Dipolar interactions and spin delocalization

[thanasis]

Hello,

I was wondering whether ES can account for dipolar interactions within exchange-coupled systems by considering the spin densities introduced due to exchange interactions.

Assuming we have set up a precise expression of the dipole-dipole interaction matrix Ddip(ij) between spins i and j, using tensors gi and gj:

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D_dip_ij = transpose(gi)*gj - 3 * (transpose(gi)*Rij) * (transpose(Rij)*gj);
dip_ij = 12993 * rij^-3 * D_dip_ij;

when we define our system so that:

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Sys.ee = etc + etc + dip_ij

then I guess that Easyspin calculates something like Si(T)*Sys.ee*Sj for the e-e interaction part of the system's spin Hamiltonian.

However, magnetic exchange may affect the spin densities on each spin (e.g when we have polynuclear systems). The spin densities can be calculated by calculating the operator matrices:

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[S1x,S1y,S1z,etc] = sop(Sys,'x1','y1','z1',etc); 

and then the expectation values (e.g. at the ground state):

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H = sham(Sys,[0 0 1e-4]);
[Vt,E]=eig(H);
S1x_expect = Vt(:,1)'*S1x*Vt(:,1);
S1y_expect = 
S1z_expect = 
etc

So my question is: can we separately calculate the dipolar contribution, not for the pure single-ion spin values, but for the spin densities due to magnetic exchange? I.e. something of the type:

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[Six_expect Siy_expect Siz_expect] * dip_ij * [Sjx_expect; Sjy_expect; Sjz_expect]

and then stick it to the rest of the spin Hamiltonian?

And more to the point, is there physical meaning to such a calculation? Please note that I am not considering delocalized spins within organic radical systems, but between exchange-coupled metal centers. So the point-dipole approximation would still be valid in terms of distances, but with recalculated spin values.

Thanks!

[Stefan Stoll]

It's not entirely clear to me what you mean. The last expression you gave is a constant, as it appears to be independent of any spin operators.

[thanasis]

Thanks Stefan,

Indeed the mathematical formulation I give is not correct. It is rather meant as an indication of what I am looking to calculate. The "how" is the question.

What I am trying to calculate is a dipolar interaction when one of the sites has a different than nominal spin density on it, due to exchange interactions. We can have an approximate idea of spin densities on each site by calculating spin expectation values (as scalars). Can we then use these to define a "tweaked" spin operator matrix, which will give rise to "tweaked" dipolar interactions?

And, the bigger question, do you agree that there is physical meaning in doing this?