Field Resonance Theory

Notice too that in the present argument the (unpaired-electron) spin density should appear primarily on the sites with an excess free-valence sum, especially for those such sites more well separated from opposite-type sites with non-zero free valence. Yet further too if distant sites need to be spin-paired, then there should be a low-lying higher-spin excited state where the spin-pairing is violated. For finite conjugated molecules this further leads to agreement with the spin result of Eq. 

Application of Mean-Field Resonance Theory to Defected Graphites 

This corresponds to the number of unpaired electrons in R also, and we term 51 the graphitic anti-molecule corresponding to R. 

Beyond these two example applications a number of others have been described. These concern not only ordinary radicaloid (finite) molecules, but also polymer ends, graphitic comers, carbene containing systems (with ferromagnetic couplings between the singly-occupied a-orbitals and the 7t-network), and even some systems with transition metal centers involved in the exchange network. See Refs. [195,198]. 

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The most simple way to accomplish this objective is to correct the external field operator post factum, as was repeatedly done in magnetic resonance theory, e.g. in [39]. Unfortunately this method is inapplicable to systems with an unrestricted energy spectrum. Neither can one use the method utilizing the Landau-Teller formula for an equidistant energy spectrum of the harmonic oscillator. In this simplest case one need correct... 

Because we are both computational chemistry researchers, we have naturally directed the book also to specialists in this field, particularly those wishing to incorporate natural bond orbital (NBO) and natural resonance theory (NRT) analysis into their methodological and conceptual toolbox. Researchers will find here a... 

Weller s review (1961) is not confined to acid-base reactions but deals with the kinetics of excited state reactions in general. Vander Donckt (1970) covers developments of the acid-base section of the Weller field but pays more attention to physical organic aspects, such as applications of resonance theory to the interpretation of pA-shifts upon excitation and the application of linear free energy relationships. The reviews by Schulman and Winefordner (1970) and by Winefordner et al. (1971a) are directed towards possible analytical applications. 

In Figs. 12 and 13 we compare the results of the present theory for quadrupole moments with the experimental data obtained for the l) line of rubidium [Budker 2002 (b)]. The calculations for our simpler system reproduce many of the qualitative aspects of the experimental data for Rb. As seen, at the center of the in-phase plots of Figs. 12 and 13, zero-field resonances arise, while resonances centered at the magnetic-field values for which = 1/2 and... 

The most precise measurements of the fine-structure parameters D and E have in fact been carried out using zero-field resonance. Figure 7.6 shows the three zero-field transitions in the Ti state of naphthalene molecules in a biphenyl crystal at T = 83 K. In these experiments, the absorption of the microwaves was detected as a function of their frequency [5]. The lines are inhomogeneously broadened and nevertheless only about 1 MHz wide. Owing to the small hnewidth of the zero-field resonances, the fine-structure constants can be determined with a high precision. This small inhomogeneous broadening is due to the hyperfine interaction with the nuclear spins of the protons (see e.g. [M2] and [M5]). For triplet states in zero field, the hyperfine structure vanishes to first order in perturbation theory, since the expectation value of the electronic spins vanishes in all three zero-field components (cf Sect. 7.2). The hyperfine structure of the zero-field resonances is therefore a second-order effect [5]. 

The substituent effects on the a protons in butatrienes correspond to 0.71 a"(R) in Table 8 (R = H, Me, Et, MeO, MeS, Cl, CHO (from 4, 229, and 239)) that is, they are reduced compared with those in allenes. Concerning the remote hydrogen atoms (H3, H4) one observes, if ever, only a slight difference between the H chemical shifts of the Z- and -protons (228). The substituent effects on the proton shifts of these last hydrogen atoms show an unexpected behavior The tt donors Me, Et, EtO shift the resonances to higher field, whereas the 7T donors Cl and MeS yield low-field shifts. Therefore, simple resonance theory which stresses a negative v electron density at the 5 carbon atoms of butatrienes with tt donors does not seem to be appropriate to represent the electron density distributions in butatrienes with second-row substituents (Cl, MeS) (Section IIl.C). 

The method ean be applied to all molecules, although a particularly useful field of applications of resonance theory can be found in the organic chemistry of aromatic systems. For example, the total electronic wave function of the benzene molecule is presented as a linear combination of resonance structures ... 

Both methods have met with outstanding success in the field of organic chemistry. The predominant importance of their contribution is due, however, to different types of achievement. Thus, the resonance theory has been... 

T. Prisner and M. J. Prandolini, Dynamic Nuclear Polarization (DNP) at High Magnetic Fields , in Multifrequency Electron Paramagnetic Resonance Theory and Applications, ed. S. K. Misra, Wiley-VCH Verlag GmbH Co. KGaA, Weinheim, Germany, 2011, p. 921. 

Magnetic and optical resonances are identical electromagnetic phenomena in the sense that there occurs an interaction of a magnetic field with matter, and both types of experiments may be described under a common mathematical formalism that is independent of experimental approach. But in developing a theoretical formalism that fuses both optical and magnetic resonance phenomena there occurs a problem reconciling the manner in which one treats the resonance condition. For example, both magnetic resonance theory and experiment deal directly with an... 

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