Except for `R2eff' and `No Rex', all models can be fit to clusterings of spins, or spin blocks. The models are described in more detail below and summarised in Table 11.1. The parameters of the models and of relaxation dispersion in general are given in Table 17.5.
For a number of models, the offresonance R_{1} value can be optimised. Normally the offresonance models will use fixed experimental R_{1} values for optimisation. However if the experimental values are not loaded, then the R_{1} values will be automatically optimised. For finer control of this optimisation behaviour, see the relax_disp.r1_fit user function (page ). The models which support offresonance R_{1} fitting include:
In the future, support for offresonance effects in the CPMG experiments is planned (see section 11.10 on page ).


Model name  Solution  Sites  Parameters  Restrictions  Reference 


Experiment independent  
R2eff      {R_{2eff},^{ ... }}  Fixed relaxation time period   
R2eff      {R_{2eff}, I_{0},^{ ... }}  Variable relaxation time period   
No Rex  Closed  1  {R_{2}^{0},^{ ... }}     
CPMGtype  
LM63  Analytic  2  {R_{2}^{0},..., Φ_{ex}, k_{ex}}  Fast exchange  Luz and Meiboom (1963) 
LM63 3site  Analytic  3  {R_{2}^{0},..., Φ_{ex, B}, k_{B}, Φ_{ex, C}, k_{C}}  Fast exchange, p_{A} > p_{B} and  Luz and Meiboom (1963) 
p_{A} > p_{C}  
CR72  Analytic  2  {R_{2}^{0},..., p_{A}, Δω, k_{ex}}  p_{A} > p_{B}, not very slow exchange  Carver and Richards (1972) 
CR72 full  Analytic  2  {R_{2A}^{0}, R_{2B}^{0},..., p_{A}, Δω, k_{ex}}  p_{A} > p_{B}, not very slow exchange  Carver and Richards (1972) 
IT99  Analytic  2  {R_{2}^{0},..., p_{A}, Δω, τ_{ex}}  p_{A} p_{B}  Ishima and Torchia (1999) 
TSMFK01  Analytic  2  {R_{2A}^{0},..., Δω, k_{AB}}  p_{A} p_{B} slow exchange  Tollinger et al. (2001) 
B14  Analytic  2  {R_{2}^{0},..., p_{A}, Δω, k_{ex}}  p_{A} > p_{B},  Baldwin (2014) 
B14 full  Analytic  2  {R_{2A}^{0}, R_{2B}^{0},..., p_{A}, Δω, k_{ex}}  p_{A} > p_{B},  Baldwin (2014) 
NS CPMG 2site expanded  Numeric  2  {R_{2}^{0},..., p_{A}, Δω, k_{ex}}  p_{A} > p_{B}  Tollinger et al. (2001) 
NS CPMG 2site 3D  Numeric  2  {R_{2}^{0},..., p_{A}, Δω, k_{ex}}  p_{A} > p_{B}   
NS CPMG 2site 3D full  Numeric  2  {R_{2A}^{0}, R_{2B}^{0},..., p_{A}, Δω, k_{ex}}  p_{A} > p_{B}   
NS CPMG 2site star  Numeric  2  {R_{2}^{0},..., p_{A}, Δω, k_{ex}}  p_{A} > p_{B}   
NS CPMG 2site star full  Numeric  2  {R_{2A}^{0}, R_{2B}^{0},..., p_{A}, Δω, k_{ex}}  p_{A} > p_{B}   
MMQ CPMGtype  
MMQ CR72  Analytic  2  {R_{2}^{0},..., p_{A}, Δω, Δω^{H}, k_{ex}}  p_{A} > p_{B}  Korzhnev et al. (2004a) 
NS MMQ 2site  Numeric  2  {R_{2}^{0},..., p_{A}, Δω, Δω^{H}, k_{ex}}  p_{A} > p_{B}  Korzhnev et al. (2005a) 
NS MMQ 3site linear  Numeric  3  {R_{2}^{0},..., p_{A}, p_{B}, Δω_{AB}, Δω_{BC},  p_{A} > p_{B} and p_{B} > p_{C}  Korzhnev et al. (2005a) 
Δω^{H}_{AB}, Δω^{H}_{BC}, k_{ex}^{AB}, k_{ex}^{BC}}  
NS MMQ 3site  Numeric  3  {R_{2}^{0},..., p_{A}, p_{B}, Δω_{AB}, Δω_{BC},  p_{A} > p_{B} and p_{B} > p_{C}  Korzhnev et al. (2005a) 
