View source for Relax disp.spin lock offset+field

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== Setting up relax_disp.spin_lock_offset and relax_disp.spin_lock_field ==
[http://www.nmr-relax.com/manual/Dispersion_model_summary.html Refer to the manual for parameter explanation]

This page is a little help to understand how to use the functions:
#relax_disp.spin_lock_offset()
#relax_disp.spin_lock_field()

=== spin lock offset ===
[http://www.nmr-relax.com/manual/relax_disp_spin_lock_offset.html Manual on relax_disp.spin_lock_offset]<br>
The relax function relax_disp.spin_lock_offset() requires the values to be provided in ppm.
 relax_disp.spin_lock_offset(spectrum_id=None, offset=None)

=== spin lock field ===
[http://www.nmr-relax.com/manual/relax_disp_spin_lock_field.html Manual on relax_disp.spin_lock_field]<br>
The relax function relax_disp.spin_lock_field() requires the values to be provided in Hz.
 relax_disp.spin_lock_field(spectrum_id=None, field=None)

== Literature comments ==
See Figure 1 and 10 in the reference:

* {{#lst:Citations|PalmerMassi06}}

[[File:Fig1 Palmer Massi 2006.png|thumb|center|upright=3|Try to reproduce Figure 1.]]
Figure produced with script [[Relax_disp.spin_lock_offset%2Bfield_figure | found here. ]]

== Calculations in relax ==
=== spin lock offset ===
In the literature, the values are often stated as "offset", "carrier offset", "offset of the spin-lock pulse" with values given in Hz, and can have values from 0-500 to 10-20.000 Hz.<br>
These values reflects offset frequencies to the carrier frequency, and in relax is noted as '''"Spin-lock offset, the frequency of of the rf field"''' : {{:omegarf}}.

Relax needs input for {{:omegarf}} in ppm, and during calculations converts to the rad/s, with the following function call.
<source lang="python">
offsets[ei][si][mi][oi] = frequency_to_rad_per_s(frq=cdp.spin_lock_offset[id], B0=frq, isotope=spin.isotope)
</source>

If you need to convert to ppm from Hz values, consider during this in your relax script. <br>
If for example you have recorded at a 800 MHz spectrometer, you could find the Carrier position for <sup>15</sup>N (Value of yCar in NMRPipe scripts). If yCAR = 118.078 ppm, then
<source lang="python">
from lib.nmr import frequency_to_Hz, frequency_to_ppm

# Spectrometer frequency
sfrq = 799.7773991 # MHz
# Carrier position
yCAR = 118.078 # ppm 

# We take the absolute value, since the gyromagnetic ratio of N15 is negative.
yCAR_Hz = abs(frequency_to_Hz(frq=yCAR, B0=sfrq*1E6, isotope='15N'))
# We add the offset (deltadof2 in varian pulse sequences) in Hz, and from 0 to 10.000
yCar_offset_Hz = yCAR_Hz + float(deltadof2)
# The convert back from Hz to ppm. Again absolute value, because of the gyromagnetic ratio of N15 is negative.
yCar_offset_ppm = abs(frequency_to_ppm(frq=yCar_offset_Hz, B0=sfrq*1E6, isotope='15N'))

relax_disp.spin_lock_offset(spectrum_id=sp_id, offset=yCar_offset_ppm)
</source>



'''Offset in the literature'''<br>

The offset is in the literature noted as Ω<sub>S</sub>, where Ω<sub>S</sub> is the (Ex. <sup>15</sup>N) resonance offset from the spin-lock carrier.

Note that Ω<sub>S</sub> is dependent of the [[wikipedia:Chemical_shift | chemical shifts]] δ in ppm for the nuclei of interest.

The [[wikipedia:Chemical_shift | Chemical Shifts]] δ in ppm for nuclei of interest (ex. <sup>15</sup>N and which have been loaded in with relax function [http://www.nmr-relax.com/manual/chemical_shift_read.html chemical_shift_read] from a [http://www.nmr-relax.com/manual/spectrum_read_intensities.html peak list formatted file]) is first converted to to the rad/s with the following function calls.

<math>
\bar{\omega}_{S,i} = 2\pi \cdot \delta_{S,i} \cdot B_0 \cdot \frac{\gamma_{^{15}N}}{\gamma_{^{1}H}}
</math>

<source lang="python">
shifts[ei][si][mi] = frequency_to_rad_per_s(frq=shift, B0=frq, isotope=spin.isotope)
</source>

Then <span style="text-decoration: overline">Ω<sub>S</sub></span> is calculated with: <span style="text-decoration: overline">Ω<sub>S,i</sub></span> = <span style="text-decoration: overline">Ω<sub>S,i</sub></span> - {{:omegarf}}, where <span style="text-decoration: overline">Ω</span> is the population averaged Larmor frequency of the spin and comes from the conversion of the [[wikipedia:Chemical_shift | Chemical Shifts]] δ<sub>S,i</sub> to frequency <span style="text-decoration: overline">Ω<sub>S,i</sub></span>.
<source lang="python">
Delta_omega = shifts[ei][si][mi] - offsets[ei][si][mi][oi]
</source>

=== spin lock field ===
The spin lock field strength is noted {{:nu1}}, and relax requires these to be provided in unit of '''rad/s'''.<br>

The spin lock field strength is converted to rad/s, with the following function call.

<math>
\omega_{S,1} = 2\pi \cdot \nu_{S,1}
</math>

<source lang="python">
omega1 = point * 2.0 * pi
</source>

Then the Rotating frame tilt angle θ is calculated.

<math>
\theta = \tan^{-1} \left( \frac{\omega_1}{\bar{\Omega}_{S,i}} \right)
</math>

<source lang="python">
if Delta_omega == 0.0:
    theta[ei][si][mi][oi].append(pi / 2.0)
# Calculate the theta angle describing the tilted rotating frame relative to the laboratory.
# If Delta_omega is negative, there follow the symmetry of atan, that atan(-x) = - atan(x).
# Then it should be: theta = pi + atan(-x) = pi - atan(x) = pi - abs(atan( +/- x))
elif omega1 / Delta_omega > 0 :
    theta[ei][si][mi][oi].append(atan(omega1 / Delta_omega))
else:
    theta[ei][si][mi][oi].append(pi + atan(omega1 / Delta_omega))
</source>

== Code reference calculations in relax ==
The code which is called resides in:

'''lib/nmr.py'''
 frequency_to_rad_per_s(frq=None, B0=None, isotope=None):
<source lang="python">
"""Convert the given frequency from ppm to rad/s units."""
return frq * 2.0 * pi * B0 / g1H * return_gyromagnetic_ratio(isotope) * 1e-6
</source>

'''specific_analyses/relax_disp/disp_data.py'''
 return_offset_data(spins=None, spin_ids=None, field_count=None, fields=None):

Data structures
<source lang="python">
"""
The data structures consist of many different index types.  These are:

- Ei:  The index for each experiment type.
- Si:  The index for each spin of the spin cluster.
- Mi:  The index for each magnetic field strength.
- Oi:  The index for each spin-lock offset.
- Di:  The index for each dispersion point, the spin-lock field strength.
"""
</source>

== Spectrometer notes ==

=== Varian / VnmrJ ===
In some pulse sequences, the following is seen:
 'trim' is a basic timeunit and the total spinlock time is calculated as '''2.0*ncyc*trim'''
 b1 = getval("b1"),                      /* spin-lock field, Hz! */  
 deltadof2 = getval("deltadof2"),        /* offset for N15 spinlock */
== See also ==
[[Category:Relaxation dispersion analysis]]