Quasirelativistic energy-consistent 5f-in-core pseudopotentials for pentavalent and hexavalent actinide elements

Quasirelativistic energy-consistent 5f-in-core pseudopotentials modeling pentavalent (5f ^n?2 occupation with n = 2–6 for Pa–Am) and hexavalent (5f ^n?3 occupation with n = 3–6 for U–Am) actinides have been adjusted. Energy-optimized (6s5p4d) and (7s6p5d) valence basis sets contracted to polarized double- to quadruple-zeta quality as well as 2f1g correlation functions have been derived. Corresponding smaller basis sets (4s4p3d) and (5s5p4d) suitable for calculations on actinide(V) and actinide(VI) ions in crystalline solids form subsets of these basis sets designed for calculations on neutral molecules. Calculations using the Hartree–Fock and the coupled-cluster method with single and double excitation operators and a perturbative estimate of triple excitations for actinide pentafluorides show satisfactory agreement with calculations using 5f-in-valence pseudopotentials and experimental data, respectively. However, in the hexavalent case the 5f-in-core approximation seems to reach its limitations except for hexavalent uranium (5f⁰), where results for both uranium hexafluoride and the uranyl ion deviate only slightly from the 5f-in-valence reference data.     

Quasirelativistic f-in-core pseudopotentials and core-polarization potentials for trivalent actinides and lanthanides: molecular test for trifluorides

Calibration studies of actinide and lanthanide trifluorides are reported for actinide and lanthanide scalar-relativistic energy-consistent f-in-core pseudopotentials, respectively, accompanying valence basis sets as well as core-polarization potentials. Results from Hartree–Fock and coupled-cluster singles, doubles, and perturbative triples f-in-core pseudopotential calculations are compared to corresponding data from f-in-valence pseudopotential and all-electron calculations as well as to experimental data. In general, good agreement is observed between the f-in-core and f-in-valence pseudopotential results, whereas due to the lack of experimental data for the actinides only a good agreement of the calculated and experimentally determined bond lengths of the lanthanide systems can be established. Nevertheless, the results indicate that the core-polarization potentials devised here for actinides improve the f-in-core results.     

Quasirelativistic energy-consistent 5f-in-core pseudopotentials for trivalent actinide elements

Quasirelativistic energy-consistent 5f-in-core pseudopotentials modelling trivalent actinides, corresponding to a near-integral 5f ⁿ occupation (n = 0–14 for Ac–Lr), have been generated. Energy-optimized (6s5p4d), (7s6p5d), and (8s7p6d) primitive valence basis sets contracted to polarized double to quadruple zeta quality as well as 2f1g correlation functions have been derived. Corresponding smaller basis sets (4s4p3d), (5s5p4d), and (6s6p5d) suitable for calculations on actinide(III) ions in crystalline solids form subsets of these basis sets designed for calculations on neutral molecules. Results of Hartree–Fock test calculations for actinide(III) monohydrates and actinide trifluorides show a satisfactory agreement with corresponding calculations using 5f-in-valence pseudopotentials. Even in the beginning of the actinide series, where the 5f shell is relatively diffuse, only quite acceptable small deviations occur as long as the 5f-shell does not participate significantly in covalent bonding. Electronic Supplementary Material Supplementary material is available in the online version of this article at and is accessible for authorized users.     

Quasirelativistic energy-consistent 5f-in-core pseudopotentials for divalent and tetravalent actinide elements

Quasirelativistic energy-consistent 5f-in-core pseudopotentials modeling divalent (5f ⁿ⁺¹ occupation with n = 5–13 for Pu–No) respectively tetravalent (5f ^n-1 occupation with n = 1–9 for Th–Cf) actinides together with corresponding core-polarization potentials have been generated. Energy-optimized (6s5p4d) and (7s6p5d) valence basis sets as well as 2f1g correlation functions have been derived and contracted to polarized double, triple, and quadruple zeta quality. Corresponding smaller (4s4p) and (5s5p) respectively (4s4p3d) and (5s5p4d) basis sets suitable for calculations on actinide(II) respectively actinide(IV) ions in crystalline solids form subsets of these basis sets designed for calculations on molecules. Results of Hartree–Fock test calculations for actinide di- and tetrafluorides show a satisfactory agreement with calculations using 5f-in-valence pseudopotentials. Electronic Supplementary Material The online version of this article doi: contains supplementary material, which is available to authorized users.     

