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Berry-phase Calculation of Dipole

(2011-04-30 22:49:51)
标签：

berry-phase

dipole

 分类： vasp
  Today(2011-04-30), I move some part of <如何用vasp计算Born有效电荷(转载)>to this blog.
 
0：上面的脚本将scf的WAVE CHG另存，或许是因为在dipole计算中，有可能破坏原来的scf的文件；否则就需要scf-berry1-scf-berry2-scf-berry3了。(In berry-phase calculation, scf can also be used. However, many kpoints are inquired in berry-phase calculation.Therefore, scf for ordinary calculation, then nscf for berry-phase. I know this from the picture pasted at 2011-04-30 )

1：R是个矢量，不能对分量求和，但或许可以对其求模(绝对值，norm)。(For every G_i direction, all the berry-phase part of electron polarization is number*R_i 2011-04-30 )

2：IPGAR的三个方向为a1,a2,a3，不是xyz；
但R的输出结果的三个分量(d1 d2 d3)是在xyz轴上的分量，而不是d1*a1,d2*a2,d3*a3。
一个固定几何构型的三个不同的方向：
三个方向会给出不同的Rev；Rev项是先求和，再平均.(Rev is the polarization originated from augment part of electron, USPP PAW.)
三个方向会给出不同的Rbp；Rbp项只求和，不平均
(【Rev的在三个方向的平均值】+【Rbp在三个方向的和】=【Relc】)
三个方向会给出相同的Rion；Rion项不求和
【Relc】+【Rion】=【Rtotal】

3：在vasp.4.6.36中，IGPAR=3，输出如下所示：
Berry-Phase term: <R>bp
<R> = (    -0.18037,    -0.18037,     0.00000 ) electrons Angst
     +(     4.51020,     4.51020,     0.00000 ) *c
最后一行的*c中的c是个任意整数。

POSCAR如下：
4.5102
0.0 0.5 0.5
0.5 0.0 0.5
0.5 0.5 0.0
因此：(     4.51020,     4.51020,     0.00000 )=4.5102*(0.5 0.5 0)*2=a3*2
a3*2即为2*e*R/V，berry phase中特有的那个量。

3：我将DIPOL设在0 0 0(一个永远不动的原子上)，Berry phase项正常，但是ion项不正常。
Rion或许可以直接手工计算。
NaF
4.5102
0.0 0.5 0.5
0.5 0.0 0.5
0.5 0.5 0.0
Na F
1 1
Direct
0.0       0.0    0.0
0.5       0.5    0.5
PAW势中显示Na为+9，F为+7。
DIPOL=0.01 0.01 0.01
ionic dipole moment: p[ion]=(   -15.06407   -15.06407   -15.06407 ) e*Angst
（-15.06407 -15.06407 -15.06407)=(0.01*a1+0.01*a2+0.01*a3)*9+(-0.49*a1-0.49*a2-0.49*a3)*7
F的坐标改为 0.51 0.51 0.49后
DIPOL=0.01 0.01 0.01，ionic dipole moment: p[ion]=(-15.06407 -15.06407 -15.37978 ) e*Angst。
(-15.06407 -15.06407 -15.37978 )=(+0.01*a1+0.01*a2+0.01*a3)*9+(-0.5*a1-0.5*a2-0.48*a3)*7
记得自己手工确定一次Rion，以防自己理解错误，切记，切记，切记

开始计算dipole前，必须确定：所有原子从一个构型变到另一个构型下时，
所有原子
在只能在单胞内移动，（这需要
修改坐标原点的位置
），绝不能有跳出单胞边界的原子。

补记：1：电子对dipole的贡献必须跟ion相反，否则就错了(对只移动一个原子的情况是对的，但是对很多原子都移动，就不一定了2011-04-30)。2
：
不考虑自旋的时候，berry-phase的对应的突变时(
2*e*R/V*整数，这个整数可正可负)，考虑自旋后，每个spin的贡献是1*e*R/V*整数。3：最好用4.6.36,它会多输出一行警告。4：必须用经典的born effective charge*displacement的方法手工计算dipole，然后跟berry-phase的方法对比，才能确定(2*e*R/V*整数)中的那个常数。5：必须确保所有原子坐标没有0出现，否则一定将所有原子平移，比如原子坐标加上[0.1 0.1 0.1]。即使加上了[0.1 0.1 0.1]，依然会在berr-phase的最后结果中发现(2*e*R/V*整数)中的整数不等于0；因此必须跟4中的方法对比，以确定这个整数.（2011-03-20）

补记：PRB,48.4442.
http://s15/middle/5f15ead2h765680780afe&690Calculation of Dipole" TITLE="Berry-phase Calculation of Dipole" />
(2011-03-26)

I try to use 4.6.36 calculate berry phase in AFM. However, the berry-phase contribution are not equal between up and down spins. I can not figure it out:(.(2011-04-27)