Δω^{H}_{AB}, Δω^{H}_{BC}, k_{ex}^{AB}, k_{ex}^{BC}, k_{ex}^{AC}}  
R_{1ρ}type  
M61  Analytic  2  {R_{1ρ}',..., Φ_{ex}, k_{ex}}  Fast exchange, onresonance,  Meiboom (1961) 
R_{1} = R_{2}  
DPL94  Analytic  2  {R_{1ρ}',..., Φ_{ex}, k_{ex}}  Fast exchange  Davis et al. (1994) 
M61 skew  Analytic  2  {R_{1ρ}',..., p_{A}, Δω, k_{ex}}  p_{A} p_{B}, onresonance  Meiboom (1961) 
TP02  Analytic  2  {R_{1ρ}',..., p_{A}, Δω, k_{ex}}  p_{A} p_{B}, not fast exchange  Trott and Palmer (2002) 
TAP03  Analytic  2  {R_{1ρ}',..., p_{A}, Δω, k_{ex}}  Weak condition of p_{A} p_{B}  Trott et al. (2003) 
TP04^{11.1}  Analytic  N  {R_{1ρ}',..., p_{1},..., p_{N},, k_{12},... k_{1N}}  One site dominant  Trott and Palmer (2004) 
MP05  Analytic  2  {R_{1ρ}',..., p_{A}, Δω, k_{ex}}  p_{A} > p_{B}  Miloushev and Palmer (2005) 
BK13  Analytic  2  {R_{2}^{0},..., p_{A}, Δω, k_{ex}}  p_{A} > p_{B},  Baldwin and Kay (2013) 
BK13 full  Analytic  2  {R_{2A}^{0}, R_{2B}^{0},..., p_{A}, Δω, k_{ex}}  p_{A} > p_{B},  Baldwin and Kay (2013) 
NS R1rho 2site  Numeric  2  {R_{1ρ}',..., p_{A}, Δω, k_{ex}}  p_{A} > p_{B}   
NS R1rho 3site linear  Numeric  3  {R_{1ρ}',..., p_{A}, p_{B}, Δω_{AB}, Δω_{BC},  p_{A} > p_{B} and p_{A} > p_{C}   
k_{ex}^{AB}, k_{ex}^{BC}}  
NS R1rho 3site  Numeric  3  {R_{1ρ}',..., p_{A}, p_{B}, Δω_{AB}, Δω_{BC},  p_{A} > p_{B} and p_{A} > p_{C}   
k_{ex}^{AB}, k_{ex}^{BC}, k_{ex}^{AC}}  




Parameter  Equation  Description  Units 
ν_{CPMG} 
1/(4τ_{CPMG})  CPMG frequency  Hz 
τ_{CPMG}  1/(4ν_{CPMG})  Delay between CPMG π pulses  s 
T_{relax}    The relaxation delay period  s 
I_{0}    Reference peak intensity when T_{relax} is zero   
I_{1}    Peak intensity for a given ν_{CPMG} or spinlock field strength ω_{1}   
R_{2}^{0}    R_{2} relaxation rate in the absence of exchange  rad.s^{1} 
R_{2A}^{0}    R_{2} relaxation rate for state A in the absence of exchange  rad.s^{1} 
R_{2B}^{0}    R_{2} relaxation rate for state B in the absence of exchange  rad.s^{1} 
R_{1ρ}'    R_{1ρ} relaxation rate in the absence of exchange  rad.s^{1} 
 ω_{rf}  The average resonance offset in the rotating frame  rad.s^{1}  
Ω_{A}  ω_{A}  ω_{rf}  The resonance offset in the rotating frame for state A  rad.s^{1} 
Ω_{B}  ω_{B}  ω_{rf}  The resonance offset in the rotating frame for state B  rad.s^{1} 
Ω_{C}  ω_{C}  ω_{rf}  The resonance offset in the rotating frame for state C  rad.s^{1} 
ω_{A}    The Larmor frequency of the spin in state A  rad.s^{1} 
ω_{B}    The Larmor frequency of the spin in state B  rad.s^{1} 
ω_{C}    The Larmor frequency of the spin in state C  rad.s^{1} 
ω^{H}_{A}    The proton Larmor frequency of the spin in state A (for MMQ data)  rad.s^{1} 
ω^{H}_{B}    The proton Larmor frequency of the spin in state B (for MMQ data)  rad.s^{1} 
ω^{H}_{C}    The proton Larmor frequency of the spin in state C (for MMQ data)  rad.s^{1} 
p_{A}ω_{A} + p_{B}ω_{B}  The population averaged Larmor frequency of the spin  rad.s^{1}  
ω_{1}    Spinlock field strength, i.e. the amplitude of the rf field  rad.s^{1} 
