The ab initio model potential method: Third-series transition metal elements

Abstract

In this paper we present nonrelativistic and relativistic core ab initio model potentials ͑AIMPs͒ and valence basis sets for La and the third-series transition metal elements. The relativistic AIMPs are derived from atomic Cowan-Griffin calculations; they are made of a spin-free part and a one-electron spin-orbit operator according to Wood and Boring. The core potentials correspond to the 62-electron core ͓Cd,4f ͔. The valence basis sets are optimized and spin-orbit corrected. We present monitoring spin-free calculations on the atoms, singly ionized ions and monohydrides of the ten elements, which show a good performance overall. A spin-free-state-shifted spin-orbit-configuration interaction calculation on Pt, which uses empirical spin-free data and which is expected to be essentially free from spin-free deficiencies, points out that the quality of the spin-orbit operators is very good.

The ab initio model potential method with the spin-free relativistic scheme by eliminating small components Hamiltonian

“…The AIMP with the reduced number of primitives (13s10p9d6 f ) of Ref. 7 gives slightly larger errors: 0.011 Å; Ϫ23 cm Ϫ1 ; and Ϫ0.06 eV at the HF level, and 0.009 Å; Ϫ35 cm Ϫ1 ; and Ϫ0.06 eV at the CCSD level. The errors of the AIMP method with the valence-only contracted basis set are similar to those with the uncontracted basis sets at the HF level: 0.007 Å; Ϫ25 cm Ϫ1 ; and Ϫ0.06 eV.…”

“…Since the spectroscopic constants are rather sensitive to the outer region of a basis set, the outermost three s and d, four p, and one f primitive functions were replaced by the corresponding three s, p, d and one f functions of the CG-AIMP (13s10p9d6 f ) basis set; 7 it must be noted that the primitive functions of the CG-AIMP valence basis set have been proven to be useful in NP-AIMP calculations. 11,12 The AIMP calculations were carried out using the uncontracted basis sets (22s17p14d9 f ) and (13s10p9d6 f ).…”

“…Several relativistic variations of the AIMP method have been proposed: the AIMP method with the CowanGriffin Hamiltonian ͑CG-AIMP͒, [5][6][7] the AIMP with the Wood-Boring Hamiltonian-͑WB-AIMP͒, 8,9 and the AIMP with the Douglas-Kroll transformed no-pair Hamiltonian ͑NP-AIMP͒. [10][11][12] Remarkable success has been achieved with these relativistic methods for systems containing heavy atoms.…”

Structure and spectroscopy of Pa4+ defects in Cs2ZrCl6. An ab initio theoretical study

“…3 and Table I under the entry sfss-ACPF-37. This simple sfss Hamiltonian has been shown to be very efficient to include electron correlation effects and spin-orbit coupling effects at a time in ab initio calculations when they can be largely decoupled, both in transition metal elements [13][14][15] and lanthanide elements. 19 …”

“…1,2 A problem remains, however, in the interpretation of the 6d 1 states: The 6d crystal field splitting, 10Dq, of Cs 2 ZrCl 6 :Pa 4ϩ is smaller than that of Ce 3ϩ in Cs 2 NaYCl 6 , whereas the larger extension of the 6d orbitals of Pa 4ϩ with respect to the 5d orbitals of Ce 3ϩ would make one expect a larger d crystal field splitting. 2 Among the theoretical methods able to calculate the structure and spectroscopy of actinide impurities in ionic crystals, the ab initio model potential method ͑AIMP͒ [10][11][12] has been shown to properly represent embedding effects in ionic hosts, 11,12 on the one hand, and scalar and spin-orbit relativistic effects in main group elements and transition elements such as Ni 2ϩ -doped MgO, 13 Ir ϩ and Pt, 14,15 on the other hand. Recently, the relativistic core ab initio model potentials of the lanthanide and actinide elements based on Cowan-Griffin-Wood-Boring 16,17 atomic calculations have been published and their good performance in scalar relativistic effects has been pointed out.…”