The molecular structure of ferrocene

Revisiting the origin of the bending in group 2 metallocenes AeCp2 (Ae = Be-Ba)

Metallocenes are well-established compounds in organometallic chemistry, and can exhibit either a coplanar structure or a bent structure according to the nature of the metal center (E) and the cyclopentadienyl ligands (Cp). Herein, we re-examine the chemical bonding to underline the origins of the geometry and stability observed experimentally. To this end, we have analysed a series of group 2 metallocenes [Ae(C₅R₅)₂] (Ae = Be-Ba and R = H, Me, F, Cl, Br, and I) with a combination of computational methods, namely energy decomposition analysis (EDA), polarizability model (PM), and dispersion interaction densities (DIDs). Although the metal-ligand bonding nature is mainly an electrostatic interaction (65-78%), the covalent character is not negligible (33-22%). Notably, the heavier the metal center, the stronger the d-orbital interaction with a 50% contribution to the total covalent interaction. The dispersion interaction between the Cp ligands counts only for 1% of the interaction. Despite that orbital contributions become stronger for heavier metals, they never represent the energy main term. Instead, given the electrostatic nature of the metallocene bonds, we propose a model based on polarizability, which faithfully predicts the bending angle. Although dispersion interactions have a fair contribution to strengthen the bending angle, the polarizability plays a major role.

Ferrocene derivatives with planar chirality and their enantioseparation by liquid-phase techniques

In the last decade, planar chiral ferrocenes have attracted a growing interest in several fields, particularly in asymmetric catalysis, medicinal chemistry, chiroptical spectroscopy and electrochemistry. In this frame, the access to pure or enriched enantiomers of planar chiral ferrocenes has become essential, relying on the availability of efficient asymmetric synthesis procedures and enantioseparation methods. Despite this, in enantioseparation science, these metallocenes were not comprehensively explored, and very few systematic analytical studies were reported in this field so far. On the other hand, enantioselective high-performance liquid chromatography has been frequently used by organic and organometallic chemists in order to measure the enantiomeric purity of planar chiral ferrocenes prepared by asymmetric synthesis. On these bases, this review aims to provide the reader with a comprehensive overview on the enantioseparation of planar chiral ferrocenes by discussing liquid-phase enantioseparation methods developed over time, integrating this main topic with the most relevant aspects of ferrocene chemistry. Thus, the main structural features of ferrocenes and the methods to model this class of metallocenes will be briefly summarized. In addition, planar chiral ferrocenes of applicative interest as well as the limits of asymmetric synthesis for the preparation of some classes of planar chiral ferrocenes will also be discussed with the aim to orient analytical scientists towards 'hot topics' and issues which are still open for accessing enantiomers of ferrocenes featured by planar chirality.

Machine Learning-Assisted Selection of Active Spaces for Strongly Correlated Transition Metal Systems

Active space quantum chemical methods could provide very accurate description of strongly correlated electronic systems, which is of tremendous value for natural sciences. The proper choice of the active space is crucial but a nontrivial task. In this article, we present a neural network-based approach for automatic selection of active spaces, focused on transition metal systems. The training set has been formed from artificial systems composed of one transition metal and various ligands, on which we have performed the density matrix renormalization group and calculated the single-site entropy. On the selected set of systems, ranging from small benchmark molecules up to larger challenging systems involving two metallic centers, we demonstrate that our machine learning models could predict the active space orbitals with reasonable accuracy. We also tested the transferability on out-of-the-model systems, including bimetallic complexes and complexes with ligands, which were not involved in the training set. Also, we tested the correctness of the automatically selected active spaces on a Fe(II)-porphyrin model, where we studied the lowest states at the DMRG level and compared the energy difference between spin states or the energy difference between conformations of ferrocene with recent studies.

Spin-state energetics of metallocenes: How do best wave function and density functional theory results compare with the experimental data?

