Molcas Forum

LucaBabetto

Member

Registered: 2018-11-21

Posts: 31

Zero Field Splitting (D-tensor) calculation

Hello,

I'm trying to calculate the D-tensor of a series of organic molecules in their triplet state using OpenMolcas. From reading the manual it seems I need to use the SINGLE_ANISO module, however I'm not sure whether this type of calculation is only suitable for metal complexes with strong spin-orbit coupling.

For instance, I already carried out similar calculations in Orca and I've noticed the spin-orbit contribution for the systems I'm studying is - as expected - basically zero, and the only contributions are spin-spin in nature.

Could you please point me towards the correct use of the SINGLE_ANISO module for Zero Field Splitting calculations in organic triplets?

Regards

Luca

nikolay

Member

From: Stuttgart

Registered: 2016-03-21

Posts: 54

Re: Zero Field Splitting (D-tensor) calculation

Hello Luca,

I may be wrong, but I think spin-spin interactions are not implemented.
Ignacio, can anybody confirm that?

General information on SINGLE_ANISO is there in the manual, and also in this long thread on the forum.

amanuv

Member

Registered: 2019-05-07

Posts: 12

Re: Zero Field Splitting (D-tensor) calculation

Hi Luca and nikolay:
I noticed that this thread is about D and E tensors, so I thought its reasobale to ask a question here.

Spin-orbit energy levels from D and E tensor:

I have Ho3+ based lanthanide complex of S=8, for which I have computed D and E tensor using &Single_aniso by providing following input:

&SINGLE_ANISO
crys
Ho
mltp
1
17
quax
2 

Then I set-up a Hamiltonian as described in output:

H_zfs^{2}= D * [S_{Za}^2 - S*(S+1)/3] + E * [S_{Xa}^2 - S_{Ya}^2]

After providing the D and E values from the output and diagonalizing the above Hamiltonian, the Eigen-values for this Hamiltonian is different than the Spin-orbit energy levels. 
But when I set-up a crystal field Hamiltonian  and privided the Crystal-Field parameters from the output the Spin-orbit energy matches.
I am wondering why I can not produce Spin-orbit energy levels from D and E tensor?

nikolay

Member

From: Stuttgart

Registered: 2016-03-21

Posts: 54

Re: Zero Field Splitting (D-tensor) calculation

Hi amanuv,

I thought it should give the same (relative) eigenvalues within the multiplet.
How much are the differences?
I also don't really understand why do you use quax=2  ?

amanuv

Member

Registered: 2019-05-07

Posts: 12

Re: Zero Field Splitting (D-tensor) calculation

Thanks for quick response,
First, by using quax=2, I was trying to control the quantization axis.

The difference between eigen-values are about 100 cm-1 which is huge. I am using Mathemtica to diagonalize the Hamiltonian.
I am using Following operators:

a=8
J = DiagonalMatrix[{a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, 
    a}];
Jz = DiagonalMatrix[{8, 7, 6, 5, 4, 3, 2, 1,  0, -1, -2, -3, -4, -5, -6, -7, -8}];
Jp = DiagonalMatrix[{4, Sqrt[30], Sqrt[42], 2 Sqrt[13], 2 Sqrt[15],  Sqrt[66], Sqrt[70], 6 Sqrt[2], 6 Sqrt[2], Sqrt[70], Sqrt[66],  2 Sqrt[15], 2 Sqrt[13], Sqrt[42], Sqrt[30], 4}, 1];
Jn = DiagonalMatrix[{4, Sqrt[30], Sqrt[42], 2 Sqrt[13], 2 Sqrt[15],   Sqrt[66], Sqrt[70], 6 Sqrt[2], 6 Sqrt[2], Sqrt[70], Sqrt[66],   2 Sqrt[15], 2 Sqrt[13], Sqrt[42], Sqrt[30], 4}, -1];
HD = DD*(Jz.Jz - 1/3 (J.J + J)) + EE*((Jp.Jp + Jn.Jn)/2);

I dont know, how can I import my Mathematica file here. Or If you prefer, I can send you by email.

Thanks in advance.

amanuv

Member

Registered: 2019-05-07

Posts: 12

Re: Zero Field Splitting (D-tensor) calculation

Hi again nikolay,
I think, I figured out why D and E are insufficient to produce Spin-orbit energy levels. I learned from following paper that:

https://aip.scitation.org/doi/10.1063/1.4739763

“In the case of relatively weak spin-orbit coupling the zero-field splitting can be described in the second order perturbation theory after spinorbit coupling leading to the following ZFS Hamiltonian in the crystal field approximation”

In my case Spin-orbit coupling is very strong that’s why I need higher-order crystal-field parameters (B44, B66).

Thanks for your help.