1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
<!--Converted with LaTeX2HTML 2019.2 (Released June 5, 2019) -->
<HTML lang="EN">
<HEAD>
<TITLE>3.1 Single-projector, norm-conserving, no semicore</TITLE>
<META NAME="description" CONTENT="3.1 Single-projector, norm-conserving, no semicore">
<META NAME="keywords" CONTENT="pseudo-gen">
<META NAME="resource-type" CONTENT="document">
<META NAME="distribution" CONTENT="global">
<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=utf-8">
<META NAME="viewport" CONTENT="width=device-width, initial-scale=1.0">
<META NAME="Generator" CONTENT="LaTeX2HTML v2019.2">
<LINK REL="STYLESHEET" HREF="pseudo-gen.css">
<LINK REL="next" HREF="node13.html">
<LINK REL="previous" HREF="node11.html">
<LINK REL="next" HREF="node13.html">
</HEAD>
<BODY >
<!--Navigation Panel-->
<A
HREF="node13.html">
<IMG WIDTH="37" HEIGHT="24" ALT="next" SRC="next.png"></A>
<A
HREF="node11.html">
<IMG WIDTH="26" HEIGHT="24" ALT="up" SRC="up.png"></A>
<A
HREF="node11.html">
<IMG WIDTH="63" HEIGHT="24" ALT="previous" SRC="prev.png"></A>
<A ID="tex2html114"
HREF="node1.html">
<IMG WIDTH="65" HEIGHT="24" ALT="contents" SRC="contents.png"></A>
<BR>
<B> Next:</B> <A
HREF="node13.html">3.2 Single-projector, norm-conserving, with</A>
<B> Up:</B> <A
HREF="node11.html">3 A worked example:</A>
<B> Previous:</B> <A
HREF="node11.html">3 A worked example:</A>
<B> <A ID="tex2html115"
HREF="node1.html">Contents</A></B>
<BR>
<BR>
<!--End of Navigation Panel-->
<!--Table of Child-Links-->
<A ID="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
<UL>
<LI><A ID="tex2html116"
HREF="node12.html#SECTION00041100000000000000">3.1.1 Generation</A>
<LI><A ID="tex2html117"
HREF="node12.html#SECTION00041200000000000000">3.1.2 Testing</A>
</UL>
<!--End of Table of Child-Links-->
<HR>
<H2><A ID="SECTION00041000000000000000">
3.1 Single-projector, norm-conserving, no semicore</A>
</H2>
<P>
<H3><A ID="SECTION00041100000000000000">
3.1.1 Generation</A>
</H3><EM>
Let us start from the simplest case with the following input:
</EM><PRE>
&input
atom='Ti', dft='PBE', config='[Ar] 3d2 4s2 4p0',
rlderiv=2.90, eminld=-2.0, emaxld=2.0, deld=0.01, nld=3,
iswitch=3
/
&inputp
pseudotype=1, nlcc=.true., lloc=1,
file_pseudopw='Ti.pbe-n-rrkj.UPF'
/
3
4S 1 0 2.00 0.00 2.9 2.9
3D 3 2 2.00 0.00 1.3 1.3
4P 2 1 0.00 0.00 2.9 2.9
</PRE><EM>
In the <TT>&input</TT> namelist,
we specify the we want to generate a PP (<TT>iswitch=3</TT>) and to
calculate <TT>nld=3</TT> logarithmic derivatives at <TT>rlderiv=2.90</TT> a.u.
from the origin, in the energy range <TT>eminld=-2.0</TT> Ry to
<TT>emaxld=2.0</TT> Ry, in energy steps <TT>deld=0.01</TT> Ry
(note that these values will not affect PP generation).
In the <TT>&inputp</TT> namelist, we specify the we want a single-projector,
NC-PP (<TT>pseudotype=1</TT>), with nonlinear core correction
(<TT>nlcc=.true.</TT>), using the <I>l</I> = 1 channel as local (<TT>lloc=1</TT>).
The output PP will be written in UPF format to file <TT>Ti.pbe-n-rrkj.UPF</TT>
(following the <SMALL>QUANTUM </SMALL>ESPRESSO convention for PP names).
Following the two namelists, there is a list of states used for pseudization:
the 4S state, with pseudization radius <I>r</I><SUB>c</SUB> = 2.9 a.u.; the 3D state,
<I>r</I><SUB>c</SUB> = 1.3 a.u.; the 4P, <I>r</I><SUB>c</SUB> = 2.9 a.u., listed as last because it is
the channel to be chosen as local potential.
