How to generate a pseudopotential

Transcription

How to generate a
pseudopotential
1
40
AE wfn l=0
PS wfn l=0
0.8
0.6
0
0.4
-20
0.2
-40
0
-60
-0.2
-80
-0.4
0
0.5
1
0
1.5
2
2.5
3
AE logder l=0
PS logder l=0
20
3.5
4
-100
-3.5 -3 -2.5 -2 -1.5 -1 -0.5
0.6
l=0 Pseudopot r
0.5
1
l=0 Pseudopot q
0.4
-2
0
0.2
-4
0
-6
-0.2
-8
-0.4
-10
-0.6
-12
-14
-0.8
0
0.5
1
1.5
2
2.5
3
3.5
4
-1
0
5
10
15
20
Objectives
Generate a norm-conserving pseudopotential using ATOM
Description of the input file of the ATOM code for a
pseudopotential generation
A title for the job
N 1s2
2s2 2p3 3d0 4f0
pg ≡ PseudopotentialI. generation
ENERGY FUNCTIONAL FOR A DIELECTRIC INSIDE AN ELECTRIC FIELD.
core
Chemical
symbol of the
atom
Principal
quantum
number
pg
n=N
1
2
2
3
4
Nitrogen
tm2 2.0
c=ca
0.0
0.0
4
0
2.00
1
3.00
2
0.00
3
0.00
1.15
1.15
Angular
quantum
number
Cutoff radii for the
Occupation
different shells
(in bohrs)
(spin up)
(spin down)
0.0
0.0
0.00
0.00
0.00
0.00
1.15
1.50
0.0
0.0
valence
Number of core
and valence
orbitals
Exchange-and correlation functional
ca ≡ Ceperley-Alder (LDA)
wi ≡ Wigner (LDA)
hl ≡ Hedin-Lundqvist (LDA)
bh ≡ von-Barth-Hedin (LDA)
gl ≡ Gunnarson-Lundqvist (LDA)
pb ≡ Perdew-Burke-Ernzerhof, PBE (GGA)
rv ≡ revPBE (GGA)
rp ≡ RPBE, Hammer, Hansen, Norvskov (GGA)
ps ≡ PBEsol (GGA)
wc ≡ Wu-Cohen (GGA)
+s if spin (no relativistic)
+r if relativistic
bl ≡ BLYP Becke-Lee-Yang-Parr (GGA)
am≡ AM05 by Armiento and Mattson (GGA)
vw ≡ van der Waals functional
How to run a pseudopotential generation with ATOM
2
I.
$ ../../Utils/pg.sh N.tm2.inp
==> Output data in directory N.tm2
==> Pseudopotential in N.tm2.vps and N.tm2.psf (and maybe in N.tm2.xml)
$ ls
N.test.inp N.tm2.inp N.tm2.vps
N.tm2 N.tm2.psf N.tm2.xml
$ cd N.tm2
$ ls
AECHARGE INP PSPOTR1 RHO pots.gplot
AELOGD0 OUT PSPOTR2 SCRPSPOTR0 pots.gps
AELOGD1 PSCHARGE PSPOTR3 SCRPSPOTR1 pseudo.gplot
AELOGD2 PSLOGD0 PSWFFMT SCRPSPOTR2 pseudo.gps
AELOGD3 PSLOGD1 PSWFNQ0 SCRPSPOTR3 scrpots.gplot
AEWFNR0 PSLOGD2 PSWFNQ1 VPSFMT scrpots.gps
AEWFNR1 PSLOGD3 PSWFNQ2 VPSOUT subps.gplot
AEWFNR2 PSPOTQ0 PSWFNQ3 VPSXML subps.gps
AEWFNR3 PSPOTQ1 PSWFNR0 charge.gplot vcharge.gplot
CHARGE PSPOTQ2 PSWFNR1 charge.gps vcharge.gps
FOURIER_AREA PSPOTQ3 PSWFNR2 coreq.gplot vspin.gplot
FOURIER_QMAX PSPOTR0 PSWFNR3 coreq.gps vspin.gps
$
Run the script
The pseudopotentials will
be on the same parent
directory:
.vps (unformatted)
.psf (formatted)
.xml (in XML format)
Different output files in a
new directory (same
name as the input file
without the .inp
extension)
An explanation of the different files can be
found in the ATOM User’s Guide (page 6)
Plotting the all electron and pseudo charge densities
$ gnuplot –persist charge.gplot
