(Absolute) sign of magnetic dipole transition matrix elements

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bksh
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Joined: 23 Jan 2018, 23:38
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Affiliation: ETH Zurich
Country: Switzerland

(Absolute) sign of magnetic dipole transition matrix elements

Post by bksh » 24 Jan 2018, 10:21

Dear DALTON community,

I am currently using DALTON to calculate the magnetic transition dipole moment associated with an electronic excitation of a chiral organic molecule ion (C3H6O+). I have calculated the ECD excitation spectrum and have a question regarding the output, in particular the section containing the elements of the magnetic transition moment. My question may be very basic (= stupid), for which I apologize in advance.

For my problem, it is necessary to know the absolute sign of this quantity.

What I need are the matrix elements of the magnetic transition dipole moment which reads in atomic units (I omit the summation over all electron coordinates for brevity):



and in terms of matrix elements:

for the ground-to-exc. state transition .

The associated interaction energy in a homogeneous field would be



In a.u., .

According to the DALTON output:

Code: Select all

@               Magnetic transition dipole moments (au)
                ---------------------------------------

  ( mu_B*<0|l_i|n>, where mu_B = 0.5 is the Bohr magneton)

 Symm.  Mode   Frequency         Conventional                  London
 ex.st.  No.     (eV)        x        y       z         x        y        z
 ==============================================================================
   1      1     2.0947    0.25318 -0.18998 -0.35026   0.25303 -0.18997 -0.35018
   1      2     3.1485   -0.38091 -0.15630 -0.21397  -0.38105 -0.15632 -0.21400
   1      3     7.9881   -0.06048 -0.16816  0.11696  -0.06054 -0.16833  0.11707
 ------------------------------------------------------------------------------



I need . Knowing that the magnetic dipole op. vector changes sign on complex conjugation and that the Bohr magneton is already included, this implies that the listed matrix element corresponds directly to the quantity I need, without the necessity of further sign flips.

I would like to ask whether my interpretation of the subject is correct.
Thank you in advance for your input.

Best regards,
bksh

hjaaj
Posts: 317
Joined: 27 Jun 2013, 18:44
First name(s): Hans Jørgen
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Affiliation: Universith of Southern Denmark
Country: Denmark

Re: (Absolute) sign of magnetic dipole transition matrix elements

Post by hjaaj » 27 Jan 2018, 23:31

You can never get a specific sign for a transition matrix element. Remember that you can multiply any solution vector to the time-independent Schrödinger equation with -1, and it is still a solution and it still corresponds to the same physical state.

-- Hans Jørgen.

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