Effect of LAMBDA on the total energy

[elise.p.kenny]

Hi there,

I am trying to do a constrained magnetic moment calculation, but I am confused about the effect of LAMBDA on the total energy due to (what I percieve as) contradictory information in the VASP documentation.

On the tutorial page wiki/index.php/Constraining_local_magnetic_moments it says:

E_p is the energy arising from the penalty function. It decreases with increasing LAMBDA.
By increasing LAMBDA stepwise one can bring E_p down (slowly so the solution remains stable from one run to another).
This way one approaches the LSDA total energy for a given magnetic configuration.

In my calculations, I find it to be true that E_p decreases with increasing LAMBDA. Eg. E_p=0.000007 eV when LAMBDA=50 and E_p=0.002 eV when LAMBDA=0.1
But, I also find that the overall energy decreases with decreasing LAMBDA. I am using VASP 6.2.1

The wiki page for I_CONSTRAINED_M states:

...applying constraints by means of a penalty functional contributes to the total energy. This contribution, however, decreases with decreasing LAMBDA and can in principle be made vanishingly small. Decreasing LAMBDA stepwise, from one run to another (slowly so the solution remains stable) one thus converges towards the DFT total energy for a given magnetic configuration.

This seems to be directly contradictory to the information about E_p. Am I missing something?
According to my understanding, the energy should approach the unconstrained solution when LAMBDA -> 0.
Should I be increasing or decreasing LAMBDA to reach a solution near the unconstrained solution?

Thanks

[elise.p.kenny]

I see that the wiki page for I_CONSTRAINED_M has now been edited, so it says the opposite than it did when I made the original post.

So, increasing LAMBDA brings the solution closer to the unconstrained solution?

[ferenc_karsai]

Yes sorry, according to your post we revised the page, but I forgot to answer you. Thank you for coming back again on that topic.

The information should be consistent both on the tutorial page and the page for I_CONSTRAINED_M.

The penalty term is like a spring, if you are allowing to be far away from the origin (small LAMBDA) the penalty energy is high.
By increasing LAMBDA you bring the energy closer to a given magnetic configuration (constrain it to that) and the penalty energy decreases.