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<H2><A ID="SECTION00042000000000000000">
3.2 Single-projector, norm-conserving, with semicore states</A>
</H2>
<P>
<EM>The results of transferability tests suggest that a Ti PP with only
3<I>d</I>, 4<I>s</I>, 4<I>p</I> states have limited transferability to cases with
different 3<I>d</I> configurations. In order to improve it, a possible
way is to put semicore 3<I>s</I> and 3<I>p</I> states in valence. The maximum
for those states (0.87 a.u. and 0.90 a.u. respectively) is in the
same range as for 3<I>d</I> (0.98 a.u.). Let us try thus the following:
</EM><PRE>
&input
atom='Ti', dft='PBE', config='[Ar] 3d2 4s2 4p0',
rlderiv=2.90, eminld=-4.0, emaxld=2.0, deld=0.01, nld=3,
iswitch=3
/
&inputp
pseudotype=1, rho0=0.001, ...
file_pseudopw='Ti.pbe-sp-rrkj.UPF'
/
3
3S 1 0 2.00 0.00 1.1 1.1
3P 2 1 6.00 0.00 1.2 1.2
3D 3 2 2.00 0.00 1.3 1.3
&test
configts(1)='3s2 3p6 3d2 4s2 4p0',
/
</PRE><EM>
Note the presence of the <TT>&test</TT> namelist: it is used in this
context to supply the electronic valence configuration, to be used
for unscreening. As a first step, we do not include the core correction.
In place of the dots we should specify the local reference potential.
If we use <TT>lloc=-1</TT> with large values of <TT>rcloc</TT>,
(comparable to pseudization radii for the previous case)
we get all kinds of mysterious errors:
</EM><PRE>
from compute_chi : error # 1
n is too large
</PRE><EM>
for <TT>rcloc=2.5</TT>, while <TT>rcloc=2.7</TT> produces an equally
mysterious
</EM><PRE>
from run_pseudo : error # 1
Errors in PS-KS equation
</PRE><EM>
while smaller values (e.g. 1.5) lead to other errors:
</EM><PRE>
WARNING! Expected number of nodes: 0 = 2-1-1, number of nodes found: 1.
</PRE><EM>
Even if the code doesn't stop, the presence of such messages
is a signal of something going wrong in the generation algorithm.
With some more experiments, though, one finds that <TT>rcloc=1.3</TT>
yields a good potential. We still have other choices. In this case,
<I>d</I> as reference potential: <TT>lloc=2</TT>, seems to work as well
(and produces a PP with less projectors: only <I>s</I> and <I>p</I>).
The generation algorithm in the latter case yields these
results for Kohn-Sham energies:
</EM><PRE>
n l nl e AE (Ry) e PS (Ry) De AE-PS (Ry)
1 0 3S 1( 2.00) -4.60347 -4.60348 0.00001
2 1 3P 1( 6.00) -2.85621 -2.85623 0.00002
3 2 3D 1( 2.00) -0.31302 -0.31301 -0.00001
2 0 4S 1( 2.00) -0.32830 -0.32892 0.00062
3 1 4P 1( 0.00) -0.10777 -0.10732 -0.00045
</PRE><EM>
Note that the 3<I>s</I>, 3<I>p</I>, 3<I>d</I> levels should be the same by construction
(the difference is numerical noise); the 4<I>s</I> and 4<I>p</I> levels are not
guaranteed to be the same. The fact that they are, to a very good degree,
is very reassuring. A look at the orbitals will reveal that <!-- MATH
$3s, 3p, 3d$
-->
3<I>s</I>, 3<I>p</I>, 3<I>d</I>
are nodeless, 4<I>s</I> and 4<I>p</I> have one node. The spherical wave basis
set confirms the absence of ghosts:
</EM><PRE>
Cutoff (Ry) : 50.0
N = 1 N = 2 N = 3
E(L=0) = -4.5385 Ry -0.3263 Ry -0.0047 Ry
E(L=1) = -2.8427 Ry -0.1071 Ry 0.0193 Ry
E(L=2) = -0.1511 Ry 0.0311 Ry 0.0685 Ry
Cutoff (Ry) : 100.0
N = 1 N = 2 N = 3
E(L=0) = -4.5883 Ry -0.3279 Ry -0.0048 Ry
E(L=1) = -2.8547 Ry -0.1073 Ry 0.0193 Ry
E(L=2) = -0.2918 Ry 0.0303 Ry 0.0649 Ry
Cutoff (Ry) : 150.0
N = 1 N = 2 N = 3
E(L=0) = -4.5899 Ry -0.3280 Ry -0.0048 Ry
E(L=1) = -2.8549 Ry -0.1073 Ry 0.0193 Ry
E(L=2) = -0.2936 Ry 0.0303 Ry 0.0649 Ry
</PRE><EM>
Note that for <I>l</I> = 0 the first (<I>N</I> = 1) level is the 3<I>s</I> level,
the second (<I>N</I> = 2) level is the 4<I>s</I> level, and the like for
<I>l</I> = 1. Let us now repeat the testing on the nine
selected configurations as for the 4-electron PP. You will
have to add <TT>3s2 3p6</TT> to all test configurations
<TT>configts</TT>. Let us see check the errors on total energy
differences:
</EM><PRE>
$ grep Delta ld1.test
dEtot_ps = 0.227291 Ry, Delta E= -0.001230 Ry
dEtot_ps = 0.540886 Ry, Delta E= -0.000918 Ry
dEtot_ps = 1.540155 Ry, Delta E= -0.002640 Ry
dEtot_ps = 0.343314 Ry, Delta E= 0.000077 Ry
dEtot_ps = 0.715061 Ry, Delta E= 0.001142 Ry
dEtot_ps = 1.849816 Ry, Delta E= -0.000820 Ry
dEtot_ps = 3.522904 Ry, Delta E= -0.004735 Ry
dEtot_ps = 6.702626 Ry, Delta E= -0.003032 Ry
</PRE><EM>
Energy differences are reproduced with an
error that does not exceed a few mRy (see column at the rhs).
Eigenvalues are also well reproduced, e.g.:
</EM><PRE>
1 0 3S 1( 2.00) -8.37382 -8.37230 -0.00152
2 1 3P 1( 6.00) -6.57173 -6.57195 0.00021
3 2 3D 1( 0.00) -3.84145 -3.83518 -0.00627
2 0 4S 1( 0.00) -2.73793 -2.74985 0.01192
3 1 4P 1( 0.00) -2.25938 -2.25525 -0.00412
</PRE><EM>
although errors may reach 0.01 Ry (still one order of magnitude
better than what we get with the previous 4-electron PP). The price
to pay is the presence of more electrons in the valence.
</EM><HR>
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