Hyperfine Splittings of Exchange Coupled System

[jchen3]

Hi All,

Again, I have a question regarding exchange coupled system when simulating hyperfine splittings.
The example case is for biradicals known with strong exchange coupling interactions. I wanted to simulate the hyperfine splittings compare to the spectrum.
The normal code for an isotropic simulation for the single radical is like below:

Code: Select all

Sys.S=1/2
Sys.g=2
Sys.Nucs='14N'
Sys.lw=0.2
Sys.A=20
Exp.Range=[330,350]
Exp.mwFreq=9.5

The normal code for an isotropic simulation for the biradicals is like below:

Code: Select all

Sys.S=[1/2 1/2]
g=[2 2]
Sys.A=[20 0;0 20]
Sys.lw=0.2
Sys.Nucs='14N,14N'
Sys.J=-3.3e7

Due to strong exchange coupling, the hyperfine splitting from the biradical will be looking like half of those from the single radical, which is what we can see base on the codes I just showed you.

Here is the problem, I am working on a more complicated system where I have a lot more Nuclei contributing to the hfi, what I thought might be reasonable to reduce the computing time is an example shown below for the same biradicals:

Code: Select all

Sys.S=1
g=2
Sys.A=[20 0;0 20]
Sys.lw=0.2
Sys.Nucs='14N,14N'

or

Code: Select all

Sys.S=1
g=2
Sys.A=[20 20]
Sys.lw=0.2
Sys.Nucs='14N,14N'

The first code gave me a mixing feature of hyperfine splittings, those on the edge will be half of hfi parameters, and the central ones are not.
The second code will just give a same looking from the single radical which is reasonable, the program just treats the S=1 spin as a single spin system.
When I define the spin system as a triplet, I thought I told the program that only triplet will populate and hence strong exchange coupling, while the result didnot like exactly what I wanted.
This might be no difference for a small system like the codes I showed here, while this become a huge difference when the spin system is much larger. The actual case I am working on have at least 4 nuclei, the A matrix will be very large and difficult to compute when I introduce an interacting spin system with exchange coupling value.
Another question related to this topic is about zero-field splitting term.
An example is shown below:

Code: Select all

     
S: [0.5000 0.5000]
g: [2 2 2; 2 2 2]
D: [550 0]
lw: 2
J: -7900000

For an exchange coupled system, I found that within the reasonable range of zero-field splitting values, there is no difference for the simulation. In order to retrieve the similar looking to the spectrum, I had to make it a S=1 system, then zero-field splitting can dominate in the simulation, while my previous trials found that might not correct in terms of hfi and so on.

So my question is, in order to do so, what should I do?
Thanks a bunch!

[Stefan Stoll]

Regarding the zero-field splitting term, there is none if you have two coupled S=1/2 spins. There is an effective zero-field splitting term once you treat the system in the coupled basis (i.e. singlet plus triplet, instead of two doublets).

[jchen3]

Regarding the zero-field splitting term, there is none if you have two coupled S=1/2 spins. There is an effective zero-field splitting term once you treat the system in the coupled basis (i.e. singlet plus triplet, instead of two doublets).

Dear Stefan,

Thanks for your reply that made the question more clear. In order to include D term, I have to set it as a "S=1". In that case, how do I specify A matrix to emphasize the strong exchange coupling effect to hyperfine splittings? My attempt to do so as shown in the codes gave me a mixture of both features. Thank you!

[Stefan Stoll]

You will have to convert the hyperfine coupling tensor from the uncoupled to the coupled representation. This is covered in textbooks, see e.g. Bencini/Gatteschi, EPR of Exchange Coupled Systems.

[jchen3]

You will have to convert the hyperfine coupling tensor from the uncoupled to the coupled representation. This is covered in textbooks, see e.g. Bencini/Gatteschi, EPR of Exchange Coupled Systems.

Dear Stefan,

Thanks for pointing that out, now it is completely clear to me.

Best,
Ju