The ABINIT Users Mailing List ( CLOSED )

[Masayoshi Mikami <mmikami@yk.rim.or.jp>]

Dear Rongqin,

Thanks for your patience to wait for replies.
(As denoted in the FAQ:
 http://www.abinit.org/ABINIT/Infos/FAQ.htm#NoResponce
 "those who have answers have less time to reply at that time,
 unfortunately. Please be patient ..." It is true for me these days.)

You raised two concerns,(1)&(2). (kindly see the citation below)

(1) Please read, 
http://www.abinit.org/ABINIT/Infos/FAQ.htm#oscillator
and the hyperlinks therein, in particular,
http://www.abinit.org/wws/arc/announce/2003-02/msg00000.html

So, the values computed in the paper (PRB66,155213,2002) 
refers to the quantities between parenthesis in Eq.(54) 
in PRB 55,10355 (1997). In other words, the values were 
computed by the definition in Phys.Rev.B 50, 13379 (1994):
  http://prola.aps.org/abstract/PRB/v50/i18/p13379_1
(Thus the values in PRB66 paper could be directly 
 compared with those in the PRB50 paper.)

The description in my paper appears misleading, indeed.
Thank you very much for pointing out this.
I will have to send the erratum to the PRB. 
(Better later than never ...)
But kindly note that the conclusions remain the same.

(2) You should have employed the Omega (wave numbers) 
in atomic unit, not in cm-1. 
Your mistake seems to come from the confusion of units.
By googling, I found several URLs about the unit conversions,
just for your references:
http://erbium.chem.ucl.ac.uk/anthony/local/units.html
http://alta1.middlebury.edu/chemistry/class/physical/quantum/help/atomic/atomic.html
(The rest may be left as your homework ...)

Best regards,
Masayoshi

(1)http://www.abinit.org/wws/arc/forum/2004-01/msg00012.html
> Dear Dr. Mikami,
> 
>     Thank you very much for your directions. Now at present I
> am reading your publication:  Lattice dynamics and dielectric
> properties f TiO2 anatase: A first principle study ( PRB,
> 66,155213,2002 ). In it you gave the relation between epsilon_0
> and epsilon_infinity by the mode oscillator strength and the
> omega. Your said that omega is the wave number of the mode m,
> however, this may be questionable as I summed over the optical
> modes to get epsilon_0 by hand. Or in other words, omega should
> be the frequency of the mode m. would you please check it? Or
> maybe I am wrong. 
>    This does no harm to the significance of your paper,
> however, a clarification will be helpful to our novices. 
>
>    Regards
>
>    Rongqin Wu 

