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在GW计算过程中考虑DFT+U

已有 10091 次阅读 2014-6-19 10:03 |个人分类:电子结构计算|系统分类:科研笔记

关注：

1）什么情况下需考虑+U

2) 什么情况下需考虑自旋轨道耦合

3）什么情况下需考虑自旋极化作用

4）什么情况下需采用GW或杂化泛函(HSE等)计算

1. Thanks to Huayun,

从你的结果看HSE杂化泛函对能隙附近的能带结构基本没什么效果，GW有些影响但没能产生带隙，其中的原因并不显而易见。

由于XH3属于电荷转移绝缘体，在理想的情况下H上应该有两个1s电子，而X上剩满壳层的[Ar]核。目前看起来没能产生带隙的原因有可能是电荷转移不完全导致，你可以检查一下费米能级附近的电子是不是还属于X。如果X上还残余有d电子，你可以用DFT+U的方法劈裂能隙。

由于XH3中没有高角动量的电子，自旋-轨道耦合我猜测帮助可能不会很大。

要进行自旋-轨道耦合计算，你需要在INCAR中设置LNONCOLLINEAR = T （可能需要重新编译VASP）和 LSORBIT = T，并且去除对称性ISYM = 0。其余的设置与标准的DFT计算没有什么不同。

wannier只是用来分析结果的，其参数不影响具体的计算，GW参数的设置没看出不妥。

究其最终原因，我感觉问题的根源在于电子的自相互作用而非电子间的关联，HSE和GW都不能完全去除电子自相互作用，你可能需要考虑包含100%Hartree-Fock交换能量泛函的方法（例如M06-HF杂化泛函），或者其它SelfInteraction Correction方法。

2.考虑DFT+U后的GW计算脚本

################## step1: a DFT groundstate calculation ###################

cat > INCAR << EOF
ISMEAR = 0
SIGMA = 0.05
GGA = PE
EDIFF = 1E-8

###DFT+U ####

ISPIN=2
LDAU = .TRUE.
LDAUTYPE = 2
LDAUL = -1 2
LDAUU = 0.00 2.10
LDAUJ = 0.0 0.1
LDAUPRINT = 0
LMAXMIX = 4
EOF

# start calculation

$PARA -n $NP -machinefile .nodelists.$$ $EXEC > STDOUT

cp OUTCAR OUTCAR-01
cp STDOUT STDOUT-01

####################################### step 2: obtain DFT virtual orbitals #####################

cat > INCAR << EOF
ISMEAR = 0
SIGMA = 0.05
GGA = PE
EDIFF = 1E-8

ALGO = Exact
NBANDS = 48
LOPTICS = .TRUE.
NEDOS = 2000
# you might try
#LPEAD = .TRUE.

###DFT+U######
ISPIN=2
LDAU = .TRUE.
LDAUTYPE = 2
LDAUL = -1 2
LDAUU = 0.00 2.10
LDAUJ = 0.0 0.1
LDAUPRINT = 0
LMAXMIX = 4
EOF

# start calculation

$PARA -n $NP -machinefile .nodelists.$$ $EXEC > STDOUT

cp WAVECAR WAVECAR.LOPTICS
cp WAVEDER WAVEDER.LOPTICS
cp OUTCAR OUTCAR-02
cp STDOUT STDOUT-02

# #######################step 3: GW + WANNIER90 #################################

cat > INCAR << EOF
ISMEAR = 0
SIGMA = 0.05
GGA = PE
EDIFF = 1E-8

###GW0 calculation####

ALGO = GW0
LSPECTRAL = .TRUE.
NOMEGA = 50
LRPA = .FALSE.

NBANDS = 48

##VASP2WANNIER90
LWANNIER90=.TRUE.

###DFT+U#####

ISPIN=2
LDAU = .TRUE.
LDAUTYPE = 2
LDAUL = -1 2
LDAUU = 0.00 2.10
LDAUJ = 0.0 0.1
LDAUPRINT = 0
LMAXMIX = 4
EOF

# start calculation

$PARA -n $NP -machinefile .nodelists.$$ $EXEC > STDOUT

cp OUTCAR OUTCAR-03
cp STDOUT STDOUT-03
cp WAVECAR WAVECAR-03
cp WAVEDER WAVEDER-03

U值为2时，自旋向上的能带与向下的能带重合，与不加U的能带相比，0eV以上分开处有上下拉开趋向，但不明显

3. 自旋轨道耦合设置

LSORBIT = .TRUE.
ICHARG = 11 ! non selfconsistent run, read CHGCAR
LMAXMIX = 4 ! for d elements increase LMAXMIX to 4, f: LMAXMIX = 6
! you need to set LMAXMIX already in the collinear calculation
SAXIS = x y z ! direction of the magnetic field
NBANDS = 2 * number of bands of collinear run
GGA_COMPAT = .FALSE. ! apply spherical cutoff on gradient field

