Correlation consistent basis sets for lanthanides: The atoms La–Lu

Potential-Energy Curves for the Ground and Several Electronic States of NdO and NdS

Potential energy curves (PECs) were calculated for 21 and 18 electronic states of NdO and NdS molecules, respectively. In each case, static electron correlation effects were described by incomplete model space multiconfiguration self-consistent field wave functions based on an active space that included the most important valence orbitals. Dynamic electron correlation was included by the multireference second-order generalized Van Vleck perturbation theory method. Scalar-relativistic contributions were included by the effective core potential approach, using def2-TZVPP basis sets. Spin-dependent relativistic corrections were determined to be small and negligible for the Nd atom and so were not included in the calculations. The 21 and 18 electronic states of NdO and NdS were predicted to be in the excitation energy range of ∼3.2 and ∼2.7 eV, respectively. The ground electronic states of NdO and NdS were determined as 15H (6s4fσ4fϕ4fδ) and 15H (4fϕ4fπ4fπ6s), with spectroscopic constants: bond length Re = 1.780 and 2.325 Å, and harmonic frequency ωe = 891 and 538 cm-1, respectively.

Unraveling the electronic structure of LuH, LuN, and LuNH: building blocks of new materials

Advances in superconductor technology have been pursued for decades, moving towards room temperature models, such as a postulated nitrogen-doped lutetium hydride network. While experimental observations have been contradictory, insight into the building blocks of potential new superconductor materials can be gained theoretically, unravelling the fascinating electronic structure of these compounds at a molecular level. Here, the fundamental building blocks of lutetium materials (LuH, LuN, and LuNH) have been examined. The structures, spectroscopic constants for the ground and excited states, and the potential energy curves have been obtained for these species using complete active self-consistent field (CASSCF) and multireference configuration interaction with Davidson's correction (MRCI+Q) methods. For LuNH, the energetic properties of its isomers are determined. The bond dissociation energies of the three building blocks are calculated with the state-of-the-art f-block ab initio correlation consistent composite approach (f-ccCA) and the high accuracy extrapolated ab initio thermochemistry (HEAT) scheme. As well, an analysis of different formation pathways of LuNH has been provided.

Element effects in endohedral metal-metal-bonding fullerenes M2@C82 (M = Sc, Y, La, Lu)

Endohedral metal-metal-bonding fullerenes have recently emerged, in which encapsulated metals form a metal-metal bond. However, the physical reasons why some metal elements prefer to form metal-metal bonds inside fullerene are still unclear. Herein, we reported first-principles calculations on electronic structures, bonding properties, dynamics, and thermodynamic stabilities of endohedral metallofullerenes M2@C82 (M = Sc, Y, La, Lu). Multiple bonding analysis approaches unambiguously reveal the existence of one two-center two-electron σ covalent metal-metal bond in M2@C82 (M = Sc, Y, Lu); however, the La-La bonding interaction in La2@C82 is weaker and could not be categorized as one metal-metal covalent bond. The energy decomposition analysis on bonding interactions between an encapsulated metal dimer and fullerene cages suggested that there exist two electron-sharing bonds between a metal dimer and fullerene cages. The reasons why La2 prefers to donate electrons to fullerene cages rather than form a standard σ covalent metal-metal bond are mainly attributed to two following facts: La2 has a lower ionization potential, while the hybridization of ns, (n - 1)d, and np atomic orbitals in La2 is higher. Ab initio molecular dynamic simulations reveal that the M-M bond length at room temperature follows the trend of Sc < Lu < Y. The statistical thermodynamics calculations at different temperatures reveal that the experimentally observed endohedral metal-metal-bonding fullerenes M2@C82 have high concentrations in the endohedral fullerene formation temperature range.

A route to high-accuracy ab initio description of electronic excited states in high-spin lanthanide-containing species: A case study of GdO

Accurate description of electronic excited states of high-spin molecular species is a yet unsolved problem in modern electronic structure theory. A composite computational scheme developed in the present work contributes to solving this task for a challenging case of lanthanide-containing molecules. In the scheme, the highest-spin states whose wavefunctions are dominated by a single Slater determinant are described at the single-reference (SR) CCSD(T) level, whereas the lower-spin states, being inherently multiconfigurational in their nature, are treated with multireference (MR) methods, MRCI and/or CASPT2. An original technique which scales MR results against SR CCSD(T) ones to improve the accuracy in the former is proposed and examined, taking the example of 12 electronic states of gadolinium monoxide, X9Σ-, Y7Σ-, A'9Δ, A1'7Δ, A9Π, A17Π, B9Σ-, B17Σ-, C9Π, C17Π, D9Σ-, and D17Σ-, up to 35 000 cm-1. A multitude of the corresponding Ω (spin-coupled) states was then studied within the state-interacting approach employing the full Breit-Pauli spin-orbit coupling operator with CASSCF-generated ΛS states as a basis. For all ΛS and Ω states, the Gd-O bond lengths, spectroscopic constants ωe, ωexe, αe, and adiabatic excitation energies are obtained. The theoretical predictions are in good agreement with the experimental data, with deviations in excitation energies not exceeding 350 cm-1 (1 kcal/mol). The spectroscopic properties of the yet unobserved electronic states, A'9Δ, A1'7Δ, C9Π, C17Π, D9Σ-, and D17Σ-, are evaluated for the first time.

