# Overtone pa.m

Overtone soft pulse-acquire experiment with frequency-domain acquisition.

## Syntax

    spectrum=overtone_pa(spin_system,parameters,H,R,K)


## Description

The function performs a soft pulse followed by frequency-domain acquisition at the overtone frequency. Because time-domain overtone spectroscopy is difficult (see http://dx.doi.org/10.1039/C4CP03994G for details), this mode of acquisition is preferable in practice. Simulations assumptions should be set to 'qnmr'.

## Arguments

    parameters.sweep        -  vector with two elements giving the spectrum frequency extents
in Hz around the overtone frequency

parameters.npoints      -  number of points in the spectrum

parameters.rho0         -  initial state

parameters.coil         -  detection state

parameters.Lx           -  X Zeeman operator on the quadrupolar nucleus

parameters.rf_frq       -  pulse frequency offset from the overtone frequency on the quadrupolar nucleus, Hz

parameters.rf_pwr       -  pulse power on the quadrupolar nucleus, Hz

parameters.rf_dur       -  pulse duration, seconds

parameters.method       -  'average' uses the average Hamiltonian theory, 'fplanck' uses Fokker-Planck formalism
for the calculation of the pulse evolution.

H                       -  Hamiltonian commutation superoperator

R                       -  unthermalised relaxation superoperator

K                       -  chemical kinetics superoperator


## Returns

The function returns the populations of the detection state at the frequencies specified.

## Examples

The following 15N overtone spectrum is produced by examples/nmr_overtone/mas_valine_2.m example file:

## Notes

1. Relaxation must be present in the system dynamics, or the matrix inverse-times-vector operation performed by the frequency domain detection module would fail to converge. The relaxation superoperator should not be thermalised.
2. Relaxation theory is not applied during the pulse.
3. Average Hamiltonian and Fokker-Planck pulses produce signals in different phases. We are trying to figure out why, but it looks non-trivial. The average Hamiltonian theory option is faster.
4. Irrespectively of the pulse algorithm option selection, the magic angle spinning is always handled with the Fokker-Planck formalism.