</EM>
<P>
<EM>There is nothing magic or especially deep in the choice of the radius
and energy range for logarithmic derivatives, of the local
potential and of pseudization radii: it is just a reasonable guess.
Running the input, one gets an error:
</EM><PRE>
Wfc 4S rcut= 2.883 Estimated cut-off energy= 14.82 Ry
l= 0 Node at 0.71997236
This function has 1 nodes for 0 < r < 2.883
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
from compute_phi : error # 1
phi has nodes before r_c
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
</PRE><EM>
This means that the 4S pseudized orbitals has one node. With RRKJ
pseudization (the default), this may occasionally happen. One can
either choose TM pseudization (<TT>tm=.true.</TT>) or set a small
value of <I>ρ</I>(<I>r</I> = 0) (e.g. <TT>rho0=0.001</TT>). Let us do the latter.
You should carefully look at the output, which will consists in
an all-electron calculation, followed by the pseudopotential generation
step, followed by a final test. In particular, notice this message
about the nonlinear core correction:
</EM><PRE>
Computing core charge for nlcc:
r > 1.73 : true rho core
r < 1.73 : rho core = a sin(br)/r a= 2.40 b= 1.56
Integrated core pseudo-charge : 3.43
</PRE><EM>
(this is actually not an ideal situation: the pseudization radius for the
charge density should be smaller than all pseudization radii; in our
case, smaller than <!-- MATH
$r_c^{(min)} = r_c^{(l=2)}=1.3$
-->
<I>r</I><SUB>c</SUB><SUP>(min)</SUP> = <I>r</I><SUB>c</SUB><SUP>(l=2)</SUP> = 1.3 a.u.).
Also notice messages on pseudization:
</EM><PRE>
Wfc 4S rcut= 2.883 Estimated cut-off energy= 5.32 Ry
Using 4 Bessel functions for this wfc, rho(0) = 0.001
This function has 0 nodes for 0 < r < 2.883
Wfc 3D rcut= 1.296 Estimated cut-off energy= 137.82 Ry
This function has 0 nodes for 0 < r < 1.296
</PRE><EM>
(note the large difference between the estimated cutoff for the <I>s</I> and
the <I>d</I> channel! Of course, it is only the latter the ``problem'' one
here); and look at the final consistency check:
</EM><PRE>
n l nl e AE (Ry) e PS (Ry) De AE-PS (Ry)
1 0 4S 1( 2.00) -0.32830 -0.32830 0.00000
3 2 3D 1( 2.00) -0.31302 -0.31302 0.00000
2 1 4P 1( 0.00) -0.10777 -0.10777 0.00000
</PRE><EM>
You should get exactly 0 (within numerical accuracy) in the columnn
at the right.
</EM>
<P>
<EM>As a further check, let's have a look at the logaritmic derivatives
and at pseudized Kohn-Sham orbitals. Logarithmic derivatives are written
to files <TT>ld1.dlog</TT> and <TT>ld1ps.dlog</TT>, for AE and PS
calculations respectively (file names can be changed using variable
<TT>prefix</TT>). They can be plotted using for instance
<TT>gnuplot</TT> and the following commands:
</EM><PRE>
plot [-2:2][-20:20] 'ld1.dlog' u 1:2 w l lt 1, 'ld1.dlog' u 1:3 w l lt 2,\
'ld1.dlog' u 1:4 w l lt 3, 'ld1ps.dlog' u 1:2 lt 1, \
'ld1ps.dlog' u 1:3 lt 2, 'ld1ps.dlog' u 1:4 lt 3
</PRE><EM>
PS orbitals and the corresponding AE ones are written to file
<TT>ld1ps.wfc</TT> (PS on the left, AE on the right). They can be
plotted using the following commands:
</EM><PRE>
plot [0:5] 'ld1ps.wfc' u 1:2 lt 1 , 'ld1ps.wfc' u 1:3 lt 3 , \
'ld1ps.wfc' u 1:4 lt 2 , 'ld1ps.wfc' u 1:5 lt 1 w l, \
'ld1ps.wfc' u 1:6 lt 3 w l, 'ld1ps.wfc' u 1:7 lt 2 w l
</PRE><EM>
One gets the following plots (AE=lines, PS=points;
<TT>lt 1</TT>=red=<I>s</I>; <TT>lt 2</TT>=green=<I>p</I>; <TT>lt 3</TT>=blue=<I>d</I>;
note that in the files, orbitals are ordered as given in input,
logarithmic derivatives as <I>s</I>, <I>p</I>, <I>d</I>).