Intensity-Borrowing Mechanisms Pertinent to Laser Cooling of Linear Polyatomic Molecules

A study of the intensity-borrowing mechanisms important to optical cycling transitions in laser-coolable polyatomic molecules arising from non-adiabatic coupling, contributions beyond the Franck-Condon approximation, and Fermi resonances is reported. It has been shown to be necessary to include non-adiabatic coupling to obtain computational accuracy that is sufficient to be useful for laser cooling of molecules. The predicted vibronic branching ratios using perturbation theory based on the non-adiabatic mechanisms have been demonstrated to agree well with those obtained from variational discrete variable representation calculations for representative molecules including CaOH, SrOH, and YbOH. The electron-correlation and basis-set effects on the calculated transition properties, including the vibronic coupling constants, the spin-orbit coupling matrix elements, and the transition dipole moments, and on the calculated branching ratios have been thoroughly studied. The vibronic branching ratios predicted using the present methodologies demonstrate that RaOH is a promising radioactive molecule candidate for laser cooling.

Probing the Chemical Bond between Lanthanides and Carbon: CeC, PrC, NdC, LuC, and TmC2

Resonant two-photon ionization experiments have been conducted to probe the bond dissociation energy (BDE) of the lanthanide-carbon bond, allowing the BDEs of CeC, PrC, NdC, LuC, and Tm-C₂ to be measured to high precision. Values of D₀(CeC) = 4.893(3) eV, D₀(PrC) = 4.052(3) eV, D₀(NdC) = 3.596(3) eV, D₀(LuC) = 3.685(4) eV, and D₀(Tm-C₂) = 4.797(6) eV are obtained. Additionally, the adiabatic ionization energy of LuC was measured, giving IE(LuC) = 7.05(3) eV. The electronic structure of these species, along with the previously measured LaC, has been further investigated using quantum chemical calculations. Despite LaC, CeC, PrC, and NdC having ground electronic configurations that differ only in the number of 4f electrons present and have virtually identical bond orders, bond lengths, fundamental stretching frequencies, and metallic oxidation states, a peculiar 1.30 eV range in bond dissociation energies exists for these molecules. A natural bond orbital analysis shows that the metal atoms in these molecules have a natural charge of +1 with a 5d² 4fⁿ 6s⁰ configuration while the carbon atom has a natural charge of -1 and a 2p³ configuration. The diabatic bond dissociation energies, calculated with respect to the lowest energy level of this separated ion configuration, show a greatly reduced energy range of 0.32 eV, with the diabatic BDE decreasing as the amount of 4f character in the σ-bond increases. Thus, the wide range of measured BDEs for these molecules is a consequence of the variation in atomic promotion energies at the separated ion limit. TmC₂ has a smaller BDE than the other LnC₂ molecules, due to the tiny amount of 5d participation in the valence molecular orbitals.

Correlated Dirac-Coulomb-Breit multiconfigurational self-consistent-field methods

The fully correlated frequency-independent Dirac-Coulomb-Breit Hamiltonian provides the most accurate description of electron-electron interaction before going to a genuine relativistic quantum electrodynamics theory of many-electron systems. In this work, we introduce a correlated Dirac-Coulomb-Breit multiconfigurational self-consistent-field method within the frameworks of complete active space and density matrix renormalization group. In this approach, the Dirac-Coulomb-Breit Hamiltonian is included variationally in both the mean-field and correlated electron treatment. We also analyze the importance of the Breit operator in electron correlation and the rotation between the positive- and negative-orbital space in the no-virtual-pair approximation. Atomic fine-structure splittings and lanthanide contraction in diatomic fluorides are used as benchmark studies to understand the contribution from the Breit correlation.

Theoretical Investigation of Single-Molecule-Magnet Behavior in Mononuclear Dysprosium and Californium Complexes

Early-actinide-based (U, Np, and Pu) single-molecule magnets (SMMs) have yet to show magnetic properties similar to those of highly anisotropic lanthanide-based ones. However, there are not many studies exploring the late-actinides (more than half-filled f shells) as potential candidates for SMM applications. We computationally explored the electronic structure and magnetic properties of a hypothetical Cf(III) complex isostructural to the experimentally synthesized Dy(dbm)₃(bpy) complex (bpy = 2,2'-bipyridine; dbm = dibenzoylmethanoate) via multireference methods and compared them to those of the Dy(III) analogue. This study shows that the Cf(III) complex can behave as a SMM and has a greater magnetic susceptibility compared to other experimentally and computationally studied early-actinide-based (U, Np, and Pu) magnetic complexes. However, Cf spontaneously undergoes α-decay and converts to Cm. Thus, we also explored the isostructural Cm(III)-based complex. The computed magnetic susceptibility and g-tensor values show that the Cm(III) complex has poor SMM behavior in comparison to both the Dy(III) and Cf(III) complexes, suggesting that the performance of Cf(III)-based magnets may be affected by α-decay and can explain the poor performance of experimentally studied Cf(III)-based molecular magnets in the literature. Further, this study suggests that the ligand field is dominant in Cf(III), which helps to increase the magnetization blocking barrier by nearly 3 times that of its 4f congener.