Improved valence basis sets for divalent lanthanide 4f-in-core pseudopotentials

Improved energy-optimized (6s5p4d) and (7s6p5d) primitive valence basis sets have been derived for energy-consistent scalar-relativistic 4f-in-core pseudopotentials of the Stuttgart-Cologne variety modeling divalent lanthanides with a $4\hbox{f}^{n+1}$ occupation (n = 0?C13 for La?CYb). Segmented contracted basis sets covering the range of polarized double-, triple-, and quadruple-zeta quality, augmented by 2f1g correlation sets, were created for use in molecular calculations. The basis sets contain smaller (4s4p3d) and (5s5p4d) primitive subsets, which are designed in particular for solid state calculations of crystals containing divalent lanthanide ions. Hartree?CFock, density functional theory and coupled cluster results obtained with the new basis sets for lanthanide atomic ionization potentials as well as of geometry optimizations of various test molecules, i.e. selected lanthanide mono- and dihydrides, mono- and difluorides, and monooxides, show a satisfactory agreement with experimental data as well as with corresponding scalar-relativistic all-electron results. Core-polarization potentials are found to improve the results, especially for the atomic first and second ionization potentials.     

Scalar-relativistic 5f-in-core pseudopotentials and core-polarization potentials for trivalent actinides: calibration calculations for Ac<Superscript>3+</Superscript>, Cm<Superscript>3+</Superscript> and Lr<Superscript>3+</Superscript> complexes

The performance of recently proposed 5f-in-core pseudopotentials for the trivalent actinides was investigated in calculations for model complexes An³⁺L ⁿ⁻ for three selected actinides (An³⁺ = Ac³⁺, Cm³⁺, Lr³⁺) and eight simple ligands with atoms from the first three periods of the table of elements (L ⁿ⁻ = F⁻, Cl⁻, OH⁻, SH⁻, CO, NH₂⁻, H₂O, H₂S, NH₃). Results of Hartree-Fock and Coupled Cluster with singles, doubles and perturbative triples calculations using basis sets of quadruple-zeta quality are compared to corresponding reference data obtained with scalar-relativistic energy-adjusted 5f-in-valence small-core pseudopotentials. The inclusion of core-polarization potentials in the 5f-in-core pseudopotential calculations and corrections of the basis set superposition error by the counterpoise correction leads to very good agreement between the 5f-in-valence and 5f-in-core pseudopotential results for bond lengths, bond angles and binding energies. Results from 5f-in-core pseudopotential calculations using different density functionals also show reasonable agreement with the more rigorous Coupled Cluster results. It is argued that the An 5f rather than the An f population is a useful criterion for the applicability of a specific An 5f-in-core pseudopotential.     

Valence basis sets for lanthanide 4f-in-core pseudopotentials adapted for crystal orbital ab initio calculations

Crystal orbital adapted Gaussian (4s4p3d), (5s5p4d) and (6s6p5d) valence primitive basis sets have been derived for calculating periodic bulk materials containing trivalent lanthanide ions modeled with relativistic energy-consistent 4f-in-core lanthanide pseudopotentials of the Stuttgart-Koeln variety. The calibration calculations of crystalline A-type Pm₂O₃ using different segmented contraction schemes (4s4p3d)/[2s2p2d], (4s4p3d)/[3s3p2d], (5s5p4d)/[2s2p2d], (5s5p4d)/[3s3p3d], (5s5p4d)/[4s4p3d], (6s6p5d)/[2s2p2d], (6s6p5d)/[3s3p3d] and (6s6p5d)/[4s4p4d] are discussed at both Hartree–Fock (HF) and density functional theory (DFT) levels for the investigation of basis set size effects. Applications to the geometry optimization of A-type Ln₂O₃ (Ln = La-Pm) show a satisfactory agreement with experimental data using the lanthanide valence basis sets (6s6p5d)/[4s4p4d] and the standard set 6-311G* for oxygen. The corresponding augmented sets (8s7p6d)/[6s5p5d] with additional diffuse functions for describing neutral lanthanide atoms were applied to calculate atomic energies of free lanthanide atoms for the evaluation of cohesive energies for A-Ln₂O₃ within both conventional Kohn-Sham DFT and the a posteriori-HF correlation DFT schemes.     