</EM>
<P>
<EM><IMG STYLE=""
SRC="img2.png"
ALT="\includegraphics[width=7.5cm]{pseudo-gen-fig1.pdf}">
<IMG STYLE=""
SRC="img3.png"
ALT="\includegraphics[width=7.5cm]{pseudo-gen-fig2.pdf}">
</EM>
<P>
<EM>We observe that our PP seems to reproduce fairly well
the logarithmic derivatives, with deviations appearing only at
relatively high (> 1 Ry) energies. AE and PS orbitals match
very well beyond the pseudization radii; the 3<I>d</I> orbital is
slightly deformed, because we have chosen a relatively large
<!-- MATH
$r_c^{(l=2)}=1.3$
-->
<I>r</I><SUB>c</SUB><SUP>(l=2)</SUP> = 1.3 a.u.. It is easy to verify that a smaller
<!-- MATH
$r_c^{(l=2)}$
-->
<I>r</I><SUB>c</SUB><SUP>(l=2)</SUP> yields a better 3<I>d</I> PS orbital, but also a harder
<I>d</I> potential: e.g., for <!-- MATH
$r_c^{(l=2)}=1.0$
-->
<I>r</I><SUB>c</SUB><SUP>(l=2)</SUP> = 1.0 a.u., you get
</EM><PRE>
Wfc 3D rcut= 1.009 Estimated cut-off energy= 225.64 Ry
</PRE><EM>
Before proceding, it is wise to verify whether our PP has ``ghosts''.
Let us prepare the following input for the testing phase
(note the variable <TT>iswitch=2</TT> and the <TT>&test</TT>
namelist):
</EM><PRE>
&input
atom='Ti', dft='PBE', config='[Ar] 3d2 4s2 4p0',
iswitch=2
/
&test
file_pseudo='Ti.pbe-n-rrkj.UPF',
nconf=1, configts(1)='3d2 4s2 4p0',
ecutmin=50, ecutmax=200, decut=50
/
</PRE><EM>
This will solve the Kohn-Sham equation for the PP read from
<TT>file_pseudo</TT>, for a single valence configuration
(<TT>nconf=1</TT>) listed in <TT>configts(1)</TT> (the ground state
in this case), using a base of spherical waves whose cutoff
(in Ry) ranges from <TT>ecutmin</TT> to <TT>ecutmax</TT> in steps of
<TT>decut</TT>. The initial part of the output looks good, but let us
look at the test with spherical waves, towards the end:
</EM><PRE>
Cutoff (Ry) : 200.0
N = 1 N = 2 N = 3
E(L=0) = -0.7483 Ry -0.3282 Ry -0.0042 Ry
E(L=1) = -0.1077 Ry 0.0192 Ry 0.0630 Ry
E(L=2) = -0.2961 Ry 0.0304 Ry 0.0654 Ry
</PRE><EM>
The lowest levels found in this way should be the same<A ID="tex2html1"
HREF="footnode.html#foot201"><SUP>1</SUP></A>
as those calculated from radial integration (see above).
This is true for the 4<I>p</I> state (-0.1077 Ry),
for the 3<I>d</I> state (-0.2961 Ry vs -0.31302 Ry, see footnote),
for the 4<I>s</I> state (-0.3282 Ry)....but note the spurious 4<I>s</I>
level at -0.7483 Ry! Our PP has a ghost and is unusable.
</EM>
<P>
<EM>What should be do now? we may try to change the definition of the
local potential. We had chosen <I>l</I> = 1, let us try <I>l</I> = 2 and <I>l</I> = 0.
The former has the same pathology, the latter has no ghosts.
So our data for PP generation are as follows:
</EM><PRE>
&input
atom='Ti', dft='PBE', config='[Ar] 3d2 4s2 4p0',
rlderiv=2.90, eminld=-2.0, emaxld=2.0, deld=0.01, nld=3,
iswitch=3
/
&inputp
pseudotype=1, nlcc=.true., lloc=0,
file_pseudopw='Ti.pbe-n-rrkj.UPF',
/
3
4P 2 1 0.00 0.00 2.9 2.9
3D 3 2 2.00 0.00 1.3 1.3
4S 1 0 2.00 0.00 2.9 2.9
</PRE><EM>
(note <TT>lloc=0</TT> and the 4<I>s</I> state at the end of the list).
