Spin-States

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. 

A single-excitation configuration interaction (CIS) calculation is probably the most common way to obtain excited-state energies. This is because it is one of the easiest calculations to perform. 

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EPR) netic) resonance [218-222] electron spin states in a magnetic field species... 

NMR Nuclear magnetic resonance [223, 224] Chemical shift of splitting of nuclear spin states in a magnetic field H [225], C [226, 227], N [228], F [229], 2 Xe [230] Other Techniques Chemical state diffusion of adsorbed species... 

Each lattice point extraneous to the sites connected by graphs also contributes a factor of two on summing over spin states. Hence all lattice points contribute a factor of 2 whether they are coimected or not, and... 

Part A shows the four possible combined spin states of a molecular fragment, taken as an example. 

These are the same states as in Figure Bl.l 1.8, but attention is now drawn to the populations of the four spin states, each reduced by subtracting the 25% population that would exist at very low field, or alternatively at infinite temperature. The figures above each level are these relative differences, in convenient units. The intensity of any one transition, i.e. of the relevant peak in the doublet, is proportional to the difference of these differences, and is therefore proportionally relative to unity for any transition at Boltzmaim equilibrium, and 4 for any transition. 

For quadnipolar nuclei, the dependence of the pulse response on Vq/v has led to the development of quadnipolar nutation, which is a two-dimensional (2D) NMR experiment. The principle of 2D experiments is that a series of FIDs are acquired as a fimction of a second time parameter (e.g. here the pulse lengdi applied). A double Fourier transfomiation can then be carried out to give a 2D data set (FI, F2). For quadnipolar nuclei while the pulse is on the experiment is effectively being carried out at low field with the spin states detemiined by the quadnipolar interaction. In the limits Vq v the pulse response lies at v and... 

A result of tlie relaxation processes is a shortened lifetime of the spin states giving rise to a broadening of the EPR line, which for most magnetic resonance lines dominated by homogeneous linewidth can be written as... 

The negative sign in equation (b 1.15.26) implies that, unlike the case for electron spins, states with larger magnetic quantum number have smaller energy for g O. In contrast to the g-value in EPR experiments, g is an inlierent property of the nucleus. NMR resonances are not easily detected in paramagnetic systems because of sensitivity problems and increased linewidths caused by the presence of unpaired electron spins. 

Stehlik D, Bock C H and Thurnauer M 1989 Transient EPR-spectroscopy of photoinduced electronic spin states in rigid matrices Advanced ERR in Biology and Biochemistry ed A J Hoff (Amsterdam Elsevier) oh 11, pp 371 03... 

CIDNP involves the observation of diamagnetic products fonned from chemical reactions which have radical intemiediates. We first define the geminate radical pair (RP) as the two molecules which are bom in a radical reaction with a well defined phase relation (singlet or triplet) between their spins. Because the spin physics of the radical pair are a fiindamental part of any description of the origins of CIDNP, it is instmctive to begin with a discussion of the radical-pair spin Hamiltonian. The Hamiltonian can be used in conjunction with an appropriate basis set to obtain the energetics and populations of the RP spin states. A suitable Hamiltonian for a radical pair consisting of radicals 1 and 2 is shown in equation (B1.16.1) below [12]. 

When the inter-radieal distanee is very small, J is large, and. S and Jq are far apart and eaimot mix. This is ealled the exehange region as the eleetron spins are eonstrained by the exehange interaetion to remain in their respeetive spin states. As the radieals diflfiise apart, J rapidly falls to zero, and the. S and levels... 

By examining the expression for Q ( equation (B1.16.4)). it should now be clear that the nuclear spin state influences the difference in precessional frequencies and, ultimately, the likelihood of intersystem crossing, tlnough the hyperfme tenn. It is this influence of nuclear spin states on electronic intersystem crossing which will eventually lead to non-equilibrium distributions of nuclear spin states, i.e. spin polarization, in the products of radical reactions, as we shall see below. 

Figure Bl.16.5. An example of the CIDNP net effect for a radical pair with one hyperfme interaction. Initial conditions g > g2, negative and the RP is initially singlet. Polarized nuclear spin states and schematic NMR spectra are shown for the recombination and scavenging products in the boxes.

In this simple case, there are just two nuclear spin states, a and (3. Equation (1.16.5) shows the calculation of the difference in electron precessional frequencies, Q, for nuclear spin states a (equation (B 1.16.5a)) and (3 (equation (B1.16.5h)). 

Since Ag is positive and is negative, Q is larger for the p state than for the a state. Radical pairs in the p nuclear spin state will experience a faster intersystem crossing rate than those in the a state with the result that more RPs in the p nuclear spin state will become triplets. The end result is that the scavenging product, which is fonned primarily from triplet RPs, will have an excess of spins in the p state while the recombination product, which is fonned from singlet RPs, will have an excess of a nuclear spin states. 

Let and be the fractions of states with odd and even total spins. Sj =0,1,2,.. ., 2s. When the 2s + 1 spin-states. Sj are iimesolved, the appropriate combination of syimnetric and antisyimnetric cross sections is the weighted mean... 

Secondly, you must describe the electron spin state of the system to be calcn lated. Electron s with their individual spin s of Sj=l /2 can combine in various ways to lead to a state of given total spin. The second input quantity needed is a description of the total spin... 

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