An Investigation of Lanthanum Coordination Compounds by Using Solid‐State 139La NMR Spectroscopy and Relativistic Density Functional Theory

Lanthanum‐139 NMR spectra of stationary samples of several solid La^III coordination compounds have been obtained at applied magnetic fields of 11.75 and 17.60 T. The breadth and shape of the ¹³⁹La NMR spectra of the central transition are dominated by the interaction between the ¹³⁹La nuclear quadrupole moment and the electric field gradient (EFG) at that nucleus; however, the influence of chemical‐shift anisotropy on the NMR spectra is non‐negligible for the majority of the compounds investigated. Analysis of the experimental NMR spectra reveals that the ¹³⁹La quadrupolar coupling constants (C_Q) range from 10.0 to 35.6 MHz, the spans of the chemical‐shift tensor (Ω) range from 50 to 260 ppm, and the isotropic chemical shifts (δ_iso) range from ?80 to 178 ppm. In general, there is a correlation between the magnitudes of C_Q and Ω, and δ_iso is shown to depend on the La coordination number. Magnetic‐shielding tensors, calculated by using relativistic zeroth‐order regular approximation density functional theory (ZORA‐DFT) and incorporating scalar only or scalar plus spin–orbit relativistic effects, qualitatively reproduce the experimental chemical‐shift tensors. In general, the inclusion of spin–orbit coupling yields results that are in better agreement with those from the experiment. The magnetic‐shielding calculations and experimentally determined Euler angles can be used to predict the orientation of the chemical‐shift and EFG tensors in the molecular frame. This study demonstrates that solid‐state ¹³⁹La NMR spectroscopy is a useful characterization method and can provide insight into the molecular structure of lanthanum coordination compounds.     

Two‐component calculations of spin–orbit effects for a van der Waals molecule Rn2

Electronic structures of the weakly bound Rn₂ were calculated by the two‐component Møller–Plesset second‐order perturbation and coupled‐cluster methods with relativistic effective core potentials including spin–orbit operators. The calculated spin–orbit effects are small, but depend strongly on the size of basis sets and the amount of electron correlations. Magnitudes of spin–orbit effects on D_e (0.7–3.0 meV) and R_e (−0.4∼−2.2 Å) of Rn₂ are comparable to previously reported values based on configuration interaction calculations. A two‐component approach seems to be a promising tool to investigate spin–orbit effects for the weak‐bonded systems containing heavy elements. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 139–143, 1999     

Full four‐component relativistic calculations of the one‐bond 77Se–13C spin‐spin coupling constants in the series of selenium heterocycles and their parent open‐chain selenides

Four‐component relativistic calculations of ⁷⁷Se–¹³C spin–spin coupling constants have been performed in the series of selenium heterocycles and their parent open‐chain selenides. It has been found that relativistic effects play an essential role in the selenium–carbon coupling mechanism and could result in a contribution of as much as 15–25% of the total values of the one‐bond selenium–carbon spin‐spin coupling constants. In the overall contribution of the relativistic effects to the total values of ¹J(Se,C), the scalar relativistic corrections (negative in sign) by far dominate over the spin‐orbit ones (positive in sign), the latter being of less than 5%, as compared to the former (ca 20%). A combination of nonrelativistic second‐order polarization propagator approach (CC2) with the four‐component relativistic density functional theory scheme is recommended as a versatile tool for the calculation of ¹J(Se,C). Solvent effects in the values of ¹J(Se,C) calculated within the polarizable continuum model for the solvents with different dielectric constants (ε 2.2–78.4) are next to negligible decreasing negative ¹J(Se,C) in absolute value by only about 1 Hz. The use of the locally dense basis set approach applied herewith for the calculation of ⁷⁷Se–¹³C spin‐spin coupling constants is fully justified resulting in a dramatic decrease in computational cost with only 0.1–0.2‐Hz loss of accuracy. Copyright © 2014 John Wiley & Sons, Ltd.     

