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Fermi level dependence on basis set
Date: 2018/07/13 23:33
Name: Dechamps Samuel   <samuel.dechamps@uclouvain.be>

Dear OpenMx users and developers,

I was wondering how the Fermi level (or chemical potential when T dependency is considered) depends on the basis set.
For a given system, in this case MoS2, I have the following trend (after optimizing the lattice and the atomic positions for each case) :

Mo-S Ef
s3p3d2f1 -0.175781250000
s3p3d2 -0.175781250000
s3p3d2-s2p1d1 -0.175781250000
s3p2d1-s2p1d1 -0.185546875000
s2p2d1 -0.185546875000
s2p2d1-s2p1d1 -0.185546875000
s2p1d1 -0.185546875000
s2p2d1-s2p1 -0.232658386230

I read that Ef is such that the total number of electrons is conserved for the KS eigenvectors.
Does that therefore means that by adding a d-orbital the KS eigenvectors are changed, modifying in turn Ef ? (for s3p2d1-s2p1d1 => s3p3d2-s2p1d1)

If not, what is the meaning of Ef changing abruptly for certain additional orbitals ?

Regards,
S. Dechamps

To detail my idea, here is the orbital decomposition :

(s3p2d1-s2p1d1)
1 Mo Up spin Down spin Sum Diff Angles(Deg)
multiple
s 0 0.993154324 0.993154324 1.986308649 0.000000000 90.0000 0.0000
sum over m 0.993154324 0.993154324 1.986308649 0.000000000
s 1 0.178391951 0.178391951 0.356783901 0.000000000 90.0000 0.0000
sum over m 0.178391951 0.178391951 0.356783901 0.000000000
s 2 0.018741606 0.018741606 0.037483211 0.000000000 90.0000 0.0000
sum over m 0.018741606 0.018741606 0.037483211 0.000000000
sum over m+mul 1.190287880 1.190287880 2.380575761 0.000000000
px 0 0.994646312 0.994646312 1.989292625 0.000000000 88.6389 -0.5319
py 0 0.994659239 0.994659239 1.989318477 0.000000000 89.5669 89.2415
pz 0 0.993252384 0.993252384 1.986504769 0.000000000 89.5145 -85.4934
sum over m 2.982557935 2.982557935 5.965115871 0.000000000
px 1 0.024185768 0.024185768 0.048371537 0.000000000 90.2588 186.9696
py 1 0.024211821 0.024211821 0.048423642 0.000000000 90.5305 -89.7055
pz 1 0.055717120 0.055717120 0.111434240 0.000000000 89.1007 113.9129
sum over m 0.104114710 0.104114710 0.208229419 0.000000000
sum over m+mul 3.086672645 3.086672645 6.173345290 0.000000000
d3z^2-r^2 0 0.547038459 0.547038459 1.094076918 0.000000000 5.4629 0.0000
dx^2-y^2 0 0.506799209 0.506799209 1.013598418 0.000000000 178.3685 0.0000
dxy 0 0.505440313 0.505440313 1.010880626 0.000000000 178.1699 0.0000
dxz 0 0.452226672 0.452226672 0.904453343 0.000000000 90.0000 0.0000
dyz 0 0.452160129 0.452160129 0.904320257 0.000000000 90.0000 0.0000
sum over m 2.463664782 2.463664782 4.927329563 0.000000000
sum over m+mul 2.463664782 2.463664782 4.927329563 0.000000000


