Two-component methods of relativistic quantum chemistry: from the Douglas–Kroll approximation to the exact two-component formalism

Influence of the Fe(II) Spin State on Iron-Ligand Bonds in Heme Model Iron-Porphyrin Complexes with 4, 5 and 6 Ligands

In this work heme models with four [Fe(II)(P)], five [Fe(II)(P)Im], [Fe(II)(P)O2] and six ligands [Fe(II)(P)(Im)O2], where P=porphyrin, with different spin states (ms=5, 3 and 1) of the iron atom were investigated using relativistic-corrected quantum chemistry methods (PW6B95-D3-DKH/jorge-TZP-DKH). Dependence of the iron-ligand bond properties on (i) spin state and (ii) number of ligands were analyzed using natural bond orbital analysis, electron density topology, electrostatic potential and electron localization function. It is shown that reversible binding of O2 is possible in case of formation of semicoordination bond between Fe(II) and imidazole. Binding of the fifth and sixth ligand from the energetic and orbital points of view is more favorable for the triplet Fe(II) state. At the same time for the six-coordinated complex [Fe(II)(P)(Im)O2] interconversion of Fe(II) electrons of valent 3d orbital from quintet to triplet and vice versa is possible under thermal fluctuations (energy barriers less than 2 kcal/mol).

A new computational framework for spinor-based relativistic exact two-component calculations using contracted basis functions

A new computational framework for spinor-based relativistic exact two-component (X2C) calculations is developed using contracted basis sets with a spin-orbit contraction scheme. Generally contracted, j-adapted basis sets of p-block elements using primitive functions in the correlation-consistent basis sets are constructed for the X2C Hamiltonian with atomic mean-field spin-orbit integrals (the X2CAMF scheme). The contraction coefficients are taken from atomic X2CAMF Hartree-Fock spinors, thereby following the simple concept of a linear combination of atomic orbitals. Benchmark calculations of spin-orbit splittings, equilibrium bond lengths, and harmonic vibrational frequencies demonstrate the accuracy and efficacy of the j-adapted spin-orbit contraction scheme.

Beyond Electrons: Correlation and Self-Energy in Multicomponent Density Functional Theory

Post-Kohn-Sham methods are used to evaluate the ground-state correlation energy and the orbital self-energy of systems consisting of multiple flavors of different fermions. Starting from multicomponent density functional theory, suitable ways to arrive at the corresponding multicomponent random-phase approximation and the multicomponent Green's functionG W ${GW}$ approximation, including relativistic effects, are outlined. Given the importance of both of this methods in the development of modern Kohn-Sham density functional approximations, this work will provide a foundation to design advanced multicomponent density functional approximations. Additionally, theG W ${GW}$ quasiparticle energies are needed to study light-matter interactions with the Bethe-Salpeter equation.

Nature of ultrafast dynamics in the lowest-lying singlet excited state of [Ru(bpy)3]2

This work presents mechanisms to rationalize the nature of ultrafast photochemical and photophysical processes on the first singlet metal-ligand charge transfer state (1MLCT1) of the [Ru(bpy)3]2+ complex. The 1MLCT1 state is the lowest-lying singlet excited state and the most important intermediate in the early evolution of photoexcited [Ru(bpy)3]2+*. The results obtained from simple but interpretable theoretical models show that the 1MLCT1 state can be very quickly formed via both direct photo-excitation and internal conversions and then can efficiently relax to its equilibrium geometry in ca. 5 fs. The interligand electron transfer (ILET) on the potential energy surface of the 1MLCT1 state is also extremely fast, with a rate constant of ca. 1.38 × 1013 s-1. The ultrafast ILET implies that the excited electron can dynamically delocalize over the three bpy ligands, despite the fact that the excited electron may be localized on either one of the three ligands at the equilibrium geometries of the three symmetric equivalent minima. Since rapid ILET essentially suggests delocalization, the long-standing controversy in inorganic photophysics-whether the excited electron is localized or delocalized-may therefore be calmed down to some extent.

Unravelling the 6sp ← 6s absorption spectra of Bi(III) complexes

We report a spectroscopic and computational study that investigates the absorption spectra of Bi(III) complexes, which often show an absorption band in the UV region (∼270-350 nm) due to 6sp ← 6s transitions. We investigated the spectra of three simple complexes, [BiCl5]2-, [BiCl6]3- and [Bi(DMSO)8]3+, which show absorption maxima at 334, 326 and 279 nm due to 3P1 ← 1S0 transitions. Theoretical calculations based on quasi-degenerate N-electron valence perturbation theory to second order (QD-NEVPT2) provide an accurate description of the absorption spectra when employing CAS(2,9) wave functions. We next investigated the absorption spectra of the [Bi(NOTA)] complex (H3NOTA = 1,4,7-triazacyclononane-1,4,7-triacetic acid), which forms ternary complexes [Bi(NOTA)X]- (X = Cl, Br or I) in the presence of excess halide in aqueous solutions. Halide binding has an important impact on the position of the 3P1 ← 1S0 transition, which shifts progressively to longer wavelengths from 282 nm ([Bi(NOTA)]) to 298 nm (X = Cl), 305 nm (X = Br) and 325 nm (X = I). Subsequent QD-NEVPT2 calculations indicate that this effect is related to the progressive stabilization of the spin-orbit free states associated with the 6s16p1 configuration on increasing the covalent character of the metal-ligand(s) bonds, rather than with significant differences in spin-orbit coupling (SOC). These studies provide valuable insight into the coordination chemistry of Bi(III), an ion with increasing interest in targeted alpha therapy due to the possible application of bismuth isotopes bismuth-212 (212Bi, t1/2 = 60.6 min) and bismuth-213 (213Bi, t1/2 = 45.6 min).