(To generate a figure on the screen using gnuplot)
$ gnuplot charge.gps
(To generate a postscript file with the figure)
The core and the charge densities are angularly integrated (multiplied by
Charge densities (electrons/bohr)
7
The PS and AE valence
charge densities are
equal beyond the cutoff
radii
AE core charge
AE valence charge
PS core charge
PS valence charge
6
)
5
Small peak in the AE
valence charge density
due to orthogonality with
AE core
4
3
2
1
0
0
0.5
1
1.5
r (bohr)
2
2.5
3
Plotting the all pseudopotenial information
$ gnuplot –persist pseudo.gplot
$ gnuplot pseudo.gps
1
40
AE wfn l=0
PS wfn l=0
0.8
0.6
0
0.4
-20
0.2
-40
0
-60
AE and PS
wavefunctions
-0.2
-0.4
0
0.5
1
0
1.5
2
2.5
3
AE logder l=0
PS logder l=0
20
AE and PS logarithmic
derivatives
-80
3.5
4
-100
-3.5 -3 -2.5 -2 -1.5 -1 -0.5
0.6
l=0 Pseudopot r
0.5
1
l=0 Pseudopot q
0.4
-2
0
0.2
-4
The more Fourier
components, the
harder the
pseudopotential
0
-6
-0.2
-8
-0.4
Real space
pseudopotential
-10
-12
Fourier transformed
pseudopotential
-0.6
-0.8
-14
-1
0
0.5
1
1.5
2
2.5
3
3.5
4
0
5
10
15
20
A figure like this for each angular momentum shell in the valence
Plotting the real-space pseudopotentials
$ gnuplot –persist pots.gplot
$ gnuplot pots.gps
0
Vs
Vp
Vd
Vf
Pseudopotential (Ry)
-5
-10
Beyond the largest cutoff
radius, the pseudopotential
-15
-20
tends to
-25
-30
-35
0
0.5
1
1.5
2
r (bohr)
2.5
3
3.5
4
Plotting the unscreened and screened pseudopoten
$ gnuplot –persist scrpots.gplot
$ gnuplot scrpots.gps
4
0
Vs
Vs(scr)
2
0
-10
Pseudopotential (Ry)
-2
-4
-15
-6
-20
-8
-25
-10
-30
-12
-14
Vp
Vp(scr)
-5
0
2
4
0
6
8
10
0
2
4
0
Vd
Vd(scr)
-5
-35
6
8
10
8
10
Vf
Vf(scr)
-2
-4
-6
-10
-8
-10
-15
-12
-14
-20
-16
-25
0
2
4
6
8
10
-18
r (bohr)
0
2
4
6
Exploring the output file
$ vi OUT
2
I.
ATM Version 3.3 (2008/09/13)
ATM3.3
28-MAR-12
Nitrogen
------------------------------------------------------------
&v&d
N pseudopotential generation
----------------------------correlation = ca
nonspin-polarized
nuclear charge
number of core orbitals
number of valence orbitals
electronic charge
ionic charge
=
=
=
=
=
7.000000
1
4
7.000000
0.000000
$ grep ’&v’ OUT
ATM3.3
28-MAR-12
Nitrogen
2s
0.0
2.0000
-1.35223895
2p
0.0
3.0000
-0.53262229
3d
0.0
0.0000
0.00000000
4f
0.0
0.0000
0.00000000
---------------------------- &v
2s
0.0
2.0000
-1.35223253
2p
0.0
3.0000
-0.53261661
3d
0.0
0.0000
0.00000000
4f
0.0
0.0000
0.00000000
---------------------------- &v
4.72576386
3.67454481
0.00142446
0.00246771
-15.36854475
-13.16757601
-0.13826878
-0.13367744
1.17006869
3.50294491
0.00142446
0.00246771
-8.02041578
-9.33629169
-0.09876341
-0.09548389
&v&d
&v
&v
&v
&v
&v
&v
&v
&v
ATM Version 3.3 (2008/09/13)
ATM3.3
28-MAR-12
Nitrogen