4. DFT+U介绍

d电子情形

ISPIN=2
LDAU = .TRUE.
LDAUTYPE = 2
LDAUL = -1 2
LDAUU = 0.00 2.10
LDAUJ = 0.0 0.1
LDAUPRINT = 0
LMAXMIX = 4

f电子情形

ISPIN=2
LDAU = .TRUE.
LDAUTYPE = 2
LDAUL = -1 3
LDAUU = 0.00 2.10
LDAUJ = 0.0 0.1
LDAUPRINT = 0
LMAXMIX =6

参数解释：

On site Coulomb interaction: L(S)DA+U

http://cms.mpi.univie.ac.at/vasp/vasp/On_site_Coulomb_interaction_L_S_DA_U.html#6627

LDAU= .TRUE. | .FALSE.

LDAUTYPE= 1 | 2 | 4

LDAUL= [0 | 1 | 2 | 3 array] LDAUU= [real array] LDAUJ= [real array]

LDAUPRINT= 0 | 1 | 2

Defaults:
LDAU	= .FALSE.
LDAUTYPE	= 2
LDAUPRINT	= 0

The L(S)DA often fails to describe systems with localized (strongly correlated) and electrons (this manifests itself primarily in the form of unrealistic one-electron energies).

In some cases this can be remedied by introducing a strong intra-atomic interaction in a (screened) Hartree-Fock like manner, as an on site replacement of the L(S)DA.

(1) This approach is commonly known as the L(S)DA+U method.
Setting LDAU=.TRUE. in the INCAR file switches on the L(S)DA+U.

By means of the LDAUTYPE-tag on specifies which type of L(S)DA+U approach will be used:

(2) LDAUTYPE=2 (Default):

The simplified (rotationally invariant) approach to the LSDA+U, introduced by Dudarev et al. [91]. This flavour of LSDA+U is of the following form:

Note: in Dudarev's approach the parameters and do not enter seperately, only the difference is meaningfull.

(3) LDAUL= ...

specifies the -quantum number (one number for each species) for which the on-site interaction is added.
(-1=no on-site terms added, 1= p, 2= d, 3= f, Default: LDAUL=2)

(4) LDAUU= ...

specifies the effective on-site Coulomb interaction parameters.

(5) LDAUJ= ... specifies the effective on-site Exchange interaction parameters.

NB: LDAUL, LDAUU, and LDAUJ must be specified for all atomic species! 【原子种类，不是每个原子】

(6) LDAUPRINT= 0 | 1 | 2 Controls the verbosity of the L(S)DA+U module.
(0: silent,

1: Write occupancy matrix to OUTCAR, 2: idem 1., plus potential matrix dumped to stdout, Default: LDAUPRINT=0)

It is important to be aware of the fact that when using the L(S)DA+U, in general the total energy will depend on the parameters and . It is therefore not meaningful to compare the total energies resulting from calculations with different and/or (c.q. in case of Dudarev's approach).

Furthermore, since LDA+U usually results in aspherical charge densities at and atoms we recommend to set LASPH = .TRUE. in the INCAR file for gradient corrected functionals (see Sec. 6.44).

For CeO for instance, identical results to the FLAPW methods can be only obtained setting LASPH = .TRUE.

(7)Note on bandstructure calculation: The CHGCAR file also contains only information up to LMAXMIX (defaulted to 2) for the on-site PAW occupancy matrices.

When the CHGCAR file is read and kept fixed in the course of the calculations (ICHARG=11), the results will be necessarily not identical to a selfconsistent run.

The deviations can be (or actually are) large for L(S)DA+U calculations.

For the calculation of band structures within the L(S)DA+U approach, it is hence strictly required to increase LMAXMIX to 4 (d elements) and 6 (f elements). (see Sec. 6.63).

If ICHARG is set to 11 or 12, it is strongly recommened to set LMAXMIX to twice the maximum l-quantum number in the pseudpotentials. Thus for s and p elements LMAXMIX should be set to 2, for d elements LMAXMIX should be set to 4, and for f elements LMAXMIX should be set to 6 (see section 6.63).

参考

PAW control tags

http://cms.mpi.univie.ac.at/vasp/vasp/PAW_control_tags.html#5802

In principle, the PAW method can be used in the same manner as the US-PP method. Only special PAW POTCAR files are required. In principle, also no additional user interference is required.

However there are a few flags that control the behavior of the PAW implementation. The first one is LMAXPAW: LMAXPAW = L

This flag sets the maximum -quantum number for the evaluation of the on-site terms on the radial support grids in the PAW method. The default for LMAXPAW is $2*l_{max}$ , where $l_{max}$ is the maximum angular quantum number of the partial waves.