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.     

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.     

An alternative to pseudopotentials: a core—valence approximation scheme for molecular calculations

A core—valence approximation scheme is described in which the integral-evaluation time varies as (N_valence)⁴ rather than (N_total)⁴. The scheme is based on expanding core—valence overlap distributions in terms of a mono-centric basis centred at the core. The method is illustrated with comparative calculations on NF₃ and PCl₃.     

On the calculation of electric dipole strengths of 4f→4f transitions in lanthanide complexes

Electric dipole strengths calculated with the combined static coupling (SC)/dynamic coupling (DC) intensity model for 4f → 4f transitions in lanthanide complexes contain SC/DC cross-term (“interference”) contributions which may add to or subtract front the purely static and dynamic contributions. Calculations for europium (III) complexes show that cross- terms cannot be neglected in characterizing 4f→4f intensities.     

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.     

Structure-based description of a step-by-step synthesis of homo- and heterodinuclear (4f, 4f ') lanthanide complexes

The stepwise course of the synthesis of homo- (4f, 4f) and heterodilanthanide (4f, 4f ') complexes has been investigated through structural determination of the intermediate and final products occurring in the process. In the first step, the tripodal ligand H(3)L is reacted with Ln(NO(3))(3) x 5H(2)O to give a complex (H(3)L)Ln(NO(3))(3) in which the ligand does exist in a zwitterionic form. This unexpected feature has been definitely supported by a structural determination performed on a closely related complex (HL')(3)Ln(NO(3))(3) (1). These species are fairly stable and may be isolated. In basic medium, (H(3)L)Ln(NO(3))(3) is deprotonated to yield a neutral LLn complex crystallized as LLnNaClO(4) (2), the lanthanide ion being linked to the inner N(4)O(3) coordination site of the ligand. Finally, addition of Ln'(NO(3))(3) x 5H(2)O (Ln' being similar or different from Ln) to the LLn complex yields the desired homo- or heterodinuclear LLnLn'(NO(3))(3) complex 3, where the Ln' ion is coordinated to the outer O(3)O(3) coordination site of the tripodal ligand. Complex 1 (Ln = La) crystallizes in the triclinic space group P1 (No. 2): a = 11.1883(7) A, b = 11.8993(9) A, c = 16.4197(10) A, alpha = 81.900 (6) degrees, beta = 79.406(5) degrees, gamma = 79.470(6) degrees, V = 2099.5(2) A(3), Z = 2. Complex 2 (Ln = Eu) crystallizes in the monoclinic space group P2(1)/n (No. 14): a = 13.6333(13) A, b = 15.3799(12) A, c = 17.1473(13) A, beta = 111.283(10) degrees, V = 3350.2(5) A(3), Z = 4. Complex 3 (Ln = Ln' = Dy) crystallizes in the trigonal space group R3 (No. 148) with a = b = 23.847(3) A, c = 42.982(2) A, V = 21168(4) A(3), Z = 18. Complex 3 possesses a Dy(O(phenoxo))(3)Dy core, and a nitrato anion has been replaced by a eta(2)-chelated o-vanillin anion. We did not succeed in obtaining crystals of any of the heterodinuclear LLnLn'(NO(3))(3) entities, but their existence was unambiguously confirmed by positive fast atom bombardment mass spectrometry experiments.     

The structure of lanthanide complexes with five membered sulfones and the specific benzene solvation

By means of a computer program based on the pseudo-contact equation, the structures of lanthanide complexes with five-membered sulfones have been established. The compounds are 1:1 bidentate complexes with the axis of complexation nearly parallel to the bisecting line of the O-S-O angle, and with the lanthanide position being at an average distance of 2.4 A from both oxygen atoms. The Ledal model, which assumes the specific benzene solvation, has been proposed as an adequate model for molecules with planar ring structure, and the distance between the benzene and solute along the preferential axis of complexation has been established as ~ 3.0 Å. The most probable conformation of the ring was taken into account because the accuracy of location of the lanthanide or benzene molecule in these complexes depends mainly on the correct model of the molecule assumed. Detailed analysis of the Eu(fod),-induced shifts in the PMR spectrum of NTBN sulfone confirmed the advanced structure of the complexes of five-membered ring sulfones with the lanthanide shift reagents.     