Cholesky Decomposition-Based Implementation of Relativistic Two-Component Coupled-Cluster Methods for Medium-Sized Molecules

A Cholesky decomposition (CD)-based implementation of relativistic two-component coupled-cluster (CC) and equation-of-motion CC (EOM-CC) methods using an exact two-component Hamiltonian augmented with atomic-mean-field spin-orbit integrals (the X2CAMF scheme) is reported. The present CD-based implementation of X2CAMF-CC and EOM-CC methods employs atomic-orbital-based algorithms to avoid the construction of two-electron integrals and intermediates involving three and four virtual indices. Our CD-based implementation extends the applicability of X2CAMF-CC and EOM-CC methods to medium-sized molecules with the possibility to correlate around 1000 spinors. Benchmark calculations for uranium-containing small molecules were performed to assess the dependence of the CC results on the Cholesky threshold. A Cholesky threshold of 10-4 is shown to be sufficient to maintain chemical accuracy. Example calculations to illustrate the capability of the CD-based relativistic CC methods are reported for the bond-dissociation energy of the uranium hexafluoride molecule, UF6, with up to quadruple-ζ basis sets, and the lowest excitation energy in the solvated uranyl ion [UO22+(H2O)12].

Effect of hydration equilibria on the relaxometric properties of Gd(III) complexes: new insights into old systems

We present a detailed relaxometric and computational investigation of three Gd(III) complexes that exist in solution as an equilibrium of two species with a different number of coordinated water molecules: [Gd(H2O)q]3+ (q = 8, 9), [Gd(EDTA)(H2O)q]- and [Gd(CDTA)(H2O)q]- (q = 2, 3). 1H nuclear magnetic relaxation dispersion (NMRD) data were recorded from aqueous solutions of these complexes using a wide Larmor frequency range (0.01-500 MHz). These data were complemented with 17O transverse relaxation rates and chemical shifts recorded at different temperatures. The simultaneous fit of the NMRD and 17O NMR data was guided by computational studies performed at the DFT and CASSCF/NEVPT2 levels, which provided information on Gd⋯H distances, 17O hyperfine coupling constants and the zero-field splitting (ZFS) energy, which affects electronic relaxation. The hydration equilibrium did not have a very important effect in the fits of the experimental data for [Gd(H2O)q]3+ and [Gd(CDTA)(H2O)q]-, as the hydration equilibrium is largely shifted to the species with the lowest hydration number (q = 8 and 2, respectively). The quality of the analysis improves however considerably for [Gd(EDTA)(H2O)q]- upon considering the effect of the hydration equilibrium. As a result, this study provides for the first time an analysis of the relaxation properties of this important model system, as well as accurate parameters for [Gd(H2O)q]3+ and [Gd(CDTA)(H2O)q]-.

Synthesis and Photophysical Properties of Lanthanide Pyridinylphosphonic Tacn and Pyclen Derivatives: From Mononuclear Complexes to Supramolecular Heteronuclear Assemblies

Synthetic methodologies were developed to achieve the preparation of ligands L1 and L2 consisting of tacn- and pyclen-based chelators decorated with pyridinylphosphonic pendant arms combined with ethylpicolinamide or acetate coordinating functions, respectively. Phosphonate functions have been selected for their high affinity toward Ln3+ ions compared to their carboxylated counterparts and for their steric hindrance that favors the formation of less-hydrated complexes. Thanks to regiospecific N-functionalization of the macrocyclic backbones, the two ligands were isolated with good yields and implicated in a comprehensive photophysical study for the complexation of Eu3+, Tb3+, and Yb3+. The coordination behavior of L1 and L2 with these cations has been first investigated by means of a combination of UV-vis absorption spectroscopy, steady-state and time-resolved luminescence spectroscopy, and 1H and 31P NMR titration experiments. Structural characterization in solution was assessed by NMR spectroscopy, corroborated by theoretical calculations. Spectroscopic characterization of the Ln3+ complexes of L1 and L2 was done in water and D2O and showed the effective sensitization of the lanthanide metal-centered emission spectra, each exhibiting typical lanthanide emission bands. The results obtained for the phosphonated ligands were compared with those reported previously for the corresponding carboxylated analogues.

Effect of Magnetic Anisotropy on the 1H NMR Paramagnetic Shifts and Relaxation Rates of Small Dysprosium(III) Complexes

We present a detailed analysis of the 1H NMR chemical shifts and transverse relaxation rates of three small Dy(III) complexes having different symmetries (C3, D2 or C2). The complexes show sizeable emission in the visible region due to 4F9/2 → 6HJ transitions (J = 15/2 to 11/2). Additionally, NIR emission is observed at ca. 850 (4F9/2 → 6H7/2), 930 (4F9/2 → 6H5/2), 1010 (4F9/2 → 6F9/2), and 1175 nm (4F9/2 → 6F7/2). Emission quantum yields of 1-2% were determined in aqueous solutions. The emission lifetimes indicate that no water molecules are present in the inner coordination sphere of Dy(III), which in the case of [Dy(CB-TE2PA)]+ was confirmed through the X-ray crystal structure. The 1H NMR paramagnetic shifts induced by Dy(III) were found to be dominated by the pseudocontact mechanism, though, for some protons, contact shifts are not negligible. The analysis of the pseudocontact shifts provided the magnetic susceptibility tensors of the three complexes, which were also investigated using CASSCF calculations. The transverse 1H relaxation data follow a good linear correlation with 1/r6, where r is the distance between the Dy(III) ion and the observed proton. This indicates that magnetic anisotropy is not significantly affecting the relaxation of 1H nuclei in the family of complexes investigated here.

Relativistic modulation of supramolecular halogen/copper interactions and phosphorescence in Cu(I) pyrazolate cyclotrimers

Described herein are the synthesis, structure, and photophysics of the iodo-substituted cyclic trinuclear copper(I) complex, Cu₃[4-I-3,5-(CF₃)₂Pz]₃ supported by a highly-fluorinated pyrazolate in comparison with its previously reported 4-Br/4-Cl analogues. The crystal structure is stabilised by multiple supramolecular interactions of Cu₃⋯I and hydrogen/halogen bonding. The photophysical properties and supramolecular interactions are investigated experimentally/computationally for all three 4-halo complexes vis-à-vis relativistic effects.

