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Let us consider the Ti atom: Z = 22
, electronic configuration:
1s22s22p63s23p63d24s2
, with PBE XC functional.
The input data for the AE calculation is simple:
&input
atom='Ti', dft='PBE', config='[Ar] 3d2 4s2 4p0'
/
and yields the total energy and Kohn-Sham levels. Let us concentrate
on the outermost states:
3 0 3S 1( 2.00) -4.6035 -2.3017 -62.6334
3 1 3P 1( 6.00) -2.8562 -1.4281 -38.8608
3 2 3D 1( 2.00) -0.3130 -0.1565 -4.2588
4 0 4S 1( 2.00) -0.3283 -0.1641 -4.4667
4 1 4P 1( 0.00) -0.1078 -0.0539 -1.4663
and on their spatial extension:
s(3S/3S) = 1.000000 <r> = 1.0069 <r2> = 1.1699 r(max) = 0.8702
s(3P/3P) = 1.000000 <r> = 1.0860 <r2> = 1.3907 r(max) = 0.8985
s(3D/3D) = 1.000000 <r> = 1.6171 <r2> = 3.5729 r(max) = 0.9811
s(4S/4S) = 1.000000 <r> = 3.5138 <r2> = 14.2491 r(max) = 2.9123
s(4P/4P) = 1.000000 <r> = 4.8653 <r2> = 27.9369 r(max) = 3.8227
Note that the 3d
state has a small spatial extension, comparable to that of
3s
and 3p
states and much smaller than for 4s
and 4p
states; the
3d
energy is instead comparable to that of 4s
and 4p
states and much
higher than the 3s
and 3p
energies.. Much of the chemistry of Ti is
determined by its 3d
states. What should we do? We have the choice among
several possibilities:
- single-projector NC-PP with 4 electrons in valence (3d24s2
),
with nonlinear core correction;
- single-projector NC-PP with 12 electrons in valence
(
3s23p63d24s2
);
- multiple-projector US-PP with 12 electrons in valence;
- multiple-projector US-PP with 4 electrons in valence and
nonlinear core correction;
- ...
The PP of case 1) will be hard due to the presence of 3d
states, and
its transferability may turn out not be sufficient for all purposes;
PP's for 2) will be even harder due to the presence of 3d
and
semicore 3s
and 3p
states; PP 3) can be made soft, but generating
one is not trivial; PP 4) may suffer from insufficient transferability.
Subsections
Next: 3.1 Single-projector, norm-conserving, no
Up: User's Guide for LD1
Previous: 2.4 Checking for transferability
Contents
Layla Martin-Samos Colomer
2012-11-21