Relativistic Ab-Initio Model Potential Calculations

The production of relativistic ab initio model potentials and valence basis sets has been complemented with calculations on atoms and molecules which have 

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Quasi-relativistic ab initio model potential calculations, Reference 60. 

L. SeijoChem. Phys., 102, 8078 (1995). Relativistic Ab Initio Model Potential Calculations... 

Relativistic correction included by perturbation theory, Reference 61. Quasi-relativistic ab initio model potential calculations. Reference 60. 

Seijo [120] has performed relativistic ab initio model potential calculations including spin-orbit interaction using the Wood-Boring Hamiltonian. Calculations ere performed for several atoms up to Rn, and several dimer... 

Relativistic Ab-Initio Model Potential Calculations for Molecules and Embedded Clusters. 

Seijo, L., Barandiatan, Z. Relativistic ab initio model potentials calculations for molecules and embedded clusters. In Schwerdtfeger, P. (ed.) Relativistic Electronic Structure Theory, Part I, pp. 417-475. Elsevier, Amsterdam (2002)... 

Barandiaran Z, Seijo L. The ab initio model potential method. Cowan-Griffin relativistic core potentials and valence basis sets from Li (Z = 3) to La (Z = 57). Can J Chem. 1992 70 409. Seijo L. Relativistic ab initio model potential calculations including spin-orbit effects trhough the Wood-Boring Hamiltonian. J Chem Phys. 1995 102 8078. 

Seijo L, Barandiaran Z. Relativistic Ab-Initio Model Potential Calculations for Molecules and Embedded Clusters. In Schwerdtfeger P, editor. Relativistic Electronic Structure Theory Part 2. Applications. Amsterdam Elsevier 2004. p. 417-475. 

Relativistic Ab Initio Model Potential embedded cluster calculations on the structure and spectroscopy of local defects created by actinide impurity ions in solid hosts are the focus of attention here. They are molecular like calculations which include host embedding effects and electron correlation effects, but also scalar and spin-orbit coupling relativistic effects, all of them compulsory for a detailed understanding of the large manifolds of states of the 5f" the 5f" 6d configurations. The results are aimed at showing the potentiality of Relativistic Quantum Chemistry as a tool for prediction and interpretation in the field of solids doped with heavy element impurities. 

In the calculations based on effective potentials the core electrons are replaced by an effective potential that is fitted to the solution of atomic relativistic calculations and only valence electrons are explicitly handled in the quantum chemical calculation. This approach is in line with the chemist s view that mainly valence electrons of an element determine its chemical behaviour. Several libraries of relativistic Effective Core Potentials (ECP) using the frozen-core approximation with associated optimised valence basis sets are available nowadays to perform efficient electronic structure calculations on large molecular systems. Among them the pseudo-potential methods [13-20] handling valence node less pseudo-orbitals and the model potentials such as AIMP (ab initio Model Potential) [21-24] dealing with node-showing valence orbitals are very popular for transition metal calculations. This economical method is very efficient for the study of electronic spectroscopy in transition metal complexes [25, 26], especially in third-row transition metal complexes. 

Atomization energies (in a.u.), bond lengths (in A), and force constants k of the breathing mode (in a.u.), from one-component SCF calculations using energy-consistent scalar-relativistic pseudopotentials (EC-PP), ab initio model potentials (AIMP) and valence basis sets of double zeta (DZ) and polarized double-zeta (DZP) quality, in comparison to all-electron (AE) relativistic SCF calculations. Numbers in parentheses are differences to corresponding non-relativistic results. 

All structures were optimized at the CASSCF(8,8) level with the cc-pVDZ basis set. For multireference calcidations involving bromine and iodine, the Cowan-Griffin ab initio model potential with a relativistic effective core potential was used.222 CASPT2 calculations were performed on all optimized CASSCF(8,8)/cc-pVDZ geometries, using the CASSCF wave functions as the reference wave functions. SOCs were computed by using the Pauli-Breit Hamiltonian. 

Some scalar relativistic effects are included implicitly in calculations if pseudopotentials for heavy atoms are used to mimic the presence of core electrons there are several families of pseudopotentials available the effective core potentials (ECP) (Cundari and Stevens 1993 Hay and Wadt 1985 Kahn et al. 1976 Stevens et al. 1984), energy-adjusted pseudopotentials (Cao and Dolg 2006 Dolg 2000 Peterson 2003 Peterson et al. 2003), averaged relativistic effective potentials (AREP) (Hurley et al. 1986 Lajohn et al. 1987 Ross et al. 1990), model core potentials (MCP) (Klobukowski et al. 1999), and ab initio model potentials (AIMP) (Huzinaga et al. 1987). 

The final consequence of such a strategy would be to try to eliminate the degrees of freedom of the core electrons as well and to introduce a possibly nonlocal effective potential (pseudopotential), the parameters of which are adjusted either to experiments, which are relativistic from the very beginning, or suitable atomic properties derived from relativistic calculations. This method has developed to the real working horse of relativistic quantum chemistry, and several variants are known as relativistic pseudopotentials, effective core potentials (ECPs) or ab initio model potentials. See Relativistic Effective Core Potential Techniques for Molecules Containing Very Heavy Atoms. 

Quasi-relativistic ab initio core model potential calculations (SCF level) the (n - l)d subshell is included in the valence space (i.e. 14-valence electrons). The reaction energies do not include ZPE from Reference 103. 

Table 3 lists the errors in excitation energies of Cs calculated with a relativistic ab initio one-valence electron PP and various forms of the cutoff-factor as well as with addition of a local potential. Clearly, for a given CPP the PP could be adjusted to reproduce (essentially exactly) the experimental energy levels, but then the PP without CPP does not model the frozen-core DHF AE case any more. 

Pacchioni has recently carried out calculations on the low-lying states of Sn2 and Pb2. This author gives the impression that he is the first to carry out a comparative ab initio Cl calculation on these systems. We would like to clarify this further. First, his calculation starts with the Hafner-Schwarz model potentials in comparison to our relativistic ab initio potentials derived from numerical Dirac-Fock solutions of the atoms. Pacchioni s calculations ignore spin-orbit interaction. Our calculations include spin-orbit interaction in a relativistic Cl scheme in comparison to the non-relativistic Cl of Pacchioni. Thus, he obtains a Z), approximately twice the experimental value which he corrects by a semi-empirical scheme to arrive at a value close to our calculated value with a relativistic Cl. Our calculations have clearly demonstrated the need to carry out an intermediate-coupling Cl calculation for Pbj as a result of large spin-orbit contamination. Calculations without spin-orbit, such as Pacchioni s, have little relationship to the real Pb2 molecule. 

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