GRECP/5e‐MRD‐CI calculation of the electronic structure of PbH

The correlation calculation of the electronic structure of PbH is carried out with the generalized relativistic effective core potential (GRECP) and multireference single‐ and double‐excitation configuration interaction (MRD‐CI) methods. The 22‐electron GRECP for Pb is used and the outer core 5s, 5p, and 5d pseudospinors are frozen using the level‐shift technique, so only five external electrons of PbH are correlated. A new configuration selection scheme with respect to the relativistic multireference states is employed in the framework of the MRD‐CI method. The [6, 4, 3, 2] correlation spin–orbit basis set is optimized in the coupled cluster calculations on the Pb atom using a recently proposed procedure, in which functions in the spin–orbital basis set are generated from calculations of different ionic states of the Pb atom and those functions are considered optimal that provide the stationary point for some energy functional. Spectroscopic constants for the two lowest‐lying electronic states of PbH (²Π_1/2, ²Π_3/2) are found to be in good agreement with the experimental data. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

GRECP/MRD‐CI calculations of spin‐orbit splitting in ground state of Tl and of spectroscopic properties of TlH

The generalized relativistic effective core potential (GRECP) approach is employed in the framework of multireference single‐ and double‐excitation configuration interaction (MRD‐CI) method to calculate the spin‐orbit splitting in the ²P^o ground state of the Tl atom and spectroscopic constants for the 0⁺ ground state of TlH. The 21‐electron GRECP for Tl is used, and the outer core 5s and 5p pseudospinors are frozen with the help of the level shift technique. The spin‐orbit selection scheme with respect to relativistic multireference states and the corresponding code are developed and applied in the calculations. In this procedure both correlation and spin‐orbit interactions are taken into account. A [4,4,4,3,2] basis set is optimized for the Tl atom and employed in the TlH calculations. Very good agreement is found for the equilibrium distance, vibrational frequency, and dissociation energy of the TlH ground state (R_e=1.870 Å, ω_e=1420 cm⁻¹, D_e=2.049 eV) as compared with the experimental data (R_e=1.872 Å, ω_e=1391 cm⁻¹, D_e=2.06 eV). © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 409–421, 2001     

Development of spin‐dependent relativistic open‐shell Hartree–Fock theory with time‐reversal symmetry (II): The restricted open‐shell approach

An open‐shell Hartree–Fock (HF) theory for spin‐dependent two‐component relativistic calculations, termed the Kramers‐restricted open‐shell HF (KROHF) method, is developed. The present KROHF method is defined as a relativistic analogue of ROHF using time‐reversal symmetry and quaternion algebra, based on the Kramers‐unrestricted HF (KUHF) theory reported in our previous study (Int. J. Quantum Chem., doi: 10.1002/qua.25356 ). As seen in the nonrelativistic ROHF theory, the ambiguity of the KROHF Fock operator gives physically meaningless spinor energies. To avoid this problem, the canonical parametrization of KROHF to satisfy Koopmans' theorem is also discussed based on the procedure proposed by Plakhutin et al. (J. Chem. Phys. 2006 , 125, 204110). Numerical assessments confirmed that KROHF using Plakhutin's canonicalization procedure correctly gives physical spinor energies within the frozen‐orbital approximation under spin–orbit interactions.     

All‐electron relativistic computations on the low‐lying electronic states,bond length,and vibrational frequency of CeF diatomic molecule with spin–orbit coupling effects

Ab initio all‐electron computations have been carried out for Ce⁺ and CeF, including the electron correlation, scalar relativistic, and spin–orbit coupling effects in a quantitative manner. First, the n‐electron valence state second‐order multireference perturbation theory (NEVPT2) and spin–orbit configuration interaction (SOCI) based on the state‐averaged restricted active space multiconfigurational self‐consistent field (SA‐RASSCF) and state‐averaged complete active space multiconfigurational self‐consistent field (SA‐CASSCF) wavefunctions have been applied to evaluations of the low‐lying energy levels of Ce⁺ with [Xe]4f¹5d¹6s¹ and [Xe]4f¹5d² configurations, to test the accuracy of several all‐electron relativistic basis sets. It is shown that the mixing of quartet and doublet states is essential to reproduce the excitation energies. Then, SA‐RASSCF(CASSCF)/NEVPT2 + SOCI computations with the Sapporo(‐DKH3)‐2012‐QZP basis set were carried out to determine the energy levels of the low‐lying electronic states of CeF. The calculated excitation energies, bond length, and vibrational frequency are shown to be in good agreement with the available experimental data. © 2018 Wiley Periodicals, Inc.     

