Periodic Trends in Lanthanide Compounds through the Eyes of Multireference ab Initio Theory

Regularities among electronic configurations for common oxidation states in lanthanide complexes and the low involvement of f orbitals in bonding result in the appearance of several periodic trends along the lanthanide series. These trends can be observed on relatively different properties, such as bonding distances or ionization potentials. Well-known concepts like the lanthanide contraction, the double–double (tetrad) effect, and the similar chemistry along the lanthanide series stem from these regularities. Periodic trends on structural and spectroscopic properties are examined through complete active space self-consistent field (CASSCF) followed by second-order <i>N</i>-electron valence perturbation theory (NEVPT2) including both scalar relativistic and spin–orbit coupling effects. Energies and wave functions from electronic structure calculations are further analyzed in terms of ab initio ligand field theory (AILFT), which allows one to rigorously extract angular overlap model ligand field, Racah, and spin–orbit coupling parameters directly from high-level ab initio calculations. We investigated the elpasolite Cs₂NaLn^IIICl₆ (Ln^III = Ce–Nd, Sm–Eu, Tb–Yb) crystals because these compounds have been synthesized for most Ln^III ions. Cs₂NaLn^IIICl₆ elpasolites have been also thoroughly characterized with respect to their spectroscopic properties, providing an exceptionally vast and systematic experimental database allowing one to analyze the periodic trends across the lanthanide series. Particular attention was devoted to the apparent discrepancy in metal–ligand covalency trends between theory and spectroscopy described in the literature. Consistent with earlier studies, natural population analysis indicates an increase in covalency along the series, while a decrease in both the nephelauxetic (Racah) and relativistic nephelauxetic (spin–orbit coupling) reduction with increasing atomic number is calculated. These apparently conflicting results are discussed on the basis of AILFT parameters. The AILFT derived parameters faithfully reproduce the underlying multireference electronic structure calculations. The remaining discrepancies with respect to experimentally derived data are mostly due to underestimation of the ligand field splittings, while the dynamic correlation and nephelauxetic effects appears to be adequately covered by CASSCF/NEVPT2

Ab Initio Ligand-Field Theory Analysis and Covalency Trends in Actinide and Lanthanide Free Ions and Octahedral Complexes

Actinide chemistry is gaining increased focus in modern research, particularly in the fields of energy research and molecular magnetism. However, the structure–function and structure–property relationships of actinides have still not been studied as intensely as those for transition metals. In this work, we report a detailed ab initio study of the spectroscopic, magnetic, and bonding properties of the trivalent actinide free ions and their associated hexachloride complexes in octahedral symmetry. The electronic structures of these systems are examined using complete active-space self-consistent-field calculations followed by second-order N-electron valence perturbation theory, including both scalar relativistic and spin–orbit-coupling effects. The computed energies and wave functions are further analyzed by means of ab initio ligand-field theory (AILFT) and finally chemically interpreted by means of the angular overlap model (AOM). The derived Slater–Condon and spin–orbit parameters have allowed us to systematically rationalize the spectroscopic and magnetic properties of the investigated free ions and complexes along the entire actinide series. Overall, the AILFT- and AOM-derived parameters accurately reproduce the multireference electronic structure calculations. The small observed discrepancies with respect to experimentally derived ligand-field parameters are essentially due to an underestimation of the electronic correlation, which arises from both the constrained size of the active space (restricted to the f orbitals) and the limit of the perturbation approach to account for dynamical correlation. Our analysis also provides insight into the metal–ligand covalency trends along the series. Consistent with natural population analysis, the nephelauxetic (Slater–Condon parameters) and relativistic nephelauxetic (spin–orbit-coupling) reductions determined for these complexes indicate a decrease in the covalency along the series. These trends also hold, to varying extents, for the corresponding tetravalent derivatives, as well as the lanthanide analogues

Cyanide-Bridged Fe^III–Cu^II Complexes: Jahn–Teller Isomerism and Its Influence on the Magnetic Properties

We report here the synthesis and characterization of four dinuclear cyanide-bridged Fe^III–Cu^II complexes, based on a tetra- or a pentadentate bispidine ligand (L¹ or L², respectively; bispidines are 3,7-diazabiyclo[3.3.1]­nonane derivatives) coordinated to the Cu^II center, and a tridentate bipyridineamide (bpca) coordinated to the <i>low-spin</i> Fe^III site, with cyanide groups completing the two coordination spheres, one of them bridging between the two metal ions. The four structurally characterized complexes [{Fe­(bpca)­(CN)₃}­{Cu­(L¹·H₂O)}]­BF₄, [{Fe­(bpca)­(CN)₃}­{Cu­(L²)}]­[Fe­(bpca)­(CN)₃]·5H₂O, [{Fe­(bpca)­(CN)₃}­{Cu­(L²·MeOH)}]­PF₆·MeOH·H₂O, and [{Fe­(bpca)­(CN)₃}­{Cu­(L²)}]­PF₆·2H₂O belong to different structural isomers. The most important differences are structurally and electronically enforced (direction of the pseudo-Jahn–Teller mode) strong or weak interactions of the copper­(II) center with the cyanide bridge. The related strength of the magnetic coupling of the two centers is analyzed with a combination of experimental magnetic, electron paramagnetic resonance (EPR), electronic spectroscopic data together with a ligand-field theory- and density functional theory (DFT)-based analysis

