# dnp_freq_scan.m

Microwave frequency scan steady-state DNP experiment. Returns the steady-state population of the user-specified states as a function of microwave irradiation frequency.

## Syntax

dnp=dnp_freq_scan(spin_system,parameters,H,R,K)

## Arguments

parameters.mw_pwr - microwave power, rad/s parameters.mw_frq - row vector of microwave frequ- ency offsets (rad/s) relative to the reference g-factor parameters.g_ref - reference g-factor around which frequency offsets are specified parameters.rho0 - thermal equilibrium state parameters.coil - coil state vector or a horizon- tal stack thereof parameters.mw_oper - microwave irradiation operator parameters.ez_oper - Lz operator on the electrons H - Hamiltonian matrix, received from context function R - relaxation superoperator, received from context function K - kinetics superoperator, received from context function

## Outputs

dnp - an array of the steady state amplitudes of the states specified in parameters.coil as at each of the microwave frequencies supplied

## Examples

Below is a simple TOTAPOL based Cross Effect DNP example (examples/dnp_solids/cross_effect_freq_scan_3.m), set to reproduce Figure 2b from http://dx.doi.org/10.1016/j.jmr.2011.09.047

Intensity differences are due to a different relaxation model and minor inconsistencies between the stated geometry and the interaction amplitudes used in the original paper.

## Notes

- The relaxation superoperator supplied to this function should NOT be thermalized.
- Backslash method is recommended for small spin systems and GMRES method for large ones.

## See also

*Version 2.5, authors: Ilya Kuprov, Walter Kockenberger, Alexander Karabanov, Maria Grazia Concilio*