Magnetic Anisotropy in “Scorpionate” First‐Row Transition‐Metal Complexes: A Theoretical Investigation

In this work we have analyzed in detail the magnetic anisotropy in a series of hydrotris(pyrazolyl)borate (Tp^?) metal complexes, namely [VTpCl]⁺, [CrTpCl]⁺, [MnTpCl]⁺, [FeTpCl], [CoTpCl], and [NiTpCl], and their substituted methyl and tert‐butyl analogues with the goal of observing the effect of the ligand field on the magnetic properties. In the [VTpCl]⁺, [CrTpCl]⁺, [CoTpCl], and [NiTpCl] complexes, the magnetic anisotropy arises as a consequence of out‐of‐state spin–orbit coupling, and covalent changes induced by the substitution of hydrogen atoms on the pyrazolyl rings does not lead to drastic changes in the magnetic anisotropy. On the other hand, much larger magnetic anisotropies were predicted in complexes displaying a degenerate ground state, namely [MnTpCl]⁺ and [FeTpCl], due to in‐state spin–orbit coupling. The anisotropy in these systems was shown to be very sensitive to perturbations, for example, chemical substitution and distortions due to the Jahn–Teller effect. We found that by substituting the hydrogen atoms in [MnTpCl]⁺ and [FeTpCl] by methyl and tert‐butyl groups, certain covalent contributions to the magnetic anisotropy energy (MAE) could be controlled, thereby achieving higher values. Moreover, we showed that the selection of ion has important consequences for the symmetry of the ground spin–orbit term, opening the possibility of achieving zero magnetic tunneling even in non‐Kramers ions. We have also shown that substitution may also contribute to a quenching of the Jahn–Teller effect, which could significantly reduce the magnetic anisotropy of the complexes studied.     

Pseudo‐Contact NMR Shifts over the Paramagnetic Metalloprotein CoMMP‐12 from First Principles

Long‐range pseudo‐contact NMR shifts (PCSs) provide important restraints for the structure refinement of proteins when a paramagnetic metal center is present, either naturally or introduced artificially. Here we show that ab initio quantum‐chemical methods and a modern version of the Kurland–McGarvey approach for paramagnetic NMR (pNMR) shifts in the presence of zero‐field splitting (ZFS) together provide accurate predictions of all PCSs in a metalloprotein (high‐spin cobalt‐substituted MMP‐12 as a test case). Computations of 314 ¹³C PCSs using g‐ and ZFS tensors based on multi‐reference methods provide a reliable bridge between EPR‐parameter‐ and susceptibility‐based pNMR formalisms. Due to the high sensitivity of PCSs to even small structural differences, local structures based either on X‐ray diffraction or on various DFT optimizations could be evaluated critically by comparing computed and experimental PCSs. Many DFT functionals provide insufficiently accurate structures. We also found the available 1RMZ PDB X‐ray structure to exhibit deficiencies related to binding of a hydroxamate inhibitor. This has led to a newly refined PDB structure for MMP‐12 (5LAB) that provides a more accurate coordination arrangement and PCSs.     

Accurate Quantum‐Chemical Prediction of Enthalpies of Formation of Small Molecules in the Gas Phase

The coupled‐cluster approach, including single and double excitations and perturbative corrections for triple excitations, is capable of predicting molecular electronic energies and enthalpies of formation of small molecules in the gas phase with very high accuracy (specifically, with error bars less than 5 kJ mol^?1), provided that the electronic wavefunction is dominated by the Hartree–Fock configuration. This capability is illustrated by calculations on molecules containing O–H and O–F bonds, namely OH, FO, H₂O, HOF, and F₂O. To achieve this very high accuracy, it is imperative to account for electron‐correlation effects in a quantitative manner, either by using explicitly correlated two‐particle basis functions (R12 functions) or by extrapolating to the limit of a complete basis. Besides taking into account harmonic zero‐point vibrational energies, it is also necessary to account for anharmonic corrections to the zero‐point vibrational energies, to include the core orbitals into the coupled‐cluster calculations, and to account for spin–orbit corrections and scalar relativistic effects. These additional corrections constitute small but significant contributions in the range of 1–4 kJ mol^?1 to the enthalpies of formation of the aforementioned molecules. The highly accurate coupled‐cluster results, obtained by employing R12 functions and by including various corrections, are compared with standard Kohn–Sham density‐functional calculations as well as with the Gaussian‐2 and complete‐basis‐set model chemistries.     

