Spin Distribution in Alternant Radicals

As the MSADs have the largest coefficients in the ground-state wave function, one may expect that for alternant free radicals or polyradicals, the dominant positive spin density will be largest on the atoms that bear an alpha spin in the MSAD. An example that was analyzed in Chapter 7 is the allyl radical, where the MSAD predicts positive spin densities at positions 1, 3 and a negative density at position 2. Similarly, the MSAD of benzyl radical predicts positive spin densities on the benzylic carbon and on the ortho and para positions. 

To get accurate numerical results, the spin densities can be deduced from the diagonalization of the spin-Hamiltonian matrix (9). To calculate the spin density of a given atom, one only has to sum up the weights (in this case, the squared coefficients) of all determinants, in which this atom is occupied by an a spin, while subtracting the weights of determinants in which this atom has a (3 spin (consult the case of allyl radical in Exercise 7.1). 

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