In Situ Ternary Adduct Formation of Yttrium Polyaminocarboxylates Leads to Small Molecule Capture and Activation

In this work the chemistry of yttrium complexes is exploited for small molecule capture and activation. Nuclear magnetic resonance (NMR) and density functional theory (DFT) studies were used to investigate the in situ formation of solution state ternary yttrium-acetate, yttrium-bicarbonate, and yttrium-pyruvate adducts with a range of polyaminocarboxylate chelates. These studies reveal that [Y(DO3A)(H₂ O)₂ ] (H₃ DO3A - 1,4,7,10-tetraazacyclododecane-1,4,7-tricarboxylic acid) and [Y(EDTA)(H₂ O)_q ]^- (H₄ EDTA - ethylenediaminetetraacetic acid, q = 2 and 3) are able to form ternary adducts with bicarbonate and pyruvate. In the latter, unusual decarboxylation of pyruvate to form acetic acid and CO₂ was observed and further studied using SABRE-hyperpolarised ¹³ C NMR (SABRE - signal amplification by reversible exchange) to provide information about the reaction timescale and lifetime of intermediates involved in this conversion. The work presented demonstrates that yttrium complexes can capture and activate small molecules, which may lead to novel and useful applications of this metal in catalysis and medical imaging.

Computational 199 Hg NMR

Theoretical background and fundamental results dealing with the computation of mercury chemical shifts and spin-spin coupling constants are reviewed with a special emphasis on their stereochemical behavior and applications.

Halogen Bonding Involving Gold Nucleophiles in Different Oxidation States

A single-crystal X-ray diffraction (XRD) study of diaryliodonium tetrachloroaurates (or, in the recent terminology, tetrachloridoaurates), [(p-XC₆H₄)₂I][AuCl₄] (X = Cl, 1; Br, 2), was performed for 1 (the structure is denoted as 1a to show similarity with the isomorphic structure 2a) and two polymorphs─2a (obtained from MeOH) and 2b (from 1,2-C₂H₄Cl₂). Examination of the XRD data for these three structures revealed 2-center C-X···Au^III (X = Cl and Br) and 3-center bifurcated C-Br···(Cl-Au) halogen bonding (abbreviated as XB) between the p-Cl or p-Br atoms of the diaryliodonium cations and the gold(III) atom of [AuCl₄]^-. The noncovalent nature of Au^III-involving interactions, the nucleophilicity of the gold(III) atoms, and the electrophilic role of p-X atoms of the diaryliodonium cations in the XBs were studied by a set of complementary computational methods. Combined experimental and theoretical studies allowed the recognition of the d-nucleophilicity of the [d⁸Au^III] atom which, regardless of its rather substantial formal 3+ charge, can function as a d-nucleophilic partner of XB. This conclusion was also supported by theoretical calculations performed for the structures' refcodes BINXOM and ICSD 62511; the obtained data verified the nucleophilicity of Au^III toward a K⁺ ions or a σ-(Cl)-hole, respectively. All our results, together with consideration of relevant literature, indicate that gold atoms in the three oxidation states (0, I, and even III) exhibit nucleophilicity in XBs.

Strong Relativistic Effects in Lanthanide-Based Single-Molecule Magnets

Lanthanide-based single-molecule magnets (SMMs) are promising building blocks for quantum memory and spintronic devices. Designing lanthanide-based SMMs with long spin relaxation time requires a detailed understanding of their electronic structure, including the crucial role of the spin-orbit coupling (SOC). While traditional calculations of SOC using the perturbation theory applied to a solution of the nonrelativistic Schrödinger equation are valid for light atoms, this approach is questionable for systems containing heavy elements such as lanthanides. We investigate the accuracy of the perturbation estimates of SOC by variationally solving the Dirac equation for the [DyO]+ molecule, a prototype of a lanthanide-based SMM. We show that the energy splittings between the M J states involved in spin relaxation depend on the interplay between strong SOC and dynamic electron correlation. We demonstrate that this interplay affects the resonances between the spin and vibrational transitions and, therefore, the spin relaxation time.

Atomic Mean-Field Approach within Exact Two-Component Theory Based on the Dirac-Coulomb-Breit Hamiltonian

An extension of the exact two-component theory with atomic mean-field integrals (the X2CAMF scheme) to the treatment of the Breit term together with efficient implementation using an atomic Dirac-Coulomb-Breit Hartree-Fock program is reported. The accuracy of the X2CAMF scheme for treating the contributions from the Breit term to the molecular properties is demonstrated using benchmark calculations of equilibrium bond lengths, harmonic frequencies, and dipole moments for molecules containing elements across the periodic table. Calculations of the properties for molecules containing period four elements aiming at high accuracy as well as for Th- and U-containing molecules are also presented and compared with experimental results to demonstrate the usefulness of the X2CAMF scheme in combination with accurate treatments of electron correlation by the coupled-cluster (CC) methods. The combination of CC methods and the X2CAMF scheme shows potential to extend the accuracy of CC calculations to heavy elements, e.g., to computational heavy-element thermochemistry.

Quantum Chemical Approaches to the Calculation of NMR Parameters: From Fundamentals to Recent Advances

Quantum chemical methods for the calculation of indirect NMR spin–spin coupling constants and chemical shifts are always in progress. They never stay the same due to permanently developing computational facilities, which open new perspectives and create new challenges every now and then. This review starts from the fundamentals of the nonrelativistic and relativistic theory of nuclear magnetic resonance parameters, and gradually moves towards the discussion of the most popular common and newly developed methodologies for quantum chemical modeling of NMR spectra.

