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Module for the calculation of RDCs.


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__package__ =

Imports: dot, sum

Calculate the ensemble average RDC, using the 5D tensor. This function calculates the average RDC for a set of XH bond vectors from a structural ensemble, using the 5D vector form of the alignment tensor. The formula for this ensemble average RDC value is: _N_ \ Dij(theta) = > pc . RDC_ijc (theta), /__ c=1 where:
The backcalculated RDC is given by the formula: RDC_ijc(theta) = (x_jc**2  z_jc**2)Axx_i + (y_jc**2  z_jc**2)Ayy_i + 2x_jc.y_jc.Axy_i + 2x_jc.z_jc.Axz_i + 2y_jc.z_jc.Ayz_i.

Calculate the ensemble average RDC, using the 3D tensor. This function calculates the average RDC for a set of XH bond vectors from a structural ensemble, using the 3D tensorial form of the alignment tensor. The formula for this ensemble average RDC value is: _N_ \ T Dij(theta) = dj > pc . mu_jc . Ai . mu_jc, /__ c=1 where:
The dipolar constant is defined as: dj = 3 / (2pi) d', where the factor of 2pi is to convert from units of rad.s^1 to Hertz, the factor of 3 is associated with the alignment tensor and the pure dipolar constant in SI units is: mu0 gI.gS.h_bar d' =    , 4pi r**3 where:

Calculate the ensemble average RDC gradient element for Amn, using the 3D tensor. This function calculates the average RDC gradient for a set of XH bond vectors from a structural ensemble, using the 3D tensorial form of the alignment tensor. The formula for this ensemble average RDC gradient element is: _N_ dDij(theta) \ T dAi  = dj > pc . mu_jc .  . mu_jc, dAmn /__ dAmn c=1 where:

Calculate the ensemble and pseudoatom averaged RDC, using the 3D tensor. This function calculates the average RDC for a set of XH bond vectors from a structural ensemble, using the 3D tensorial form of the alignment tensor. The RDC for each pseudoatom is calculated and then averaged. The formula for this ensemble and pseudoatom average RDC value is: _N_ _M_ \ 1 \ T Dij(theta) = dj > pc .  > mu_jcd . Ai . mu_jcd, /__ M /__ c=1 d=1 where:
The dipolar constant is defined as: dj = 3 / (2pi) d', where the factor of 2pi is to convert from units of rad.s^1 to Hertz, the factor of 3 is associated with the alignment tensor and the pure dipolar constant in SI units is: mu0 gI.gS.h_bar d' =    , 4pi r**3 where:

Calculate the ensemble and pseudoatom average RDC gradient element for Amn, using the 3D tensor. This function calculates the average RDC gradient for a set of XH bond vectors from a structural ensemble, using the 3D tensorial form of the alignment tensor. The formula for this ensemble average RDC gradient element is: _N_ _M_ dDij(theta) \ 1 \ T dAi  = dj > pc .  > mu_jcd .  . mu_jcd, dAmn /__ M /__ dAmn c=1 d=1 where:

Calculate the RDC, using the 3D alignment tensor. The RDC value is: T Dij(theta) = dj . mu_j . Ai . mu_j, where:
The dipolar constant is defined as: dj = 3 / (2pi) d', where the factor of 2pi is to convert from units of rad.s^1 to Hertz, the factor of 3 is associated with the alignment tensor and the pure dipolar constant in SI units is: mu0 gI.gS.h_bar d' =    , 4pi r**3 where:

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