On the conceptual meaning of magnetic related directives

[ivansc...@gmail.com]

Dear all,

I come across three different directives, which are all related but confused me, somehow. According to the definition of the manual, we find

MULTIPLICITY: "Two times the total spin plus one. Specify 3 for a triplet, 4 for a quartet, and so on. Default is 1 (singlet) for an even number and 2 (doublet) for an odd number of electrons." 

FIXED_MAGNETIC_MOMENT: "Imposed difference between the numbers of electrons of spin up and spin down: m = n(up) - n(down). A negative value (default) allows for a change of the magnetic moment. -1 specifically keeps an integer number of spin up and spin down electrons."

 MAGNETIZATION: "The magnetization used in the atomic initial guess. Adds magnetization/2 spin-alpha electrons and removes magnetization/2 spin-beta electrons"

I am trying to set magnetic simulations with and without DFT+U corrections for bulk and slabs, both for Ferro-Magnetic (FM) and Anti-Ferro-Magnetic (AFM) ordering. From my experience with other codes, it is first required to set the initial magnetization for the atomic sites. Thus, I would use directive magnetization (BS can be also used but we will not consider it here) when setting the &SUBSYS block. However, I am not sure what this magnetization/2 spin-alpha (-beta) means. 

Question 1) Can you clarify the meaning of the magnetization/2 is for alpha and beta? What are the units for the magnetization? 

Now let us consider two different cases.

Case A. Solution via diagonalization, smearing and mixing

In section &SMEAR we can set FIXED_MAGNETIC_MOMENT to define the difference between electrons up-down (if positive) or allow it to change (if negative). This is very convenient for FM ordering calculations. However, I find it confusing what I should set for MULTIPLICITY in this case. For AFM, one should set FIXED_MAGNETIC_MOMENT=0

and MULTIPLICITY=1. 

Question 2) For FM systems, one can set the value of FIXED_MAGNETIC_MOMENT and the corresponding value for MULTIPLICITY. However, if I set FIXED_MAGNETIC_MOMENT < 0 (to allow the magnetization to change) what should be the value for MULTIPLICITY? Should it be 0.0? What is the meaning of defining MULTIPLICITY = 0.0 (default)?

Case B. Solution only via OT for systems with band gap

In this case there is no need to introduce &SMEAR. 

Question 3: CP2K still runs if one sets &OT+&SMEAR+(ADDED_MOL>0, why? Should not the code prevent such simulation?

Assuming that we do not include &SMEAR, thus we do not have a way to define the value for FIXED_MAGNETIC_MOMENT. Even tough we can set the initial magnetization, the only way to control the total magnetization/spin is through MULTIPLICITY, but I am not sure if this works correctly for condensed phase systems.

Question 4: For AFM states, could I set an initial value of zero from the initial MAGNETIZATION values, and set MULTIPLICITY=1? How do I properly FM states with OT using MAGNETIZATION and MULTIPLICITY?

Thanks a lot for your patience and help to answer my questions

Ivan

[Sigma-Jun Lu]

As far as i can concern:
1)Regularly, if alpha/beta corresponds to spin polarizability, there should be a relationshipf between charge/spin(specifically for each orbital, or combination of them as a whole, the quantity to set total spin is magnetization):

charge=-(alpha+beta)/2, magnetization=(alpha-beta)/2, or inversely alpha=magnetization-charge, beta=-charge-magnetization.

2) Multiplicity, is a little bit complex concept. Normally, you can only use 0~2 in cp2k--
0: not consider the spin contribution;
1: fixed FM state without flipping of spins;
2: consider two degree of freedom, up and down;

3 and above, only consider deeply magnetic interaction, rather than single electrons, take 2 electrons for example, you might get one singlet plus a set of triplets. * i have not seen any signal that cp2k can handle this issue.

3) Perhaps you need add more MOs for proper smearing, usually, empty orbitals does not dirty your calculation result of gap energy.

4) Use $BS instead with seperating atoms of spin up and down in your &coord section, and forget multiplity and magnetization with a # symbol or deleting the line. See page 35/36 in this document- https://www.cp2k.org/_media/events:2015_cecam_tutorial:ling_hybrids.pdf . Nevertheless, during the optimization process, you may not use $BS, but magnetization, and foget #multiplicity.

hope these helps.

Sigma-Jun LU