Approaching actinide(+III) hydration from first principles

A systematic computational approach to An(III) hydration on a density-functional level of theory, using quasi-relativistic 5f-in-core pseudopotentials and valence-only basis sets for the An(III) subsystems, is presented. Molecular structures, binding energies, hydration energies, and Gibbs free energies of hydration have been calculated for [An(III)(OH(2))(h)](3+) (h = 7, 8, 9) and [An(III)(OH(2))(h-1) * OH(2)](3+) (h = 8, 9), using large (7s6p5d2f1g)/[6s5p4d2f1g] An(III) and cc-pVQZ O and H basis sets within the COSMO implicit solvation model. An(III) preferred primary hydration numbers are found to be 8 for all An(III) at the gradient-corrected density-functional level of theory. Second-order M?ller-Plesset perturbation theory predicts preferred primary hydration numbers of 9 and 8 for Ac(III)-Md(III) and No(III)-Lr(III), respectively.     

Density functional theory studies of actinide(III) motexafins (An-Motex2+, An = Ac, Cm, Lr). Structure, stability, and comparison with lanthanide(III) motexafins

Newly developed relativistic energy-consistent 5f-in-core actinide pseudopotentials and corresponding (7s6p5d1f)/[5s4p3d1f] basis sets in the segmented contraction scheme, combined with density functional theory methods, have been used to study the molecular structure and chemical properties of selected actinide(III) motexafins (An-Motex2+, An = Ac, Cm, Lr). Structure and stability are discussed, and a comparison to the lanthanide(III) motexafins (Ln-Motex2+, Ln = La, Gd, Lu) is made. The actinide element is found to reside above the mean N5 motexafin plane, and the larger the cation, the greater the observed out-of-plane displacement. It is concluded that the actinium(III), curium(III), and lawrencium(III) cations are tightly bound to the macrocyclic skeleton, yielding stable structures. However, the calculated metal-ligand gas-phase binding energy for An-Motex2+ is about 1-2 eV lower than that of Ln-Motex2+, implying a lower stability of An-Motex2+ compared to Ln-Motex2+. Results including solvent effects imply that Ac-Motex2+ is the most stable complex in aqueous solution and should be the best candidate for experimentalists to get stable actinide(III) motexafin complexes.     

Energy-consistent relativistic pseudopotentials for the 4d elements: atomic and molecular applications

Recently reported energy-consistent relativistic pseudopotentials have been used with series of matching correlation consistent basis sets in benchmark calculations of various atomic and molecular properties. The basis set convergence of the 4d metal electron affinities and 5s2-->5s0 excitation energies are reported at the CCSD(T) level of theory, and the effects of valence and 4s4p correlation are investigated. In addition the impact of correlating the low-lying 3d electrons was also studied in all-electron Douglas-Kroll-Hess (DKH) calculations, which also included the ionization potentials and 5s2-->5s1 excitation energies. For all four atomic properties, higher order coupled cluster calculations through CCSDTQ are reported. The final calculated values are generally all within 1 kcal/mol of experiment. A notable exception is the ionization potential of Tc, the currently accepted experimental value of which is suggested to be too high by about 3 kcal/mol. Molecular calculations are also reported for the low-lying electronic states of ZrO and RuF, as well as the ground electronic state of Pd2. The effects of spin-orbit coupling are investigated for these cases in pseudopotential calculations. Wherever possible, the pseudopotential results have been calibrated against DKH calculations with correlation consistent basis sets of triple-zeta quality. In all cases the calculated data for these species are in very good agreement with experiment. In particular, the correct electronic ground state for the RuF molecule (4Phi92) was obtained, which was made possible by utilizing systematic sequences of correlation consistent basis sets.     

Energy-adjusted pseudopotentials for the rare earth elements

Nonrelativistic and quasirelativistic energy-adjusted pseudopotentials and optimized (7s6p5d)/[5s4p3d]-GTO valence basis sets for use in molecular calculations for fixed f-subconfigurations of the rare earth elements, La through Lu, have been generated. Atomic excitation and ionization energies from numerical HF, as well as SCF pseudopotential calculations using the derived basis sets, differ by less than 0.1 eV from numerical HF all-electron results. Corresponding values obtained from CI(SD), CEPA-1, as well as density functional calculations using the quasirelativistic pseudopotentials, are in reasonable agreement with experimental data.     

