Spin state determination

Line shape and line Spin-spin relaxation T2 (s) Lifetime of spin state determined by... 

For quadmpolar nuclei, the dependence of the pulse response on Vq/Vj has led to the development of quadmpolar nutation, which is a two-dimensional (2D) NMR experiment. The principle of 2D experiments is that a series of FIDs are acquired as a function of a second time parameter (e.g. here the pulse length applied). A double Fourier transformation can then be carried out to give a 2D data set (FI, FI). For quadmpolar nuclei while the pulse is on the experiment is effectively being carried out at low field with the spin states determined by the quadmpolar interaction. In the limits Vq 4 Vj and Vq Vj the pulse response lies at Vj and (/ -I- )vj respectively so is not very discriminatory. However, for Vq Vj the pulse response is complex and... 

Lineshape and linewidth Spin-spin relaxation time T2 = (1/hAv) (s) Peak width at half-maximum intensity (Av, Hz) Lifetime of spin state determined by dynamic processes and local magnetic environment... 

Using a table of nuclear spin states, determine... 

Tin has 10 stable isotopes. Using a table of nuclear spin states, determine q uz for each of them. How many different... 

Ah initio programs attempt to compute the lowest-energy state of a specified multiplicity. Thus, calculations for different spin states will give the lowest-energy state and a few of the excited states. This is most often done to determine singlet-triplet gaps in organic molecules. 

Nuclear magnetic resonance (NMR) spectroscopy (Section 13 3) A method for structure determination based on the effect of molecular environment on the energy required to promote a given nucleus from a lower energy spin state to a higher energy state... 

In this section, we compare our results for the magnetic moments of Ni, Fe and Co, n< 55, clusters with available experimental data. We point out that the determination of the exact ground state of these clusters is a very difficult task because these clusters exhibit a number of various spin states with energies lying very close to the ground state and within the range of both the calculational and the experimental errors. 

According to the law for the eigenvalues, our determinant could possibly be a mixture of spin states associated with the quantum numbers S = m, m- -1,. . N. However, in the special case... 

A single Slater determinant with N+ N represents a pure spin state if, and only if, the number of doubly filled orbitals defined by Eq. 11.57 equals AL. 

More abstractly the condition Tr (p+p ) = iV implies that the part of the Hilbert space defined by the projection operator p should be fully contained in the part defined by the projection operator p+. If we now vary p slightly so that this condition is no longer fulfilled, Eq. II.GO shows that the pure spin state previously described by the Slater determinant becomes mixed up with states of higher quantum numbers S = m+1,. . . . The idea of the electron pairing in doubly occupied orbitals is therefore essential in the Hartree-Fock scheme in order to secure that the Slater determinant really represents a pure spin state. This means, however, that, in the calculation of the best spin orbitals y>k(x), there is a new auxiliary condition of the form... 

Leaving the question of pure spin states entirely aside, Wigner studied a system containing an even number of electrons (N = 2n) by considering the product of two determinants built up from or-bitals only... 

As shown in Section II.D(2), the determinant of Eq. III.133 can be brought to correspond to a pure spin state by imposing a certain condition (11.61) on the relation between p+ and p. which corresponds to the pairing of the electrons. If p+ and p are permitted to vary independently of each other, the determinant is no longer a pure spin state but a mixture of states associated with the quantum numbers... 

It is now possible to formulate an extension of the conventional Hartree-Fock scheme by considering a wave function (25+1) IP which is a pure spin state and which is simply defined by the component of the single Slater determinant Eq. III. 133 as has the spin property required ... 

A common feature of the Hartree-Fock scheme and the two generalizations discussed in Section III.F is that all physical results depend only on the two space density matrices p+ and p, which implies that the physical and mathematical simplicity of the model is essentially preserved. The differences lie in the treatment of the total spin in the conventional scheme, the basic determinant is a pure spin function as a consequence of condition 11.61, in the unrestricted scheme, the same determinant is a rather undetermined mixture of different spin states, and, in the extended scheme, one considers only the component of the determinant which has the pure spin desired. 

According to these equations, the effect of selectively perturbing the spin states of spins i and j is to isolate the cross-relaxation paths common to these two spins. Combining Eqs. 15 and 19, the individual cross-relaxation terms are readily determined from single-selective and double-selective relaxation-rate measurements, that is. 

Spin-state transitions have been studied by the application of numerous physical techniques such as the measurement of magnetic susceptibility, optical and vibrational spectroscopy, the Fe-Mbssbauer effect, EPR, NMR, and EXAFS spectroscopy, the measurement of heat capacity, and others. Most of these studies have been adequately reviewed. The somewhat older surveys [3, 19] cover the complete field of spin-state transitions. Several more recent review articles [20, 21, 22, 23, 24, 25] have been devoted exclusively to spin-state transitions in compounds of iron(II). Two reviews [26, 27] have considered inter alia the available theoretical models of spin-state transitions. Of particular interest is the determination of the X-ray crystal structures of spin transition compounds at two or more temperatures thus approaching the structures of the pure HS and LS electronic isomers. A recent survey [6] concentrates particularly on these studies. 

---