Structural orbital exchange

Table I. Structural and antiferromagnetic orbital exchange parameters...

The frozen-core (fc) approach is not restricted to spin-independent electronic interactions the spin-orbit (SO) interaction between core and valence electrons can be expressed by a sum of Coulomb- and exchange-type operators. The matrix element formulas can be derived in a similar way as the Sla-ter-Condon rules.27 Here, it is not important whether the Breit-Pauli spin-orbit operators or their no-pair analogs are employed as these are structurally equivalent. Differences with respect to the Slater-Condon rules occur due to the symmetry properties of the angular momentum operators and because of the presence of the spin-other-orbit interaction. It is easily shown by partial integration that the linear momentum operator p is antisymmetric with respect to orbital exchange, and the same applies to t = r x p. Therefore, spin-orbit... 

Future applications of the AOM will include the analysis of the optical spectra and magnetic properties of transition metal ions located in polynuclear systems. Calculations on infinite structures (chains) have already been reported [110], and a parametrization scheme for the evaluation of orbital-exchange parameters in magnetically coupled dinuclear complexes was presented recently [111]. Another interesting aspect concerns the dynamic extension of the AOM which allows, for example, Jahn-Teller energies to be calculated [112, 113]. Finally, it should be... 

The mobility of the proton in position 2 of a quaternized molecule and the kinetics of exchange with deuterium has been studied extensively (18-20) it is increased in a basic medium (21-23). The rate of exchange is close to that obtained with the base itself, and the protonated form is supposed to be the active intermediate (236, 664). The remarkable lability of 2-H has been ascribed to a number of factors, including a possible stabilizing resonance effect with contributions of both carbene and ylid structure. This latter may result from the interaction of a d orbital at the sulfur atom with the cr orbital out of the ring at C-2 (21). 

The tetramethylammonium salt [Me4N][NSO] is obtained by cation exchange between M[NSO] (M = Rb, Cs) and tetramethylammonium chloride in liquid ammonia. An X-ray structural determination reveals approximately equal bond lengths of 1.43 and 1.44 A for the S-N and S-O bonds, respectively, and a bond angle characteristic bands in the IR spectrum at ca. 1270-1280, 985-1000 and 505-530 cm , corresponding to o(S-N), o(S-O) and (5(NSO), respectively. Ab initio molecular orbital calculations, including a correlation energy correction, indicate that the [NSO] anion is more stable than the isomer [SNO] by at least 9.1 kcal mol . ... 

The atoms X, Y, and Z in the general structure might be C, N, O, F, or S, and the asterisk ( ) might mean that the p orbital on atom Z is vacant, that it contains a single electron, or that it contains a lone pair of electrons. The two resonance forms differ simply by an exchange in position of the multiple bond and the asterisk from one end to the other. 

Fig. 11. Top molecular orbital energies for precursor, structure C (broken lines) and for bridged intermediate, structure D (full lines). Bottom bridging energy (AE) for N =0 (full line) and N = 1 (broken line), where N is the number of electrons transferred from the carbon residue to the platinum. The energies are plotted as functions of the 7rC3-to-platinum overlap integral (S). The energy unit 0 [ is the absolute value of the exchange integral between a pair of p1 orbitals in benzene. For structures C and D, cf. reaction (7). After J. R. Anderson and N. R. Avery, J. Calal. 7, 315 (1967).

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