------------------------------------------------------------
Comparing AE and PS eigenvalues
N pseudopotential generation
$ grep
----------------------------correlation = ca
&v&d
‘&v’ OUT
nonspin-polarized
nuclear charge
number of core orbitals
number of valence orbitals
electronic charge
ionic charge
=
=
=
=
7.000000
1
4
7.000000
$ grep ’&v’ OUT
ATM3.3
28-MAR-12
Nitrogen
2s
0.0
2.0000
-1.35223895
2p
0.0
3.0000
-0.53262229
3d
0.0
0.0000
0.00000000
4f
0.0
0.0000
0.00000000
---------------------------- &v
2s
0.0
2.0000
-1.35223253
2p
0.0
3.0000
-0.53261661
3d
0.0
0.0000
0.00000000
4f
0.0
0.0000
0.00000000
---------------------------- &v
Eigenvalues (in Ry)
4.72576386
3.67454481
0.00142446
0.00246771
-15.36854475
-13.16757601
-0.13826878
-0.13367744
1.17006869
3.50294491
0.00142446
0.00246771
-8.02041578
-9.33629169
-0.09876341
-0.09548389
&v&d
&v
&v
&v
&v
&v
&v
&v
&v
The AE and PS eigenvalues are not exactly identical because the
pseudopotentials are changed slightly to make them approach their limit tails
faster
I.
Cite1,2 .
If the cutoff radii are negative
un!k (!r ) =
!
!
!
!
cnµ (!k)eik·(!rµ +R−!r) φµ (!r − !rµ − R),
(1)
!
Rµ
pe
No semicore
tm2
Ti
pb
0.000
0.000
0.000
0.000
0.000
0.000
5
4
4
0
2.000
0.000
#4s
4
1
0.000
0.000
#4p
ENERGY FUNCTIONAL
INSIDE #3d
AN ELECTRIC FIELD.
3 FOR
2 A DIELECTRIC
2.000
0.000
4
3
0.000
0.000
#4f
-1.20
-1.20000 -1.30000
2.48000
1.00000 -1.00000
#23456789012345678901234567890123456789012345678901234567890
!
! r)
i!
k·(!
+R−!
!
nr )==4 lcnµ
= (0!k)es
=rµ0.0
un!k (!
φµ (!r − !rµ − R),
a
extr
0.087
-0.154
0.259 -0.585
!
Rµ
r extr
0.035
0.220
0.752
2.943
No semicore
r zero
0.092
0.393
1.252
r 90/99 %
5.320
7.740
Cite1,2 .
pe
tm2
Ti
pb
0.000
0.000
0.000
0.000
0.000
0.000
5
4
4
0
2.000
0.000
#4s
4
1
0.000
0.000
#4p
3
2
2.000
0.000
#3d
4
3
0.000
0.000
#4f
-1.20
-1.20000 -1.30000
2.48000
1.00000 -1.00000
I. ENERGY FUNCTIONAL FOR A
#23456789012345678901234567890123456789012345678901234567890
In the OUT file,
these radii are written in
n = 4
l = 0
Citea1,2extr
.
r extr
r zero
r 90/99 %
-0.154
0.220
0.393
7.740
0.259
0.752
1.252
un!k (!r ) =
= 0 s = 0.0
extr
0.087
extr
0.035
zero
0.092
position of the last node: 1.252 Bohr
-0,2
0,0
-0.154
0.220
0.393
0.259
0.752
1.252
-0.585
2.943
(1)
2
rc set to 3.28
Core radius ( 3.28) outside wfn extremum ( 2.94)
l
a
r
r
0,2
!
!
!
cnµ (!k)eik·(!rµ +R−!r) φµ (!r −0,0
!rµ − R),
!
Rµ
n = 4
0,4
DIELECTRIC
INSIDE AN ELECTRIC FIELD.
Ruler
-0.585
2.943
!
(1)
position of the last peak: 2.943 Bohr
s = 0.0
0.087
0.035
0.092
5.320
Ruler
0,6
radial part of the 4s orbital
I.
10,0
5,0
15,0
distance to nuclei (Bohr)
20,0

How to generate a pseudopotential

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