Question about total and molecular dipoles

[Hana]

Hello,

I am trying to calculate the dipole moment of my non-periodic system. The system has more than one molecule, and I am interested in calculating both molecular and total dipole moment. Currently, I use two sections (section1: FORCE_EVAL/DFT/LOCALIZE, section 2: FORCE_EVAL/DFT/PRINT/MOMENTS) in my input, as elaborated at the end of this message. Section 2 outputs a total dipole moment of 18.9465 Debye. From section 1 and using the Wannier centers, I get a total dipole moment of 18.9876 Debye. Here is my first question: Is this discrepancy normal? According to CP2K documentation, the first value (from section 2) is based on "simple operator". However, I am not sure what that is, and whether it justifies the discrepancy?

Also, I have another question. In section 1, I have the TOTAL_DIPOLE and MOLECULAR_DIPOLES subsections as well. The dipole values that I get from these two are completely (orders of magnitude) different from the values mentioned in the previous paragraph (~19 Debye), although I set all the reference points to zero. Moreover, for the molecular dipole, the output file shows zero for most of the atoms, and non-zero values for the rest of them. Therefore, I cannot find the "molecule" concept there. Here is my second question: Am I missing anything when using these two subsections (TOTAL_DIPOLE and MOLECULAR_DIPOLES)?

Thanks in advance for your help, and sorry for the long message!

section 1:

    &LOCALIZE
      MAX_ITER 1000
      METHOD JACOBI
      EPS_LOCALIZATION 1.0E-6
      &PRINT
        &WANNIER_CENTERS
           IONS+CENTERS .TRUE.
        &END
        &TOTAL_DIPOLE
           PERIODIC F
           REFERENCE ZERO
           FILENAME total
        &END
        &MOLECULAR_DIPOLES
           PERIODIC F
           REFERENCE ZERO
           FILENAME molecular
        &END
      &END
    &END

section 2:

    &PRINT
      &MOMENTS

            PERIODIC F
            REFERENCE ZERO
            FILENAME dipole
      &END
    &END

[Fangyong Yan]

Dear Hana, 

Wannier function is only for periodic systems. (see for example, our paper: Infrared Spectroscopy of Li+ Solvation in EmimBF4 and in Propylene Carbonate: Ab Initio Molecular Dynamics and Experiment, JPCB, 2022)

The wannier center is treated as the expectation value of the position of individual electrons. That is why we can obtain molecules, or cation with +1 charge, and anion with -1 charge. Because 

all the charges (electrons, nuclei), are integer.

Wannier function is one way to partition the electron density, there are other methods to partition the charge density. 

For a molecule, the dipole moment is invariant to your chosen origin. For a cation or anion, dipole is dependent on your origin, but the change of dipole is not, and IR intensity is related to the change of dipole. 

Good luck!!

Fangyong

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[Fangyong Yan]

The Wannier center does not mean the electron is there, because electron is only known by a probability and electrons are indistinguishable. 

You can think the dipole moment operator is Wannier center multiplying the electron charge. 

For non-periodic electrons, there should be methods just like Wannier functions for periodic electrons. 

FY

[Fangyong Yan]

The electron density is the summation of all the Wannier functions squares, so if an electron density at a cartesian coordinate is 0.1, this is contributed by 

all the wannier functions at this position. 

So you can think wannier function is one way of partitioning the electron density.

FY

[Fangyong Yan]

Also, for the wannier function using GAPW method, the electron density can be calculated by summing up the square of all the wannier functions. On the other hand,

if you use print electron density, then the electron density is not the exact electron density.  [We consulted with Professor Hutter and Dr. Iannuzzi on this because we 

want to make sure the electron density is correct.]  FY