Let us plot again logarithmic derivatives and orbitals (they look
quite the same as before) and run again the test with spherical
waves. We get (see the last section in the output):
</EM><PRE>
Cutoff (Ry) : 50.0
N = 1 N = 2 N = 3
E(L=0) = -0.3282 Ry -0.0049 Ry 0.0361 Ry
E(L=1) = -0.1077 Ry 0.0192 Ry 0.0630 Ry
E(L=2) = -0.1469 Ry 0.0311 Ry 0.0682 Ry
Cutoff (Ry) : 100.0
N = 1 N = 2 N = 3
E(L=0) = -0.3282 Ry -0.0049 Ry 0.0361 Ry
E(L=1) = -0.1077 Ry 0.0192 Ry 0.0630 Ry
E(L=2) = -0.2959 Ry 0.0303 Ry 0.0652 Ry
Cutoff (Ry) : 150.0
N = 1 N = 2 N = 3
E(L=0) = -0.3282 Ry -0.0049 Ry 0.0361 Ry
E(L=1) = -0.1077 Ry 0.0192 Ry 0.0630 Ry
E(L=2) = -0.2961 Ry 0.0303 Ry 0.0652 Ry
</PRE><EM>
This time the first column yields (with a small discrepancy for 3<I>d</I>)
the expected levels, and only those levels. It is wise to inspect
the second column as well for absence of suspiciously low levels:
ghosts may appear also as spurious excited states close to occupied
states. Note how bad the energy for the 3<I>d</I> level is at 50 Ry.
At 100 Ry however we are close to convergence and at 150 Ry
well converged, in agreement with the estimate given during
the PP generation (138 Ry).
</EM>
<P>
<EM>We have now our first candidate (i.e. not surely wrong) PP.
In order to 1) verify if it really does the job, 2) quantify
its transferability, 3) quantify its hardness, and 4) improve
it, if possible, we need to perform some more testing.
</EM>
<P>
<H3><A ID="SECTION00041200000000000000">
3.1.2 Testing</A>
</H3>
<P>
<EM>As a first idea of how good our PP is, let us verify how it
behaves on differente electronic configuration. The code
allows to test several configurations in the following way:
</EM><PRE>
&input
atom='Ti', dft='PBE', config='[Ar] 3d2 4s2 4p0',
iswitch=2
/
&test
file_pseudo='Ti.pbe-n-rrkj.UPF',
nconf=9
configts(1)='3d2 4s2 4p0'
configts(2)='3d2 4s1 4p1'
configts(3)='3d2 4s1 4p0'
configts(4)='3d2 4s0 4p0'
configts(5)='3d1 4s2 4p1'
configts(6)='3d1 4s2 4p0'
configts(7)='3d1 4s1 4p0'
configts(8)='3d1 4s0 4p0'
configts(9)='3d0 4s0 4p0'
/
</PRE><EM>
here we have chosen 9 different valence configurations
(the corresponding AE configurations are obtained by
superimposing <TT>configts</TT> to core states in <TT>config</TT>).
