Quasirelativistic energy-consistent 4f-in-core pseudopotentials for tetravalent lanthanide elements

Quasirelativistic energy-consistent 4f-in-core pseudopotentials modeling tetravalent lanthanides (4f ^n?1 occupation with n = 1, 2, 3, 8, 9 for Ce, Pr, Nd, Tb, Dy) 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 (4s4p3d) and (5s5p4d) basis sets suitable for calculations on lanthanide(IV) ions in crystalline solids form subsets of these basis sets designed for calculations on neutral molecules. Calculations for lanthanide tetrafluorides using the 4f-in-core pseudopotentials at the Hartree–Fock level show satisfactory agreement with calculations using 4f-in-valence pseudopotentials. For cerium tetrafluoride the experimental bond length is well reproduced using the 4f-in-core pseudopotential at the coupled-cluster level with single and double excitation operators and a perturbative estimate of triple excitations. For cerium dioxide 4f-in-core and 4f-in-valence pseudopotential calculations agree quite well, if a proper f basis set instead of f polarization functions is applied.     

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.     

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 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.     

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.     

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.     

Study of the An–Cl bond contraction in actinide trichlorides

The variation of the An–Cl bond distance in ground-state actinide trichloride (AnCl₃) molecules has been studied by density functional theory calculations using the B3LYP exchange–correlation functional in conjunction with small-core relativistic energy-consistent pseudopotentials for the actinides. The ground electronic states and the ground-state molecular properties of the trichlorides of heavy actinides (An = Bk–Lr) are reported in this paper the first time. Extending the present results with literature data on the light actinide trichlorides (AnCl₃, An = Th–Cm), the trend in the bond distance has been evaluated for the whole actinide row. The contraction is well manifested in the major part of the actinide row (An = U–Fm). The deviations at the beginning (Th, Pa) and end of the row (Md, No) have been explained by minor differences in the bonding interactions.     

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.     

Evaluation of radiation stability of N,N-didodecyl N′,N′-di-octyl diglycolamide: a promising reagent for actinide partitioning

The radiation stability of N,N-di-dodecyl-N′,N′-di-octyl-3-oxapentane-1,5-diamide (D³DODGA) was studied by γ-irradiation of the solvent up to a absorbed dose of 1,000 kGy. The effect of γ-irradiation on the radiolytic degradation of D³DODGA was assessed by measuring the distribution ratio of Am(III) (D _Am(III)) as well as the third phase formation in the irradiated D³DODGA-n-dodecane solution. The D _Am(III) in the irradiated solution decreased with increase of absorbed dose. The critical aqueous concentration of Nd(III) above which the third phase forms, increased with increase of absorbed dose. However, the limiting organic concentration of Nd(III) remained at ~25 mM irrespective of the absorbed dose. Recovery of Am(III) from the radiolytically degraded organic phase showed that back extraction of Am(III) was quantitative in a few contacts using dilute nitric acid. Our studies clearly indicated that radiolytic degradation of D³DODGA in n-dodecane is marginal even at the absorbed dose of 1,000 kGy, and therefore D³DODGA is a potential candidate for minor actinide partitioning.     

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.     

Comparative studies on co-extraction of uranium(VI) and different mineral acid from aqueous feed solutions using TBP,TOPO and TOA

Equilibrium and kinetics of co-extraction of hexavalent uranium and mineral acids from aqueous solutions into a hydrocarbon phase (paraffin) using tri n-butyl phosphate (TBP), tri-n-octyl phosphine oxide (TOPO) and tri-n-octyl amine (TOA) has been studied. Relative rates of extraction of uranium(VI) and mineral acid by different complexing ligands were measured simultaneously using bulk-liquid membrane system. Acid extraction by complexing ligands was found to be significant. Wherever there was a possibility of the formation of the third phase, isodecanol was used as an organic phase modifier. Study revealed that isodecanol promotes acid extraction and substantially reduces distribution coefficient of U(VI) into the hydrocarbon phase. The rate of acid extraction by different ligand was in the order of TOPO > TOA > TBP–isodecanol > TBP, whereas the rate of extraction of uranium(VI) was in the order TOPO > TOA > TBP > TBP–isodecanol. A kinetic model was developed to predict concentration of acid and U(VI) in the feed, organic and the strip phase during extraction. The mass transfer coefficients for acid and metal were determined by fitting the model to the observed concentration–time data.     

