Pseudocontact shift analysis

In progress - don't judge too harshly!

Spinach offers several ways to process the experimental PCS data:

1) Point-dipole approximation, where the spin center is assumed to be a point with dipole magnetic moment that depends linearly on magnetic field. This approximation is valid for the distant nuclei. This approach requires PCSs and nuclear coordinates as an input and gives susceptibility tensor, position of the paramagnetic center and theoretical PCSs as an output. For more details see ippcs.m

2) DFT approximation. This method requires the hyperfine tensors from DFT calculation (ORCA or Gaussian) and fit the susceptibility tensor to experimental PCS data. See pcs2chi.m

2) Analytical non-point approximation, where the spin center is assumed to have some spacial distribution. It can be due to fast mobility of a spin label or when paramagnetic center is formed by several metal ions. All nuclei assumed to be outside the bounding sphere of the spin density. This method requires similar input as point-dipole approximation and the level of approximation L that accounts for the non-point density. If L=0 it is identical to the point approximation. Additional output includes the information about spin distribution in a form of multipole moments for more details see [ipcs_gen]

3) Numerical non-point approximation does the same job as analytical approach but without an assumption that all nuclei are outside the bounding sphere. This approach recover the density distribution on the three-dimensional grid. For more details see ipcs.m

There are also several ways to compute PCS for a given molecular structure. PCS is computed as the trace of the product of hyperfine tensor and susceptibility tensor divided by corresponding gyromagnetic ratios (see paper on PCS for details):

1) Point-dipole approximation. Hyperfine tensor here is computed assuming the point electron spin. This approach is valid for distant nuclei. This method requires the nuclear coordinates, coordinates of paramagnetic center and susceptibility tensor defined in the same frame as the molecule. See ppcs.m

2) DFT hyperfine tensor can be read from output file of ORCA or Gaussian programs. PCS can be predicted for a given susceptibility tensor by hfc2pcs.m

3) Analytically evaluated dipolar hyperfine for a spin distribution can be done using multipole expansion of the spin density distribution. This approach is valid outside the bounding sphere.Multipole moments can be entered manually or one can evaluate them with the function dens2mult.m

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