Spin correlation

To calculate the spin correlation fiinctions between any two sites, multiply the expression for (.Sq) by Z when... 

The spin correlation fiinctions and their dependence on the distance between sites and the coupling between adjacent sites are of great interest in understanding the range of these correlations. In general, for a closed chain... 

Utilizing FT-EPR teclmiques, van Willigen and co-workers have studied the photoinduced electron transfer from zinc tetrakis(4-sulfonatophenyl)porphyrin (ZnTPPS) to duroquinone (DQ) to fonn ZnTPPS and DQ in different micellar solutions [34, 63]. Spin-correlated radical pairs [ZnTPPS. . . DQ ] are fomied initially, and the SCRP lifetime depends upon the solution enviromnent. The ZnTPPS is not observed due to its short T2 relaxation time, but the spectra of DQ allow for the detemiination of the location and stability of reactant and product species in the various micellar solutions. While DQ is always located within the micelle, tire... 

Figure Bl.16.22. Schematic representations of CIDEP spectra for hypothetical radical pair CH + R. Part A shows the A/E and E/A RPM. Part B shows the absorptive and emissive triplet mechanism. Part C shows the spin-correlated RPM for cases where J and J a.. ...

Buckley C D, Hunger D A, Here P J and McLauchlan K A 1987 Electron spin resonance of spin-correlated radical pairs Chem. Phys. Lett. 135 307-12... 

Avdievich N I and Forbes M D E 1995 Dynamic effects in spin-correlated radical pair theory J modulation and a new look at the phenomenon of alternating line widths in the EPR spectra of flexible biradicals J. Phys. Chem. 99 9660-7... 

Forbes M D E, Avdievich N I, Schulz G R and Ball J D 1996 Chain dynamics cause the disappearance of spin-correlated radical pair polarization in flexible biradicals J. Phys. Chem. 100 13 887-91... 

To see how and under what conditions stability is enhanced or diminished, we need to consider the symmetry of the orbital (9-32), Flectrons in the antisymmetric orbital r r have a 7ero probability of occurring at the node in u where U] = rj. Electron mutual avoidance of the node due to spin correlation reduces the total energy of the system because it reduces electron repulsion energy due to charge... 

K. Binder, P. C. Hoehenberg. Phase transitions and static spin correlations in Ising models with free surfaces. Phys Rev B 6 3461-3487, 1972. 

Since the coiTelation between opposite spins has both intra- and inter-orbital contributions, it will be larger than the correlation between electrons having the same spin. The Pauli principle (or equivalently the antisymmetry of the wave function) has the consequence that there is no intraorbital conelation from electron pairs with the same spin. The opposite spin correlation is sometimes called the Coulomb correlation, while the same spin correlation is called the Fermi correlation, i.e. the Coulomb correlation is the largest contribution. Another way of looking at electron correlation is in terms of the electron density. In the immediate vicinity of an electron, here is a reduced probability of finding another electron. For electrons of opposite spin, this is often referred to as the Coulomb hole, the corresponding phenomenon for electrons of the same spin is the Fermi hole. 

Linear rules have the important property that all single-spin expectations and multi- spin correlations are decoupled. Calculating the expectation < Sk >t+ii for example, we see that... 

In a famous paper, Bell [bell64] showed that locality and the notion that the components of the particles spins are determinate are fundamentally incompatible with the spin correlations as predicted by quantum mechanics. Bell s result, in effect, rules out the possibility of having a local, deterministic theory. 

Using a variety of transient and CW spectroscopies spanning the time domains from ps to ms, we have identified the dominant intrachain photoexcitations in C )-doped PPV films. These are spin-correlated polaron pairs, which are formed within picoseconds following exciton diffusion and subsequent dissociation at photoinduced PPV+/Cw> defect centers. We found that the higher-energy PA band of polaron pairs is blue-shifted by about 0.4 eV compared to that of isolated polarons in PPV. 