Guided Ion Beam Studies of the Dy + O → DyO+ + e- Chemi-ionization Reaction Thermochemistry and Dysprosium Oxide, Carbide, Sulfide, Dioxide, and Sulfoxide Cation Bond Energies

Guided ion beam tandem mass spectrometry (GIBMS) was used to measure the kinetic energy dependent product ion cross sections for reactions of the lanthanide metal dysprosium cation (Dy⁺) with O₂, SO₂, and CO and reactions of DyO⁺ with CO, O₂, and Xe. DyO⁺ is formed through an exothermic process when Dy⁺ reacts with O₂, whereas all other processes observed are found to be endothermic. The kinetic energy dependences of these cross sections were analyzed to yield 0 K bond dissociation energies (BDEs) for DyO⁺, DyC⁺, DyS⁺, DyO₂⁺, and DySO⁺. The 0 K BDE for DyO⁺ is determined to be 5.60 ± 0.02 eV from the weighted average of six independent thresholds, which are dominated by the slightly endothermic reaction of Dy⁺ with SO₂. Combined with the well-established Dy ionization energy (IE), this value indicates that the chemi-ionization reaction, Dy + O → DyO⁺ + e^-, is endothermic by 0.33 ± 0.02 eV. Theoretical BDEs for Dy⁺-O, Dy⁺-C, Dy⁺-S, ODy⁺-O, and Dy⁺-SO were calculated at several levels of theory and basis sets for comparison with experiment with reasonable agreement achieved.

Norm-Conserving 4f-in-Core Pseudopotentials and Basis Sets Optimized for Trivalent Lanthanides (Ln = Ce-Lu)

We present here a set of scalar-relativistic norm-conserving 4f-in-core pseudopotentials, together with complementary valence-shell Gaussian basis sets, for the lanthanide (Ln) series (Ce-Lu). The Goedecker, Teter, and Hutter (GTH) formalism is adopted with the generalized gradient approximation (GGA) for the exchange-correlation Perdew-Burke-Ernzerhof (PBE) functional. The 4f-in-core pseudopotentials are built through attributing 4f-subconfiguration 4fⁿ (n = 1-14) for Ln (Ln = Ce-Lu) into the atomic core region, making it possible to circumvent the difficulty of the description of the open 4fⁿ valence shell. A wide variety of computational benchmarks and tests have been carried out on lanthanide systems including Ln³⁺-containing molecular complexes, aqueous solutions, and bulk solids to validate the accuracy, reliability, and efficiency of the optimized 4f-in-core GTH pseudopotentials and basis sets. The 4f-in-core GTH pseudopotentials successfully replicate the main features of lanthanide structural chemistry and reaction energetics, particularly for nonredox reactions. The chemical bonding features and solvation shells, hydrolysis energetics, acidity constants, and solid-state properties of selected lanthanide systems are also discussed in detail by utilizing these new 4f-in-core GTH pseudopotentials. This work bridges the idea of keeping highly localized 4f electrons in the atomic core and efficient pseudopotential formalism of GTH, thus providing a highly efficient approach for studying lanthanide chemistry in multi-scale modeling of constituent-wise and structurally complicated systems, including electronic structures of the condensed phase and first-principles molecular dynamics simulations.

Synthesis and Characterisation of Novel Bis(diphenylphosphane oxide)methanidoytterbium(III) Complexes

Reaction of [YbCp₂(dme)] (Cp = cyclopentadienyl, dme = 1,2 dimethoxyethane) with bis(diphenylphosphano)methane dioxide (H₂dppmO₂) leads to deprotonation of the ligand H₂dppmO₂ and oxidation of ytterbium, forming an extremely air-sensitive product, [Yb^III(HdppmO₂)₃] (1), a six-coordinate complex with three chelating (OPCHPO) HdppmO₂ ligands. Complex 1 was also obtained by a redox transmetallation/protolysis synthesis from metallic ytterbium, Hg(C₆F₅)_2, and H₂dppmO₂. In a further preparation, the reaction of [Yb(C₆F₅)₂] with H₂dppmO₂, not only yielded compound 1, but also gave a remarkable tetranuclear cage, [Yb₄(µ-HdppmO₂)₆(µ-F)₆] (2) containing two [Yb(µ-F)]₂ rhombic units linked by two fluoride ligands and the tetranuclear unit is encapsulated by six bridging HdppmO₂ donors. The fluoride ligands of the cage result from C-F activation of pentafluorobenzene and concomitant formation of p-H₂C₆F₄ and m-H₂C₆F₄, the last being an unexpected product.

Ab initio composite strategies and multireference approaches for lanthanide sulfides and selenides

The f-block ab initio correlation consistent composite approach was used to predict the dissociation energies of lanthanide sulfides and selenides. Geometry optimizations were carried out using density functional theory and coupled cluster singles, doubles, and perturbative triples with one- and two-component Hamiltonians. For the two-component calculations, relativistic effects were accounted for by utilizing a third-order Douglas-Kroll-Hess Hamiltonian. Spin-orbit coupling was addressed with the Breit-Pauli Hamiltonian within a multireference configuration interaction approach. The state averaged complete active space self-consistent field wavefunctions obtained for the spin-orbit coupling energies were used to assign the ground states of diatomics, and several diagnostics were used to ascertain the multireference character of the molecules.