Versatile Macrocyclic Platform for the Complexation of [natY/90Y]Yttrium and Lanthanide Ions

We report a macrocyclic ligand (H3L6) based on a 3,6,10,13-tetraaza-1,8(2,6)-dipyridinacyclotetradecaphane platform containing three acetate pendant arms and a benzyl group attached to the fourth nitrogen atom of the macrocycle. The X-ray structures of the YL6 and TbL6 complexes reveal nine coordination of the ligand to the metal ions through the six nitrogen atoms of the macrocycle and three oxygen atoms of the carboxylate pendants. A combination of NMR spectroscopic studies (1H, 13C, and 89Y) and DFT calculations indicated that the structure of the YL6 complex in the solid state is maintained in an aqueous solution. The detailed study of the emission spectra of the EuL6 and TbL6 complexes revealed Ln3+-centered emission with quantum yields of 7.0 and 60%, respectively. Emission lifetime measurements indicate that the ligand offers good protection of the metal ions from surrounding water molecules, preventing the coordination of water molecules. The YL6 complex is remarkably inert with respect to complex dissociation, with a lifetime of 1.7 h in 1 M HCl. On the other hand, complex formation is fast (∼1 min at pH 5.4, 2 × 10-5 M). Studies using the 90Y-nuclide confirmed fast radiolabeling since [90Y]YL6 is nearly quantitatively formed (radiochemical yield (RCY) > 95) in a short time over a broad range of pH values from ca. 2.4 to 9.0. Challenging experiments in the presence of excess ethylenediaminetetraacetic acid (EDTA) and in human serum revealed good stability of the [90Y]YL6 complex. All of these experiments combined suggest the potential application of H3L6 derivatives as Y-based radiopharmaceuticals.

The Dual Descriptor Reveals the Janus–Faced Behaviour of Diiodine

The Janus–faced ligand behavior of diiodine (I₂) was evidenced after applying the dual descriptor (DD or second-order Fukui function), thus providing additional support to the work performed by Rogachev and Hoffmann in 2013. Along with its capacity to reveal sites susceptible to undergo attacks simultaneously of nucleophilic and electrophilic types, another advantage of DD lies in being an orbital-free descriptor. That means it is based only upon total electron densities when written in its most accurate operational formula. This quality is not exclusive of DD because when Fukui functions are written in terms of electron densities instead of densities of frontier molecular orbitals, they become orbital-free descriptors too. Furthermore, the present work is an application of the generalized operational formula of the dual descriptor published in 2016 that takes into account any possible degeneracy in frontier molecular orbitals. As a proof about capabilities of DD, the possible sites for a favorable interaction between I₂ with two organometallic compounds [Rh₂(O₂CCF₃)₄] and [(C₈H₁₁N₂)Pt (CH₃)] were correctly revealed by overlapping the biggest lobe for receiving nucleophilic attacks of one molecule with the biggest lobe for receiving electrophilic attacks of the other molecule, so allowing to predict the same coordination modes as experimentally known: linear “end–on” for the [(C₈H₁₁N₂)Pt (CH₃)]…I₂, and bent “end–on” for the [Rh₂(O₂CCF₃)₄]…I₂ interactions.

Rigidified Derivative of the Non-macrocyclic Ligand H4OCTAPA for Stable Lanthanide(III) Complexation

The stability constants of lanthanide complexes with the potentially octadentate ligand CHXOCTAPA^4–, which contains a rigid 1,2-diaminocyclohexane scaffold functionalized with two acetate and two picolinate pendant arms, reveal the formation of stable complexes [log K_LaL = 17.82(1) and log K_YbL = 19.65(1)]. Luminescence studies on the Eu³⁺ and Tb³⁺ analogues evidenced rather high emission quantum yields of 3.4 and 11%, respectively. The emission lifetimes recorded in H₂O and D₂O solutions indicate the presence of a water molecule coordinated to the metal ion. ¹H nuclear magnetic relaxation dispersion profiles and ¹⁷O NMR chemical shift and relaxation measurements point to a rather low water exchange rate of the coordinated water molecule (k_ex²⁹⁸ = 1.58 × 10⁶ s^–1) and relatively high relaxivities of 5.6 and 4.5 mM^–1 s^–1 at 20 MHz and 25 and 37 °C, respectively. Density functional theory calculations and analysis of the paramagnetic shifts induced by Yb³⁺ indicate that the complexes adopt an unprecedented cis geometry with the two picolinate groups situated on the same side of the coordination sphere. Dissociation kinetics experiments were conducted by investigating the exchange reactions of LuL occurring with Cu²⁺. The results confirmed the beneficial effect of the rigid cyclohexyl group on the inertness of the Lu³⁺ complex. Complex dissociation occurs following proton- and metal-assisted pathways. The latter is relatively efficient at neutral pH, thanks to the formation of a heterodinuclear hydroxo complex.

A non-macrocyclic ligand containing a rigid cyclohexyl spacer forms thermodynamically stable complexes with the lanthanide(III) ions in aqueous solution. The complexes also show remarkable kinetic inertness, though a structural change facilitates dissociation through the metal-assisted mechanism for the small lanthanides. The Gd(III) complex displays a relatively high relaxivity due to the presence of a water molecule coordinated to the metal ion, while the Eu(III) and Tb(III) analogues display strong metal-centered luminescence.