Some of them are neutral, some are ionic, the first five leave
the 3<I>d</I> states unchanged, the last one is a completely ionized
Ti<SUP>4+</SUP>. For each configuration, the code writes results
(e.g. orbitals) into files <TT>ld1</TT><I>N</I>.* and <TT>ld1ps</TT><I>N</I>.*,
where <I>N</I> is the index of the configuration. A summary is written to
file <TT>ld1.test</TT>. For the first configuration, AE and PS
eigenvalues and total energies are written:
</EM><PRE>
3 2 3D 1( 2.00) -0.31302 -0.31302 0.00000
1 0 4S 1( 2.00) -0.32830 -0.32830 0.00000
2 1 4P 1( 0.00) -0.10777 -0.10777 0.00000
Etot = -1707.131006 Ry, -853.565503 Ha, -23226.698556 eV
Etotps = -9.748745 Ry, -4.874372 Ha, -132.638416 eV
</PRE><EM>
(AE and PS eigenvalues are in this case the same, since this is the
reference configuration used to build the PP). For the following
configurations, AE and PS eigenvalues, plus total energy
<EM>differences</EM><A ID="tex2html2"
HREF="footnode.html#foot219"><SUP>2</SUP></A>wrt configuration 1 are printed:
</EM><PRE>
3 2 3D 1( 2.00) -0.40319 -0.40457 0.00138
1 0 4S 1( 1.00) -0.38394 -0.38420 0.00026
2 1 4P 1( 1.00) -0.15248 -0.15237 -0.00011
dEtot_ae = 0.226061 Ry
dEtot_ps = 0.226250 Ry, Delta E= -0.000189 Ry
</PRE><EM>
The discrepancy between AE and PS energy differences (in this case,
wrt the ground state) as well as the discrepancies in AE and PS
eigenvalues, are a measure of how transferrable a PP is. In this case,
the AE-PS discrepancy on <!-- MATH
$\delta E = E(4s^14p^13d^2) - E(4s^24p^03d^2)$
-->
<I>δE</I> = <I>E</I>(4<I>s</I><SUP>1</SUP>4<I>p</I><SUP>1</SUP>3<I>d</I><SUP>2</SUP>) - <I>E</I>(4<I>s</I><SUP>2</SUP>4<I>p</I><SUP>0</SUP>3<I>d</I><SUP>2</SUP>)
(look at <TT>Delta E</TT>) is quite small, < 0.2 mRy, while the
maximum discrepancy of the eigenvalues (rightmost column) ∼1 mRy.
These are very good results.
Unfortunately this is also a configuration that doesn't differ much
from the reference one. Let us see the other cases:
</EM><PRE>
3 2 3D 1( 2.00) -0.83550 -0.83256 -0.00295
1 0 4S 1( 1.00) -0.76075 -0.76163 0.00088
2 1 4P 1( 0.00) -0.48549 -0.48617 0.00068
dEtot_ae = 0.539968 Ry
dEtot_ps = 0.540344 Ry, Delta E= -0.000376 Ry
3 2 3D 1( 2.00) -1.44648 -1.44538 -0.00110
1 0 4S 1( 0.00) -1.24186 -1.24652 0.00465
2 1 4P 1( 0.00) -0.91224 -0.91599 0.00375
dEtot_ae = 1.537516 Ry
dEtot_ps = 1.540285 Ry, Delta E= -0.002769 Ry
3 2 3D 1( 1.00) -0.68514 -0.74236 0.05722
1 0 4S 1( 2.00) -0.45729 -0.45802 0.00073
2 1 4P 1( 1.00) -0.18855 -0.18471 -0.00383
dEtot_ae = 0.343391 Ry
dEtot_ps = 0.371650 Ry, Delta E= -0.028259 Ry
3 2 3D 1( 1.00) -1.16621 -1.21438 0.04817
1 0 4S 1( 2.00) -0.87720 -0.87620 -0.00100
2 1 4P 1( 0.00) -0.56807 -0.56137 -0.00670
dEtot_ae = 0.716203 Ry
dEtot_ps = 0.739110 Ry, Delta E= -0.022907 Ry
3 2 3D 1( 1.00) -1.82248 -1.87471 0.05223
1 0 4S 1( 1.00) -1.39447 -1.39936 0.00489
2 1 4P 1( 0.00) -1.03942 -1.03465 -0.00476
dEtot_ae = 1.848995 Ry
dEtot_ps = 1.873240 Ry, Delta E= -0.024245 Ry
3 2 3D 1( 1.00) -2.54976 -2.61959 0.06983
1 0 4S 1( 0.00) -1.94361 -1.96745 0.02383
2 1 4P 1( 0.00) -1.53584 -1.54419 0.00835
dEtot_ae = 3.518170 Ry
dEtot_ps = 3.554733 Ry, Delta E= -0.036564 Ry
3 2 3D 1( 0.00) -3.84145 -3.95251 0.11106
1 0 4S 1( 0.00) -2.73793 -2.81405 0.07612
2 1 4P 1( 0.00) -2.25938 -2.28768 0.02831
dEtot_ae = 6.699594 Ry
dEtot_ps = 6.831938 Ry, Delta E= -0.132344 Ry
</PRE><EM>
It is evident that configurations with 3<I>d</I><SUP>2</SUP> occupancy are well
reproduced, with errors on total energy differences < 3 mRy and
on eigenvalues< 5 mRy. Configurations with different 3<I>d</I> occupancy,
however, have errors one order of magnitude higher. For the extreme
case of Ti<SUP>4+</SUP>, the error is ∼ 0.1 Ry.
