Bonding analysis at HOMO, could you please give me some hints.

[zhaohs]

Hi all,

Currently, I'm reading the paper: Direct to indirect band gap transition in ultrathin ZnO nanowires under uniaxial compression [APPLIED PHYSICS LETTERS 94, 113114, 2009].

You can download this paper from the following url:

http://h1.ripway.com/zhaohs/Direct%20to%20indirect%20band%20gap%20transition%2 0in%20ultrathin%20ZnO%20nanowires%20under.pdf

At the top of page 3, the author said:

--------------
A detailed analysis on the characteristics of atomic orbital contribution of the
highest occupied molecular orbital (HOMO) shows that
bonding at Gamma-point is mainly contributed from the O pz and
Zn dz2 states, with equal components from all the six Zn and
O in the supercell. For point E and F in Fig. 4, the key
bonding characteristics are also the O pz and Zn dz2, but from
only two (L=0.48 nm) or four (L=0.47 nm) Zn and O atoms.
The analyses indicate that bonding of HOMO at
Gamma-point is much stronger than that at E or F point. Therefore,
during uniaxial compression, the energy lowering at Gamma-point
will be much faster than that at E or F point.
--------------

But I cann't figure out what calculations should I performed in order to obtain the above information within siesta.

Furthermore, the author said that the bonding are mainly contributed from O pz and Zn dz2. But in my mind, all of the three sub-orbitals of p (px,py, pz) are exactly equivalent, and that is also the case for the five sub-orbitals of d (dz2, dxz, dxy, dx2-y2, dyz). So, how should they know the bonding are mainly contributed from O pz and Zn dz2?

Could you please give me some hints? Thanks in advance.

Regards.

[SpectraCat]

Hi all,

Currently, I'm reading the paper: Direct to indirect band gap transition in ultrathin ZnO nanowires under uniaxial compression [APPLIED PHYSICS LETTERS 94, 113114, 2009].

You can download this paper from the following url:

http://h1.ripway.com/zhaohs/Direct%20to%20indirect%20band%20gap%20transition%2 0in%20ultrathin%20ZnO%20nanowires%20under.pdf

At the top of page 3, the author said:

--------------
A detailed analysis on the characteristics of atomic orbital contribution of the
highest occupied molecular orbital (HOMO) shows that
bonding at Gamma-point is mainly contributed from the O pz and
Zn dz2 states, with equal components from all the six Zn and
O in the supercell. For point E and F in Fig. 4, the key
bonding characteristics are also the O pz and Zn dz2, but from
only two (L=0.48 nm) or four (L=0.47 nm) Zn and O atoms.
The analyses indicate that bonding of HOMO at
Gamma-point is much stronger than that at E or F point. Therefore,
during uniaxial compression, the energy lowering at Gamma-point
will be much faster than that at E or F point.
--------------

But I cann't figure out what calculations should I performed in order to obtain the above information within siesta.

Furthermore, the author said that the bonding are mainly contributed from O pz and Zn dz2. But in my mind, all of the three sub-orbitals of p (px,py, pz) are exactly equivalent, and that is also the case for the five sub-orbitals of d (dz2, dxz, dxy, dx2-y2, dyz). So, how should they know the bonding are mainly contributed from O pz and Zn dz2?

Could you please give me some hints? Thanks in advance.

Regards.

Well, I don't know what siesta is .. I guess it's some sort of solid-state computational physics package .. so I'm afraid I can't be much help there.

However, I can perhaps help with your confusion about the spatial orbitals. The spatial orbitals (i.e. px, py, pz, or the 5 d-orbitals) are only "equivalent" (I assume you meant degenerate), when an atom is in isotropic space. In this case, the atoms are participating in a covalent bonding network, and thus are most definitely NOT in isotropic space. As to how the authors know specifically that it is the pz and dz[sup2[/sup] orbitals contributing .. that is one of the things you can keep track of with a computational quantum electronic structure package.