An alternative stream came from the valence bond (VB) theory. Ovchinnikov judged the ground-state spin for the alternant diradicals by half the difference between the number of starred and unstarred ir-sites, i.e., S = (n -n)l2 [72]. It is the simplest way to predict the spin preference of ground states just on the basis of the molecular graph theory, and in many cases its results are parallel to those obtained from the NBMO analysis and from the sophisticated MO or DFT (density functional theory) calculations. However, this simple VB rule cannot be applied to the non-alternate diradicals. The exact solutions of semi-empirical VB, Hubbard, and PPP models shed light on the nature of spin correlation [37, 73-77]. 

Figure 17. Contour plot of the 360MHz homonuclear spin correlation mpa of 10 (2 mg, CDCL, high-field expansion) with no delay inserted in the pulse sequence shown at the top of the figure. Assignments of cross peaks indicating coupled spins in the E-ring are shown with tljie dotted lines. The corresponding region of the one-dimensional H NMR spectra is provided on the abscissa. The 2-D correlation map is composed of 128 x 512 data point spectra, each composed of 16 transients. A 4-s delay was allowed between each pulse sequence (T ) and t was incremented by 554s. Data was acquired with quadrature phase detection in both dimensions, zero filled in the t dimension, and the final 256 x 256 data was symmetrized. Total time of the experiment was 2.31 h (17).

O.G. Poluektov, L.M. Utschig, A.A. Dubinskij and M. Thurnauer, ENDOR of spin-correlated radical pairs in photosynthesis at high magnetic field A tool for mapping electron transfer pathways, J. Am. Chem. Soc., 2004, 126, 1644. 

An alternative way to describe the phenomenon is to consider that the ground state of a chain is already divided into domains at any temperatures. In order for the system to follow a small variation of the magnetic field some domains have to reverse their spin orientation. This occurs through a random walk of the DWs, that is, equal probability for the DW to move backward or forward, which implies that the DW needs a time proportional to d2 to reach the other end of a domain of length d. Given that d scales as the two spins correlation length, ., which, for the Ising model, is proportional to exp(2///rB7 ), for unitary spins, the same exponential relaxation is found... 

The exact high- and low-density limits can be found from arguments given in Ref. [57]. For = 0 in the high-density limit (where the random phase approximation becomes exact), the parallel-spin and anti-parallel-spin correlation energies are equal [57], so... 

Eq. (23) is at Erst surprising, since it implies that the parallel-spin correlation energy for = 0 is slightly positive [-0.02ec(/ = 0)] in the low-density limit. But this cannot be ruled out, since the total correlation energy is of course properly negative. Eqs. (22) and (23) are at least consistent with the increase with r, of the GSB ratio - 0)/e(r, = 0), as shown in Table... 

We focus in this Section on particular aspects relating to the direct interpretation of valence bond wavefunctions. Important features of a description in terms of modem valence bond concepts include the orbital shapes (including their overlap integrals) and estimates of the relative importance of the different stmctures (and modes of spin coupling) in the VB wavefunction. We address here the particular question of defining nonorthogonal weights, as well as certain aspects of spin correlation analysis. 

Spin correlation analysis [68-71] is an attractive means of representing the coupling between electron spins, having the important advantage of being independent of the spin basis used. We shall consider in the following the particular case of a spin-coupled... 

The dimensions of the spin spaces for the active electrons in Table 2, cf. Eq. (9)) are certainly not small. It proved difficult to find a spin basis in which very few of the coefficients were large and so we adopted instead a spin correlation scheme cf. Section 4.2). In the present work, we exploited the way in which expectation values of the two-electron spin operator evaluated over the total spin eigenfunction 4, depend on the coupling of the individual spins associated with orbitals ( )/ and j. Negative values indicate singlet character and positive values triplet character. Special cases of the expectation value are ... 

Table 3 Overlap (upper triangle) and spin correlation (lower triangle) matrices successive values in the boxes relate to S = 0, 1, 2, and 3...

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