Exploiting the Fluxionality of Lanthanide Complexes in the Design of Paramagnetic Fluorine Probes

Fluorine-19 MRI is increasingly being considered as a tool for biomolecular imaging, but the very poor sensitivity of this technique has limited most applications. Previous studies have long established that increasing the sensitivity of ¹⁹F molecular probes requires increasing the number of fluorine nuclei per probe as well as decreasing their longitudinal relaxation time. The latter is easily achieved by positioning the fluorine atoms in close proximity to a paramagnetic metal ion such as a lanthanide(III). Increasing the number of fluorine atoms per molecule, however, is only useful inasmuch as all of the fluorine nuclei are chemically equivalent. Previous attempts to achieve this equivalency have focused on designing highly symmetric and rigid fluorinated macrocyclic ligands. A much simpler approach consists of exploiting highly fluxional lanthanide complexes with open coordination sites that have a high affinity for phosphated and phosphonated species. Computational studies indicate that Ln^III-TREN-MAM is highly fluxional, rapidly interconverting between at least six distinct isomers. In neutral water at room temperature, Ln^III-TREN-MAM binds two or three equivalents of fluorinated phosphonates. The close proximity of the ¹⁹F nuclei to the Ln^III center in the ternary complex decreases the relaxation times of the fluorine nuclei up to 40-fold. Advantageously, the fluorophosphonate-bound lanthanide complex is also highly fluxional such that all ¹⁹F nuclei are chemically equivalent and display a single ¹⁹F signal with a small LIS. Dynamic averaging of fluxional fluorinated supramolecular assemblies thus produces effective ¹⁹F MR systems.

The critical role of ligand topology: strikingly different properties of Gd(iii) complexes with regioisomeric AAZTA derivatives

Two regioisomeric Gd(III) complexes with heptadentate AAZTA-like ligands show different hydration state (q = 1 and 2) and astonishingly different thermodynamic stability and dissociation kinetics.

Surprising Complexity of the [Gd(AAZTA)(H2O)2]- Chelate Revealed by NMR in the Frequency and Time Domains

Typically, Ln(III) complexes are isostructural along the series, which enables studying one particular metal chelate to derive the structural features of the others. This is not the case for [Ln(AAZTA)(H₂O)_x]⁻ (x = 1, 2) systems, where structural variations along the series cause changes in the hydration number of the different metal complexes, and in particular the loss of one of the two metal-coordinated water molecules between Ho and Er. Herein, we present a ¹H field-cycling relaxometry and ¹⁷O NMR study that enables accessing the different exchange dynamics processes involving the two water molecules bound to the metal center in the [Gd(AAZTA)(H₂O)₂]⁻ complex. The resulting picture shows one Gd-bound water molecule with an exchange rate ∼6 times faster than that of the other, due to a longer metal–water distance, in accordance with density functional theory (DFT) calculations. The substitution of the more labile water molecule with a fluoride anion in a diamagnetic-isostructural analogue of the Gd-complex, [Y(AAZTA)(H₂O)₂]⁻, allows us to follow the chemical exchange process by high-resolution NMR and to describe its thermodynamic behavior. Taken together, the variety of tools offered by NMR (including high-resolution ¹H, ¹⁹F NMR as a function of temperature, ¹H longitudinal relaxation rates vs B₀, and ¹⁷O transverse relaxation rates vs T) provides a complete description of the structure and exchange dynamics of these Ln-complexes along the series.

Herein, we present a ¹H field−cycling relaxometry and ¹⁷O NMR study that enables accessing the different exchange dynamics processes involving the two water molecules bound to the metal center in the [Gd(AAZTA)(H₂O)₂]⁻ complex.

Vibrational frequencies and intramolecular force constants for cisplatin: assessing the role of the platinum basis set and relativistic effects

The role of platinum basis set (PTBS) and relativistic effects for predicting the vibrational frequencies and intramolecular force constants for cisplatin are discussed. Nonrelativistic and relativistic computational protocols were built at B3LYP/PTBS/jorge-DZP/C-PCM and B3LYP-DKH2/PTBS/jorge-DZP-DKH/C-PCM levels, respectively, where 19 distinct PTBS were tested. As expected, the structural parameters were not very sensitive to the PTBS, however, the inclusion of relativistic effects improves the description of the cisplatin structure. When it comes to the vibrational frequencies, the results show that the PTBS, and mainly the relativistic effects, are both important. Moreover, the PBE0 functional led to better results than B3LYP in the protocols PBE0/LANL2TZ(f)/jorge-DZP/C-PCM (P20) and PBE0-DKH2/Sapporo-DKH3-DZP-2012/jorge-DZP-DKH/C-PCM (P22), which provided a mean absolute deviation (MAD) of only 10.8 cm^-1 and 9.5 cm^-1, respectively, for vibrational frequencies, which are excellent choices to study Pt complexes. Finally, a discussion of the intramolecular force constants for cisplatin is carried out, with the calculated bond and angles force constants with P20 and P22 protocols being recommended for the parameterization of the force field of cisplatin.

Reactions of U+ with H2, D2, and HD Studied by Guided Ion Beam Tandem Mass Spectrometry and Theory

The kinetic energy-dependent reactions of the atomic actinide uranium cation (U⁺) with H₂, D₂, and HD were examined by guided ion beam tandem mass spectrometry. An average 0 K bond dissociation energy of D₀(U⁺ - H) = 2.48 ± 0.06 eV is obtained by analysis of the endothermic product ion cross sections. Quantum chemistry calculations were performed for comparison with experimental thermochemistry, including high-level CASSCF-CASPT2-RASSI calculations of the spin-orbit corrections. CCSD(T) and the CASSCF levels show excellent agreement with experiment, whereas B3LYP and PBE0 slightly overestimate and the M06 approach badly underestimates the bond energy for UH⁺. Theory was also used to investigate the electronic structures of the reaction intermediates and potential energy surfaces. The experimental product branching ratio for the reaction of U⁺ with HD indicates that these reactions occur primarily via a direct reaction mechanism, despite the presence of a deep-well for UH₂⁺ formation according to theory. The reactivity and hydride bond energy for U⁺ are compared with those for transition metal, lanthanide, and actinide cations, and periodic trends are discussed. These comparisons suggest that the 5f electrons on uranium are largely core and uninvolved in the reactive chemistry.

