Function for the calculation of the transformed relaxation gradients.
The transformed relaxation gradients
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Data structure: self.data.dri_prime
Dimension: 2D, (parameters, transformed relaxation data)
Type: Numeric matrix, Float64
Dependencies: self.data.jw, self.data.djw
Required by: self.data.dri, self.data.d2ri
Formulae
~~~~~~~~
Components
~~~~~~~~~~
Dipolar
~~~~~~~
1 / mu0 \ 2 (gH.gN.h_bar)**2
d = - . | ---- | . ----------------
4 \ 4.pi / <r**6>
3 / mu0 \ 2 (gH.gN.h_bar)**2
d' = - - . | ---- | . ----------------
2 \ 4.pi / <r**7>
CSA
~~~
(wN.csa)**2
c = -----------
3
2.wN**2.csa
c' = -----------
3
R1()
~~~~
J_R1_d = J(wH-wN) + 3J(wN) + 6J(wH+wN)
dJ(wH-wN) dJ(wN) dJ(wH+wN)
J_R1_d_prime = --------- + 3 . ------ + 6 . ---------
dmf dmf dmf
J_R1_c = J(wN)
dJ(wN)
J_R1_c_prime = ------
dmf
R2()
~~~~
J_R2_d = 4J(0) + J(wH-wN) + 3J(wN) + 6J(wH) + 6J(wH+wN)
dJ(0) dJ(wH-wN) dJ(wN) dJ(wH) dJ(wH+wN)
J_R2_d_prime = 4 . ----- + --------- + 3 . ------ + 6 . ------ + 6 . ---------
dmf dmf dmf dmf dmf
J_R2_c = 4J(0) + 3J(wN)
dJ(0) dJ(wN)
J_R2_c_prime = 4 . ----- + 3 . ------
dmf dmf
sigma_noe()
~~~~~~~~~~~
J_sigma_noe = 6J(wH+wN) - J(wH-wN)
dJ(wH+wN) dJ(wH-wN)
J_sigma_noe_prime = 6 . --------- - ---------
dmf dmf
Spectral density parameter
~~~~~~~~~~~~~~~~~~~~~~~~~~
dR1()
----- = d . J_R1_d_prime + c . J_R1_c_prime
dJj
dR2() d c
----- = - . J_R2_d_prime + - . J_R2_c_prime
dJj 2 6
dsigma_noe()
------------ = d . J_sigma_noe_prime
dJj
Chemical exchange
~~~~~~~~~~~~~~~~~
dR1()
----- = 0
dRex
dR2()
----- = 1
dRex
dR2()
------ = (2.pi.wH)**2
drhoex
dsigma_noe()
------------ = 0
dRex
CSA
~~~
dR1()
----- = c' . J_R1_c
dcsa
dR2() c'
----- = - . J_R2_c
dcsa 6
dsigma_noe()
------------ = 0
dcsa
Bond length
~~~~~~~~~~~
dR1()
----- = d' . J_R1_d
dr
dR2() d'
----- = - . J_R2_d
dr 2
dsigma_noe()
------------ = d' . J_sigma_noe
dr
|
