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 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 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.     

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.     

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.     

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.     

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.     

Contracted Gaussian-type basis functions revisited. IV. Atoms Rb to Xe

We report minimal-type contracted Gaussian-type function (GTF) sets, #n=(n3333/n33/n3) with n=5 and 6, #7= (74333/743/74), and #8= (84333/843/75), for the fourth-row atoms from Rb to Xe. Test calculations are performed on the Ag₂ molecule. Spectroscopic constants given by split valence sets derived from #5 and #6 are a little contaminated by basis set superposition error. However, we find that the fully valence split #8 set, (8433111/84111/711111), yields essentially the same results as a large GTF set, (22s15p12d), with a general contraction, when p-, d-, and f-type polarization functions are augmented. The present #7 and #8 CGTF sets are recommended for ab initio molecular calculations including fourth-row atoms. Received: 15 January 2002 / Accepted: 16 April 2002 / Published online: 24 June 2002     

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.     

Understanding structure and bonding in early actinide 6d(0)5f0 MX6q (M = Th-Np; X = H, F) complexes in comparison with their transition metal 5d0 analogues

The relationship between structure and bonding in actinide 6d(0)5f(0) MX(6)(q)() complexes (M = Th, Pa, U, Np; X = H, F; q = -2,-1, 0, +1) has been studied, based on density functional calculations with accurate relativistic actinide pseudopotentials. The detailed comparison of these prototype systems with their 5d(0) transition metal analogues (M = Hf, Ta, W, Re) reveals in detail how the 5f orbitals modify the structural preferences of the actinide complexes relative to the transition metal systems. Natural bond orbital analyses on the hydride complexes indicate that 5f orbital involvement in sigma-bonding favors classical structures based on the octahedron, while d orbital contributions to sigma-bonding favor symmetry lowering. The respective roles of f and d orbitals are reversed in the case of pi-bonding, as shown for the fluoride complexes.     

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 relativistic energy-consistent pseudopotentials for 3d-transition metals

Energy-consistent relativistic pseudopotentials for 3d-transition metals Sc to Ni based on modified valence energies are proposed. The pseudopotentials are adjusted at the finite difference level within the intermediate coupling scheme with respect to multi-configuration Dirac–Hartree–Fock data based on the Dirac–Coulomb Hamiltonian with an estimate of the Breit contributions in quasidegenerate perturbation theory. Typically a few hundred to thousand J levels arising from about 35 to 40 configurations ranging from the anion down to the highly charged cation are considered as references. It is shown that introducing a small common energetic shift of all valence energies reduces the errors in the parameter adjustment considerably. Results of highly correlated atomic and molecular test calculations using large basis sets and basis set extrapolation techniques are presented. To be submitted to Theoretical Chemistry Accounts (special volume on the occasion of Prof. Dr. H. Stoll's 60th birthday)     

Theoretical study of the conformational structure and thermodynamic properties of 5-(4-oxo-1,3-thiazolidine-2-ylidene)-rhodanine and ethyl-5-(4-oxo-1,3-thiazolidine-2-ylidene)-rhodanine-3-acetic acid as acceptor groups of indoline dyes

The quantum chemical DFT method with the B3LYP hybrid functional in 6–31++G(d,p) and 6–311+G(d,p) basis sets is used to calculate the equilibrium geometric parameters of different conformations of 5-(4-oxo-1,3-thiazolidine-2-ylidene)-rhodanine and its substituted form ethyl–5-(4-oxo-1,3-thiazolidine-2-ylidene)-rhodanine-3′-acetic acid applied in the synthesis of indoline and some other sensitizing dyes for solar cells. The thermodynamic parameters of four conformers and their synthesis reactions are calculated. The effect of substituents on the thermodynamic stability of the studied isomers is shown.     

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.     

Segmented contracted basis sets for atoms H through Xe: Sapporo-(DK)-<Emphasis Type="Italic">n</Emphasis>ZP sets (<Emphasis Type="Italic">n</Emphasis> = D,T, Q)

For the 54 atoms from H to Xe, compact yet accurate segmented Gaussian-type basis sets have been constructed for all electron calculations. Non-relativistic nZP (Sapporo-nZP) sets for Li–Xe and relativistic nZP (Sapporo-DK-nZP) sets for K–Xe are developed (n = D, T, Q), which efficiently incorporate valence and core electron correlations. Test calculations at the coupled-cluster level of theory are performed for spectroscopic constants of 12 hydrides of s- and d-block atoms and 12 diatomics of p-block atoms in their ground states. For all molecules, the calculated spectroscopic constants approach to the experimental values smoothly as the basis set quality increases.     

A study of factors affecting the accurac of combined calculation methods

By the example of combined calculation methods (CCMs) corresponding to calculations in MP4/6–311+G(fd,p)//MP2/6-31G(d,p) and MP4/aug-cc-pvTZ//MP2/cc-pvDZ approximations the factors affecting their accuracy are considered. By total energy calculations made for a number of compounds it is shown that the accuracy of CCMs reduces when valence double- and triple-split basis sets are applied together, and also when different methods are used to allow for electron correlation. The use of empirical corrections taking into account the character of the electron distribution in a molecule allows an enhancement of the accuracy of CCMs. The mentioned factors taken into account enable us to obtain CCM, for which the mean absolute deviation of calculation data is 1.0 kJ/mol and the largest maximum deviation is 8.0 kJ/mol in the total energy calculation in the MP4/6-311+G(f,d,p) approximation.