total charge question

[paulzim]

Hello,

I am wondering about the quantity "Charge" in the properties output. I ran a twoprobe calculation, which converged to:

# sc 26 : q =  193.26029 e  Etot = -3687.65468 Ry  dRho =  2.6318E-04  dEtot =  7.0024E-06 Ry

and then the properties section says:

# ----------------------------------------------------------------
# Total Energy           = -26398.6064 eV             
# Potential Energy       = -26398.6064 eV             
# Ion Kinetic Energy     = 0.0000 eV
# ----------------------------------------------------------------             
# NumOrb: Energy of system
# ----------------------------------------------------------------             
# Charge                  = 195.1892
# Band Structure Energy   = -726.1524 eV               
# ----------------------------------------------------------------

The final iteration giving charge is not equal to the charge given in the properties output. Any explanation would be helpful.

Thanks!
--Paul

[zh]

# sc 26 : q =  193.26029 e  Etot = -3687.65468 Ry  dRho =  2.6318E-04  dEtot =  7.0024E-06 Ry

By examining  the log file of Li-H2-Li system during the self-consistent calculation, one may find that the charge printed here is computed by the Mulliken population analysis for the scattering region (i.e., center region).   see below for the last iteration step:


# sc 14 : q =    7.95068 e  Etot =  -12.91021 Ry  dRho =  7.6522E-06  dEtot = -9.6834E-07 Ry
#-------------------------------------------------------------------------------
# Mulliken Population for sc 14
#-------------------------------------------------------------------------------
 4 Li     q =  0.98680 [ s:  0.987 ]
 5 Li     q =  1.02999 [ s:  1.030 ]
 6 Li     q =  0.94415 [ s:  0.944 ]
 7  H     q =  1.01437 [ s:  0.535, s:  0.454, py:  0.000, pz:  0.025, px:  0.000 ]
 8  H     q =  1.01424 [ s:  0.535, s:  0.454, py:  0.000, pz:  0.025, px:  0.000 ]
 9 Li     q =  0.94416 [ s:  0.944 ]
10 Li     q =  1.02998 [ s:  1.030 ]
11 Li     q =  0.98699 [ s:  0.987 ]
#-------------------------------------------------------------------------------
# Total Charge =    7.95068

# ----------------------------------------------------------------
# Total Energy           = -26398.6064 eV             
# Potential Energy       = -26398.6064 eV             
# Ion Kinetic Energy     = 0.0000 eV
# ----------------------------------------------------------------             
# NumOrb: Energy of system
# ----------------------------------------------------------------             
# Charge                  = 195.1892
# Band Structure Energy   = -726.1524 eV               
# ----------------------------------------------------------------

The final iteration giving charge is not equal to the charge given in the properties output. Any explanation would be helpful.

I guess that the charge printed below "# NumOrb: Energy of system" may be estimated by the density matrix (i.e.[tex]\rho_{c,c}[/tex]) of scattering region.  In addition, the "Band Structure Energy" printed below "# NumOrb: Energy of system" may be computed by the Eq.(22) in PRB 63, 245407(2001). i.e.,
[tex]E_{BS}=Tr_c[\rho H]=\rho_{c,l}h_{l,c}+\rho_{c,c}h_{c,c}+\rho_{c,r}h_{r,c}[/tex]

[zzhang]

For these charges referred below, the calculation is done with zero applied voltage.  When you refer to the equilibrium and non-equilibrium cases, do you mean with and without applied potential?

Supposedly both charges are calculated from the coefficients of the scattering states. During the iteration steps of the two probe calculation, are the Mulliken charges calculated from the scattering state coefficients only, as opposed to the charge, supposedly calculated with the Fermi distribution function, in the properties section?

Could some body please clarify how these charges are calculated in more detail?

Thanks,
Zhiyong

[zh]

For these charges referred below, the calculation is done with zero applied voltage.  When you refer to the equilibrium and non-equilibrium cases, do you mean with and without applied potential?

Yes.  You may refer to PHYSICAL REVIEW B 63, 245407(2001). Especially, take a look at  page 245407-5 there.