Ab initio quasirelativistic calculations on electronic transitions in ICl by the multireference many‐body perturbation theory

A quasirelativistic perturbative method of ab initio calculations on ground and excited molecular electronic states and transition properties within the relativistic effective core potential approximation is presented and discussed. The method is based on the construction of a state‐selective many‐electron effective Hamiltonian in the model space spanned by an appropriate set of Slater determinants by means of the second‐order many‐body multireference perturbation theory. The neglect of effective spin–orbit interactions outside of the model space allows the exploitation of relatively high nonrelativistic symmetry during the evaluation of perturbative corrections and therefore dramatic reduction of the cost of computations without any contraction of the model‐space functions. One‐electron transition properties are evaluated via the perturbative construction of spin‐free transition density matrices. Illustrative calculations on the X0⁺ ? A1, B0⁺, and (ii)1 transitions in the ICl molecule are reported. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Synthesis and Structure of Ag4Te(SO4) – a New Compound Featuring a Silver‐Telluride Framework

Tetrasilver telluride sulfate was obtained as a black air‐stable polycrystalline powder; its structure was determined from X‐ray powder diffraction data. The new compound crystallizes in the cubic space group P2₁3, with the unit cell parameter a = 8.6263(2) Å and Z = 4. The crystal structure of Ag₄Te(SO₄) is composed of a positively charged silver‐telluride three‐dimensional framework, in which the isolated tetrahedral SO₄^2– anions are embedded. The framework features an irregular coordination for tellurium atoms with a coordination number of six and manifold Ag–Ag contacts ranging from 2.99 to 3.14 Å. The distortion of the SO₄^2– anion as well as the interactions within the framework and between the framework and the SO₄^2– anions are analyzed with the help of the structural data, vibrational spectra, and band structure calculations.     

2,2,2‐trifluoroacetophenone‐based D‐π‐A type photoinitiators for radical and cationic photopolymerizations under near‐UV and visible LEDs

Two D‐π‐A‐type 2,2,2‐trifluoroacetophenone derivatives, namely, 4′‐(4‐( N,N‐diphenyl)amino‐phenyl)‐phenyl‐2,2,2‐trifluoroacetophenone (PI‐Ben) and 4′‐(4‐(7‐(N,N‐diphenylamino)‐9,9‐dimethyl‐9H‐fluoren‐2‐yl)‐phenyl‐2,2,2‐trifluoroacetophenone (PI‐Flu), are developed as high‐performance photoinitiators combined with an amine or an iodonium salt for both the free‐radical polymerization of acrylates and the cationic polymerization of epoxides and vinyl ether upon exposure to near‐UV and visible light‐emitting diodes (LEDs; e.g., 365, 385, 405, and 450 nm). The photochemical mechanisms are investigated by UV‐Vis spectra, molecular‐orbital calculations, fluorescence, cyclic voltammetry, photolysis, and electron‐spin‐resonance spin‐trapping techniques. Compared with 2,2,2‐trifluoroacetophenone, both photoinitiators exhibit larger redshift of the absorption spectra and higher molar‐extinction coefficients. PI‐Ben and PI‐Flu themselves can produce free radicals to initiate the polymerization of acrylate without any added hydrogen donor. These novel D‐π‐A type trifluoroacetophenone‐based photoinitiating systems exhibit good efficiencies (acrylate conversion = 48%–66%; epoxide conversion = 85%–95%; LEDs at 365–450 nm exposure) even in low‐concentration initiators (0.5%, w/w) and very low curing light intensities (1–2 mW cm^?2). © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1945–1954     

Calculations of solid‐state 43Ca NMR parameters: A comparison of periodic and cluster approaches and an evaluation of DFT functionals

