Spin density populations

Figure 2. Spin-density populations for the high-spin form (S=6) of Co...

Symmetry and stability analysis. The semi-empirical unrestricted Hartree-Fock (UHF) method was used for symmetry and stability analysis of chemical reactions at early stage of our theoretical studies.1,2 The BS MOs for CT diradicals are also expanded in terms of composite donor and acceptor MOs to obtain the Mulliken CT theoretical explanations of their electronic structures. Instability in chemical bonds followed by the BS ab initio calculations is one of the useful approaches for elucidating electronic structures of active reaction intermediates and transition structures.2 The concept is also useful to characterize chemical reaction mechanisms in combination with the Woodward-Hoffman (WH) orbital symmetry criterion,3 as illustrated in Figure 1. According to the Woodward-Hoffmann rule,3 there are two types of organic reactions orbital-symmetry allowed and forbidden. On the other hand, the orbital instability condition is the other criterion for distinguishing between nonradical and diradical cases.2 The combination of the two criteria provides four different cases (i) allowed nonradical (AN), (ii) allowed radical (AR), (iii) forbidden nonradical (FN), and (iv) forbidden radical (FR). The charge and spin density populations obtained by the ab initio BS MO calculations are responsible for the above classifications as shown in Fig. 1. 

The consistent total energy makes it possible to compute singlet-triplet gaps using RHF for the singlet and the half-electron calculation for the triplet. Koopman s theorem is not followed for half-electron calculations. Also, no spin densities can be obtained. The Mulliken population analysis is usually fairly reasonable. 

Extended Hiickel calculations are performed with a nonorthogonalized AO basis set therefore, the spin densities are to be evaluated by gross atomic populations and not simply by squares of expansion coefficients. 

An approach to solving the inverse Fourier problem is to reconstruct a parametrized spin density based on axially symmetrical p orbitals (pz orbitals) centered on all the atoms of the molecule (wave function modeling). In the model which was actually used, the spin populations of corresponding atoms of A and B were constrained to be equal. The averaged populations thus refined are displayed in Table 2. Most of the spin density lies on the 01, N1 and N2 atoms. However, the agreement obtained between observed and calculated data (x2 = 2.1) indicates that this model is not completely satisfactory. 

The hexaphenyldilead radical anion almost certainly has a similar structure since the g values are all less than 2.0023. Calculation of the unpaired spin population in the lead 6s and 6p orbitals leads to values of 0.11 and 0.99. Once again the spin population is too large, especially for the 6p orbital. Nevertheless, the calculations do show that the spin density is probably entirely associated with the lead atoms. 

The calculation of the indices requires the overlap matrix S of atomic orbitals and the first-order density (or population) matrix P (in open-shell systems in addition the spin density matrix Ps). The summations refer to all atomic orbitals /jl centered on atom A, etc. These matrices are all computed during the Hartree-Fock iteration that determines the molecular orbitals. As a result, the three indices can be obtained... 

Considering a five-point spin density distribution (central ion and four nitrogens) for the determination of the dipolar proton hfs tensors in Ag(TPP) (5.5), the computed ADD principal values are found to be close to the experimental results. It should be noted that in Ag(TPP) the Mulliken population, UN, on the nitrogen nearest to the pyrrole proton provides a larger contribution to ADD along the Ag-H direction than the population UAg. 

The sensitivity on the other hand is dictated by the spin density and the polarization (the relative population of a- and y3-states). The latter in turn depends on the energy separation of a- and y3-states, which increases concomitantly with field strength. Changing to a higher field will therefore not only increase spectral dispersion but also increase sensitivity because the polarization increases. The remarkable increase in resolution that is gained by going from 600 to 800 MHz is shown in Fig. 3.1. 

The different shift mechanisms may be understood in more detail by considering the effect of the magnetic field on the populations and energies of the different crystal orbitals (Figure 7a). Transfer of electron density via the 90° interaction arises due to a direct delocalization of spin density due to overlap between the half-filled tzg. oxygen jt, and empty Li 2s atomic orbitals (the delocalization mechanism. Figure 7b).This overlap is responsible for the formation of the tzg (antibonding) molecular orbital in a molecule or the tzg crystal orbital (or band) in a solid. No shift occurs for the 180° interaction from this mechanism as the eg orbitals are empty. 

Methyl tricyclo[4.1.0.0 ]heptane-l-carboxylate gives a cation-radical in which the spin density is almost completely localized on C-1 while the positive charge is on C-7. The revealed structural feature of the intermediate cation-radical fairly explains the regioselectivity of N,N-dichlorobenzenesulfonamide addition to the molecular precursor of this cation-radical. In the reaction mentioned, the nucleophilic nitrogen atom of the reactant adds to electrophilic C-7, and the chlorine radical attacks C-1 whose spin population is maximal (Zverev and Vasin 1998, 2000). 

Both theory and experiment point to an almost perpendicular orientation of the two butadiene H2C=C(t-Bu) moieties (see Scheme 3.53). On passing from the neutral molecule to its anion-radical, this orthogonal orientation should flatten because the LUMO of 1,3-butadiene is bonding between C-2 and C-3. Therefore, C2-C3 bond should be considerably strengthened after the anion-radical formation. The anion-radical will acquire the cisoidal conformation. This conformation places two bulky tert-butyl substituents on one side of the molecule, so that the alkali metal counterion (M+) can approach the anion-radical from the other side. In this case, the cation will detain spin density in the localized part of the molecular skeleton. A direct transfer of the spin population from the SOMO of the anion-radical into the alkali cation has been proven (Gerson et al. 1998). 

To disrupt the carbon-chloride bond at position 5 of the substrate anion-radical, population of this bond with an unpaired electron should be increased. However, if a spin density at carboncarrying chlorine is too great, the initial chlorine-containing anion-radicals dimerize instead of cleaving the chloride ion. Thus, in the isomeric 6-chloro-27/,3//-benzo[b]thiophenedione-2,3 anion-radical, unpaired electron density at C-6 is five times greater than at C-5, and the dimerization proceeds much more rapidly than the cleavage of carbon-chlorine bond (Alberti et al. 1981). 

According to CASSCF (and nonhybrid functionals), the spin population on the Fe atom is close to 1.0, whereas the NO moiety does not carry a significant amount of spin density. Based on that, the Fe(I)-NO+ electronic structure was assigned to the FeP-NO complex. Earlier, (147) based on Car-Parinello MD simulations, the Fe(III)-NO electronic structure was suggested for the FeP-NO complex. Additional complications came from the comparison of N-0 bond length while the experimentally measured bond... 

Fig.12. Qualitative MO scheme for complex 1 (St = 0, BS(1,1)) (top) and spin density plot with Mulliken spin populations (bottom).

The analysis of the data of PS I gave quite accurate information on the distance of the spin centres (25.4 0.3 A)301 that compared well with the crystal structure data.68 A problem is the extended it-spin density distribution in the donor and acceptor. For a solid comparison a centre of gravity for the spin must be calculated from experimental or theoretical spin density distributions of the two radicals. Similar data with almost unaltered distances were obtained for PS I with other quinones substituted into the Ai site.147-302This work has been extended to other electron acceptors,303 which show a larger heterogeneity in distances. It has been shown that the lifetime of the RP can also be measured and can even be controlled in the experiments by an additional mw pulse prior to the 2-pulse echo sequence.302 This pulse transfers population to triplet levels which cannot directly recombine to the singlet ground state. This has earlier been shown for the bRC.304,305 The OOP-ESEEM technique has also been applied to various mutants of PS I to characterize them by the measured distances between fixed donor and variable acceptors.254 256-263-264... 

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