On the effect of 4f electrons on the structural characteristics of lanthanide trihalides: computational and electron diffraction study of dysprosium trichloride

The molecular and electronic structure of dysprosium trichloride, DyCl(3), was calculated by high-level quantum chemical methods in order to learn about the effect of the partially filled 4f subshell and of the possible spin-orbit coupling on them. High-temperature electron diffraction studies of DyCl(3) were also carried out so that we could compare the computed geometry with the experimental one, after thermal corrections on the latter. Dysprosium monochloride, DyCl, and the dimer of dysprosium trichloride, Dy(2)Cl(6), were also investigated by computation. We found that the electron configuration of the 4f subshell does not influence the geometry of the trichloride monomer molecule as the ground state and first excited state molecules have the same geometry. Nonetheless, taking the 4f electrons into account in the calculation, together with the 5s and 5p electrons, is important in order to get geometrical parameters consistent with the results from experiment. Based on electron diffraction and different levels of computation, the suggested equilibrium bond length (r(e)) of DyCl(3) is 2.443(14) A, while the thermal average distance (r(g)) from electron diffraction is 2.459(11) A. The molecule is trigonal planar in equilibrium. Although the ground electronic state splits due to spin-orbit coupling, the lowering of the total electronic energy is very small (about 0.025 hartree) and the geometrical parameters are not affected. In contrast with the monomeric trichloride molecule, the bond angles of the dimer seem to be different for different electronic states, indicating the influence of the 4f electronic configuration on their structure. We carried out an anharmonic analysis of the out-of-plane vibration of the trichloride monomer and found that the vibration is considerably anharmonic at 39.5 cm(-1), compared with the 30.5 cm(-1) harmonic value.     

4-Nitro and 4-chloro pyridine-N-oxide complexes of lanthanide perchlorates

Adducts of lanthanide perchlorates with 4-nitro and 4-chloro pyridine-Noxides (4-NPNO and 4-CPNO respectively) have been synthesised for the first time and characterised by analysis, electrolytic conductance, infrared, proton-NMR and electronic spectral data. The complexes are of the compositions Ln₂(NPNO)₁₅ (ClO₄)₆ (Ln = La, Pr, Nd and Gd), Tb(NPNO), (C1O₄)₆), Ln₂(NPNO)₁₃ (C1O₄)₆) (Ln = Dy, Ho, and Yb); Ln (CPNO)₈ (C10₄)₃) (Ln = La, Pr, Nd, Tb, Dy, Ho and Yb) and Ln(CPNO), (C1O₄)₃) (Ln = Sm and Gd). Conductivity and IR data provide evidence for the non-coordinated nature of the perchlorate groups. IR and NMR spectra suggest coordinationvia the oxygen of the N-oxide group. Electronic spectral shapes of the Nd⁺³ and Ho⁺³ complexes are interpreted in terms of eight-and seven-coordinate environments in the case of 4-NPNO complexes and eight-coordination in the case of 4-CPNO complexes. IR data indicate bridged structure in NPNO complexes of lanthanides other than Tb.     

Synthesis, structural studies, theoretical calculations, and linear and nonlinear optical properties of terpyridyl lanthanide complexes: new evidence for the contribution of f electrons to the NLO activity

The synthesis and structural, photophysical, and second-order nonlinear optical (NLO) properties of a novel lanthanide terpyridyl-like complex family LLn(NO(3))(3) (Ln = La, Gd, Dy, Yb, and Y) are reported. The isostructural character of this series in solution and in the solid state has been established on the basis of X-ray diffraction analysis in the cases of yttrium and gadolinium complexes, theoretical optimization of geometry (DFT), and NMR spectroscopy. The absorption, emission, and solvatochromic properties of the free terpyridyl-like ligand L were thoroughly investigated, and the twist intramolecular charge transfer (TICT) character of the lowest energy transition was confirmed by theoretical calculation (TDDFT and CIS). The similar ionochromic effect of the different lanthanide ions was evidenced by the similar UV-visible spectra of the complete family of complexes. On the other hand, the quadratic hyperpolarizability coefficient beta, measured by the harmonic light scattering (HLS) technique, is clearly dependent on the nature of the metal, and a careful examination of the particular case of yttrium unambiguously confirms the contribution of metal f electrons to the NLO activity.     

Lanthanide complexes for second order nonlinear optics: evidence for the direct contribution of f electrons to the quadratic hyperpolarizability

This study descibes for the first time the nonlinear optical (NLO) properties of multipolar lanthanide complexes, Na3[Ln(dipic)3]. The "metal-induced" NLO activity enhancement is confirmed as a general property of f-block elements, and the direct participation of f electrons to the hyperpolarizability beta is strongly supported by experimental data.     

