All-electron double zeta basis sets for the lanthanides: Application in atomic and molecular property calculations

The solution structures and relative stability constants of lanthanide-EDTA complexes predicted from computation

Ligand selectivity to specific lanthanide (Ln) ions is key to the separation of rare earth elements from each other. Ligand selectivity can be quantified with relative stability constants (measured experimentally) or relative binding energies (calculated computationally). The relative stability constants of EDTA (ethylenediaminetetraacetic acid) with La3+, Eu3+, Gd3+, and Lu3+ were predicted from relative binding energies, which were quantified using electronic structure calculations with relativistic effects and based on the molecular structures of Ln-EDTA complexes in solution from density functional theory molecular dynamics simulations. The protonation state of an EDTA amine group was varied to study pH ∼7 and ∼11 conditions. Further, simulations at 25 °C and 90 °C were performed to elucidate how structures of Ln-EDTA complexes varying with temperature are related to complex stabilities at different pH conditions. Relative stability trends are predicted from computation for varying Ln3+ ions (La, Eu, Gd, Lu) with a single ligand (EDTA at pH ∼11), as well as for a single Ln3+ ion (La) with varying ligands (EDTA at pH ∼7 and ∼11). Changing the protonation state of an EDTA amine site significantly changes the solution structure of the Ln-EDTA complex resulting in a reduction of the complex stability. Increased Ln-ligand complex stability is correlated to reduced structural variations in solution upon an increase in temperature.

Laser-Controlled Implementation of Controlled-NOT, Hadamard, SWAP, and Pauli Gates as Well as Generation of Bell States in a 3d-4f Molecular Magnet

Using high-level ab initio many-body theory, we theoretically propose that the Dy and the Ni atoms in the [Dy₂Ni₂(L)₄(NO₃)₂(DMF)₂] real molecular magnet as well as in its core, that is, the [Dy₂Ni₂O₆] system, act as two-level qubit systems. Despite their spatial proximity we can individually control each qubit in this highly correlated real magnetic system through specially designed laser-pulse combinations. This allows us to prepare any desired two-qubit state and to build several classical and quantum logic gates, such as the two-qubit (binary) CNOT gate with three distinct laser pulses. Other quantum logic gates include the single-qubit (unary) quantum X, Y, and Z Pauli gates; the Hadamard gate (which necessitates the coherent quantum superposition of two many-body electronic states); and the SWAP gate (which plays an important role in Shor's algorithm for integer factorization). Finally, by sequentially using the achieved CNOT and Hadamard gates we are able to obtain the maximally entangled Bell states, for example, (12)(|00⟩ + |11⟩).

Lanthanide-dependent coordination interactions in lanmodulin: a 2D IR and molecular dynamics simulations study

The biological importance of lanthanides, and the early lanthanides (La³⁺-Nd³⁺) in particular, has only recently been recognized, and the structural principles underlying selective binding of lanthanide ions in biology are not yet well established. Lanmodulin (LanM) is a novel protein that displays unprecedented affinity and selectivity for lanthanides over most other metal ions, with an uncommon preference for the early lanthanides. Its utilization of EF-hand motifs to bind lanthanides, rather than the Ca²⁺ typically recognized by these motifs in other proteins, has led it to be used as a model system to understand selective lanthanide recognition. Two-dimensional infrared (2D IR) spectroscopy combined with molecular dynamics simulations were used to investigate LanM's selectivity mechanisms by characterizing local binding site geometries upon coordination of early and late lanthanides as well as calcium. These studies focused on the protein's uniquely conserved proline residues in the second position of each EF-hand binding loop. We found that these prolines constrain the EF-hands for strong coordination of early lanthanides. Substitution of this proline results in a more flexible binding site to accommodate a larger range of ions but also results in less compact coordination geometries and greater disorder within the binding site. Finally, we identify the conserved glycine in the sixth position of each EF-hand as a mediator of local binding site conformation and global secondary structure. Uncovering fundamental structure-function relationships in LanM informs the development of synthetic biology technologies targeting lanthanides in industrial applications.

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.

