| Actually, I think the number reported are the trace for each symmetry operation and not for the symmetry class. In the case of D_{3d}^5, there is 12 symmetry operations. The other of the operation is probably the one listed in the output file of the electronic structure. With that information, we can figure out the irreducible representation.
Michel Le 08-04-15 à 18:01, Bo Qiu a écrit : Thanks a lot, the case is Bi2Te3, rhombohedral cell, 5 atoms inside the unitcell, and its space group is 166 and belongs to point group D_{3d}^5, I checked the output file when producing the DDB's, ABINIT had identified the space group correctly which is 166. And the anaddb output for phonon eigenfrequencies and eigenvectors are attached below, thanks again and eager for your help!
By the way, I checked with the character table, the only two point groups having 12 symmetry classes are : C_{6h} and D_{6h}, and they are not likely the case for Bi2Te3... thanks!
================================================================================
-outvars9: echo values of input variables ----------------------
Flags :
ifcflag 1
Miscellaneous information :
eivec 1
asr 1
chneut 1
Interatomic Force Constants Inputs :
dipdip 1
ifcana 0
ifcout 0
Description of grid 1 :
brav 1
ngqpt 2 2 2
nqshft 1
q1shft
0.00000000E+00 0.00000000E+00 0.00000000E+00
First list of wavevector (reduced coord.) :
nph1l 3
qph1l
0.00000000E+00 0.00000000E+00 0.00000000E+00 1.000E+00
3.75000000E-02 3.75000000E-02 7.50000000E-02 1.000E+00
7.50000000E-02 7.50000000E-02 1.50000000E-01 1.000E+00
Second list of wavevector (cart. coord.) :
nph2l 1
qph2l
1.00000000E+00 0.00000000E+00 0.00000000E+00 0.000E+00
================================================================================
read the DDB information and perform some checks
-begin at tcpu 0.040 and twall 0.042 sec
Real(R)+Recip(G) space primitive vectors, cartesian coordinates (Bohr,Bohr^-1):
R(1)= 4.7530203 0.0000000 18.8131213 G(1)= 0.1402617 0.0000000 0.0177181
R(2)= -2.3765102 4.1162364 18.8131213 G(2)= -0.0701308 0.1214702 0.0177181
R(3)= -2.3765102 -4.1162364 18.8131213 G(3)= -0.0701308 -0.1214702 0.0177181
Unit cell volume ucvol= 1.1042110E+03 bohr^3
Angles (23,13,12)= 2.44944933E+01 2.44944933E+01 2.44944933E+01 degrees
Now the whole DDB is in central memory
================================================================================
Dielectric Tensor and Effective Charges
-begin at tcpu 0.050 and twall 0.058 sec
anaddb : Zero the imaginary part of the Dynamical Matrix at Gamma,
and impose the ASR on the effective charges
The violation of the charge neutrality conditions
by the effective charges is as follows :
atom electric field
displacement direction
1 1 4.249851 0.000000
1 2 0.509536 0.000000
1 3 5.187664 0.000000
2 1 0.277559 0.000000
2 2 4.704303 0.000000
2 3 7.149061 0.000000
3 1 -0.108162 0.000000
3 2 -0.128731 0.000000
3 3 3.496086 0.000000
Effective charge tensors after
imposition of the charge neutrality,
and eventual restriction to some part :
atom displacement
1 1 -4.925456E+00 3.161922E-01 3.727469E+00
1 2 -5.014190E-02 -4.771856E+00 3.556130E+00
1 3 -9.955571E-02 -7.988403E-02 -5.915701E+00
2 1 -3.698630E+00 2.817443E-01 2.916057E+00
2 2 1.326859E-01 -3.459363E+00 3.870740E+00
2 3 -6.283830E-02 -7.118099E-02 -2.282296E+00
3 1 6.161366E+00 -4.398404E-01 -4.779758E+00
3 2 -1.076101E-01 5.845291E+00 -5.648786E+00
3 3 1.126177E-01 1.111230E-01 5.240153E+00
4 1 6.161363E+00 -4.398404E-01 -4.779772E+00
4 2 -1.076060E-01 5.845291E+00 -5.648770E+00
4 3 1.126189E-01 1.111230E-01 5.240158E+00
5 1 -3.698643E+00 2.817443E-01 2.916004E+00
5 2 1.326720E-01 -3.459363E+00 3.870685E+00
5 3 -6.284257E-02 -7.118099E-02 -2.282313E+00
Now, the imaginary part of the dynamical matrix is zeroed
================================================================================
Calculation of the interatomic forces
-begin at tcpu 0.050 and twall 0.059 sec
Homogeneous q point set in the B.Z.