Observation of Selectively Populated Monohalide Excited States from the Reactions of Group 3 Metal (Sc, Y, and La) Monomers and Dimers with Halogen-Containing Molecules

The chemiluminescent reactions of the group 3 metals Sc and Y with F₂, Cl₂, Br₂, ClF, ICl (Sc), IBr (Y), and SF₆ and La with F₂, SF₆, Cl₂, and ClF have been studied at low pressures (6 × 10^-6 to 4 × 10^-4 Torr) using a beam-gas arrangement and extended to the 10^-3 Torr multiple collision pressure range. Contrary to previous reports, the observed chemiluminescent spectra are primarily attributed to emission from the metal monohalides. Extensive pressure and temperature dependence studies and high-level correlated molecular orbital theory calculations of the bond dissociation energies support this conclusion and the attribution of the chemiluminescence. Evidence for the "selective" production of a monohalide excited electronic state is obtained for several of the Sc and Y reactions. All reactions producing the metal monofluorides are first order with respect to the oxidant, while reactions producing the monochlorides and monobromides are found to be "faster than first order" with respect to the oxidant. This difference is associated with the metal halide bond dissociation energies and the metal halide product internal density of states. Analysis of the temperature dependence for six representative reactions indicates that the "selective" excited-state formation of the metal monohalides proceeds via a direct mechanism with negligible activation energy. We compare and contrast the present results with previous experiments and interpretations which have assigned the selective emission from these systems to the group 3 dihalides produced in a two-step reaction sequence analogous to an electron jump process. The current results suggest a distinctly different interpretation of the observed processes in these systems. The observed selectivity observed in these studies is remarkable given the significant number of known and potential excited states in the scandium and yttrium halides as well as their different electronic configurations.

Bonding properties of molecular cerium oxides tuned by the 4f-block from ab initio perspective

Probing chemical bonding in molecules containing lanthanide elements is of theoretical interest, yet it is computationally challenging because of the large valence space, relativistic effects, and considerable electron correlation. We report a high-level ab initio study that quantifies the many-body nature of Ce–O bonding with the coordination environment of the Ce center and particularly the roles of the 4 f orbitals. The growing significance of the overlap between Ce 4 f and O 2 p orbitals with the increasing coordination of Ce atoms enhances Ce–O bond covalency and in return directs the molecular geometry. Upon partial reduction from neutral to anionic ceria, the excessive electrons populate the Ce-centered localized 4 f orbital. The interplay between the admixture and localization of the 4 f-block dually modulates bonding patterns of cerium oxide molecules, underlying the importance of many-body interactions between ligands and various lanthanide elements.

Ab Initio Composite Approaches for Heavy Element Energetics: Ionization Potentials for the Actinide Series of Elements

The first, second, and third gas-phase ionization potentials have been determined for the actinide series of elements using an ab initio composite scalar and fully relativistic approach, employing the coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) and Dirac Hartree-Fock (DHF) methods, extrapolated to the complete basis set (CBS) limit. The impact of electron correlation and basis set choice within this framework are examined. Additionally, the first three ionization potentials were obtained using an ab initio heavy element correlation-consistent Composite Approach (here referred to as α-ccCA). This is the first utilization of a ccCA for actinide species.

Computational Chemistry Derivation of Cr, Mn, and La Hydroxide and Oxyhydroxide Thermodynamics

Thermodynamic quantities are calculated for gaseous hydroxides and oxyhydroxides of Cr, Mn, and La. These would form due to water-vapor-containing environments reacting with Cr-forming alloys or oxide components of potential fuel cell interconnects or anode materials. Structures and vibrational modes for the expected hydroxides and oxyhydroxides are calculated with the B3LYP hybrid functional. Enthalpies of formation from selected reactions for each species are calculated using the CCSD(T)/CBS approach. Results show good agreement with literature estimates, measurements, and calculations. The resultant data is reported as Δ_fH°(298), S°(298), and C_p(T) and put into the database for a free-energy minimizer code. Calculations are presented to show the hydroxide and oxyhydroxide vapor pressures above H₂O + Cr₂O₃, Mn₃O₄, and La₂O₃, as well as the anode material La_0.75Sr_0.25Cr_0.5Mn_0.5O_3-δ (LSCM).

Spin-Orbit Natural Transition Orbitals and Spin-Forbidden Transitions

Natural transition orbitals (NTOs) are in widespread use for visualizing and analyzing electronic transitions. The present work introduces the analysis of formally spin-forbidden transitions with the help of complex-valued spin-orbit (SO) NTOs. The analysis specifically focuses on the components in such transitions that cause their intensity to be nonzero because of SO coupling. Transition properties such as transition dipole moments are partitioned into SO-NTO hole-particle pairs, such that contributions to the intensity from specific occupied and unoccupied orbitals are obtained. The method has been implemented within the restricted active space (RAS) self-consistent field wave function theory framework, with SO coupling treated by RAS state interaction. SO-NTOs have a broad range of potential applications, which is illustrated by the T₂-S₁ state mixing in pyrazine, spin-forbidden versus spin-allowed 4f-5d transitions in the Tb³⁺ ion, and the phosphorescence of tris(2-phenylpyridine) iridium [Ir(ppy)₃].

Property-optimized Gaussian basis sets for lanthanides

Property-optimized Gaussian basis sets of split-valence, triple-zeta valence, and quadruple-zeta valence quality are developed for the lanthanides Ce-Lu for use with small-core relativistic effective core potentials. They are constructed in a systematic fashion by augmenting def2 orbital basis sets with diffuse basis functions and minimizing negative static isotropic polarizabilities of lanthanide atoms with respect to basis set exponents within the unrestricted Hartree-Fock method. The basis set quality is assessed using a test set of 70 molecules containing the lanthanides in their common oxidation states and f electron occupations. 5d orbital occupation turns out to be the determining factor for the basis set convergence of polarizabilities in lanthanide atoms and the molecular test set. Therefore, two series of property-optimized basis sets are defined. The augmented def2-SVPD, def2-TZVPPD, and def2-QZVPPD basis sets balance the accuracy of polarizabilities across lanthanide oxidation states. The relative errors in atomic and molecular polarizability calculations are ≤8% for augmented split-valence basis sets, ≤ 2.5% for augmented triple-zeta valence basis sets, and ≤1% for augmented quadruple-zeta valence basis sets. In addition, extended def2-TZVPPDD and def2-QZVPPDD are provided for accurate calculations of lanthanide atoms and neutral clusters. The property-optimized basis sets developed in this work are shown to accurately reproduce electronic absorption spectra of a series of LnCp₃ ^'- complexes (Cp' = C₅H₄SiMe₃, Ln = Ce-Nd, Sm) with time-dependent density functional theory.

