Exp.Ordering in fitting

[hbaruch]

Dear all,
I am a newcomer to easyspin. I have some elementary questions, as well as specific ones, I'd appreciate your help on any of these:
1. What does chili assume on the relative orientation of the molecular frame relative to the lab frame? Does it average on all 3-dimensional orientations?
2. Do both chili and pepper alow for rotational relaxation times?
3. To fix the relative orientation I tried the command Exp.Ordering = @(phi,theta) gaussian(theta,0,pi/8), is it valid in fitting data with pepper?
3. Can I vary the variables of Exp.Ordering so that the fit will find the best values? e.g. Vary.theta=[pi/2 pi/2] ? I had to define also Sys.theta=[0,pi/8] to make it run.
4. I add below a program that I tried, it does run including iterations on theta, but stops being rather far from a good fit. I will appreciate any comments on how to improve the program. (the data is a text file 4b.txt which somehow the attachment option does not allow me).
5. I couldn't make this run with chili, which seems to me more suitable to allow for correlation times. Is there such an option with more changes?
Thanks for any help,
Baruch

clear, clf
Sys.S = [1]; % two spins
Sys.g = [2.01, 2.007, 2.0024];
Sys.Nucs = '14N';
Sys.I=1;
Sys.A = mt2mhz([0.65,0.55,3.35]);
Sys.lwpp = [2];
Sys.logtcorr = [-11 -5 -8]; % seconds
Sys.D=[270];
Sys.theta=[0,pi/8]
Exp.Field = 23.0; % [B-static] = mT
Exp.mwCenterSweep = [0.68 0.34]; % [Radio Frequency] = GHz
Exp.nPoints = 9199;
Exp.Harmonic = 0;
Exp.Ordering = @(phi,theta) gaussian(theta,0,pi/8)
% vary parameters in fit
Vary.logtcorr = [3.5,3.5,3.5];
Exp.Ordering = @(phi,theta) gaussian(theta,0,pi/8)
Vary.theta=[pi/2 pi/2]
Vary.lwpp = [10];
Vary.D = [1000];
spc=textread('4b.txt');

SimOpt.Method = 'perturb'
esfit('pepper',spc,Sys,Vary,Exp,SimOpt)

[Stefan Stoll]

1. chili assumes the molecule tumbles around all three axis in the lab frame. If you specify an ordering potential, then the tumbling is hindered.
2. Only chili allows for tumbling.
3. Restricting orientations this way with pepper is possible.
4. Use a custom fitting function - see the documentation on least-squares fitting.
5. To specify motional restriction in chili, uses Sys.lambda (if you are using 5.2.x) or Sys.Potential (if you are using 6.0-dev).

[hbaruch]

Dear Stefan,
Thanks so much for your help. I am still confused:
1. In addition to tumbling it seems to me that an orientation needs to be specified. E.g. suppose that the correlation time in z is very slow, while correlation times in x,y are very fast. Then the molecule's z axis is almost fixed, i.e. its a zxis orientation in the molecule frame hardly varies (I hope I got the definition right). Without specifying an ordering potential, what does chili assume about the orientation of this z axis in the lab frame? The latter orientation must affect the spectra.
2. When I ran the program that I showed it did update correlation times during the fit, yet I was running pepper, allowing for Vary.logtcorr = [3.5,3.5,3.5]. Has this any meaning?
3. The same program also uses Exp.Ordering = @(phi,theta) gaussian(theta,0,pi/8), with Vary.theta=[pi/2 pi/2]. I expect theta to be a positive spherical angle measured from the z axis, yet the fit gives sometimes a negative value?
I will highly appreciate further help,
Baruch

[Stefan Stoll]

pepper assumes the spin center is immobilized, such as in a powder or a frozen solution. Exp.Ordering describes a non-uniform distribution of these fixed orientations.

In contrast, use chili to simulate spectra of spin centers that are rotationally tumbling in the sample tube, e.g. when they are in fluid solution. Sys.logtcorr = [1e-9 2e-9 5e-9] specifies three different rates of tumbling (in terms of the rotational correlation times) around the molecular x, y, and z axes.

[hbaruch]

-- just to make sure: Suppose we do not use Sys.lambda, then is it true that chili averages on all orientations, i.e. all the relative orientations of the molecular frame relative to those of the lab frame?
Thanks!

[Stefan Stoll]

In the absence of a orienting potential, all orientations are equally accessible to the spin label.

[hbaruch]

I apologize, yet I do not understand what does "accessible" mean in this context. The question is a practical one -- i.e. how does chili handle the parameters that define the orientation of the molecule relative to the lab. It seems to me natural that it averages all orientations -- is that right?

[Stefan Stoll]

chili simulates the situation where the spin label reorients dynamically in a process called Brownian rotational diffusion. If no ordering is given, all orientations are treated as equally likely.