We present a computational study of magnetic‐shielding and quadrupolar‐coupling tensors of ⁴³Ca sites in crystalline solids. A comparison between periodic and cluster‐based approaches for modeling solid‐state interactions demonstrates that cluster‐based approaches are suitable for predicting ⁴³Ca NMR parameters. Several model chemistries, including Hartree–Fock theory and 17 DFT approximations (SVWN, CA‐PZ, PBE, PBE0, PW91, B3PW91, rPBE, PBEsol, WC, PKZB, BMK, M06‐L, M06, M06‐2X, M06‐HF, TPSS, and TPSSh), are evaluated for the prediction of ⁴³Ca NMR parameters. Convergence of NMR parameters with respect to basis sets of the form cc‐pVXZ (X = D, T, Q) is also evaluated. All DFT methods lead to substantial, and frequently systematic, overestimations of experimental chemical shifts. Hartree–Fock calculations outperform all DFT methods for the prediction of ⁴³Ca chemical‐shift tensors. © 2017 Wiley Periodicals, Inc.     

Spin‐orbit ab initio and density functional theory investigation of bismuth monoboronyl,BiBO

The molecular properties of bismuth monoboronyl, BiBO, were investigated using high‐level ab initio and density functional theory calculations by including the effect of spin‐orbit coupling (SOC). SOC does not cause any change in the Bi? B bond length of BiBO, by contrast it causes significant elongation of the Bi? B bond of BiBO^?, by ～0.03 Å. The Bi? B bond length of BiBO^? that is calculated by considering SOC is almost identical to that of BiBO; this result is consistent with a recent experimental study. The term values of excited states of BiBO calculated by including SOC are in good agreement with the experimental results. One excited state which was not assigned in the previous experimental study is the Ω = 0⁺ state generated by strong SOC. In the theoretical calculations on molecules containing 6p‐block elements, including SOC is crucial for obtaining results that are consistent with the corresponding experimental results.     

An Investigation of 1:1 Adducts of Gallium Trihalides with Triarylphosphines by Solid‐State 69/71Ga and 31P NMR Spectroscopy

Several 1:1 adducts of gallium trihalides with triarylphosphines, X₃Ga(PR₃) (X=Cl, Br, and I; PR₃=triarylphosphine ligand), were investigated by using solid‐state ^69/71Ga and ³¹P NMR spectroscopy at different magnetic‐field strengths. The ^69/71Ga nuclear quadrupolar coupling parameters, as well as the gallium and phosphorus magnetic shielding tensors, were determined. The magnitude of the ⁷¹Ga quadrupolar coupling constants (C_Q(⁷¹Ga)) range from approximately 0.9 to 11.0 MHz . The spans of the gallium magnetic shielding tensors for these complexes, δ₁₁?δ₃₃, range from approximately 30 to 380 ppm; those determined for phosphorus range from 10 to 40 ppm. For any given phosphine ligand, the gallium nuclei are most shielded for X=I and least shielded for X=Cl, a trend previously observed for In^III–phosphine complexes. This experimental trend, attributed to spin‐orbit effects of the halogen ligands, is reproduced by DFT calculations. The signs of C_Q(^69/71Ga) for some of the adducts were determined from the analysis of the ³¹P NMR spectra acquired with magic angle spinning (MAS). The ¹J(^69/71Ga,³¹P) and ΔJ(^69/71Ga, ³¹P) values, as well as their signs, were also determined; values of ¹J(⁷¹Ga,³¹P) range from approximately 380 to 1590 Hz. Values of ¹J(^69/71Ga,³¹P) and ΔJ(^69/71Ga,³¹P) calculated by using DFT have comparable magnitudes and generally reproduce experimental trends. Both the Fermi‐contact and spin‐dipolar Fermi‐contact mechanisms make important contributions to the ¹J(^69/71Ga,³¹P) tensors. The ³¹P NMR spectra of several adducts in solution, obtained as a function of temperature, are contrasted with those obtained in the solid state. Finally, to complement the analysis of NMR spectra for these adducts, single‐crystal X‐ray diffraction data for Br₃Ga[P(p‐Anis)₃] and I₃Ga[P(p‐Anis)₃] were obtained.     