Electronic structure of NdO via slow photoelectron velocity-map imaging spectroscopy of NdO--

Electronically excited NdO is a possible product of the chemistry associated with the release of Nd into the ionosphere, and emission from these states may contribute to the observations following such experiments. To better characterize the energetics and spectroscopy of NdO, we report a combined experimental and theoretical study using slow photoelectron velocity-map imaging spectroscopy of cryogenically cooled NdO^- anions (cryo-SEVI) supplemented by wave function-based quantum-chemical calculations. Using cryo-SEVI, we measure the electron affinity of NdO to be 1.0091(7) eV and resolve numerous transitions to low-lying electronic and vibrational states of NdO that are assigned with the aid of the electronic structure calculations. Additionally, temperature-dependent data suggest contributions from the (2)4.5 state of NdO^- residing 2350 cm^-1 above the ground anion state. Photodetachment to higher-lying excited states of NdO is also reported, which may help to clarify observations from prior release experiments.

Improving the theoretical description of Ln(III)/An(III) separation with phosphinic acid ligands: a benchmarking study of structure and selectivity

The efficient separation of trivalent lanthanides from minor actinides with soft-donor ligands, while showing experimental promise, has theorists continuing to search for suitable approaches for describing and interpreting selectivity. To remedy this, we employ several computational methods in describing the structure of model M(H₂PX₂)₃ complexes, with M = Eu and Am, and X = O, S, Se, and Te, and predicting the selectivity of model phosphinic acid ligands in Eu(III)/Am(III) separation. After first establishing a set of MP2 and CCSD(T)-DKH3 results as benchmarks, we evaluate several density functionals and descriptions of valence shells for their accuracy with respect to metal-ligand bonding and selectivity. We find that commonly employed functionals with a 0-27% range of exact exchange used with small-core effective core potentials or with an explicit treatment of the relativistic effects (DKH2) incorrectly predict a decrease in the metal-ligand bond distance in going from Eu(III) to Am(III) and completely fail to track a selectivity trend, even giving a wrong sign for some or all ligands. Surprisingly, when these functionals are used in conjunction with an f-in-core description of metal ions, the correct trend in selectivity is recovered, though Am-X distances are overestimated in relation to Eu-X. Functionals with high components of exact exchange (50%) and double-hybrid functionals are reasonably aligned with benchmark results, pointing to the problems of DFT with small exact exchange fractions to handle f-electrons. Natural bond orbital analyses reveal that these poorly performing functionals disproportionately overpopulate outer f orbitals in the model complexes. We anticipate that recommendations resulting from this work will lead to more accurate theoretical descriptions of lanthanide/actinide selectivity with soft-donor chalcogen-based ligands in the future.

Holmium (Ho) oxide, carbide, and dioxide cation bond energies and evaluation of the Ho + O → HoO+ + e- chemi-ionization reaction enthalpy

Guided ion beam tandem mass spectrometry (GIBMS) and quantum chemical calculations are employed to evaluate the title chemi-ionization reaction with holmium. Exchange reactions of Ho⁺ with O₂, CO, and SO₂ and HoO⁺ with CO, as well as collision-induced dissociation (CID) reactions of HoO⁺ with Xe, O₂, and CO, were performed using GIBMS. Formation of HoO⁺ is exothermic in reactions with O₂ and SO₂ but endothermic for reaction with CO, as is the exchange reaction of HoO⁺ with CO. Quantitative analysis of these reactions and the three CID reactions provides a robust method to determine the bond dissociation energy (BDE) of Ho⁺-O, 6.02 ± 0.13 eV. BDEs for Ho⁺-C and OHo⁺-O are also measured as 2.27 ± 0.19 and 2.70 ± 0.27 eV, respectively. All three measurements are the first direct determinations of these BDEs. By combining the BDE of HoO⁺ with the well-established ionization energy of Ho, the exothermicity of Ho in the title chemi-ionization reaction can also be obtained as 0.00 ± 0.13 eV. All experimental thermochemistry was then compared to quantum chemical calculations for the purpose of establishing benchmarks and validation. BDEs determined via these calculations are in agreement with the experiment within the inherent experimental and theoretical uncertainties, with results obtained at the coupled-cluster with single, double, and perturbative triple excitations, CCSD(T), using all-electron basis sets yielding the most accurate results.

Accurate prediction and measurement of vibronic branching ratios for laser cooling linear polyatomic molecules

We report a generally applicable computational and experimental approach to determine vibronic branching ratios in linear polyatomic molecules to the 10^-5 level, including for nominally symmetry-forbidden transitions. These methods are demonstrated in CaOH and YbOH, showing approximately two orders of magnitude improved sensitivity compared with the previous state of the art. Knowledge of branching ratios at this level is needed for the successful deep laser cooling of a broad range of molecular species.

Unsupported Lanthanide-Transition Metal Bonds: Ionic vs Polar Covalent?