Electronic Structure of Ytterbium(III) Solvates-a Combined Spectroscopic and Theoretical Study

The wide range of optical and magnetic properties of lanthanide(III) ions is associated with their intricate electronic structures which, in contrast to lighter elements, is characterized by strong relativistic effects and spin-orbit coupling. Nevertheless, computational methods are now capable of describing the ladder of electronic energy levels of the simpler trivalent lanthanide ions, as well as the lowest energy term of most of the series. The electronic energy levels result from electron configurations that are first split by spin-orbit coupling into groups of energy levels denoted by the corresponding Russell-Saunders terms. Each of these groups are then split by the ligand field into the actual electronic energy levels known as microstates or sometimes m_J levels. The ligand-field splitting directly informs on the coordination geometry and is a valuable tool for determining the structure and thus correlating the structure and properties of metal complexes in solution. The issue with lanthanide complexes is that the determination of complex structures from ligand-field splitting remains a very challenging task. In this paper, the optical spectra-absorption, luminescence excitation, and luminescence emission-of ytterbium(III) solvates were recorded in water, methanol, dimethyl sulfoxide (DMSO), and N,N-dimethylformamide (DMF). The electronic energy levels, that is, the microstates, were resolved experimentally. Subsequently, density functional theory calculations were used to model the structures of the solvates, and ab initio relativistic complete active space self-consistent field calculations (CASSCF) were employed to obtain the microstates of the possible structures of each solvate. By comparing the experimental and theoretical data, it was possible to determine both the coordination number and solution structure of each solvate. In water, methanol, and N,N-dimethylformamide, the solvates were found to be eight-coordinated and have a square antiprismatic coordination geometry. In DMSO, the speciation was found to be more complicated. The robust methodology developed for comparing experimental spectra and computational results allows the solution structures of homoleptic lanthanide complexes to be determined.

Benchmarking the Fluxional Processes of Organometallic Piano-Stool Complexes

The correlation consistent Composite Approach for transition metals (ccCA-TM) and density functional theory (DFT) computations have been applied to investigate the fluxional mechanisms of cyclooctatetraene tricarbonyl chromium ((COT)Cr(CO)3) and 1,3,5,7-tetramethylcyclooctatetraene tricarbonyl chromium, molybdenum, and tungsten ((TMCOT)M(CO)3 (M = Cr, Mo, and W)) complexes. The geometries of (COT)Cr(CO)3 were fully characterized with the PBEPBE, PBE0, B3LYP, and B97-1 functionals with various basis set/ECP combinations, while all investigated (TMCOT)M(CO)3 complexes were fully characterized with the PBEPBE, PBE0, and B3LYP methods. The energetics of the fluxional dynamics of (COT)Cr(CO)3 were examined using the correlation consistent Composite Approach for transition metals (ccCA-TM) to provide reliable energy benchmarks for corresponding DFT results. The PBE0/BS1 results are in semiquantitative agreement with the ccCA-TM results. Various transition states were identified for the fluxional processes of (COT)Cr(CO)3. The PBEPBE/BS1 energetics indicate that the 1,2-shift is the lowest energy fluxional process, while the B3LYP/BS1 energetics (where BS1 = H, C, O: 6-31G(d'); M: mod-LANL2DZ(f)-ECP) indicate the 1,3-shift having a lower electronic energy of activation than the 1,2-shift by 2.9 kcal mol-1. Notably, PBE0/BS1 describes the (CO)3 rotation to be the lowest energy process, followed by the 1,3-shift. Six transition states have been identified in the fluxional processes of each of the (TMCOT)M(CO)3 complexes (except for (TMCOT)W(CO)3), two of which are 1,2-shift transition states. The lowest-energy fluxional process of each (TMCOT)M(CO)3 complex (computed with the PBE0 functional) has a ΔG‡ of 12.6, 12.8, and 13.2 kcal mol-1 for Cr, Mo, and W complexes, respectively. Good agreement was observed between the experimental and computed 1H-NMR and 13C-NMR chemical shifts for (TMCOT)Cr(CO)3 and (TMCOT)Mo(CO)3 at three different temperature regimes, with coalescence of chemically equivalent groups at higher temperatures.

Quantum chemical calculations of 77 Se and 125 Te nuclear magnetic resonance spectral parameters and their structural applications

An accurate quantum chemical (QC) modeling of ⁷⁷ Se and ¹²⁵ Te nuclear magnetic resonance (NMR) spectra is deeply involved in the NMR structural assignment for selenium and tellurium compounds that are of utmost importance both in organic and inorganic chemistry nowadays due to their huge application potential in many fields, like biology, medicine, and metallurgy. The main interest of this review is focused on the progress in QC computations of ⁷⁷ Se and ¹²⁵ Te NMR chemical shifts and indirect spin-spin coupling constants involving these nuclei. Different computational methodologies that have been used to simulate the NMR spectra of selenium and tellurium compounds since the middle of the 1990s are discussed with a strong emphasis on their accuracy. A special accent is placed on the calculations resorting to the relativistic methodologies, because taking into account the relativistic effects appreciably influences the precision of NMR calculations of selenium and, especially, tellurium compounds. Stereochemical applications of quantum chemical calculations of ⁷⁷ Se and ¹²⁵ Te NMR parameters are discussed so as to exemplify the importance of integrated approach of experimental and computational NMR techniques.

Lanthanide(III) Complexes Based on an 18-Membered Macrocycle Containing Acetamide Pendants. Structural Characterization and paraCEST Properties

We report a detailed investigation of the coordination properties of macrocyclic lanthanide complexes containing a 3,6,10,13-tetraaza-1,8(2,6)-dipyridinacyclotetradecaphane scaffold functionalized with four acetamide pendant arms. The X-ray structures of the complexes with the large Ln³⁺ ions (La and Sm) display 12- and 10-coordinated metal ions, where the coordination sphere is fulfilled by the six N atoms of the macrocycle, the four O atoms of the acetamide pendants, and a bidentate nitrate anion in the La³⁺ complex. The analogous Yb³⁺ complex presents, however, a 9-coordinated metal ion because one of the acetamide pendant arms remains uncoordinated. ¹H NMR studies indicate that the 10-coordinated form is present in solution throughout the lanthanide series from La to Tb, while the smaller lanthanides form 9-coordinated species. ¹H and ⁸⁹Y NMR studies confirm the presence of this structural change because the two species are present in solution. Analysis of the ¹H chemical shifts observed for the Tb³⁺ complex confirms its D₂ symmetry in aqueous solution and evidences a highly rhombic magnetic susceptibility tensor. The acetamide resonances of the Pr³⁺ and Tb³⁺ complexes provided sizable paraCEST effects, as demonstrated by the corresponding Z-spectra recorded at different temperatures and studies on tube phantoms recorded at 22 °C.