ω_{e}  Effective field in the rotating frame  rad.s^{1}  
ω_{rf}    Spinlock offset, i.e. the frequency of the rf field  rad.s^{1} 
θ  arctan  Rotating frame tilt angle  rad 
k_{AB}  p_{B}k_{ex}  The forward exchange rate from state A to state B (2site)  rad.s^{1} 
k_{BA}  p_{A}k_{ex}  The reverse exchange rate from state B to state A (2site)  rad.s^{1} 
k_{AB}  p_{B}k_{ex}^{AB}  The forward exchange rate from state A to state B (3site)  rad.s^{1} 
k_{BA}  p_{A}k_{ex}^{AB}  The reverse exchange rate from state B to state A (3site)  rad.s^{1} 
k_{BC}  p_{C}k_{ex}^{BC}  The forward exchange rate from state B to state C (3site)  rad.s^{1} 
k_{CB}  p_{B}k_{ex}^{BC}  The reverse exchange rate from state C to state B (3site)  rad.s^{1} 
k_{AC}  p_{C}k_{ex}^{AC}  The forward exchange rate from state A to state C (3site)  rad.s^{1} 
k_{CA}  p_{A}k_{ex}^{AC}  The reverse exchange rate from state C to state A (3site)  rad.s^{1} 
k_{ex}  1/τ_{ex}  Chemical exchange rate constant  rad.s^{1} 
k_{ex}^{AB}  k_{AB} + k_{BA}  Chemical exchange rate constant between sites A and B  rad.s^{1} 
k_{ex}^{BC}  k_{BC} + k_{CB}  Chemical exchange rate constant between sites B and C  rad.s^{1} 
k_{ex}^{AC}  k_{AC} + k_{CA}  Chemical exchange rate constant between sites A and C  rad.s^{1} 
k_{B}  k_{ex}^{AB}  Approximate chemical exchange rate constant between sites A and B  rad.s^{1} 
k_{C}  k_{ex}^{AC}  Approximate chemical exchange rate constant between sites A and C  rad.s^{1} 
τ_{ex}  1/k_{ex}  Time of exchange  s.rad^{1} 
p_{A}    Population of state A   
p_{B}  1  p_{A}  Population of state B (2site)   
p_{B}  1  p_{A}  p_{C}  Population of state B (3site)   
p_{C}  1  p_{A}  p_{B}  Population of state C (3site)   
Δω  ω_{B}  ω_{A}  Chemical shift difference between sites A and B (2site)  rad.s^{1} (stored as ppm) 
Δω_{AB}  ω_{B}  ω_{A}  Chemical shift difference between sites A and B (3site)  rad.s^{1} (stored as ppm) 
Δω_{BC}  ω_{C}  ω_{B}  Chemical shift difference between sites B and C (3site)  rad.s^{1} (stored as ppm) 
Δω_{AC}  Δω_{AB} + Δω_{BC}  Chemical shift difference between sites A and C (3site)  rad.s^{1} (stored as ppm) 
Δω^{H}  ω^{H}_{B}  ω^{H}_{A}  Proton chemical shift difference between sites A and B (2site)  rad.s^{1} (stored as ppm) 
Δω^{H}_{AB}  ω^{H}_{B}  ω^{H}_{A}  Proton chemical shift difference between sites A and B (3site)  rad.s^{1} (stored as ppm) 
Δω^{H}_{BC}  ω^{H}_{C}  ω^{H}_{B}  Proton chemical shift difference between sites B and C (3site)  rad.s^{1} (stored as ppm) 
Δω^{H}_{AC}  Δω^{H}_{AB} + Δω^{H}_{BC}  Proton chemical shift difference between sites A and C (3site)  rad.s^{1} (stored as ppm) 
Φ_{ex}  p_{A}p_{B}Δω^{2}  Fast exchange factor  rad^{2}.s^{2} (stored as ppm^{2}) 
Φ_{ex, B}  See 11.20a on page  Fast exchange factor between sites A and B  rad^{2}.s^{2} (stored as ppm^{2}) 
Φ_{ex, C}  See 11.20b on page  Fast exchange factor between sites A and C  rad^{2}.s^{2} (stored as ppm^{2}) 
The relax user manual (PDF), created 20190308.