4-Aminoantipyrine schiff-base complexes of lanthanide and uranyl ions

Using a new tridentate ligand, acetylacetone-4-aminoantipyrine (AAP) complexes of lanthanide nitrates having the general formula [Ln(AAP)₂](NO₃)₃ (where Ln = Pr, Nd, Sm, Gd, Dy or Y) have been prepared. Uranyl complexes of salicylaldehyde-4-aminoantipyrine (SAAP) of general formulae [UO₂(SAAP)₂](X)₂ (where X = NO₃ or I) and [UO₂(SAAP)₂(OAc)₂] have also been prepared. The complexes have been characterized by IR, electronic, NMR, conductivity and analytical techniques. While SAAP acts as bidentate ligand without using its hydroxyl group, AAP acts as tridentate ligand involving hydroxyl coordination. The covalency parameter δ has been calculated for the Pr and Nd complexes.     

4f-4f hypersensitivity in the absorption spectra and NMR studies on paramagnetic lanthanide chloride complexes with 1,10-phenanthroline in non-aqueous solutions

The optical absorption and NMR studies of trivalent lanthanide chloride complexes with 1,10-phenanthroline (phen) are presented and discussed. The 1H NMR spectra of the complexes of La, Pr, Nd, Eu and Yb have been studied in methanol-d(4). The resonances of phen in the NMR spectra of the paramagnetic complexes have been shifted to lower as well as higher fields, which is a manifestation of dipolar interaction. The H (2) protons of the heterocyclic amine display broad resonances. The degree of broadening in Pr, Nd, and Yb complexes follows the order Pr < Nd < Yb. The inter- and intra-molecular shift ratios show that the paramagnetic shift is predominantly due to dipolar interaction. The electronic spectra of Pr, Nd, Ho and Er complexes have been investigated in methanol, pyridine, DMSO and DMF, which reveal that the hypersensitive transitions exhibit larger variation in oscillator strength values and band shapes. The change in the coordination geometry of the complexes and relative basicity of ligand are found responsible for oscillator strength and band shape variation. The interelectronic repulsion and covalency parameters show covalent nature of bonding between the metal and the ligand.     

某些镧系化合物化学键特性的INDO研究

本文用INDO方法研究了不同价态镧系化合物的成键性质和4f轨道在成键中的作用,结果表明, 镧系化合物的成键受许多因素, 如价态、半径、配位数、空间构型等影响。不同配体与镧系元素成键的强度差别较大; 高价态的共价性大于低价态的; 配位数低的大于配位数高的。某些特殊构型的镧系化合物除σ键外, 还形成重叠较好的π配键,使Ln-L键共价性大大增强。4f轨道在成键中的作用比5d的少得多, 三价(二价态)的4f轨道基本定域(<0.1%), 四价态的4f轨道对成键的贡献明显增大, 可接近1%。     

Additive character of shift of W4f line in X-ray photoelectronic spectra of phosphine complexes of tungsten

Conclusions The position of the W4f_7/2 line in the XP spectra of the phosphine complexes of tungsten can be described by the additive scheme of partial shifts, caused by the ligands that enter into the complex.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 7, pp. 1631–1633, July, 1981.     

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.     

An open library of relativistic core electron density function for the QTAIM analysis with pseudopotentials

Based on two‐component relativistic atomic calculations, a free electron density function (EDF) library has been developed for nearly all the known ECPs of the elements Li (Z = 3) up to Ubn (Z = 120), which can be interfaced into modern quantum chemistry programs to save the .wfx wavefunction file. The applicability of this EDF library is demonstrated by the analyses of the quantum theory of atoms in molecules (QTAIM) and other real space functions on HeCuF, , OgF₄, and TlCl₃(DMSO)₂. When a large‐core ECP is used, it shows that the corrections by EDF may significantly improve the properties of some density‐derived real space functions, but they are invalid for the wavefunction‐depending real space functions. To classify different chemical bonds and especially some nonclassical interactions, a list of universal criteria has also been proposed. © 2018 Wiley Periodicals, Inc.     

Ab initio valence bond calculations and the spin-paired diradical character of S 4 2+

The results of some ab initio valence bond calculations, with STO-6G basis sets for the s and p orbitals, are reported for the ground state of cyclic S ₄ ²⁺ . The sum of the weights for two long-bond (or spin-paired diradical) structures is approximately 50% of the total.     

Extended Gaussian-type valence basis sets for calculations involving nonempirical core pseudopotentials. II. PS-21 G Basis for Li to Ca and Ga to Kr atoms

Split valence basis sets adapted to Durand and Barthelat core pseudopotentials have been optimized for the three first rows of the main group elements. The reliability of these PS -21G basis functions has been checked by performing test calculations on about 30 small molecule and crystalline systems. These studies indicate a satisfactory overall agreement between the PS -21G results and those of all-electron calculations carried out with basis sets having similar valence-shell contractions.