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Dear colleagues,

we are trying to calculate the shear (\rho v_{T}^{2}) and longitudinal (\rho v_{L}^{2}) moduli of fcc Ce at high pressures (from 0 to 1 GPa). These moduli are measured experimentally (Decremps et al., PRB 80, 132103 (2009)).
The zero pressure values are in a good agreement with the experimental

Decremps we (GPa)
-------------------------
35.6 37.8 long.
11.2 11.7 shear
21 22.3 bulk modulus

But when we calculate these at pressures up to 1 GPa, only for the shear modulus we obtain a good agreement, i.e. we obtain the correct behaviour with increasing pressure. On the other hand, long. and bulk moduli should decrease after about 0.1-0.2 GPa, but we get that they increase all the way. And this is our problem.

We are using TM LDA (zion 4) and abinit 5.8.4 on a linux cluster. We tried with TM GGA (zion 4) and HGH LDA (zion 12) pseudos, but even the results at zero pressure were much much worse than with TM LDA. Input file is attached.

Moduli are calculated using formulas given in Karki et al., American Mineralogist 82, 51 (1997), with the pressure corrections (p in GPa) to elastic constants (from Karki et al., J. Phys. Condens. Matter 9, 8579 (1997)):
c11 -> c11
c12 -> c12 + p
c44 -> c44 - 1/2p

All atoms are fixed by symmetry, so there is no internal strain contribution. there are no warnings in the rf elast output file. We are using occopt 4 (we tried occopt 3, but its even worse)

Does anyone have an idea why this happens or how could we improve our results?

Although the lattice constant was optimized at each pressure from 0 to 1 GPa in steps of 0.1 GPa, in the end of the 1st DS of the rf calc, the value of pressure differs from the one targeted in the structural optimization by an amount of about 0.02-0.05 GPa. Could this be a source of error? We used all the same parameters in our optimization and rf calcs.

Thank You in advance!

Igor Lukacevic

Hi Igor, interesting problem.

Your calculations sound well converged and all. Have you tried the 12 electron HGH for higher pressures? It could be that the basic structure is not great (acell underestimated) but the pressure derivative is the correct sign. This would confirm that the pseudopotential is the problem. As soon as you apply pressure you can change the hybridization etc... and the semicore may become important. You could also try with an LAPW code for reference (e.g. elk - find it on sourceforge, or through the www.etsf.eu software links), to see where the semicore levels are going. Another check is that the pseudopotential radius is still less than 1/2 the interatomic distance!

For the residual pressure, it's not a big problem, but it is strange. With identical basis (ecut ecutsm dilatmx etc...) you should get the same forces, although they may not correspond to the last forces reported, which could be the penultimate ones... Needs more investigation

Ciao

Matthieu

Hi Matthieu, and thanks for answering!
I apologize for the late reply, but I have the notification problems.

mverstra wrote:Have you tried the 12 electron HGH for higher pressures? It could be that the basic structure is not great (acell underestimated) but the pressure derivative is the correct sign. This would confirm that the pseudopotential is the problem. As soon as you apply pressure you can change the hybridization etc... and the semicore may become important.

Yes, we have. They are also horrible.

mverstra wrote:You could also try with an LAPW code for reference (e.g. elk - find it on sourceforge, or through the http://www.etsf.eu software links), to see where the semicore levels are going.

OK, thanks for the suggestion. I'll try. But, it is a very small pressure range (0 - 1 GPa) and the cell changes very little, at most by 0.14 Bohr, while acell is about 10 Bohr. And the problem arises at even lower pressures. Do you still think semicores could be the thing?

mverstra wrote:Another check is that the pseudopotential radius is still less than 1/2 the interatomic distance!

Is it reported in the header of the pseudo? If not, how could I check this (maybe using opium to construct the pseudo again)?

mverstra wrote:For the residual pressure, it's not a big problem, but it is strange. With identical basis (ecut ecutsm dilatmx etc...) you should get the same forces, although they may not correspond to the last forces reported, which could be the penultimate ones... Needs more investigation

Do you think about the forces on atoms? In Ce atoms are fixed by symmetry.


Thanks again!

Igor