     I spent almost two days for Berry-phase calculation. Vasp5.2.8 give reasonable results, while vasp4.6.28 and 4.6.36 give unphysical results. Furthermore, results of vasp4 depend on EDIFF and ENCUT. In the end, I find my mistake. I put atom on the origin of unit cell. When I add <0.01 0.01 0.01> to all the atoms, vasp5 and vasp4 give the same results:)
     e<r>_ev and e<r>_bp has nothing to do with DIPOL. Only p[ion] is changed with DIPOL.
     1: Rev is the 'expectation value' term, which comes from the augmentation charge distribution (please see refs 54 and 56 of the online handbook) which is particular to the US-PPs. 
     2:Question:I am trying to do berry phase calculation (LCALCPOL=.TRUE.) combined with HSE06 functional. I got a gap in DOS and a gap, but the program complains it is not insulating. 
In source code, the way it judges if the system is insulating or not is checking the order number of highest occupied eigenvalue. But if we do hybrid functional calculation, the eigenvalues are not listed in the order of from lower energy to high energy. For example, 
97 5.6463 1.00000 
98 5.9726 1.00000 
99 7.2118 1.00000 
100 9.6729 0.00000 
101 7.4302 1.00000 
102 9.3828 0.00000 
103 10.4377 0.00000 
highest occupied eigenvalue is supposed to be 100, however, VASP will take 99 because 100th eigenvalue is not occupied. I think it will work if we sort the order of eigenvalues, but I do not know how to do it right now. Any suggestions? Thanks.
Answer: the reason of this behaviour is that the band indices are not changed during one electronic scf run. the occupancies, the levels are correct 
       3:Question:I was trying to calculate sp. polarization of tetragonal BaTiO3 using vasp 5.2. Therefore, I switched on the LCALCPOL tag, and provided PREC = Med, EDIFF = 1E-6, ISMEAR = 0 and DIPOL = 0.25 0.25 0.25 ( according to the manual) In the OUTCAR file I obtained the following line: 
CALCP: cpu time 221.71: real time 72.93 
Total macroscopic dipole moment: p[mac]=( 0.00000 0.00000 2.58238 ) electrons Angst 
According to the manual I should obtain two lines, one for ionic dipole moment and the other for electronic dipole moment. I am not getting that. can anyone help me sort this out ? 
Answer:I was confused about this question weeks ago and I figure it out now. If you use LCALCPOL tag, you will get only one line (as you got), which is the electronic part of total polarization. To get the total polarization, you need to calculate ionic part by hand, which is not too hard.
 
The following content is obtained from vasp websit.
http://s6/middle/5f15ead2ha2246b2af895&690Calculation of Dipole" TITLE="Berry-phase Calculation of Dipole" />

http://s6/middle/5f15ead2ha2246b3a5485&690Calculation of Dipole" TITLE="Berry-phase Calculation of Dipole" />

http://s6/middle/5f15ead2ha2246fcf8c45&690Calculation of Dipole" TITLE="Berry-phase Calculation of Dipole" />



http://s3/middle/5f15ead2ha2246b680e82&690Calculation of Dipole" TITLE="Berry-phase Calculation of Dipole" />

http://s9/middle/5f15ead2ha2246b775678&690Calculation of Dipole" TITLE="Berry-phase Calculation of Dipole" />

http://s3/middle/5f15ead2ha2246b775d62&690Calculation of Dipole" TITLE="Berry-phase Calculation of Dipole" />

http://s13/middle/5f15ead2ha2246b867e6c&690Calculation of Dipole" TITLE="Berry-phase Calculation of Dipole" />

http://s14/middle/5f15ead2ha2246ba5059d&690Calculation of Dipole" TITLE="Berry-phase Calculation of Dipole" />
 
I use the INCAR:
System = XXX
ISPIN   = 2
MAGMOM = 1*3 1*-3 8*0
ISMEAR = -5
PREC = Medium
DIPOL  = 0.1 0.1 0.1
LCALCPOL = .TRUE.
And get the right result in OUTCAR, which is the same with tranditional LBERRY, IGPAR, NPPSTR, method. 
   LPEAD      =     T    switch on PEAD
   IPEAD      =     4    finite difference order for dpsi/dk
   LCALCPOL   =     T    calculate macroscopic polarization
   LCALCEPS   =     F    calculate dielectric tensor
   EFIELD_PEAD=    0.0000    0.0000    0.0000
   SKIP_EDOTP =     F
   LRPA       =     F
   SKIP_SCF   =     F
            Ionic dipole moment: p[ion]=(    13.47766    13.47766   -14.51603 ) electrons Angst
    Spin resolved dipole moment: p[sp1]=(    -3.82339    -3.82339     4.11796 ) electrons Angst
                                 p[sp2]=(     0.34152     0.34152    -0.36783 ) electrons Angst
 Total electronic dipole moment: p[elc]=(    -3.48186    -3.48186     3.75013 ) electrons Angst
(2011-04-30)

   When I use DIPOL=0.1 0.1 0.1, the dipole of ION is unexpected，although the dipole difference of ION between PE and FE are correct. At this time the dipole of ION is not the VAL*(position-ref). When I change DIPOL to 0.5 0.5 0.5, the dipole of ION is in my understanding. (2011-05-31)

                 http://s15/bmiddle/5f15ead207ac478ff235e&690Calculation of Dipole" TITLE="Berry-phase Calculation of Dipole" />(2012-10-10)


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