(2)http://www.abinit.org/wws/arc/forum/2004-01/msg00013.html
> Dear Dr. Ph.Ghosez and all ABINIT users,
> 
>     Thank you very much for your directions to us. Recently I
> encountered a matter.
>     Two ways to calculate the dielectric constant at zero frequency: one
> is the Generalized Lyddane-Sachs-Teller relation and the other is the
> formula (55) in Dynamical matrices, born effective charges, dielectric
> permittivity tensors and interatomic force constants from density
> functional perturbation theory, PRB, volume 55, 10355, using the
> oscillator strengths and TO mode frequency and then summing. 
>     However when I check these two using IFC utilities in the ABINIT
> package, I find that these two results are not consistent! ( see the
> data in the following! An example of AlAs case)
> 
>     Using the Generalized LST fomula:  
>     (Epsilon_zero/epsilon_infinity) = frequency(LO)**2/frequency(TO)**2=
> 4.150255**2/3.843146**2=1.1662074
>      so Epsilon_zero=
> epsilon_infinity*1.1662074=9.49791778*1.1662074=11.07654. quite good!
> 
>     Using the formula summing over IR active TO mode (PRB, volume 55,
> 10355, formula 55):
>     2 mode to consider: mode 4 and mode 6 for Sxx 
>       Mode 4:  Sxx=9.8172E-5(au), omega = 384.3846(cm-1)=11.52129E+12/s,
> V0=298.5975(au**3)
>        So mode 4 contribution to dielectric constant is
> ((4*3.1416)/V0)*Sxx/omega**2 = 0.07184  
>       Mode 6 : Sxx=1.6844E-5(au), omega =415.0255(cm-1)=12.4420E+12/s
>       So mode contribution to dielectric constant is : 0.01057
>       So the modes contribution is only   0.08241!!!!!!!!!!!!!!!!!!!!!
> 
>       So the discrepancy between the formula (55) and Generalized LST is
> so great!
> 
>     Maybe I have some mistake in the understanding of formula 55 but can
> you point out my mistake in the calculation?
> ------------------------------------------------------------------------
> ------------------------------------------------------------------------
> --------
> Phonon at Gamma, with non-analyticity in the
>   direction (cartesian coordinates)  0.00000  0.00000  1.00000
>  Phonon energies in Hartree :
>    0.000000E+00  0.000000E+00  0.000000E+00  1.751066E-03  1.751067E-03
>    1.890995E-03
>  Phonon frequencies in cm-1    :
> -  0.000000E+00  0.000000E+00  0.000000E+00  3.843146E+02  3.843147E+02
> -  4.150255E+02
> 
> 
> Oscillator strengths (in a.u. ; 1 a.u.=0.342036 m3/s2)
>  Mode number.  xx         yy          zz          xy          xz
> yz      
> ;  1  Real  1.5513E-17  1.6137E-26  3.5013E-18 -5.0033E-22 -7.3699E-18
> 
> 2.3770E-22
> ;         Imag    0.0000E+00  0.0000E+00  0.0000E+00  0.0000E+00
> 0.0000E+00  0.0000E+00
> ;   2     Real    1.7549E-25  3.4641E-18  1.6735E-26  7.7968E-22
> -5.4191E-26 -2.4077E-22
> ;         Imag    0.0000E+00  0.0000E+00  0.0000E+00  0.0000E+00
> 0.0000E+00  0.0000E+00
> ;   3     Real    2.8061E-17  2.7806E-27  3.3842E-21 -2.7933E-22
> -3.0816E-19  3.0676E-24
> ;         Imag    0.0000E+00  0.0000E+00  0.0000E+00  0.0000E+00
> 0.0000E+00  0.0000E+00
> ;   4     Real    9.8172E-05  8.2837E-20  1.6844E-05 -2.8517E-12
> -4.0665E-05  1.1812E-12
> ;         Imag    0.0000E+00  0.0000E+00  0.0000E+00  0.0000E+00
> 0.0000E+00  0.0000E+00
> ;   5     Real    6.2468E-24  1.1502E-04  5.7476E-19 -2.6805E-14
> 1.8948E-21 -8.1306E-12
> ;         Imag    0.0000E+00  0.0000E+00  0.0000E+00  0.0000E+00
> 0.0000E+00  0.0000E+00
> ;   6     Real    1.6844E-05  4.9192E-19  9.8172E-05  2.8785E-12
> 4.0665E-05  6.9493E-12
> ;         Imag    0.0000E+00  0.0000E+00  0.0000E+00  0.0000E+00
> 0.0000E+00  0.0000E+00
> 
>  Electronic dielectric tensor  
>       9.49791778      0.00000000      0.00000000
>       0.00000000      9.49791778      0.00000000
>       0.00000000      0.00000000      9.49791778
>         
>  Full dielectric tensor at frequency  0.0000E+00 Hartree
>   1.10765387E+01  6.48260627E-14 -3.60293620E-07
>   6.48260627E-14  1.10765380E+01  8.51600863E-14
>  -3.60293620E-07  8.51600863E-14  1.10765380E+01
>  
>  Generalized Lyddane-Sachs-Teller relation at zero frequency :
>  Direction                     Dielectric constant
>    1.00000   0.00000   0.00000    1.10765387E+01
>    0.00000   0.00000   1.00000    1.10765380E+01