(s3p3d2-s2p1d1)
1 Mo Up spin Down spin Sum Diff Angles(Deg)
multiple
s 0 0.992793152 0.992793152 1.985586303 0.000000000 90.0000 0.0000
sum over m 0.992793152 0.992793152 1.985586303 0.000000000
s 1 0.250243464 0.250243464 0.500486929 0.000000000 90.0000 0.0000
sum over m 0.250243464 0.250243464 0.500486929 0.000000000
s 2 0.014419247 0.014419247 0.028838495 0.000000000 90.0000 0.0000
sum over m 0.014419247 0.014419247 0.028838495 0.000000000
sum over m+mul 1.257455863 1.257455863 2.514911727 0.000000000
px 0 0.999105042 0.999105042 1.998210084 0.000000000 77.3896 180.5616
py 0 0.999055612 0.999055612 1.998111224 0.000000000 87.2947 -89.6237
pz 0 0.992719169 0.992719169 1.985438337 0.000000000 90.0000 113.5993
sum over m 2.990879823 2.990879823 5.981759645 0.000000000
px 1 0.045832578 0.045832578 0.091665156 0.000000000 90.0000 0.0000
py 1 0.045675659 0.045675659 0.091351317 0.000000000 91.3008 84.9812
pz 1 0.049870267 0.049870267 0.099740533 0.000000000 90.3018 254.4468
sum over m 0.141378503 0.141378503 0.282757006 0.000000000
px 2 0.012320894 0.012320894 0.024641788 0.000000000 90.0000 0.0000
py 2 0.012308760 0.012308760 0.024617520 0.000000000 90.0000 0.0000
pz 2 0.012265221 0.012265221 0.024530442 0.000000000 90.0000 0.0000
sum over m 0.036894875 0.036894875 0.073789750 0.000000000
sum over m+mul 3.169153201 3.169153201 6.338306402 0.000000000
d3z^2-r^2 0 0.469804787 0.469804787 0.939609575 0.000000000 10.4487 8.7655
dx^2-y^2 0 0.458486279 0.458486279 0.916972557 0.000000000 170.3790 0.0000
dxy 0 0.457284974 0.457284974 0.914569949 0.000000000 175.2825 0.0000
dxz 0 0.414626830 0.414626830 0.829253661 0.000000000 90.0000 0.0000
dyz 0 0.414561010 0.414561010 0.829122020 0.000000000 90.0000 0.0000
sum over m 2.214763881 2.214763881 4.429527762 0.000000000
d3z^2-r^2 1 -0.044505930 -0.044505930 -0.089011861 0.000000000 42.5285 0.0000
dx^2-y^2 1 -0.030563386 -0.030563386 -0.061126773 0.000000000 96.3623 -54.2331
dxy 1 -0.030639273 -0.030639273 -0.061278547 0.000000000 99.7196 -13.0622
dxz 1 -0.000653534 -0.000653534 -0.001307068 0.000000000 90.0000 0.0000
dyz 1 -0.000689465 -0.000689465 -0.001378930 0.000000000 90.0000 0.0000
sum over m -0.107051589 -0.107051589 -0.214103178 0.000000000
sum over m+mul 2.107712292 2.107712292 4.215424583 0.000000000

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Re: Fermi level dependence on basis set ( No.1 )
Date: 2018/07/13 23:37
Name: Dechamps Samuel  <samuel.dechamps@uclouvain.be>

PS: I'm sorry about the text not being well spaced out.
メンテ
Re: Fermi level dependence on basis set ( No.2 )
Date: 2018/07/18 00:52
Name: Dechamps Samuel  <samuel.dechamps@uclouvain.be>

Dear OpenMX users and developers,

I found the solution to my question.

The problem is due to a non-zero temperature.

In the case of MoS2, the conduction band has mainly Mo-d orbital contribution.
When T /= 0; adding a d orbital shifts the conduction bands, therefore changing Ef due to the tail of the fermi-dirac distribution going in the conduction region.

For T = 0, I have :

s3p3d2-s2p1d1 :
-0.156250000000
s3p2d1-s2p1d1 :
-0.156250000000

This is also confirmed by plotting the band structure for s3p3d2-s2p1d1 and s3p2d1-s2p1d1.

Best,
S. Dechamps

メンテ
Re: Fermi level dependence on basis set ( No.3 )
Date: 2018/08/07 17:18
Name: T. Ozaki

Hi,

For a gapped system, the determination of Fermi level at T=0K is rather
an ill-defined problem. Any energy in the gap can be a Fermi level at T=0K.
OpenMX just starts from a trial energy and search a Fermi level at a given temperature
so that the total number of electrons can be conserved. At T=0K, once the trial energy
falls in the gap, this becomes a Fermi energy.

Regards,

TO
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