About the Fermi energy defined in VASP

[pengx]

Dear all,
I understand for periodic boundary system, the absolute values of energy eigenvalue (thus the fermi energy) is meaningless. If the system contains enough vacuum space, the energy values can be referenced to the potential at the vacuum center. My question is how VASP define the fermi energy? Some posts by admin say the Fermi level is generally calculated from the highest occupied state. Does that mean the fermi energy reported in OUTCAR is same as the energy of the highest occupied level? If yes, it is obviously not the case in my calculations. I played with an armchair graphenen nanoribbon in which the direct band gap located at Gamma. I got
E-fermi : -2.3869 XC(G=0): -3.2794 alpha+bet : -2.5830
and energy levels at Gamma
53 -2.8253 2.00000
54 -2.6556 2.00000
55 -1.7744 0.00000
56 -1.6349 0.00000

This is a result of band structure calculation. I already have scf converged CHGCAR. For your reference, the following are my input
INCAR:
SYSTEM = graphene ribbon

PREC = Medium
NSW = 0
ISIF = 2
NELM = 200
NELMIN = 4
EDIFF = 1.0e-05
ENCUT = 400
ISTART = 0
ICHARG = 11
LWAVE = .False.
LCHARG = .False.
IALGO = 38
LREAL = .True.
ISMEAR = 0
SIGMA = 0.05

KPOINTS:
k-points
21 !21 intersections
line mode
rec
0.00000 0.00000 0.00000 ! Gamma
0.50000 0.00000 0.0 ! X

POSCAR
armchair graphene nano-ribbon
1.00000000000000
4.2465238590999999 0.0000000000000000 0.0000000000000000
0.0000000000000000 30.0000000000000000 0.0000000000000000
0.0000000000000000 0.0000000000000000 8.0000000000000000
26 4
Direct
0.1733135916919932 0.0412264349034275 0.0000000000000000
0.4933540390416342 0.0412264349034275 0.0000000000000000
0.0013645121440287 0.0810691862249105 0.0000000000000000
0.6653031185895917 0.0810691862249105 0.0000000000000000
0.1662858375607499 0.1216119632844744 0.0000000000000000
0.5003817931728776 0.1216119632844744 0.0000000000000000
0.9991036002666018 0.1624638469732930 0.0000000000000000
0.6675640304670256 0.1624638469732930 0.0000000000000000
0.1661992284664219 0.2031442094527499 0.0000000000000000
0.5004660473999426 0.2031442094527499 0.0000000000000000
0.0002978133006326 0.2436519001930938 0.0000000000000000
0.6663674625657319 0.2436519001930938 0.0000000000000000
0.1673405771302399 0.2843859999999978 0.0000000000000000
0.4993270536033875 0.2843859999999978 0.0000000000000000
0.0002978133006326 0.3251197664735764 0.0000000000000000
0.6663674625657319 0.3251197664735764 0.0000000000000000
0.1661992284664219 0.3656277905472528 0.0000000000000000
0.5004660473999426 0.3656277905472528 0.0000000000000000
0.9991036002666018 0.4063078196933772 0.0000000000000000
0.6675640304670256 0.4063078196933772 0.0000000000000000
0.1662858375607499 0.4471600367155283 0.0000000000000000
0.5003817931728776 0.4471600367155283 0.0000000000000000
0.0013645121440287 0.4877028137750851 0.0000000000000000
0.6653031185895917 0.4877028137750851 0.0000000000000000
0.1733135916919932 0.5275455650965751 0.0000000000000000
0.4933540390416342 0.5275455650965751 0.0000000000000000
0.0497607157597652 0.0093466774156693 0.0000000000000000
0.6169069149738624 0.0093466774156693 0.0000000000000000
0.0497607157597652 0.5594249892509937 0.0000000000000000
0.6169069149738624 0.5594249892509937 0.0000000000000000

Any comments are appreciated!

[giacomo giorgi]

Maybe I am wrong but one is the Valence Band eigenvalue, the other one is the Fermi energy.

[tlchan]

From a computational point of view, integrating the density of states from the lowest energy level to the Fermi level should give you the total number of electrons in the unit cell. Your system has an energy gap. This means that the Fermi level can be anywhere between -2.66 eV to -1.77 eV because any value within this range can give the correct number of electrons. Typically, the Fermi level is calculated by an iterative approach. Depending on the initial guess and the iterative algorithm, the computed Fermi level can end up anywhere in the energy gap.

Depending on your application, if thermodynamics is of concern, you may want to define the Fermi level to be at the middle of the energy gap. Otherwise, computationally, it does not really matter as long as the Fermi level is inside the gap.