Grid q points : 8
1) 0.00000000E+00 0.00000000E+00 0.00000000E+00
2) 5.00000000E-01 0.00000000E+00 0.00000000E+00
3) 0.00000000E+00 5.00000000E-01 0.00000000E+00
4) 5.00000000E-01 5.00000000E-01 0.00000000E+00
5) 0.00000000E+00 0.00000000E+00 5.00000000E-01
6) 5.00000000E-01 0.00000000E+00 5.00000000E-01
7) 0.00000000E+00 5.00000000E-01 5.00000000E-01
8) 5.00000000E-01 5.00000000E-01 5.00000000E-01
================================================================================
Treat the first list of vectors
-begin at tcpu 11.790 and twall 23.309 sec
Phonon wavevector (reduced coordinates) : 0.00000 0.00000 0.00000
Phonon energies in Hartree :
-2.909783E-07 -2.907722E-07 0.000000E+00 2.486419E-04 2.486541E-04
2.975502E-04 5.170214E-04 5.170274E-04 5.208795E-04 5.702163E-04
5.702346E-04 6.439805E-04 6.472644E-04 6.472710E-04 6.872440E-04
Phonon frequencies in cm-1 :
- -6.386235E-02 -6.381713E-02 0.000000E+00 5.457059E+01 5.457327E+01
- 6.530472E+01 1.134731E+02 1.134744E+02 1.143198E+02 1.251480E+02
- 1.251520E+02 1.413374E+02 1.420581E+02 1.420596E+02 1.508326E+02
Eigendisplacements
(will be given, for each mode : in cartesian coordinates
for each atom the real part of the displacement vector,
then the imaginary part of the displacement vector)
Mode number 1 Energy -2.909783E-07
Attention : low frequency mode.
(Could be unstable or acoustic mode)
; 1 6.26893703E-04 5.35084910E-04 7.58917934E-05
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 2 6.26164177E-04 5.35850575E-04 7.64272977E-05
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 3 6.26117999E-04 5.35921800E-04 7.64712863E-05
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 4 6.26117955E-04 5.35921512E-04 7.64457077E-05
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 5 6.26164124E-04 5.35850460E-04 7.64623686E-05
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
Mode number 2 Energy -2.907722E-07
Attention : low frequency mode.
(Could be unstable or acoustic mode)
; 1 5.07981148E-04 -5.43718732E-04 -3.62489693E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 2 5.08844067E-04 -5.42957733E-04 -3.62363998E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 3 5.08965988E-04 -5.42895218E-04 -3.62374210E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 4 5.08957305E-04 -5.42910464E-04 -3.62367034E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 5 5.08852273E-04 -5.42943699E-04 -3.62373924E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
Mode number 3 Energy 0.000000E+00
Attention : low frequency mode.
(Could be unstable or acoustic mode)
; 1 1.84473116E-04 -3.21133796E-04 7.40213009E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 2 1.84474472E-04 -3.21108456E-04 7.40218801E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 3 1.84467130E-04 -3.21157701E-04 7.40209980E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 4 1.84486686E-04 -3.21123179E-04 7.40216078E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 5 1.84456065E-04 -3.21139916E-04 7.40210635E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
Mode number 4 Energy 2.486419E-04
; 1 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 2 -6.93124817E-04 -2.89339378E-04 1.38095525E-05
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 3 9.01655798E-04 3.93579994E-04 -6.31157523E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 4 -9.01673177E-04 -3.93612419E-04 6.34567010E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 5 6.93105926E-04 2.89317334E-04 -1.37790974E-05
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
Mode number 5 Energy 2.486541E-04
; 1 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 2 2.89338558E-04 -6.93205344E-04 1.28559970E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 3 -3.93640955E-04 9.01683400E-04 0.00000000E+00
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 4 3.93626507E-04 -9.01706351E-04 0.00000000E+00
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 5 -2.89344263E-04 6.93181549E-04 -1.26267153E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
Mode number 6 Energy 2.975502E-04
; 1 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 2 -1.11691996E-05 -6.03085491E-06 -1.00840630E-03
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 3 7.17330598E-06 3.76693596E-06 8.31539970E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 4 -7.20081570E-06 -3.81496826E-06 -8.31537217E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 5 1.11450296E-05 5.98928834E-06 1.00841048E-03
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
Mode number 7 Energy 5.170214E-04
; 1 1.55732785E-03 -3.50662172E-04 -4.51253098E-05
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 2 3.18541699E-04 -6.08648160E-05 9.85056288E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 3 -6.70086285E-04 1.43532933E-04 7.49823675E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 4 -6.70064851E-04 1.43544453E-04 7.51675699E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 5 3.18541168E-04 -6.09059193E-05 9.83922450E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
Mode number 8 Energy 5.170274E-04
; 1 3.49886535E-04 1.55770974E-03 -3.97804559E-05
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 2 6.07649242E-05 3.18501570E-04 8.70810132E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 3 -1.43250425E-04 -6.70179849E-04 6.57204905E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 4 -1.43219439E-04 -6.70117025E-04 6.63083790E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 5 6.07049239E-05 3.18415382E-04 8.67204580E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
Mode number 9 Energy 5.208795E-04
; 1 4.75983809E-05 2.61010448E-05 1.89996286E-03