Molecular structure of diatomic lanthanide compounds

The molecular constants of selected diatomic lanthanide compounds (LaH, LaO, LaF, EuH, EuO, EuF, EuS, GdO, GdF, GdH, YbH, YbO, YbF, YbS, LuH, LuO and LuF) have been calculated by using relativistic small-core pseudopotentials and optimized (14s13p10d8f6g)/ [6s6p5d4f3g] valence basis sets. The results are in good agreement with available experimental data, with exception of YbO and LuF. The reasons for the discrepancies in case of YbO are due to a complicated mixing of configurations in the ground state, whereas in case of LuF the binding energy estimated by experimentalists appears to be too low.     

Relativistic segmented contraction basis sets with core-valence correlation effects for atoms 57La through 71Lu: Sapporo-DK-nZP sets (n?=?D, T, Q)

For the 15 lanthanide atoms ₅₇La through ₇₁Lu, we report Sapporo-DK-nZP sets (n?=?D, T, Q), which are natural extensions of the Sapporo-(DK)-nZP sets for lighter atoms and efficiently incorporate the correlation among electrons in the N through P shells as well as the relativistic effect. The present sets well describe the correlation among the 4s and 4p electrons, which are important in the excitation of 4f electrons. Atomic test calculations of ₅₇La, ₅₈Ce, ₅₉Pr, and ₆₀Nd at configuration interaction with the Davidson correction level of theory confirm high performance of the present basis sets. Molecular test calculations are carried out for ₅₇LaF and ₇₀YbF diatomics at the coupled-cluster level of theory. The calculated spectroscopic constants approach smoothly to the experimental values as the quality of the basis set increases.     

Accurate relativistic energy-consistent pseudopotentials for the superheavy elements 111 to 118 including quantum electrodynamic effects

Energy-consistent two-component semi-local pseudopotentials for the superheavy elements with atomic numbers 111-118 have been adjusted to fully relativistic multi-configuration Dirac-Hartree-Fock calculations based on the Dirac-Coulomb Hamiltonian, including perturbative corrections for the frequency-dependent Breit interaction in the Coulomb gauge and lowest-order quantum electrodynamic effects. The pseudopotential core includes 92 electrons corresponding to the configuration [Xe]4f(14)5d(10)5f(14). The parameters for the elements 111-118 were fitted by two-component multi-configuration Hartree-Fock calculations in the intermediate coupling scheme to the total energies of 267 up to 797 J levels arising from 31 up to 62 nonrelativistic configurations, including also anionic and highly ionized states, with mean absolute errors clearly below 0.02 eV for averages corresponding to nonrelativistic configurations. Primitive basis sets for one- and two-component pseudopotential calculations have been optimized for the ground and excited states and exhibit finite basis set errors with respect to the finite-difference Hartree-Fock limit below 0.01 and 0.02 eV, respectively. General contraction schemes have been applied to obtain valence basis sets of polarized valence double- to quadruple-zeta quality. Results of atomic test calculations in the intermediate coupling scheme at the Fock-space coupled-cluster level are in good agreement with those of corresponding fully relativistic all-electron calculations based on the Dirac-Coulomb-Breit Hamiltonian. The results demonstrate besides the well-known need of a relativistic treatment at the Dirac-Coulomb level also the necessity to include higher-order corrections for the superheavy elements.     

Accuracy and efficiency of atomic basis set methods versus plane wave calculations with ultrasoft pseudopotentials for DNA base molecules

Recent results from Preuss et al. (J Comput Chem 2004, 25, 112) on DNA base molecules, obtained by plane wave density functional calculations using ultrasoft pseudopotentials, are compared with calculations using Gaussian basis sets. Bond lengths and angles agree closely, but dihedral angles and vibrational frequencies show significant differences. The Gaussian basis calculations are at least an order of magnitude more efficient than the plane wave/ultrasoft pseudopotential calculations at a similar level of accuracy; the advantage is even larger if the Fourier Transform Coulomb method is used. To obtain definite benchmark values, the geometries of the four DNA bases were optimized at the MP2 level with large basis sets, up to cc-pVQZ and aug-cc-pVTZ.     

Pseudopotential study of the rare earth monohydrides,monoxides and monofluorides

Nonrelativistic and quasirelativistic energy-adjusted pseudopotentials for fixed 4f subconfigurations of the rare earth elements La through Lu together with corresponding optimized valence basis sets have been used in SCF and CI(SD) calculations to determine the spectroscopic constants for the energetically low lying superconfigurations of the lanthanide monohydrides, monoxides and monofluorides. The experimentally observed trends in dissociation energies, bond lengths and vibrational frequencies for the ground states of the calculated superconfigurations of the monoxides and monofluorides are well reproduced. The results for the monohydrides are mainly predictions.