reliability of pseudopotentials for TM
Concerning the accuracy of pseudopotentials for transition metals (TM),
I'd like to make the following comments on the contribution of Jan
Hrusak, Nov. 4, 92. In my opinion, his comments, especially the table
summarizing some results for the iron metal, give a completely wrong
picture concerning the reliability of the Hay-Wadt pseudopotentials.
Using pseudopotentials one should keep in mind the following:
1. In order to judge the accuracy of a pseudopotential one should
compare results of pseudopotential to all-electron calculations
performed at a corresponding level of theory, e.g. the HF level.
One should always exclude basis set effects since pseudopotentials
and basis sets are different things. I suggest to do such
comparisions always at the finite-difference level. In case of
the iron atom one can take the numerical all-electron data
(nonrelativistic and spin-orbit averaged quasirelativistic)
from Martin and Hay, JCP 75, 4539 (1981). Their Cowan-Griffin
results for ionisation and excitation energies agree with values
calculated by us using the related Wood-Boring scheme within 0.01 eV.
It is not correct to compare UHF results (which give no well-defined
LS-state anyhow) to such RHF results.
2. Errors due to the valence basis sets can be checked by comparision
of the corresponding results to finite difference pseudopotential
results or at least pseudopotential calculations performed with
very large basis sets (we used 15s15p15d before we applied the
finite-difference code).
3. Correlation errors can finally be checked by comparing correlated
quasirelativistic pseudopotential calculations to experimental data.
One should not forget to average the experimental numbers over
spin-orbit components when doing the pseudopotential calculation
in LS-coupling (Gaussian). This was not done by Jan Hrusak.
There is much literature on correlation effects in transition metals
and MP2 is definitely not the method to be used. I suppose that the
excellent results Jan Hrusak obtains with his Ar-core pseudopotential,
a 6s3p8d/5s3p5d basis (how can one describe 4p or 4s2->4p2 correlation
with this basis set?) in the framework of MP2 are not due to an
excellent pseudopotential, but rather to an excellent error
cancelation (pseudopotential error, basis set error, correlation
error, error in averaging the experimental numbers).
I really have no idea how
Jan Hrusak can 'publish' an all-electron excitation energy for iron
for 5D->3F (most likely s2d6 -> d8) of 7.53 eV, compare
this to pseudopotential results for 5D->3F (most likely s2d6 -> s1d7)
of 2.08 eV (error 5.45 eV) and 3.37 eV (error 4.16 eV) and state
(without any doubts, that his comparison is affected by errors), that
this is due to the 'ground state oriented parametrization procedure
more than with the valence space'. In order to discuss this, one
needs to know frozen-core results for Ne and Ar core: The frozen-core
errors in excitation and ionisation energies for 13 LS states of Fe and
Fe(+) are less than 0.02 eV for the Ne core and less than 0.25 eV for
the Ar core in finite difference all-electron HF calculations, when
this core is taken from the s2d6 5D ground state. I don't see, how
4 or 5 eV errors should arise from this in pseudopotential work.
Therefore, in order to prove that Hay-Wadt pseudopotentials are quite
accurate, in the following table I summarize some numbers for iron
pseudopotentials of Hay and Wadt and ourselves (Dolg, Wedig, Stoll,
Preuss, JCP 86, 866, 1987) in comparison to the all-electron data
published by Martin and Hay:
5D -> 5F 5D -> 3F 5D -> 6D 5D ->
4F
s2d6 s1d7 s2d6 d8 s2d6 s1d5 s2d6 d7
num. RHF, nonrelativistic
AE,HF (Martin,Hay) 1.80 7.46 6.28 7.95
ECP (Ar, Hay,Wadt) 1.53 7.28 6.06 7.73
ECP (Ne, Hay,Wadt) 1.96 7.72 6.28 8.12
PP (Ne, Dolg,Stoll,Preuss) 1.78 7.50 6.28 7.95
with 7s6p5d/5s4p3d basis set 1.79 7.48 6.33 7.99
num. RHF, quasirelativistic
AE,HF (Martin,Hay) 2.06 7.87 6.34 8.33
PP (Ne, Dolg,Stoll,Preuss) 2.06 7.94 6.35 8.36
with 7s6p5d/5s4p3d basis set 2.07 7.93 6.40 8.40
(This is the data for 4 out of 13 states I looked on in 1986; the
results for the other states are of the same quality.)
It is clearly seen that all pseudopotentials give reliable results at the
HF or SCF level. The same is true for the pseudopotentials published
by the Christiansen group or the Toulouse group (I don't have the
numbers for Fe, but e.g. for Ni the Christiansen pseudopotential HF
results agree with all-electron HF results within 0.1 eV).
Finally, I would like to remark that it is rather a matter of a proper
initial guess and not a problem of the Hay-Wadt pseudopotential, if
Gaussian calculations often converge to an excited state.
The message should be:
Distinguish pseudopotential, basis set and computational method
as well as the errors occuring at in all of these. Although the
final results might be 'excellent', it could be accidential.
Michael Dolg
Institut fuer Theoretische Chemie
Universit{t Stuttgart
Pfaffenwaldring 55
W 7000 Stuttgart 80
CFAT .at. DS0RUS1I