From CFAT@DS0RUS1I.bitnet Tue Nov 10 11:44:41 1992 Date: Tue, 10 Nov 92 16:31:08 MEZ From: CFAT%DS0RUS1I.BITNET@OHSTVMA.ACS.OHIO-STATE.EDU Subject: reliability of pseudopotentials for TM To: chemistry mailbox 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