Quantitative analysis of trivalent uranium and lanthanides in a molten chloride by absorption spectrophotometry

As an analytical application for pyrochemical reprocessing using molten salts, quantitative analysis of uranium and lanthanides by UV/Vis/NIR absorption spectrophotometry was performed. Electronic absorption spectra of LiCl–KCl eutectic at 773 K including trivalent uranium and eight rare earth elements (Y, La, Ce, Pr, Nd, Sm, Eu, and Gd as fission product elements) were measured in the wavenumber region of 4,500–33,000 cm^?1. The composition of the solutes was simulated for a reductive extraction condition in a pyroreprocessing process for spent nuclear fuels, that is, about 2 wt% U and 0.1–2 wt% rare earth elements. Since U(III) possesses strong absorption bands due to f–d transitions, an optical quartz cell with short light path length of 1 mm was adopted in the analysis. The quantitative analysis of trivalent U, Nd, Pr, and Sm was possible with their f–f transition intensities in the NIR region. The analytical results agree with the prepared concentrations within 2σ experimental uncertainties.     

Reinvestigation of the Structure of Protonated Lysine Dimer

To better understand inconsistencies between the predicted infrared (IR) spectra of previously suggested isomers of Lys₂H⁺ reported by Wu et al. (J. Am. Soc. Mass Spectrom. 22:1651–1659, 18) and the experimental IR photon dissociation (IRPD) spectrum obtained by Oh et al. (J. Am. Chem. Soc. 127:4076–4083, 4), the structure of Lys₂H⁺ was reinvestigated using IRPD spectroscopy in the extended region 2700–3700 cm^?1 and theoretical calculations. The new experimental IRPD spectrum is in good agreement with Oh’s spectrum in the corresponding wavelength range. Based on calculations at the MP2/6-311++G(d,p)//B3LYP/6-311++G(d,p) and MP2/6-31?+?G(d,p)//MP2/6-31?+?G(d,p) levels, a new salt-bridged isomer, ZW1, was found to be the most stable isomer; it is more energetically favored than the previously suggested charge-solvated isomer LL-CS01 by 10 or 26 kJ mol^?1. Although the calculated IR spectrum of ZW1 is in good agreement with the experimental one in the range 2700–3700 cm^?1, it is in poor agreement with the previous IRPD spectrum in the range 1000–1900 cm^?1. This investigation shows that the intermolecular interactions inside the dimer are more complex than previously supposed. It is possible that both salt-bridged and charge-solvated isomers of Lys₂H⁺ are stable in the gas phase, and the isomers generated during ionization are sensitive to the experimental conditions.

Isotope shift studies in the spectra of Gadolinium in UV region and term shifts of high even levels of Gd I

Isotope shift Δσ(¹⁵⁶Gd?¹⁶⁰Gd) is reported in 70 spectral lines of neutral gadolinium atom (Gd I) in the 3290- 3920 Å region providing isotope shift data in UV lines of Gd I spectrum for the first time. The measurements were carried out on a photoelectric recording Fabry-Perot Spectrometer using highly enriched isotopic samples of gadolinium. Term isotope shifts ΔT(¹⁵⁶Gd?¹⁶⁰Gd) have been evaluated for 48 high lying even parity energy levels of Gd I using this data; new ΔT values have been obtained for 24 levels. Electronic configurations 4f⁷5d6s6p, 4ff⁷5df²6p and 4f⁸5d6s assigned earlier to these even levels have been either confirmed or configuration mixing pointed out in some of these levels. Probable assignment of 4f⁸5d6s configuration to 8 even levels between 32 930 and 35 500 cm^-1 have been confirmed.     

Studies on the separation treatment of high-level liquid waste by bisamide podand(I): Extraction and separation of An(III) from Ln(III)

A process for actinide(III) and lanthanum(III) extraction separation from high-level liquid waste (HLLW) was proposed, with N,N,N',N'-tetraoctyl diglycolamide (TODGA) as the extractant, tri-n?butyl phosphate (TBP) as the phase modifier and 2,6-bis[1-(propan-1-ol)-1,2,3-triazol-4-yl]pyridine (PyTri-Diol or PTD) as hydrophilic stripping agent. This ‘hot test’ was successfully carried out, achieving 99.92% removal of americium-241 (²⁴¹Am) with a separation factor SF_(Eu/Am) of 3.8 × 10³ in the actinide(III) product solution. The results show that bisamide podand extractants can effectively realize the extraction and separation of actinide(III) and lanthanum(III) from Chinese commercial HLLW and thus have a bright practical application potential for the treatment of commercial HLLW.     

