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Dear all abinitioners,

The traditional method to find effevtive masses of electrons and holes is 
k.p method. I find a simple but effective method to acquire effective 
masses of semiconductors/insulators from ABINIT package. The mechanism is 
as follows: first, I do a band structure calculation of ground state 
calculation; second, I directly extract the eigenvalues from ABINIT output 
files; at last, use polynomial of degree two curve fitting to find three 
diagonal components(as we know, the off-diagonal components will be zero if 
we properly choose the axes directions).  We know the electronic effevtive 
mass is close relevant to charge transfer process in semiconductors. With 
this simple method, you can easily report your theoretical effevtive mass 
from first-principles when you submit a paper concerning with the transfer 
property of charge carrier. 

Here I give an example to illustrate how to get the effective masses of 
electrons of silicon.
-----------------------------------------------------------------------------------------------

EffectiveMass_IN  //the ABINIT input file
---------------------------------------------------------------------
#Computation:
#   Electronic and hole efficient masses of Crystalline Silicon
#Structure:
#    FCC unit cell.
#Pseudopotential:
#    GTH, Si.
#Date:
#    Mon-July-10-2002 @OS:Linux;Machine:MikeZhang

ecut          35.0
enunit        2             

ndtset        3

#Dataset 1: usual self-consistent calculation
kptopt1       1 
nshiftk1      3
shiftk1
             0.0 0.5 0.5
             0.5 0.0 0.5
             0.5 0.5 0.0
ngkpt1        6 6 6
prtden1       1
toldfe1       1.0d-8

#Definition of the SCF procedure
nstep         20
diemac        12.0
nband         12
ecutsm        0.5

#Dataset 2,3:  determination of the curvature of band at CBM
getden2       -1
iscf2         -2
tolwfr2       1.0d-12
kptopt2       -1
ndivk2        40 
kptbounds2
             0.0    0.415  0.415 # along Delta line
             0.0    0.435  0.435

getden3       -2
iscf3         -2
tolwfr3       1.0d-12
kptopt3       -1
ndivk3        40 
kptbounds3
            -0.01   0.425 0.415   # perpendicular to Delta line
             0.01   0.425 0.435 

#-----------------------------------------------------------
acell         3*10.25
rprim         0.0  0.5  0.5
             0.5  0.0  0.5
             0.5  0.5  0.0
natom         2
zatnum        14
ntype         1
type          2*1
xred          -0.125   -0.125   -0.125
              0.125    0.125    0.125
#-----------------------------------------------------------

I found the CBM is accurately at (0, 0, 0.844) in Cartesian coordinate of k 
in BZ from ABINIT(it is generally acknowledged that is located at (0, 0, 
0.85)). Then I use MatLab to analyze the data of output file. I edited a .m 
file named effMass.m based on mexData() function and polyfit() function. 
Function mexData can be found on www.abinit.org(but it is an old version; I 
found mexData.C on www.abinit.org was a wrong version: in fact, it couldn't 
dispose of three-dimension data:( ). Function polyfit is contained in 
MatLab. If you are interseted in effMass.m and mexData.C, you can send me 
an E-mail. I'ld also like to submit the proper version of mexData.C to 
www.abinit.org if they ask for me. 

Using effMass.m, a simple command is enough to gain the eventual results 
like that:
[effm sK E]=effmass('silicon\effectivemass_linux\effectivemass_out', 5, 2);
effectivemass_out is your ABINIT output file, 5 means the fifth band(for 
silicon, it is LUMO), 2 means disposing of dataset 2 to 3;
The MatLab output is as follows:
EffectiveMass(:,:,1) =

   0.6817
   0.8947
   0.9760
   0.9448
   0.9641
   0.9611
   0.9581
   0.9481
   0.9470
   0.9491
   0.9485
   0.9477
   0.9496
   0.9507
   0.9500
   0.9502
   0.9496
   0.9500
   0.9499
   0.9495


EffectiveMass(:,:,2) =

   0.1859
   0.1884
   0.1934
   0.1916
   0.1914
   0.1920
   0.1917
   0.1916
   0.1918
   0.1917
   0.1917
   0.1915
   0.1916
   0.1916
   0.1915
   0.1916
   0.1916
   0.1917
   0.1917
   0.1917