Zero-Field Splitting in a Series of Structurally Related Mononuclear Ni^II–Bispidine Complexes

The synthesis, single-crystal X-ray structures, electronic absorption spectra, and magnetic properties of six Ni^II complexes with a tetradentate (L¹) and three pentadentate (L², L³, L⁴) bispidine ligands (3,7-diazabicyclo[3.3.1]­nonane derivatives), Ni­(L¹·H₂O)­(OH₂)₂]­(PF₆)₂, [Ni­(L¹·H₂O)­(O₂NO)]­NO₃, [Ni­(L¹·H₂O)­(OOCCH₃)]­PF₆, [Ni­(L²·H₂O)­NCMe]­(PF₆)₂, [Ni­(L³·H₂O)­OH₂]­(PF₆)₂, and [Ni­(L⁴·H₂O)­NCMe]­(PF₆)₂ are reported. The Ni–donor bonding to pyridine and tertiary amine groups and oxygen- or nitrogen-bound coligands, completing the octahedral coordination sphere of Ni^II, is analyzed using a combination of ab initio electronic structure calculations (complete active space self-consistent field, CASSCF, followed by N-electron valence perturbation theory, NEVPT2) and angular overlap ligand field analysis. Magnetic properties are rationalized with an analysis of the magnetic anisotropy in terms of zero-field splitting and <i>g</i>-tensor parameters, obtained from first principles, and their correlation with the Ni^II–donor bonding parameters from the ligand field analysis of the ab initio results. A two-dimensional spectrochemical series of the ligands considered, according to their σ and π bonding to Ni^II, is also derived

Zero-Field Splitting in a Series of Structurally Related Mononuclear Ni^II–Bispidine Complexes

The synthesis, single-crystal X-ray structures, electronic absorption spectra, and magnetic properties of six Ni^II complexes with a tetradentate (L¹) and three pentadentate (L², L³, L⁴) bispidine ligands (3,7-diazabicyclo[3.3.1]­nonane derivatives), Ni­(L¹·H₂O)­(OH₂)₂]­(PF₆)₂, [Ni­(L¹·H₂O)­(O₂NO)]­NO₃, [Ni­(L¹·H₂O)­(OOCCH₃)]­PF₆, [Ni­(L²·H₂O)­NCMe]­(PF₆)₂, [Ni­(L³·H₂O)­OH₂]­(PF₆)₂, and [Ni­(L⁴·H₂O)­NCMe]­(PF₆)₂ are reported. The Ni–donor bonding to pyridine and tertiary amine groups and oxygen- or nitrogen-bound coligands, completing the octahedral coordination sphere of Ni^II, is analyzed using a combination of ab initio electronic structure calculations (complete active space self-consistent field, CASSCF, followed by N-electron valence perturbation theory, NEVPT2) and angular overlap ligand field analysis. Magnetic properties are rationalized with an analysis of the magnetic anisotropy in terms of zero-field splitting and <i>g</i>-tensor parameters, obtained from first principles, and their correlation with the Ni^II–donor bonding parameters from the ligand field analysis of the ab initio results. A two-dimensional spectrochemical series of the ligands considered, according to their σ and π bonding to Ni^II, is also derived

Molecular and Electronic Structures of Homoleptic Six-Coordinate Cobalt(I) Complexes of 2,2′:6′,2″-Terpyridine, 2,2′-Bipyridine, and 1,10-Phenanthroline. An Experimental and Computational Study