HgH2 meets relativistic quantum crystallography. How to teach relativity to a non-relativistic wavefunction

The capability of X-ray constrained wavefunction (XCW) fitting to introduce relativistic effects into a non-relativistic wavefunction is tested. It is quantified how much of the reference relativistic effects can be absorbed in the non-relativistic XCW calculation when fitted against relativistic structure factors of a model HgH₂ molecule. Scaling of the structure-factor sets to improve the agreement statistics is found to introduce a significant systematic error into the XCW fitting of relativistic effects.

Picture-change correction in relativistic density functional theory

Relativistic quantum chemical calculations are performed based on one of two physical pictures, namely the Dirac picture and the Schrödinger picture. With regard to the latter, the so-called picture-change effect (PCE) and picture-change correction (PCC) have been studied. The PCE, which is the change in the expectation value associated with the transformation, is not commonly a minor effect. The electron density, which is given by the expectation value of the density operator, is a fundamental variable in relativistic density functional theory (RDFT). Thus, performing the PCC in RDFT calculations is essential not only in terms of numerical agreement with the Dirac picture, but also from the viewpoint of fundamental theory. This paper explains theories and numerical studies of PCE and PCC in RDFT after overviewing those in properties, which involves the authors' works on the development of RDFT in the Schrödinger picture and relativistic exchange-correlation functionals based on picture-change-corrected variables.

Scrutinising the role of intramolecular hydrogen bonding in water exchange dynamics of Gd(iii) complexes

The water exchange rate in Gd^III-complexes bearing substituted acetophenone moieties is modulated by the ability of peripherical substituents to establish hydrogen bonds with the coordinated and/or second sphere water molecules.

Non-Bonded Radii of the Atoms Under Compression

We present quantum mechanical estimates for non-bonded, van der Waals-like, radii of 93 atoms in a pressure range from 0 to 300 gigapascal. Trends in radii are largely maintained under pressure, but atoms also change place in their relative size ordering. Multiple isobaric contractions of radii are predicted and are explained by pressure-induced changes to the electronic ground state configurations of the atoms. The presented radii are predictive of drastically different chemistry under high pressure and permit an extension of chemical thinking to different thermodynamic regimes. For example, they can aid in assignment of bonded and non-bonded contacts, for distinguishing molecular entities, and for estimating available space inside compressed materials. All data has been made available in an interactive web application.

Computation of NMR Shielding Constants for Solids Using an Embedded Cluster Approach with DFT, Double-Hybrid DFT, and MP2

In this work, we explore the accuracy of post-Hartree–Fock (HF) methods and double-hybrid density functional theory (DFT) for the computation of solid-state NMR chemical shifts. We apply an embedded cluster approach and investigate the convergence with cluster size and embedding for a series of inorganic solids with long-range electrostatic interactions. In a systematic study, we discuss the cluster design, the embedding procedure, and basis set convergence using gauge-including atomic orbital (GIAO) NMR calculations at the DFT and MP2 levels of theory. We demonstrate that the accuracy obtained for the prediction of NMR chemical shifts, which can be achieved for molecular systems, can be carried over to solid systems. An appropriate embedded cluster approach allows one to apply methods beyond standard DFT even for systems for which long-range electrostatic effects are important. We find that an embedded cluster should include at least one sphere of explicit neighbors around the nuclei of interest, given that a sufficiently large point charge and boundary effective potential embedding is applied. Using the pcSseg-3 basis set and GIAOs for the computation of nuclear shielding constants, accuracies of 1.6 ppm for ⁷Li, 1.5 ppm for ²³Na, and 5.1 ppm for ³⁹K as well as 9.3 ppm for ¹⁹F, 6.5 ppm for ³⁵Cl, 7.4 ppm for ⁷⁹Br, and 7.5 ppm for ²⁵Mg as well as 3.8 ppm for ⁶⁷Zn can be achieved with MP2. Comparing various DFT functionals with HF and MP2, we report the superior quality of results for methods that include post-HF correlation like MP2 and double-hybrid DFT.

Gadolinium Complexes of Highly Rigid, Open-Chain Ligands Containing a Cyclobutane Ring in the Backbone: Decreasing Ligand Denticity Might Enhance Kinetic Inertness

In an effort to explore novel ligand scaffolds for stable and inert lanthanide complexation in magnetic resonance imaging contrast agent research, three chiral ligands containing a highly rigid (1S,2S)-1,2-cyclobutanediamine spacer and different number of acetate and picolinate groups were efficiently synthesized. Potentiometric studies show comparable thermodynamic stability for the Gd³⁺ complexes formed with either the octadentate (L3)^4- bearing two acetate or two picolinate groups or the heptadentate (L2)^4- analogue bearing one picolinate and three acetate groups (log K_GdL = 17.41 and 18.00 for [Gd(L2)]^- and [Gd(L3)]^-, respectively). In contrast, their dissociation kinetics is revealed to be very different: the monohydrated [Gd(L3)]^- is considerably more labile, as a result of the significant kinetic activity of the protonated picolinate function, as compared to the bishydrated [Gd(L2)]^-. This constitutes an uncommon example in which lowering ligand denticity results in a remarkable increase in kinetic inertness. Another interesting observation is that the rigid ligand backbone induces an unusually strong contribution of the spontaneous dissociation to the overall decomplexation process. Thanks to the presence of two inner-sphere water molecules, [Gd(L2)]^- is endowed with high relaxivity (r₁ = 7.9 mM^-1 s^-1 at 20 MHz, 25 °C), which is retained in the presence of large excess of endogenous anions, excluding ternary complex formation. The water exchange rate is similar for [Gd(L3)]^- and [Gd(L2)]^-, while it is 1 order of magnitude higher for the trishydrated tetraacetate analogue [Gd(L1)]^- (k_ex²⁹⁸ = 8.1, 10, and 127 × 10⁶ s^-1, respectively). A structural analysis via density functional theory calculations suggests that the large bite angle imposed by the rigid (1S,2S)-1,2-cyclobutanediamine spacer could allow the design of ligands based on this scaffold with suitable properties for the coordination of larger metal ions with biomedical applications.

