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One can control the multiplicity using the NUPDOWN keyword. The manual states that "If no value is set (or NUPDOWN=-1) a full relaxation will be performed. This is also the default."

How is the initial multiplicity determined if no value is set (NUPDOWN = -1)? Is the value random, or does the code assume the lowest possible multiplicity?

Thank you,
Aaron

if NUPDOWN is not set explicitely, it is set to -1 by default and the magnetization is calculated from the difference of the self-consistent spin up and spin down charges. If NUPDOWN is set (>0!), the numbers of spin up and spin down electrons (and hence the spin multiplicity) are kept fixed according to the input.

Maybe I should rephrase my question. For a DFT code with local basis sets (gaussians), one must explicitly specify the multiplicity (singlet, doublet, triplet, etc.). This does not appear the case for VASP. Why?

Perhaps there are some papers or references that may shed more light on this.

I looked at some of the code and it appears that the initial magnetic moment on each atom is assigned a value of 1. Then the system is relaxed to the ground electronic state? Does this mean that the number of up/down electrons is allowed to change? I.e. the number of up minus number of down electrons is allowed to change during relaxation?

Thank you,

Aaron

If your system is an isolated molecule, the total magnetization will be integer (etc. 0, 1, 2 ...).
In this case, you should check the totral energy according to different NUPDOWN values to find out the minimum energy spin state. (NUPDOWN=0 => singlet, NUPDOWN=1 => triplet ...)

However, if your system is periodic system and the total magnetization in the unit cell is 1 (equivalent to NUPDOWN=1), we cannot say that the spin multiplicity of the system is triplet, because the spin multiplicity is defined for the total system not for the unit cell as far as I know. (however, in the case of the isolated molecular system, we can consider the system in a unit cell as the total system.)

VASP is not a local basis set code; as for any other PW and mixed basis set code, the 'local' magnetic moments are calculated self-consistently from the difference of the iintegrated spin up and down charge densities over the spheres defined by r=RWIGS.
Thus, any input of the magnetic moments is an initial GUESS, which may help to improve the convergence of the calculation.
NUPDOWN can of course be fixed to enfoce a certain spin multiplicity (eg for molecules or clusters) , but this is not the standard default setting;

If a molecule or cluster has an intermediate value at a transition state, is it possible to assign a physical significance to this value (e.g. curve crossing) or is it simply an artifact of the way VASP optimizes the 'local' magnetic moments?

vasp is not based on localized wavefuntions, therefore by setting NUPDOWN, the total magnetic moment of the cluster is fixed. as clusters and molecules have discrete spectra, the results obtained for calculations with different fixed moments correspond to the respective measured (excited) spin multiplet states.

Just noticed the statement above about SINGLET, TRIPLET etc.
Surely this is incorrect. We are specifying the number of excess ELECTRONS, each with spin 1/2. Therefore
NUPDOWN = 0 => S=0, SINGLET
NUPDOWN = 1 => S=1/2, 2S+1 = 2 = DOUBLET
NUPDOWN = 2 +> S=1, 2S+1 = 3 = TRIPLET.
I'm sure this was meant, but just to be clear