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["Wu Rongqin" <g0203654@nus.edu.sg>]

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