Spurious Electron in the Conduction Band

[sankh]

Dear all,

I am wondering whether someone could interpret and propose a solution to the problem that I have recently encountered in band structure calculations, following conventional VASP prescription, as cited below.

I have been doing band structure calculations on 48 atoms supercells of anatase systems (pure and doped) at spin-polarized PBEsol level of XC effects for the valence electrons while PAW PBE PP (partial p-valence for Ti and metal cations while full-core for O and second-row anions) for the core electrons, reading in the converged charges (ICHARG = 11) with Gaussian integration for BZ (ISMEAR = 0) with moderate smearing width (Sigma = 0.1), where the local charges were previously determined through an SCF process with Tetrahedron integration with Blöchl correction (ISMEAR = -5). Although the band energies (eigen values) and hence band gap computed seem OK, I am finding that VASP is giving an artifically high occupation number of about 0.5 to the first conduction band, while the number of total electrons NELEC in the OUTCAR is accurate, which is exactly as half number as the number of occupied (valence) bands that are fully occupied with occupation number of 1 (NELEC/2 number of spin-polarized alpha and beta sets of bands) and which is exactly equal to the total number of valence electrons of the atoms (POTCAR). Therefore, something went wrong in the band structure calculation that artificially suggests sizably high population of the first conduction band (0.5), which is equlivalent to "one" spurious electron in the CB, making the CB partially occupied VB and that the O atoms have spuriouly gained one extra electron!

NELECT in OUTCAR does not account this extra electron.

Interestingly, DOS calculation, which was performed through Tetrahedron integration+Blöchl correction and of course with denser K-mesh, on the same convered charges, does not give this spurious occupation number (0.5) to the first CB but rather gives exactly "0" occupation number to the CB, while band energies are same as those of band structure calculation! Futhermore, although the band structure calculation gives 0.5 occupation to an extra band, it gives surprisingly correct magnetic moment (which is "0" for full-shell anatase comprising of 352 valence electrons) in the same calculation!

Eventually, the only differences between DOS and band structure calculations are:

1. BZ Integration algorithm (Tetrahedron+Blöchl with default Sigma Vs Gaussian with Sigma 0.1)

2. K point sampling (denser Gamma-centered or MP k-points Vs line-mode high-symmetry k-vectors), although this should not really affect, I guess.

However, I would appreciate if someone could spot the reason that underlies this issue and that undermines, and could pescribe a solutio. Thanks a lot in advance for these.

Best regards,
Sankh
<span class='smallblacktext'>[ Edited ]</span>

[sankh]

Further to this issue, I add two specific examples to elaborate, as follows:

VASP predicts for 48 atom anatase TiO2 a total number of valence electrons 352 (6 O valence electrons and 10 Ti valence electrons, stemming from full-core and pv PP for O and Ti, respectively), while it is giving 176 alpha (beta) bands with occupation number 1 and 177th band (both alpha and beta) with occupation number 0.52. In case of 48 atoms TiO2 with one Ti being substituted wih a Cr atom, VASP predicts total 354 valence electrons, but giving only 176 alpha (as well as beta) occupied bands (occ no = 1), instead of 177 (177th alpha/beta bands got occ no. 0). Therefore, I am not seeing any correspondance between total number of valence electrons and band occupation number, at all. It then raises the question how one would predict correctly which band is occupied and which one unoccupied to assess VB and CB of a system!

I am now inclined to believe that there should be a bug in assigning the number of bands to be occupied (to be used for constructing density matrix), but I am surprised, as well, it seems that other users didn't encounter/recognize this problem, as I didn't find any report in the forum!

Any help to throw lights will be much appreciated.

Thanks,
Sankh