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 2 5.39806158E-06 3.25541981E-06 -3.75199713E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 3 -1.74635769E-05 -9.77118225E-06 -3.50962357E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 4 -1.74678809E-05 -9.77951409E-06 -3.50969103E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 5 5.39533019E-06 3.24970050E-06 -3.75194106E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
Mode number 10 Energy 5.702163E-04
; 1 5.15026372E-04 8.93681893E-04 -5.83521116E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 2 -5.67373345E-04 -1.01889773E-03 2.44862880E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 3 1.89333221E-04 3.48816224E-04 0.00000000E+00
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 4 1.89491539E-04 3.49101878E-04 0.00000000E+00
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 5 -5.67100349E-04 -1.01842658E-03 2.42477532E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
Mode number 11 Energy 5.702346E-04
; 1 8.93827256E-04 -5.15138530E-04 -3.52285838E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 2 -1.01866350E-03 5.67238558E-04 1.46501461E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 3 3.48865546E-04 -1.89356597E-04 0.00000000E+00
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 4 3.48897439E-04 -1.89369751E-04 0.00000000E+00
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 5 -1.01861614E-03 5.67220565E-04 1.46469155E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
Mode number 12 Energy 6.439805E-04
; 1 3.01937508E-06 1.68427199E-06 -2.48562809E-05
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 2 -1.01687053E-06 0.00000000E+00 -1.15046849E-03
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 3 0.00000000E+00 0.00000000E+00 7.10047648E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 4 0.00000000E+00 0.00000000E+00 7.10043602E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 5 -1.09573167E-06 0.00000000E+00 -1.15047188E-03
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
Mode number 13 Energy 6.472644E-04
; 1 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 2 4.26512843E-04 1.18435044E-03 -7.21155251E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 3 1.90015647E-04 5.55473543E-04 0.00000000E+00
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 4 -1.89915351E-04 -5.55296592E-04 0.00000000E+00
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 5 -4.26777272E-04 -1.18482547E-03 7.35041276E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
Mode number 14 Energy 6.472710E-04
; 1 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 2 1.18455329E-03 -4.26732788E-04 -5.97011927E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 3 5.55376609E-04 -1.89923701E-04 0.00000000E+00
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 4 -5.55353764E-04 1.89954149E-04 0.00000000E+00
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 5 -1.18464191E-03 4.26669491E-04 5.99594082E-06
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
Mode number 15 Energy 6.872440E-04
; 1 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 2 7.64340492E-06 4.58865530E-06 1.06416449E-03
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 3 0.00000000E+00 0.00000000E+00 7.88045399E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 4 0.00000000E+00 0.00000000E+00 -7.88048138E-04
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
; 5 -7.64628596E-06 -4.59360838E-06 -1.06415842E-03
; 0.00000000E+00 0.00000000E+00 0.00000000E+00
Analysis of degeneracies and characters (maximum tolerance=1.00E-06 a.u.)
Symmetry characters of vibration mode # 1
degenerate with vibration modes # 2 to 3
3.0 -3.0 1.0 -1.0 0.0 0.0 1.0 -1.0 0.0 0.0 1.0 -1.0
Symmetry characters of vibration mode # 4
degenerate with vibration mode # 5
2.0 2.0 0.0 0.0 -1.0 -1.0 0.0 0.0 -1.0 -1.0 0.0 0.0
Symmetry characters of vibration mode # 6
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
Symmetry characters of vibration mode # 7
degenerate with vibration mode # 8
2.0 -2.0 0.0 0.0 -1.0 1.0 0.0 0.0 -1.0 1.0 0.0 0.0
Symmetry characters of vibration mode # 9
1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0
Symmetry characters of vibration mode # 10
degenerate with vibration mode # 11
2.0 -2.0 0.0 0.0 -1.0 1.0 0.0 0.0 -1.0 1.0 0.0 0.0
Symmetry characters of vibration mode # 12
1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0
Symmetry characters of vibration mode # 13
degenerate with vibration mode # 14
2.0 2.0 0.0 0.0 -1.0 -1.0 0.0 0.0 -1.0 -1.0 0.0 0.0
Symmetry characters of vibration mode # 15
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
==============================================
On Tue, Apr 15, 2008 at 5:57 PM, Michel Cote < Michel.Cote@umontreal.ca> wrote: These numbers are the character of the degenerate modes to help you figure out the irreducible representation of a given set of degenerate modes. Now, if you think your system should have only 6 symmetry classes and Abinit gives you 12, it seem that the you do not agree on the symmetry of the system.
Have a look at the output file to make sure the reported space group is what you think. Please include your output file if you want more help.
Michel
Le 08-04-15 à 13:01, Bo Qiu a écrit : As a supplement to my question:
The point group of the crystal I'm calculating is D_{3d}^5 , so I look at the character table, there are only 6 columns, so I'm just confused why there are 12 columns? What do they mean? Thanks so much!
Sincerely,
Bo
Michel Cote
Departement de physique
Universite de Montreal
email: Michel.Cote@umontreal.ca
web: http://www.phys.umontreal.ca/~michel_cote
--
Thanks and Best Wishes.
Sincerely yours,
Bo Qiu
http://web.ics.purdue.edu/~qiub/homepage/ _____________________________________ Michel Cote Departement de physique Universite de Montreal
|