</EM>
<P>
<EM>In order to better understand what is going on, let us have a
look at the AE vs PS orbitals and logarithmic derivatives for
configuration 9 (i.e. for the bare PP). Let us add a line
like this:
</EM><PRE>
rlderiv=2.90, eminld=-4.0, emaxld=0.0, deld=0.01, nld=3,
</PRE><EM>
and plot files <TT>ld19ps.wfc</TT>, <TT>ld19.dlog</TT>,
<TT>ld19ps.dlog</TT> using <TT>gnuplot</TT> as above :
</EM>
<P>
<EM><IMG STYLE=""
SRC="img4.png"
ALT="\includegraphics[width=7.5cm]{pseudo-gen-fig3.pdf}">
<IMG STYLE=""
SRC="img5.png"
ALT="\includegraphics[width=7.5cm]{pseudo-gen-fig4.pdf}">
</EM>
<P>
<EM>Both the orbitals and the logarithmic derivatives (note the
different energy range) start to exhibit some visible
discrepancy now.
</EM>
<P>
<EM>One can try to fiddle with all generation parameters,
better if one at the time, to see whether things improve.
Curiously enough, the pseudization radius for the core
correction, which in principle should be as small as
possible, seems to improve things if pushed slightly
outwards (try <TT>rcore=2.0</TT>). Also surprisingly,
a smaller pseudization radius for the 3<I>d</I> state, 0.9
or 1.0 a.u., doesn't bring any visible improvement
to transferability
(but it increases a lot the required cutoff!).
Changing the pseudization radii for 4<I>s</I> and 4<I>p</I> states
doesn't affect much the results.
</EM>
<P>
<EM>A different local potential – a pseudized version
of the total self-consistent potential – can be chosen
by setting <TT>lloc=-1</TT> and setting <TT>rcloc</TT>
to the desired pseudization radius (a.u.). For small
<TT>rcloc</TT> ghosts re-appear; <TT>rcloc=2.9</TT>
yields slighty better total energy differences but slightly worse
eigenvalues. Note that the PP so generated will also have a
<I>s</I> projector, while the previous
ones had only <I>p</I> and <I>d</I> projectors.
</EM>
<P>
<EM>One could also generate the PP from a different electronic
configuration. Since Ti tends to lose rather than to attract
electrons, it will be more easily found in a ionized state than
in the neutral one. One might for instance use the electronic
configuration of the Bachelet-Hamann-Schlüter paper[<A
HREF="node21.html#BHS">4</A>]:
<!-- MATH
$3d^2 4s^{0.75} 4p^{0.25}$
-->
3<I>d</I><SUP>2</SUP>4<I>s</I><SUP>0.75</SUP>4<I>p</I><SUP>0.25</SUP>. This however doesn't seem to improve
much.
</EM>
<P>
<EM>Finally we end up with these generation data:
</EM><PRE>
&input
atom='Ti', dft='PBE', config='[Ar] 3d2 4s2 4p0',
iswitch=3
/
&inputp
pseudotype=1, nlcc=.true., rcore=2.0, lloc=0,
file_pseudopw='Ti.pbe-n-rrkj.UPF'
/
3
4P 2 1 0.00 0.00 2.9 2.9
3D 3 2 2.00 0.00 1.3 1.3
4S 1 0 2.00 0.00 2.9 2.9
</PRE>
<P><HR>
<!--Navigation Panel-->
<A
HREF="node13.html">
<IMG WIDTH="37" HEIGHT="24" ALT="next" SRC="next.png"></A>
<A
HREF="node11.html">
<IMG WIDTH="26" HEIGHT="24" ALT="up" SRC="up.png"></A>
<A
HREF="node11.html">
<IMG WIDTH="63" HEIGHT="24" ALT="previous" SRC="prev.png"></A>
<A ID="tex2html114"
HREF="node1.html">
<IMG WIDTH="65" HEIGHT="24" ALT="contents" SRC="contents.png"></A>
<BR>
<B> Next:</B> <A
HREF="node13.html">3.2 Single-projector, norm-conserving, with</A>
<B> Up:</B> <A
HREF="node11.html">3 A worked example:</A>
<B> Previous:</B> <A
HREF="node11.html">3 A worked example:</A>
<B> <A ID="tex2html115"
HREF="node1.html">Contents</A></B>
<!--End of Navigation Panel-->
</BODY>
</HTML>
|