The ABINIT-output eigenvalues is fixed to the format of five-digit decimal 
fraction, so the first several values of EffectiveMass(:,:,1) and 
EffectiveMass(:,:,2) is NOT accurate and should be get rid of. (Here I 
suggest the future ABINIT should develop parameters to control output 
format; in some occasion we need more accurate output data) Then use mean() 
function to get the mean of other values.   
Please see the file 'EffectiveMass_IN' listed above. EffectiveMass(:,:,1) 
is derived from (0.0,0.415,0.415)-(0.0,0.435,0.435), which is along Delta 
line in BZ. So EffectiveMass(:,:,1) is $m_l^*$ (longitudinal effective 
mass) and EffectiveMass(:,:,2) is $m_t^*$ (traverse effective mass). At 
last we get the ab initio theoretical values comparing with experimental 
data as follows:
            $m_l^*$ (longitudinal effective mass)       $m_t^*$ (traverse 
effective mass)
This work                 0.9511                                     0.1916
Expt.                     0.9163                                     0.1905
(Error)                     3.8%                                       0.6%

----------------------WOW!!! The results are rather 
satisfying!!!-----------------------
NOTICE: here is something you should notice when using this method.
1. Use 'band buffer' to get accurate eigenvalues(see lesson three) because 
ABINIT uses iterative diagonalizational method.
2. The parameter kptbounds should be carefully tried when handling with 
other materials. 


------------------------------------- Y   A       T 
----------------------------------
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Yet Another 
Thing!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

As above you have seen, I share my experience about using ABINIT to you. I 
also have a questions which troubles me for a long time to ask. I am sure 
that someone know how to handle them. Currently I am doing some 
response-function (static dielectric tensor) calculations on material 
rutile TiO2, which is a wide band gap semiconductor. But I always got the 
ERROR as follows:

 The lowest mode appears to be a "true" negative mode,
 and not an acoustic mode. This precludes the computation
 of the frequency-dependent dielectric tensor.
 Action : likely there is no action to be taken, although you,
 could try to raise your convergence parameters (ecut and k-points).
For your information, here are the four lowest frequencies :
-1.44436452E-03 -1.44432637E-03 -1.40826927E-03 -1.00781976E-03

leave_new : decision taken to exit ...

I know Xavier Gonze know how to dispose of the problem because he had 
successfully done that(PRB50,13379(1994), 'Lattice dynamics and dielectric 
properties of incipent ferroelectric TiO2 rutile').  But no one give me any 
suggestion. So here I expect someone can give me any instruction. I really 
appreciate for you.
--------------------------------------My Input 
File------------------------------------ 
#Computation:
#    Response function calculation of TiO2(Rutile).
#Structure:
#    Tetregonal unit cell.
#Pseudopotential:
#    HGH, nonSemiCore, Ti and O.
#Date:
#    Sat-July-07-2002 @OS:Linux;Machine:MikeZhang

ndtset        3

ecut          30.0
prtvol        1

kptopt1       1
tolvrs1       1.0d-18
iscf1         5

getwfk2       -1
kptopt2       2
rfelfd2       2
rfdir2        1      1      1
nqpt2         1
qpt2          0.0    0.0    0.0
tolwfr2       1.0d-22
iscf2         -3

getwfk3       -2
getddk3       -1
kptopt3       2
rfphon3       1
rfatpol3      1      6
rfelfd3       3
rfdir3        1      1      1
nqpt3         1
qpt3          0.0    0.0    0.0
tolvrs3       1.0d-11
iscf3         5

nstep         100
diemac        100.0
ngkpt         4 4 6
nshiftk       1
shiftk        0.5 0.5 0.5
             
#-------------------------------------------------------------------------------

#Define the unit cell
acell         8.6806      8.6806      5.5911
ntype         2
zatnum        22          8
natom         6
type
             1  1  2  2  2  2
xred
             0.0     0.0     0.0
             0.5     0.5     0.5
             0.3048  0.3048  0.0
             0.6952  0.6952  0.0
             0.8048  0.1952  0.5
             0.1952  0.8048  0.5
#-------------------------------------------------------------------------------



Mike Zhang
09/06/2002



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