Lanthanide-transition metal complexes continue to be of interest, not only because of their synthetic challenge but also of their promising magnetic properties. Computational work examining the chemical bonding between lanthanides and transition metals in PyCp₂Ln-TMCp(CO)₂ (DyPyCp₂^2- = [2,6-(CH₂C₅H₃)₂C₅H₃N]^2-) reveals strong Ln-TM dative bonds. Gas-phase optimized geometries are in good agreement with experimental structures at the density functional theory (DFT) level with large-core pseudopotentials. From La to Lu, there is a small increase in the bond dissociation energy, as well as a decrease in Ln-Fe bond lengths. Energy decomposition analyses attribute this trend to an increase in the electrostatic contribution from the decreasing bond length and a modest increase in the orbital contribution. The natural bond orbital analysis clearly indicates that 3d⁶ "lone pairs" in the [FeCp(CO)₂]^- fragment act as a Lewis bases donating nearly 0.5 electron to Ln virtual orbitals of mainly d character. The interfragment bonding was also quantified by the quantum theory of atoms in molecules, which indicates that the Ln-Fe bond is more covalent than the Ca-Fe bond in the hypothetical CpCa-FeCp(CO)₂ but less covalent than the Zn-Fe bond in the hypothetical CpZn-FeCp(CO)₂. Further comparisons suggest that to the [PyCp₂Ln]⁺ cation the [FeCp(CO)₂]^- anion appears much like a halide. Overall, these Ln-TM dative bonds appear to have strong electrostatic contributions as well as significant orbital mixing and dispersion contributions.

The electron affinity of the uranium atom

The results of a combined experimental and computational study of the uranium atom are presented with the aim of determining its electron affinity. Experimentally, the electron affinity of uranium was measured via negative ion photoelectron spectroscopy of the uranium atomic anion, U^-. Computationally, the electron affinities of both thorium and uranium were calculated by conducting relativistic coupled-cluster and multi-reference configuration interaction calculations. The experimentally determined value of the electron affinity of the uranium atom was determined to be 0.309 ± 0.025 eV. The computationally predicted electron affinity of uranium based on composite coupled cluster calculations and full four-component spin-orbit coupling was found to be 0.232 eV. Predominately due to a better convergence of the coupled cluster sequence for Th and Th^-, the final calculated electron affinity of Th, 0.565 eV, was in much better agreement with the accurate experimental value of 0.608 eV. In both cases, the ground state of the anion corresponds to electron attachment to the 6d orbital.

Coupled Cluster Studies of Platinum-Actinide Interactions. Thermochemistry of PtAnOn+ (n = 0-2 and An = U, Np, Pu)

Accurate Pt-An bond dissociation enthalpies (BDEs) for PtAnOⁿ⁺ (An = U, Np, Pu and n = 0-2) and the corresponding enthalpies for the Pt + OAnOⁿ⁺ substitution reactions have been studied for the first time using an accurate composite coupled cluster approach. Analogous O-AnOⁿ⁺ bond dissociation enthalpies are also presented. To make the study possible, new correlation consistent basis sets optimized using the all-electron third-order Douglas-Kroll-Hess (DKH3) scalar relativistic Hamiltonian are developed and reported for Pt and Au, with accompanying benchmark calculations of their atomic ionization potentials to demonstrate the effectiveness of the new basis sets. For the charged PtAnOⁿ⁺ species (n = 1, 2), a low-spin state (LSS) for which the Pt-An σ bond is doubly occupied is studied together with a high-spin state (HSS) obtained by unpairing the σ bond orbital and placing one electron into the An 5f shell. The relative energies of the two spin states have been compared and qualitatively assessed via natural population and natural bond analyses. The enthalpies for the Pt substitution reactions, i.e., Pt + OAnOⁿ⁺ → PtAnOⁿ⁺ + O, are calculated to range from about 14-62 kcal/mol, and the Pt-AnOⁿ⁺ bond dissociation enthalpies range from about 78-149 kcal/mol for the ground electronic states. For the PtAnO⁺ species, the LSSs were all predicted to be the ground state, whereas the PtAnO²⁺ molecules all favored the HSSs. The prediction for PtUO²⁺ is consistent with previous theoretical findings. The natural bond orbital analyses indicate a triple bond between An and O, with a double to quadruple bond between the An and Pt.

Thermochemistry of Gaseous Ytterbium and Gadolinium Hydroxides and Oxyhydroxides

Gd₂O₃ and Yb₂O₃ are the proposed constituents of advanced coating systems in combustion environments. In such environments, they are exposed to high-temperature water vapor, which would lead to gaseous hydroxide formation. Thermodynamic parameters are reported for YbO_n(OH)_m and GdO_n(OH)_m species. We first study the MH, MO, MF, and MCl (M = Yb and Gd) species, where some experimental data exist. Structures and spectroscopic constants were calculated at the B3LYP level. For YbO_n(OH)_m, the B3LYP approach is used in conjunction with an effective core potential, while for GdO_n(OH)_m, it was necessary to use all-electron basis sets. Enthalpies of formation were calculated with a BD(T) approach. The enthalpies of formation, entropies, and heat capacities were added to a thermochemical database. Hydroxide and oxyhydroxide vapor pressures are calculated above pure Yb₂O₃, Gd₂O₃, and Y₂O₃ in 50% H₂O/Ar from 1000 to 3000 K. Hydroxide and oxyhydroxide vapor pressures are also calculated for potential coating compositions.