Uranium (VI) recovery from saline environment by a marine unicellular cyanobacterium, Synechococcus elongatus

Sequestration of uranium from simulated sea water and reverse osmosis concentrates by the marine cyanobacterium, Synechococcus elongatus was assessed. Short term experiments established removal of 90–98 % uranium by the strain from simulated sea water containing 13 nM uranyl carbonate at pH 7.8, resulting in a loading of 7–42 μg U g^?1 over a period of 1–5 days respectively. Long term experiments involving repeated exposure of Synechococcus biomass to fresh simulated sea water every third day, showed a loading of 2,960 μg U g^?1 in 4 weeks. Nearly 85–90 % of cell bound uranium could be desorbed using 0.1 N HCl. The organism could sequester uranium (13,306 μg U g^?1 in 24 h) from aqueous solutions supplemented with 0.6 M NaCl and 21 μM [UO₂(CO₃)₂]^2? at pH 7.8. The results demonstrate noteworthy potential of this organism for harnessing uranium from marine environments.     

Conformational stability of chlorocyclohexane from temperature-dependent FT-IR spectra of xenon solutions, r 0 structural parameters, and vibrational assignment

Variable temperature (?55 to ?105 °C) studies of the infrared spectra (4000–400 cm^?1) of chlorocyclohexane (c-C₆H₁₁Cl) dissolved in liquefied xenon have been carried out. The infrared spectra of the gas and solid have also been recorded from 4000–100 cm^?1. By analyzing six conformer pairs in the xenon solution, a standard enthalpy difference of 132 ± 13 cm^?1 (1.58 ± 0.16 kJ/mol) was obtained with the equatorial conformer the more stable form. At ambient temperature, the abundance of the axial conformer is 34 ± 1%. The potential surface describing the conformational interchange has been determined and the Fourier coefficients were obtained. From MP2 ab initio calculations utilizing various basis sets with and without diffuse functions, the equatorial conformer is predicted to be more stable by 161 ± 18 cm^?1 from the four largest basis set calculations, which is consistent with the experimental results. However, the average from the corresponding B3LYP density functional theory calculations is 274 ± 15 cm^?1 which is certainly too large. By utilizing the previously reported microwave rotational constants for two isotopomers (³⁵Cl, ³⁷Cl) combined with the structural parameters predicted from the MP2(full)/6-311+G(d,p) calculations, adjusted r ₀ structural parameters have been obtained. The determined heavy atom distances for the most stable chair-equatorial conformer in Å are: r ₀(C₁–C₇,₈) = 1.532(3); r ₀(C₇,₈–C₁₃,₁₄) = 1.536(3); r ₀(C₄–C₁₃,₁₄) = 1.524(3); and r ₀(C₄–Cl₆) = 1.802(5) and the angles in degrees: ∠C₁C₇,₈C₁₃,₁₄ = 111.3(5)º; ∠Cl₆C₄C₁₃,₁₄ = 109.7(5)º with the two dihedral angles ∠C₈C₁C₇C₁₃ = 56.3(10)º and ∠C₁₄C₄C₁₃C₇ = 56.7(10)º. These parameters are in good agreement with those reported earlier from microwave and electron diffraction studies where the CC and CH distances were all assumed to be equal. A few of the previously reported vibrational assignments have been corrected. The results of these spectroscopic and theoretical studies are discussed and compared to the corresponding results for some similar molecules.     

Isotope shifts in the energy levels of the singly ionized neodymium atom

Isotope shifts ΔT (142–144) have been evaluated for odd and even energy levels of the singly ionised neodymium atom from the measurements carried out in 168 spectral lines in the 3930–5820 Å region, employing a recording Fabry-Perot spectrometer and highly enriched isotopes excited in liquid-air cooled hollow cathodes. The electronic configurations 4f³5d6s, 4f³5d6p and 4f⁴6p could be assigned to some of the energy levels on the basis of the present study.     

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.