Two-component Relativistic Effective Core Potentials Research Articles

Coupled cluster study of spectroscopic constants of ground states of heavy rare gas dimers with spin–orbit interaction

The CCSD(T) approach based on two-component relativistic effective core potential with spin–orbit interaction just included in coupled cluster iteration is adopted to study the spectroscopic constants of ground states of Kr2, Xe2 and Rn2 dimers. The spectroscopic constants have significant basis set dependence. Extrapolation to the complete basis set limit provides the most accurate values. The spin–orbit interaction hardly affects the spectroscopic constants of Kr2 and Xe2. However, the equilibrium bond length is shortened about 0.013Å and the dissociation energy is augmented about 18cm−1 by the spin–orbit interaction for Rn2 in the complete basis set limit.

A High-Precision Calculation of Bond Length and Spectroscopic Constants of Hg2 Based on the Coupled-Cluster Theory with Spin—Orbit Coupling**Supported by the Start-Up Funds of Xi'an Polytechnic University under Grant No BS1211, and the Scientific Research Program Funded by Shaanxi Provincial Education Department under Grant No 2013JK0679.

Based on the two-component relativistic effective core potential and matched basis sets cc-pwcvnz-pp (n=Q, 5), combining the completed basis-set extrapolation of electronic correlation energy and the fourth-order polynomial fitting technique, the bond length and spectroscopic constants of Hg2 are studied by the coupled cluster theory with spin—orbit coupling. Spin—orbit coupling is included in the post Hartree—Fock procedure, i.e., in the coupled-cluster iteration, to obtain more reliable theoretical results. The results show that our theoretical values agree with the experimental values very well and will be helpful to understand the spectral character of Hg2.

The spin−orbit energy estimated from two-component spin−orbit calculations as correction terms for the Gaussian-2 (G2) theory

Two-component relativistic effective core potential (RECP) approaches are employed to derive spin–orbit energies from the energy difference of spin–orbit two-component RECP and spin averaged RECP calculations. These spin–orbit energies include both the spin–orbit splitting of open-shell species and the higher order spin–orbit contributions for all species. The present spin–orbit energies, which can be estimated from the single reference configuration calculations at various levels of theory such as Hartree–Fock and coupled-cluster methods, are utilized as additional correction terms in the Gaussian-2 (G2) theory for Br and I containing species. The improvement in reaction energies due to the present scheme is similar to those reported for other types of spin–orbit calculations based on multireference configuration interaction calculations. The present scheme straightforwardly provides spin–orbit correction terms for the compounded methods such as the G2 theory. Even the spin–orbit corrections at the HF level are reliable enough to improve the performance of the G2 theory, reducing the error to the chemical accuracy (±0.1 eV or 2 kcal mol−1) that is the target prescribed in G2 theory.

Accounting for the Breit interaction in relativistic effective core potential calculations of actinides

The accuracy of accounting for the Breit effects in calculations of atoms and molecules in the framework of the two-component relativistic effective core potential (RECP) formalism is analysed theoretically and illustrated in calculations. Contributions of the Breit interaction between different core and valence shells are studied in the framework of the four-component SCF approximation for uranium and plutonium. It is shown that two-electron Breit effects between valence electrons can be neglected for the calculation of valence energies in systems containing actinides with ‘chemical accuracy’ (1 kcal mol−1 or 350 cm−1), whereas large core–core and core–valence Breit contributions can be efficiently described by one-electron RECP operators. Different versions of generalized RECPs with the Breit interaction taken into account are constructed for uranium and plutonium and compared for accuracy with the corresponding all-electron four-component calculations.

Structures and Stabilities for Halides and Oxides of Transactinide Elements Rf, Db, and Sg Calculated by Relativistic Effective Core Potential Methods

The ground states of the halides and oxides containing transactinide elements Rf (element 104), Db (element 105), and Sg (element 106) were calculated at the HF, MP2, QCISD, CCSD, and CCSD(T) levels of theory using one- and two-component relativistic effective core potentials. Spin−orbit effects are rather small for geometries, harmonic vibrational frequencies, charge distributions, overlap populations, and dipole moments, but considerable for atomization energies. Electron correlations are necessary for any accurate determination of the molecular properties, in particular for the evaluation of atomization energies. The bond lengths of Sg compounds are consistently longer than those of the corresponding W compounds by 0.04−0.06 Å. The atomization energies for Sg compounds are slightly smaller than those for the corresponding W compounds due to spin−orbit and correlation effects. The differences tend to increase with the number of oxygen atoms in the compounds. Metal charges and dipole moments are larger for the Sg compounds than for the W compounds, implying that Sg is more ionic than W. The D3h structures are calculated to be more stable by about 2 kcal/mol than the C4v ones for TaCl5, TaBr5, DbCl5, and DbBr5.

On the consistent definition of spin–orbit effects calculated by relativistic effective core potentials with one-electron spin–orbit operators: Comparison of spin–orbit effects for Tl, TlH, TlH3, PbH2, and PbH4

The spin–orbit effects for Tl, TlH, TlH3, PbH2, and PbH4 are evaluated by two-component calculations using several relativistic effective core potentials (RECP) with one-electron spin–orbit operators. The used RECPs are shape-consistent RECPs derived by Wildman et al. [J. Chem. Phys. 107, 9975 (1997)] and three sets of energy-consistent (or adjusted) RECPs published by Schwerdtfeger et al. [Phys. Scr. 36, 453 (1987); J. Chem. Phys. 90, 762 (1989)], Küchle et al. [Mol. Phys. 74, 1245 (1991)], and Leininger et al. [Chem. Phys. 217, 19 (1997)]. The shape-consistent RECP results are in very good agreement with the Küchle et al. energy-consistent RECP results for all the molecules studied here and all-electron results for TlH. The RECPs of Schwerdtfeger et al. and Leininger et al. seem to provide qualitatively different spin–orbit effects. If one defines spin-free RECP as the potential average of the corresponding two-component RECP, all RECPs give very similar spin–orbit effects for all the cases. Most of the discrepancies of molecular spin–orbit effects among various RECPs reported in the literature may originate from different definitions of RECPs with or without a spin–orbit term and not from the inherent difference in spin–orbit operators.

Two-component calculations for the molecules containing superheavy elements: Spin–orbit effects for (117)H, (113)H, and (113)F

We have calculated bond lengths, harmonic vibrational frequencies, and dissociation energies for (117)H, (113)H, and (113)F using relativistic effective core potentials (RECPs) with one-electron spin–orbit operators at the two-component coupled-cluster levels of theory. It is shown that any reasonable theoretical descriptions of the electronic structures of molecules containing superheavy elements require consideration of relativistic interactions and electron correlations. Comparisons with available all-electron Dirac–Fock (DF) based results indicate that our two-component approaches are very promising tools in the calculations for the molecules containing superheavy elements. The spin–orbit effects calculated from one- and two-component RECPs are in good agreement with those from all-electron Douglas–Kroll and DF results, implying that the potential average scheme is useful for obtaining one-component RECPs even for superheavy elements. Spin–orbit and electron correlation effects are not additive for molecular properties of (117)H, (113)H, and (113)F, but spin–orbit effects are qualitatively similar at all levels of theory considered. Spin–orbit effects contract Re and increase ωe for (113)H and (113)F, whereas they expand Re and decrease ωe for (117)H. Spin–orbit effects decrease De for all molecules considered, but the amount of decrease for (113)H and (117)H is substantially smaller than that estimated from the atomic splittings. For (117)H, our best calculations yield 1.983 Å (Re), 1403 cm−1(ωe), and 1.60 eV (De).