The crystal structures of nine homoleptic, pseudooctahedral cobalt complexes, <b>1</b>–<b>9</b>, containing either 2,2′:6′,2″-terpyridine (tpy), 4,4′-di-<i>tert</i>-butyl-2,2′-bipyridine (^tbpy), or 1,10-phenanthroline (phen) ligands have been determined in three oxidation levels, namely, cobalt­(III), cobalt­(II), and, for the first time, the corresponding presumed cobalt­(I) species. The intraligand bond distances in the complexes [Co^I(tpy⁰)₂]⁺, [Co^I(^tbpy⁰)₃]⁺, and [Co^I(phen⁰)₃]⁺ are identical, within experimental error, not only with those in the corresponding trications and dications but also with the uncoordinated neutral ligands tpy⁰, bpy⁰, and phen⁰. On this basis, a cobalt­(I) oxidation state assignment can be inferred for the monocationic complexes. The trications are clearly low-spin Co^III (<i>S</i> = 0) species, and the dicationic species [Co^II(tpy⁰)₂]²⁺, [Co^II(^tbpy⁰)₃]²⁺, and [Co^II(phen⁰)₃]²⁺ contain high-spin (<i>S</i> = ³/₂) Co^II. Notably, the cobalt­(I) complexes do not display any structural indication of significant metal-to-ligand (t_2g → π*) π-back-donation effects. Consistent with this proposal, the temperature-dependent molar magnetic susceptibilities of the three cobalt­(I) species have been recorded (3–300 K) and a common <i>S</i> = 1 ground state confirmed. In contrast to the corresponding electronic spectra of isoelectronic (and isostructural) [Ni^II(tpy⁰)₂]²⁺, [Ni^II(bpy⁰)₃]²⁺, and [Ni^II(phen⁰)₃]²⁺, which display d → d bands with very small molar extinction coefficients (ε < 60 M^–1 cm^–1), the spectra of the cobalt­(I) species exhibit intense bands (ε > 10³ M^–1 cm^–1) in the visible and near-IR regions. Density functional theory (DFT) calculations using the B3LYP functional have validated the experimentally derived electronic structure assignments of the monocations as cobalt­(I) complexes with minimal cobalt-to-ligand π-back-bonding. Similar calculations for the six-coordinate neutral complexes [Co^II(tpy^•)₂]⁰ and [Co^II(bpy^•)₂(bpy⁰)]⁰ point to a common <i>S</i> = ³/₂ ground state, each possessing a central high-spin Co^II ion and two π-radical anion ligands. In addition, the excited-states and ground state magnetic properties of [Co^I(tpy⁰)₂]­[Co^I−(CO)₄] have been explored by variable-temperature variable-magnetic-field magnetic circular dichroism (MCD) spectroscopy. A series of strong signals associated with the paramagnetic monocation exhibit pronounced <i>C</i>-term behavior indicative of the presence of metal-to-ligand charge-transfer bands [in contrast to d–d transitions of the nickel­(II) analogue]. Time-dependent DFT calculations have allowed assignment of these transitions as Co­(3d) → π*­(tpy) excitations. Metal-to-ligand charge-transfer states intermixing with the Co­(d⁸) multiplets explain the remarkably large (and negative) zero-field-splitting parameter <i>D</i> obtained from SQUID and MCD measurements. Ground-state electron- and spin-density distributions of [Co^I(tpy⁰)₂]⁺ have been investigated by multireference electronic structure methods: complete active-space self-consistent field (CASSCF) and N-electron perturbation theory to second order (NEVPT2). Both correlated CASSCF/NEVPT2 and spin-unrestricted B3LYP-based DFT calculations show a significant delocalization of the spin density from the Co^I d_{<i>xz</i>,<i>yz</i>} orbitals toward the empty π* orbitals located on the two central pyridine fragments in the trans position. This spin density is of an alternating α,β-spin polarization type (McConnel mechanism I) and is definitely not due to magnetic metal-to-radical coupling. A comparison of these results with those for [Ni^II(tpy⁰)₂]²⁺ (<i>S</i> = 1) is presented

Kβ Mainline X‑ray Emission Spectroscopy as an Experimental Probe of Metal–Ligand Covalency

The mainline feature in metal Kβ X-ray emission spectroscopy (XES) has long been recognized as an experimental marker for the spin state of the metal center. However, even within a series of metal compounds with the same nominal oxidation and spin state, significant changes are observed that cannot be explained on the basis of overall spin. In this work, the origin of these effects is explored, both experimentally and theoretically, in order to develop the chemical information content of Kβ mainline XES. Ligand field expressions are derived that describe the behavior of Kβ mainlines for first row transition metals with any d^<i>n</i> count, allowing for a detailed analysis of the factors governing mainline shape. Further, due to limitations associated with existing computational approaches, we have developed a new methodology for calculating Kβ mainlines using restricted active space configuration interaction (RAS–CI) calculations. This approach eliminates the need for empirical parameters and provides a powerful tool for investigating the effects that chemical environment exerts on the mainline spectra. On the basis of a detailed analysis of the intermediate and final states involved in these transitions, we confirm the known sensitivity of Kβ mainlines to metal spin state via the 3p–3d exchange coupling. Further, a quantitative relationship between the splitting of the Kβ mainline features and the metal–ligand covalency is established. Thus, this study furthers the quantitative electronic structural information that can be extracted from Kβ mainline spectroscopy

