deer_analyt.m

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Analytical expression for a DEER trace for two spins in the presence of dipolar and exchange (EPR) or J (NMR) coupling. This function returns the powder averaged dipolar modulation signal in DEER, PELDOR and in-phase ESEEM type experiments, as well as in solid state NMR spectroscopy where dipolar modulation has been isolated by selective recoupling.

Syntax

    deer=deer_analyt(D,J,t)

Arguments

    D - dipolar coupling, angular frequency units, the
        coefficient in front of (1-3*cos(theta)^2)*Lz*Sz
        in the spin Hamiltonian

    J - exchange coupling, angular frequency units, NMR
        convention (no factor of 2 in front), the coef- 
        ficient in front of Lz*Sz in the spin Hamiltonian

    t - array of time points, seconds

Outputs

    deer - an array of DEER form factor values of the same
           dimension as t

Examples

See examples/esr_solids directory for multiple examples from EPR spectroscopy.

An example DEER modulation trace: numerical simulation vs. analytical expression used by this function.

Notes

  1. Distance distributions in real molecules are rarely delta functions. If the distribution has a width, it would impose and additional exponential or Gaussian decay on the modulation produced by this function.
  2. The presence of observer spins can generate a background signal that may be approximately described by a stretched exponential.

See also

deer_3p_hard_deer.m, deer_3p_soft_deer.m, deer_4p_soft_deer.m, eseem.m, oopeseem.m, xyz2dd.m


Version 2.2, authors: Ilya Kuprov