Activation of D2 by Neodymium Cation (Nd+): Bond Energy of NdH+ and Mechanistic Insights through Experimental and Theoretical Studies

The kinetic-energy-dependent cross section for the reaction of Nd⁺ with D₂ was studied by using a guided ion beam tandem mass spectrometer. The formation of NdD⁺ is endothermic, and analysis of the reaction cross section gave an NdH⁺ 0 K bond dissociation energy (BDE) of 1.99 ± 0.06 eV. Theoretical calculations for the NdH⁺ BDE were performed for comparison with the experimental thermochemistry and generally gave accurate results. Additionally, relaxed potential energy surfaces for NdH₂⁺ were performed, and no strongly bound dihydride intermediate was located. The Nd⁺ + D₂ reactivity and BDE of NdH⁺ are compared with analogous results for the lanthanide cations La⁺, Ce⁺, Pr⁺, Sm⁺, Gd⁺, and Lu⁺ to establish periodic trends and insight into the role of the electronic configurations on this reactivity and the lanthanide hydride cation bond strengths.

Predicting lanthanide coordination structures in solution with molecular simulation

The chemical and physical properties of lanthanide coordination complexes can significantly change with small variations in their molecular structure. Further, in solution, coordination structures (e.g., lanthanide-ligand complexes) are dynamic. Resolving solution structures, computationally or experimentally, is challenging because structures in solution have limited spatial restrictions and are responsive to chemical or physical changes in their surroundings. To determine structures of lanthanide-ligand complexes in solution, a molecular simulation approach is presented in this chapter, which concurrently considers chemical reactions and molecular dynamics. Lanthanide ion, ligand, solvent, and anion molecules are explicitly included to identify, in atomic resolution, lanthanide coordination structures in solution. The computational protocol described is applicable to determining the molecular structure of lanthanide-ligand complexes, particularly with ligands known to bind lanthanides but whose structures have not been resolved, as well as with ligands not previously known to bind lanthanide ions. The approach in this chapter is also relevant to elucidating lanthanide coordination in more intricate structures, such as in the active site of enzymes.

Analytic evaluation of energy first derivatives for spin-orbit coupled-cluster singles and doubles augmented with noniterative triples method: General formulation and an implementation for first-order properties

A formulation of analytic energy first derivatives for the coupled-cluster singles and doubles augmented with noniterative triples [CCSD(T)] method with spin-orbit coupling included at the orbital level and an implementation for evaluation of first-order properties are reported. The standard density-matrix formulation for analytic CC gradient theory adapted to complex algebra has been used. The orbital-relaxation contributions from frozen core, occupied, virtual, and frozen virtual orbitals to analytic spin-orbit CCSD(T) gradients are fully taken into account and treated efficiently, which is of importance to calculations of heavy elements. Benchmark calculations of first-order properties including dipole moments and electric-field gradients using the corresponding exact two-component property integrals are presented for heavy-element containing molecules to demonstrate the applicability and usefulness of the present analytic scheme.

Evaluation of the Pr + O → PrO+ + e- chemi-ionization reaction enthalpy and praseodymium oxide, carbide, dioxide, and carbonyl cation bond energies

Guided ion beam tandem mass spectrometry (GIBMS) was used to measure the kinetic energy dependent product ion cross sections for reactions of the lanthanide metal praseodymium cation (Pr+) with O2, CO2, and CO and reactions of PrO+ with CO, O2, and Xe. PrO+ is formed through barrierless exothermic processes when the atomic metal cation reacts with O2 and CO2, whereas all other reactions are observed to be endothermic. Analyses of the kinetic energy dependences of these cross sections yield 0 K bond dissociation energies (BDEs) for PrO+, PrC+, PrCO+, and PrO2+. The 0 K BDE for PrO+ is determined to be 7.62 ± 0.09 eV from the weighted average of five independent thresholds. This value is combined with the well-established ionization energy (IE) of Pr to indicate an exothermicity of the chemi-ionization reaction, Pr + O → PrO+ + e-, of 2.15 ± 0.09 eV. Additionally, BDEs of Pr+-C, OPr+-O, and Pr+-CO are determined to be 2.97 ± 0.10. 2.47 ± 0.11, and 0.31 ± 0.07 eV. Theoretical Pr+-O, Pr+-C, OPr+-O, and Pr+-CO BDEs are calculated for comparison with experimental values. The Pr+-O BDE is underestimated at the B3LYP and PBE0 level of theory but better agreement is obtained using the coupled-cluster with single, double, and perturbative triple excitations, CCSD(T), level. Density functional theory approaches yield better agreement for the BDEs of Pr+-C, OPr+-O, and Pr+-CO.

Electron-Nucleus Hyperfine Coupling Calculated from Restricted Active Space Wavefunctions and an Exact Two-Component Hamiltonian

Exact two-component (X2C) relativistic nuclear hyperfine magnetic field operators were incorporated in X2C ab initio wavefunction calculations at the multireference restricted active space (RAS) level for calculations of nuclear hyperfine magnetic properties. Spin-orbit coupling was treated via RAS state interaction (SO-RASSI). The method was tested by calculations of electron-nucleus hyperfine coupling constants. The approach, implemented in the OpenMolcas program, overcomes a major limitation of a previous SO-RASSI implementation for hyperfine coupling that relied on nonrelativistic hyperfine operators [J. Chem. Theor. Comput. 2015, 11, 538-549] and therefore had limited applicability. Results from calculations on systems with light and heavy main group elements, transition metals, lanthanides, and one actinide complex demonstrate reasonably good agreement with experimental data, where available, as long as the active space can generate sufficient spin polarization.