Magnetic Transitions in Iron Porphyrin Halides by Inelastic Neutron Scattering and Ab Initio Studies of Zero-Field Splittings

Zero-field splitting (ZFS) parameters of nondeuterated metalloporphyrins [Fe­(TPP)­X] (X = F, Br, I; H₂TPP = tetraphenylporphyrin) have been directly determined by inelastic neutron scattering (INS). The ZFS values are <i>D</i> = 4.49(9) cm^–1 for tetragonal polycrystalline [Fe­(TPP)­F], and <i>D</i> = 8.8(2) cm^–1, <i>E</i> = 0.1(2) cm^–1 and <i>D</i> = 13.4(6) cm^–1, <i>E</i> = 0.3(6) cm^–1 for monoclinic polycrystalline [Fe­(TPP)­Br] and [Fe­(TPP)­I], respectively. Along with our recent report of the ZFS value of <i>D</i> = 6.33(8) cm^–1 for tetragonal polycrystalline [Fe­(TPP)­Cl], these data provide a rare, complete determination of ZFS parameters in a metalloporphyrin halide series. The electronic structure of [Fe­(TPP)­X] (X = F, Cl, Br, I) has been studied by multireference ab initio methods: the complete active space self-consistent field (CASSCF) and the N-electron valence perturbation theory (NEVPT2) with the aim of exploring the origin of the large and positive zero-field splitting <i>D</i> of the ⁶A₁ ground state. <i>D</i> was calculated from wave functions of the electronic multiplets spanned by the d⁵ configuration of Fe­(III) along with spin–orbit coupling accounted for by quasi degenerate perturbation theory. Results reproduce trends of <i>D</i> from inelastic neutron scattering data increasing in the order from F, Cl, Br, to I. A mapping of energy eigenvalues and eigenfunctions of the <i>S</i> = 3/2 excited states on ligand field theory was used to characterize the σ- and π-antibonding effects decreasing from F to I. This is in agreement with similar results deduced from ab initio calculations on CrX₆^3– complexes and also with the spectrochemical series showing a decrease of the ligand field in the same directions. A correlation is found between the increase of <i>D</i> and decrease of the π- and σ-antibonding energies <i>e</i>_λ^X (λ = σ, π) in the series from X = F to I. Analysis of this correlation using second-order perturbation theory expressions in terms of angular overlap parameters rationalizes the experimentally deduced trend. <i>D</i> parameters from CASSCF and NEVPT2 results have been calibrated against those from the INS data, yielding a predictive power of these approaches. Methods to improve the quantitative agreement between ab initio calculated and experimental <i>D</i> and spectroscopic transitions for high-spin Fe­(III) complexes are proposed

Mössbauer Spectroscopy as a Probe of Magnetization Dynamics in the Linear Iron(I) and Iron(II) Complexes [Fe(C(SiMe₃)₃)₂]^1–/0

The iron-57 Mössbauer spectra of the linear, two-coordinate complexes, [K­(crypt-222)]­[Fe­(C­(SiMe₃)₃)₂], <b>1</b>, and Fe­(C­(SiMe₃)₃)₂, <b>2</b>, were measured between 5 and 295 K under zero applied direct current (dc) field. These spectra were analyzed with a relaxation profile that models the relaxation of the hyperfine field associated with the inversion of the iron cation spin. Because of the lifetime of the measurement (10^–8 to 10^–9 s), iron-57 Mössbauer spectroscopy yielded the magnetization dynamics of <b>1</b> and <b>2</b> on a significantly faster time scale than was previously possible with alternating current (ac) magnetometry. From the modeling of the Mössbauer spectral profiles, Arrhenius plots between 5 and 295 K were obtained for both <b>1</b> and <b>2</b>. The high-temperature regimes revealed Orbach relaxation processes with <i>U</i>_eff = 246(3) and 178(9) cm^–1 for <b>1</b> and <b>2</b>, respectively, effective relaxation barriers which are in agreement with magnetic measurements and supporting ab initio calculations. In <b>1</b>, two distinct high-temperature regimes of magnetic relaxation are observed with mechanisms that correspond to two distinct single-excitation Orbach processes within the ground-state spin–orbit coupled manifold of the iron­(I) ion. For <b>2</b>, Mössbauer spectroscopy yields the temperature dependence of the magnetic relaxation in zero applied dc field, a relaxation that could not be observed with zero-field ac magnetometry. The ab initio calculated Mössbauer hyperfine parameters of both <b>1</b> and <b>2</b> are in excellent agreement with the observed hyperfine parameters