Relativistic quantum crystallography of diphenyl- and dicyanomercury. Theoretical structure factors and Hirshfeld atom refinement

Quantum crystallographic refinement of heavy-element-containing compounds is a challenge, because many physical effects have to be accounted for adequately. Here, the impact and magnitude of relativistic effects are compared with those of electron correlation, polarization through the environment, choice of basis set and treatment of thermal motion effects on the structure factors of diphenylmercury(II) [Hg(Ph)₂] and dicyanomercury(II) [Hg(CN)₂]. Furthermore, the individual atomic contributions to the structure factors are explored in detail (using Mulliken population analysis and the exponential decay of atomic displacement parameters) to compare the contributions of lighter atoms, especially hydrogen atoms, against mercury. Subsequently, relativistic Hirshfeld atom refinement (HAR) is validated against theoretical structure factors of Hg(Ph)₂ and Hg(CN)₂, starting from perturbed geometries, to test if the relativistic variant of HAR leads to multiple solutions. Generally, relativistic HAR is successful, leading to a perfect match with the reference geometries, but some limitations are pointed out.

PIDAZTA: Structurally Constrained Chelators for the Efficient Formation of Stable Gallium-68 Complexes at Physiological pH

Two structurally constrained chelators based on a fused bicyclic scaffold, 4-amino-4-methylperhydro-pyrido[1,2-a][1,4]diazepin-N,N',N'-triacetic acids [(4R*,10aS*)-PIDAZTA (L1) and (4R*,10aR*)-PIDAZTA (L2)], were designed for the preparation of Ga^III -based radiopharmaceuticals. The stereochemistry of the ligand scaffold has a deep impact on the properties of the complexes, with unexpected [Ga(L2)OH] species being superior in terms of both thermodynamic stability and inertness. This peculiar behavior was rationalized on the basis of molecular modeling and appears to be related to a better fit in size of Ga^III into the cavity of L2. Fast and efficient formation of the Ga^III chelates at room temperature was observed at pH values between 7 and 8, which enables ⁶⁸ Ga radiolabeling under truly physiological conditions (pH 7.4).

Squeezing All Elements in the Periodic Table: Electron Configuration and Electronegativity of the Atoms under Compression

We present a quantum mechanical model capable of describing isotropic compression of single atoms in a non-reactive neon-like environment. Studies of 93 atoms predict drastic changes to ground-state electronic configurations and electronegativity in the pressure range of 0-300 GPa. This extension of atomic reference data assists in the working of chemical intuition at extreme pressure and can act as a guide to both experiments and computational efforts. For example, we can speculate on the existence of pressure-induced polarity (red-ox) inversions in various alloys. Our study confirms that the filling of energy levels in compressed atoms more closely follows the hydrogenic aufbau principle, where the ordering is determined by the principal quantum number. In contrast, the Madelung energy ordering rule is not predictive for atoms under compression. Magnetism may increase or decrease with pressure, depending on which atom is considered. However, Hund's rule is never violated for single atoms in the considered pressure range. Important (and understandable) electron shifts, s→p, s→d, s→f, and d→f are essential chemical and physical consequences of compression. Among the specific intriguing changes predicted are an increase in the range between the most and least electronegative elements with compression; a rearrangement of electronegativities of the alkali metals with pressure, with Na becoming the most electropositive s¹ element (while Li becomes a p group element and K and heavier become transition metals); phase transitions in Ca, Sr, and Ba correlating well with s→d transitions; spin-reduction in all d-block atoms for which the valence d-shell occupation is d ⁿ (4 ≤ n ≤ 8); d→f transitions in Ce, Dy, and Cm causing Ce to become the most electropositive element of the f-block; f→d transitions in Ho, Dy, and Tb and a s→f transition in Pu. At high pressure Sc and Ti become the most electropositive elements, while Ne, He, and F remain the most electronegative ones.

Weak Interactions in Alkaline Earth Metal Dimers by Pair-Density Functional Theory

Alkaline earth dimers have small bond energies (less than 5 kcal/mol) that provide a difficult challenge for electronic structure calculations. They are especially challenging for Kohn-Sham density functional theory (KS-DFT) using generalized gradient approximations (GGAs) as the exchange-correlation density functional because GGAs often do not provide accurate results for weak interactions. Here we treat alkaline earth dimers from six different rows of the periodic table. We show that the dominant correlating configurations are the same in all six dimers. We also show that multiconfiguration pair-density functional theory (MC-PDFT) using a fully translated GGA as the on-top density functional not only performs much better than KS-DFT with GGAs in predicting equilibrium distances and dissociation energies but also performs better than the more computationally demanding complete active space second-order perturbation theory (CASPT2) with large basis sets and performs even better than CASPT2 with smaller basis sets.

The role of ligand to metal charge-transfer states on the luminescence of Europium complexes with 18-membered macrocyclic ligands

The stabilization of a divalent Europium provides an efficient pathway for the quenching of the luminescence in ten-coordinate macrocyclic complexes.