Computational Prediction of All Lanthanide Aqua Ion Acidity Constants

The protonation state of lanthanide-ligand complexes, or lanthanide-containing porous materials, with many Brønsted acid sites can change due to proton loss/gain reactions with water or other heteroatom-containing compounds. Consequently, variations in the protonation state of lanthanide-containing species affect their molecular structure and desired properties. Lanthanide(III) aqua ions undergo hydrolysis and form hydroxides; they are the best characterized lanthanide-containing species with multiple Brønsted acid sites. We employed constrained ab initio molecular dynamics simulations and electronic structure calculations to determine all acidity constants of the lanthanide(III) aqua ions solely from computation. The first, second, and third acidity constants of lanthanide(III) aqua ions were predicted, on average, within 1.2, 2.5, and 4.7 absolute pK_a units from experiment, respectively. A table includes our predicted pK_a values alongside most experimentally measured pK_a values known to date. The approach presented is particularly suitable to determine the Brønsted acidity of lanthanide-containing systems with multiple acidic sites, including those whose measured acidity constants cannot be linked to specific acid sites.

Application of the Molecular Invariom Model for the Study of Interactions Involving Fluorine Atoms in the {$${\text{Yb}}_{{\text{2}}}^{{{\text{II}}}}$$(μ2-OCH(CF3)2)3(μ3-OCH(CF3)2)2YbIII(OCH(CF3)2)2(THF)(Et2O)} Complex

Abstract

The electron density distributions obtained by the quantum-chemical (density functional theory) calculations and molecular invariom model in the trimeric ytterbium complex with the hexafluoroisopropoxide ligands {$${\text{Yb}}_{{\text{2}}}^{{{\text{II}}}}$$(μ2-OR)3(μ3-OR)2YbIII(OR)2(THF)(Et2O)} (I) (where R is CH(CF3)2, and THF is tetrahydrofuran) are compared. The main topological characteristics of the electron density at the critical points (3, –1) corresponding to the interactions of the ytterbium atoms in the coordination sphere obtained using two studied approaches demonstrate excellent agreement. The maximum divergence between the density functional calculations and molecular invariom model is observed for the intramolecular interactions involving the fluorine atoms (F···F, F···H, and F···O) in the structure of complex I. Geometry optimization leads to a higher number of these interactions in the complex. The energy corresponding to these interactions also increases. However, the main topological characteristics for the F···X interactions (X = F, H, O), which can be localized in the framework of both methods, remain within the transferability index range. An analysis of the deformation electron density shows that the Fδ–···Fδ– interactions are determined by the correspondence of the region of electron density concentration on one of the fluorine atoms to the region of electron density depletion on the second fluorine atom regardless of the method of measuring the electron density distribution.

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.

Solution structure of a europium–nicotianamine complex supports that phytosiderophores bind lanthanides

The structures of europium–EDTA (known lanthanide chelator) and europium–nicotianamine (biochemical precursor of phytosiderophores) complexes are resolved, in solution, with ab initio molecular dynamics as well as excitation and emission spectroscopy.

Structural and Electronic Characterization of a Photoresponsive Lanthanum(III) Complex Incorporated into Electrospun Fibers for Phosphate Ester Catalysis

Herein, we present the light-induced synthesis and characterization of a La³⁺/spiropyran derivative complex (LaMC) and its application as a catalyst when incorporated into electrospun polycaprolactone (PCL) fibers. In addition to experimental methods, computational calculations were also essential to better understand the structure and electronic characteristics of LaMC. The LaMC complex was identified as a 10-coordinated structure with the La³⁺ ion coordinated by four oxygens from the phenolate and the carbonyl of the carboxyl acid group from both MC ligands and by six oxygens from three nitrate ligands. In addition, LaMC was capable of getting reversibly isomerized by UV or visible light cycling. All PCL fibers were successively obtained, and their morphologies, surface properties, and catalytic behavior were studied. Results showed that PCL/LaMC fibers were capable of catalyzing bis(2,4-dinitrophenyl)phosphate degradation efficiently. Complete hydrolysis was accomplished in only 1.5 days relative to the half-life time of 35 days for the uncatalyzed hydrolysis at pH 8.1 and 25 °C.