All-electron relativistic spin-orbit multireference computation to elucidate the ground state of CeH

The all-electron relativistic spin-orbit multiconfiguration/multireference computations with the Sapporo basis sets were carried out to elucidate the characters of the low-lying quasi-degenerate electronic states for the CeH diatomic molecule. The present computations predict the ground state of CeH to be a pure quartet state of 4f15d1(5dσ-H1s)26s1 configuration (Ω = 3.5). The first excited state (Ω = 2.5) shows a doublet dominant of 4f1(5dσ-H1s)26s2 configuration at a short bond length while it changes to a quartet dominant at a long bond length. The Ce-H stretching fundamental frequency was calculated to be 1345 cm-1 in the ground state, which is in good agreement with the experimental value, 1271 cm-1, measured by a matrix-isolation technique.

Cerium Cation (Ce+) Reactions with H2, D2, and HD: CeH+ Bond Energy and Mechanistic Insights from Guided Ion Beam and Theoretical Studies

Reactions of the atomic lanthanide cerium cation (Ce⁺) with H₂, D₂, and HD were studied by using guided ion beam tandem mass spectrometry. Analysis of the kinetic-energy-dependent endothermic reactions to form CeH⁺ (CeD⁺) led to a 0 K bond dissociation energy (BDE) for CeH⁺ of 2.19 ± 0.09 eV. Theoretical calculations for CeH⁺ were performed at the B3LYP, BHLYP, and PBE0 levels of theory and overestimate the experimental BDE. In contrast, extrapolation to the complete basis set limit using coupled-cluster with single, double, and perturbative triple excitations, CCSD(T), gave a value (2.33 eV) in reasonable agreement with the experimental BDE. The branching ratio of the CeH⁺ and CeD⁺ products in the HD reaction suggests that the reaction occurs via a statistical mechanism involving a long-lived intermediate. Relaxed potential energy surfaces for CeH₂⁺ were computed and are consistent with the availability of such an intermediate, but the crossing point between quartet and doublet surfaces helps explain the inefficiency of the association reaction observed in the literature. The reactivity and CeH⁺ BDE are compared with previous results for group 4 transition metal cations (Ti⁺, Zr⁺, and Hf⁺), other lanthanides (La⁺, Sm⁺, Gd⁺, and Lu⁺), and the isovalent actinide Th⁺. Periodic trends and insight into the role of the electronic configuration on metal-hydride bond strength are discussed.

Polarizabilities, dispersion coefficients, and retardation functions at the complete basis set CCSD limit: From Be to Ba plus Yb

Static and dynamic polarizabilities of alkaline earth metal atoms Be-Ba and of the Yb atom, as well as dispersion coefficients and retardation functions for their long-range interactions, are used as a benchmark for the restricted coupled cluster method with singles and doubles (CCSD) and noniterative triples added [CCSD(T)] and related polarization propagator CCSD(3) methods at the complete basis set limit. The latter is attained through the sequence of the augmented correlation-consistent polarized weighted core valence n-zeta basis sets with the exact 2-component approximation for the scalar relativistic effects and with the small-core effective core potentials (for Ca, Sr, and Ba). At the converged level of core correlation treatment, the finite-field CCSD(T) method reproduces the best available data for the static dipole and quadrupole polarizabilities better than 1% and 4%, respectively. Systematic cancelation of the triple contribution in the CCSD(3) calculations of the dynamic polarizabilities of alkaline earth metal atoms makes their dispersion coefficients accurate within 3%. The retardation functions are computed and used for the analysis of the long-range interactions in the homonuclear dimers. Implications to accurate ab initio calculations of the global interaction potentials are discussed.

Formation of Cerium and Neodymium Isocyanides in the Reactions of Cyanogen with Ce and Nd Atoms in Argon Matrices

Laser ablation of metallic Ce and Nd reacting with cyanogen in excess argon during codeposition at 4 K forms Ce(NC)_x and Nd(NC)_x for x = 1-3, which are identified from their matrix infrared spectra using cyanogen substituted with ¹³C and ¹⁵N. The electronic structure calculations were performed for isocyano and cyano Cd and Nd compounds for up to n = 4. The frequencies were calculated at the density functional theory level with three different functionals as well as correlated molecular orbital theory (MP2) and are consistent with the experimental assignments and the corresponding ¹²C/¹³C isotopic frequency ratios for the isocyano species. The computed frequencies for the analogous cyanide complexes are significantly higher than those for the isocyano isomers, and they are not observed in the spectra. The high spin isocyano complexes are the lowest energy structures. On the basis of the natural population analysis results, the bonding in ⁴CeNC and ⁶NdNC is essentially purely ionic with the Ce/Nd in the +I-oxidation state. The bonding for disocyano (³Ce(NC)₂ and ⁵Nd(NC)₂) and triisocyano (²Ce(NC)₃ and ⁴Nd(NC)₃) complexes is still quite ionic with the lanthanide in the +II and +III formal oxidation states, respectively. For ¹Ce(NC)₄, the oxidation state is best described as being between +III and +IV. Formation of ⁵Nd(NC)₄ does not really change the electron configuration on the Nd from that in ⁴Nd(NC)₃ and the oxidation state on the Nd remains at +III. Although Nd compounds with up to 3 NC^- groups have more ionic binding than do the corresponding Ce compounds, Ce(NC)₄ has more ionic binding than does Nd(NC)₄. The ionic nature of isocyano Ce and Nd complexes decreases as the number of isocyano groups increases. The energetics of formation of the isocyano Ce and Nd complexes using cyanogen or CN radicals are calculated to be mostly due to exothermic processes, with the exothermicity decreasing as the number of isocyano groups increases.