. Within this picture the hybridization tetrahedra interact and the interaction energy depends on separations between centers of the tetrahedra, their mutual orientation, with respect to the bond axis. 

P is the total spinless density matrix (P = P + P ) and P is the spin density matrix (P = p" + P ). For a closed-shell system Mayer s definition of the bond order reduces to ... 

In PMD radicals, the bond orders are the same as those in the polymethines with the closed electron shell, insofar as the single occupied MO with its modes near atoms does not contribute to the bond orders. Also, an unpaired electron leads the electron density distribution to equalize. PMD radicals are characterized by a considerable alternation of spin density, which is confirmed by epr spectroscopy data (3,19,20). 

These methods can give us useful information on radicals in a manner similar to that for closed-shell systems, provided the exploitation is correct. Of course, in expressions for total energy, bond orders, etc., a singly occupied orbital must be taken into account. One should be aware of areas where the simple methods give qualitatively incorrect pictures. The HMO method, for example, cannot estimate negative spin densities or disproportionation equilibria. On the other hand, esr spectra of thousands of radicals and radical ions have been interpreted successfully with HMO. On the basis of HMO orbital energies and MO symmetry... 

One He atom has two electrons, so a He2 cation has three electrons. Following the aufbau process, two electrons fill the lower-energy cr 1 orbital, so the third must be placed in the antibonding crj orbital in either spin orientation. A shorthand form of the MO diagram appears at right. The bond order 1... 

From the inspection of the data in Table 2.4, it is clear that NO changes its original molecular character after adsorption. In general, coordination of nitric oxide leads to a pronounced redistribution of the electron and spin densities, accompanied by modification of the N-0 bond order and its polarization. Thus, in the case of the (MNO 7 10 and ZnNO 11 species, slender shortening of the N-0 bond is observed, whereas for the MNO 6 and CuNO 11 complexes it is distinctly elongated. Interestingly, polarization of the bound nitric oxide assumes its extreme values in the complexes of the same formal electron count ( NiNO 10 and CuNO 10) exhibiting however different valence. 

A fascinating feature of the G 2 species occurs in the excited singlet state. The 1G 2 species is bound by 29.0 kcalmol-1 at Re = 2.7444 A and has ordinarylooking bond order b = 1. However, the bonding character is remarkably different in the ot and (3 spin sets, corresponding to bent banana bonds of opposite curvature with respect to the internuclear axis. Figure 3.32 displays the form of one of these spin-NBOs, showing the off-axis curvature with respect to the Ga—Ga line of... 

The ground state (0 kJ/mol) for the CL molecule is represented by the term symbol 3v . The first excited state (92 kJ/mol above the ground state) is a 1 singlet (electrons spin paired with both electrons in either the n x or the n y level). The 1 v state with paired spin electrons, one each in the 7i v and n y levels, is the next excited level 155 kJ/mol above the ground state. Reduction of 02 by one electron yields the superoxide ion (02), a radical anion. Reduction by two electrons yields the peroxide ion, (02 ). Bond lengths and bond orders for these are given in Table 4.2. As noted in equation 4.2, the reduction potential for 02 in the presence of protons is thermodynamically favorable. Therefore, reversible binding of O2 to a metal can only be achieved if competition with protons and further reduction to superoxide and peroxide are both controlled.8... 

In the alternative approach, the HN(i), 15N( j, 13C (i/i— 1) correlations in the HNCA-TROSY spectrum can be supplemented with the data from the HN(CO)CA-TROSY experiment72 73 yielding solely 11 IN(/), 15N( ), 13C (i- 1) correlations. To this end, the HNCO-TROSY experiment is extended with the 13C —> 13C INEPT step, which utilizes rather large (ca. 51-55 Hz) one-bond scalar coupling between the 13C and 13C spins in order to transfer magnetization from the 13C (< — 1) nucleus further to the 13C ( — 1) spin. 

Lepidocrocite is paramagnetic at room temperature. The Neel temperature of 77 K is much lower than that of the other iron oxides and is the result of the layer-like structure of this mineral. The sheets of Fe(0,0H)6 octahedra are linked by weak hydrogen bonds, hence magnetic interactions are relatively weak. The saturation hyperfine field is also lower than for any other iron oxide (Tab. 6.2). In the antiferromagnetic state, the spins are ordered parallel to the c-axis with spins in alternate layers having opposite signs. A decrease of T by 5 K was observed for Al-lepidocrocites with an Al/(Fe-i-Al) ratio of 0.1 (De Grave et al., 1995). 

Aromatic substitution reactions are often complicated and multistep processes. A correlation, however, in many cases can be found between the charged attacking species and the electron density distribution in the molecule attacked during electrophilic and nucleoph c substitution. No such correlation is expected in radical substitution where the attacking particles are neutral, rather a correlation between the reactivities of separate bonds and a free valency index of the bond order. This allows the prediction of the most reactive bonds. Such an approach has been used by researchers who applied quantum calculations to estimate the reactivities of the isomeric thienothiophenes and to compare them with thiophene or naphthalene. " Until recently quantum methods for studying reactivities of aromatics and heteroaromatics were developed mainly in the r-electron approximation (see, for example, Streitwieser and Zahradnik ). The M orbitals of a sulfur atom were shown not to contribute substantially to calculations of dipole moments, polarographic reduction potentials, spin-density distribution, ... 

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