Temperature Dependence of Interactions between Stable Piperidine‐1‐yloxyl Derivatives and an Ionic Liquid

2,2,6,6‐Tetramethylpiperidine‐1‐yloxyl derivatives substituted with either hydrogen bonding [‐OH, ‐OSO₃H] or ionic [‐OSO₃^?Na⁺, ‐OSO₃^?K⁺, N⁺(CH₃)₃I^?, N⁺(CH₃)₃ N^?(SO₂‐CF₃)₂] substituents are investigated in 1‐butyl‐3‐methylimidazolium tetrafluoroborate over a wide temperature range covering both glassy and viscous states. The Vogel–Fulcher–Tammann equation describes the temperature dependence of the ionic liquid viscosity. Quantum chemical calculations of the spin probes at the UB3LYP/6‐311(2d,p++) level are done to describe the dependence of the spin density on nitrogen on the substitution pattern of the 4‐position of the probe. The results of these calculations are also used to understand the experimental results obtained by applying the Spernol–Gierer–Wirtz theory to analyze the viscosity dependence of the rotational correlation time of the spin probes. Significant differences are found between 2,2,6,6‐tetramethylpiperidine‐1‐yloxyl and its derivatives containing substituents that are able to form hydrogen bonds with the ionic liquid. Moreover, derivatives substituted with ionic groups at the 4‐position have a large effect on temperature‐induced solvent viscosity, as this is particularly dependent on the nature of the substituent at the 4‐position. These dependencies include the temperature region that can be used to describe interactions between the spin probes and the ionic liquid, diffusion into the free volume during non‐activated (neutral spin probes) and activated (charged spin probes) processes. Additional parameters are the radii of the ionic liquid and the spin probes, which are calculated and measured approximately. In addition, the temperature dependence of the isotropic hyperfine coupling constants of the spin probes results in information about the micropolarity of the ionic liquid. At room temperature, this is comparable to that of the solvent dimethylsulfoxide.     

Two Extended 5‐Methyltetrazolate‐Based Magnetic Complexes: Synthesis,Structure, and Magnetic Properties

Two 5‐methyl‐tetrazolate (mtz^–)‐based paramagnetic metal coordination polymers, {[Cu₂(H₂O)₂(mtz)(μ₃‐OH)(nip)] · H₂O}_n ( 1 ) and [Cu(H₂O)(mtz)₂]_n ( 2 ), were obtained in the presence and absence of aromatic 5‐nitroisophathalate (nip^2–) coligand by varying the preparation methods. Structural determinations reveal that 1 is a three‐dimensional (3D) framework with corner‐sharing triangular ribbons infinitely extended by ditopic nip^2– connectors. In contrast, 2 is a coplanar (4,4) layer constructed from square‐pyramidal Cu^II ions and μ‐N1,N4‐mtz^– linkers, which is further assembled into a 3D supramolecular network by interlayer hydrogen‐bonding interactions. Magnetically, spin‐frustrated antiferromagnetic ordering is observed in the 3D framework of 1 and canted antiferromagnetic behavior with a slight spin‐flop transition is presented in 2 , which are structurally resulting from the locally Δ‐ribbon in 1 and asymmetric magnetic superexchange mediated by the μ‐N1,N4‐mtz^– bridge of 2 .     

Ba3V2S4O3: A Mott Insulating Frustrated Quasi‐One‐Dimensional S=1 Magnet

Through a solid‐state reaction, a practically phase pure powder of Ba₃V₂S₄O₃ was obtained. The crystal structure was confirmed by X‐ray single‐crystal and synchrotron X‐ray powder diffraction (P6₃, a=10.1620(2), c=5.93212(1) Å). X‐ray absorption spectroscopy, in conjunction with multiplet calculations, clearly describes the vanadium in charge‐disproportionated V^IIIS₆ and V^VSO₃ coordinations. The compound is shown to be a strongly correlated Mott insulator, which contradicts previous predictions. Magnetic and specific heat measurements suggest dominant antiferromagnetic spin interactions concomitant with a weak residual ferromagnetic component, and that intrinsic geometric frustration prevents long‐range order from evolving.