We benchmark the accuracy of quantum-chemical methods, including wave function theory methods [coupled cluster theory at the CCSD(T) level, multiconfigurational perturbation-theory (CASPT2, NEVPT2) and internally contracted multireference configuration interaction (MRCI)] and 30 density functional theory (DFT) approximations, in reproducing the spin-state splittings of metallocenes. The reference values of the electronic energy differences are derived from the experimental spin-crossover enthalpy for manganocene and the spectral data of singlet-triplet transitions for ruthenocene, ferrocene, and cobaltocenium. For ferrocene and cobaltocenium we revise the previous experimental interpretations regarding the lowest triplet energy; our argument is based on the comparison with the lowest singlet excitation energy and herein reported, carefully determined absorption spectrum of ferrocene. When deriving vertical energies from the experimental band maxima, we go beyond the routine vertical energy approximation by introducing vibronic corrections based on simulated vibrational envelopes. The benchmarking result confirms the high accuracy of the CCSD(T) method (in particular, for UCCSD(T) based on Hartree-Fock orbitals we find for our dataset: maximum error 0.12 eV, weighted mean absolute error 0.07 eV, weighted mean signed error 0.01 eV). The high accuracy of the single-reference method is corroborated by the analysis of a multiconfigurational character of the complete active space wave function for the triplet state of ferrocene. On the DFT side, our results confirm the non-universality problem with approximate functionals. The present study is an important step toward establishing an extensive and representative benchmark set of experiment-derived spin-state energetics for transition metal complexes.

Comparison of Methods for Active Orbital Selection in Multiconfigurational Calculations

Several methods of constructing the active orbital space for multiconfigurational wave functions are compared on typical moderately strongly or strongly correlated ground-state molecules. The relative merits of these methods and problems inherent in multiconfigurational calculations are discussed. Strong correlation in the ground electronic state is found typically in larger conjugated and in antiaromatic systems, transition states which involve bond breaking or formation, and transition metal complexes. Our examples include polyenes, polyacenes, the reactant, product and transition state of the Bergman cyclization, and two transition metal complexes: Hieber's anion [(CO)3FeNO]- and ferrocene. For the systems investigated, the simplest and oldest selection method, based on the fractional occupancy of unrestricted Hartree-Fock natural orbitals (the UNO criterion), yields the same active space as much more expensive approximate full CI methods. A disadvantage of this method used to be the difficulty of finding broken spin symmetry UHF solutions. However, our analytical method, accurate to fourth order in the orbital rotation angles (Tóth and Pulay J. Chem. Phys. 2016, 145, 164102.), has solved this problem. Two further advantages of the UNO criterion are that, unlike most other methods, it measures not only the energetic proximity to the Fermi level but also the magnitude of the exchange interaction with strongly occupied orbitals and therefore allows the estimation of the correlation strength for orbital selection in Restricted Active Space methods.

Determination of cholic acid in body fluids by β‑cyclodextrin-modified N-doped carbon dot fluorescent probes

An easy, dependable, and sensitive cholic acid activity experiment was designed based on β‑cyclodextrin-modified carbon dot (β‑CD-CD) nanoprobes with specific host-guest recognizing ability and photoelectron transfer capability. The β‑CD-CD nanoprobes were characterized by infrared, ultraviolet-visible, and fluorescence spectroscopy and transmission electron microscopy. The fluorescence of the probes under optimized conditions linearly responded to cholic acid concentration from 0 to 650 μmol·L^-1 with a detection limit of 25 nmol·L^-1. The probes also performed well in detecting cholic acid in serum and urine samples with an average recovery rate of 97.1%-103.4%. Thus, this study provides a reliable, rapid, and easy method of cholic acid detection in body fluids that can be potentially applied in medical studies.

Choosing the right precursor for thermal decomposition solution-phase synthesis of iron nanoparticles: tunable dissociation energies of ferrocene derivatives

Pathways to low-temperature thermal dissociation of ferrocene derivatives as iron nanoparticle precursors.

Recent progress in ferrocene- and azobenzene-based photoelectric responsive materials

Ferrocene- and azobenzene-based derivatives are commonly used photoelectric responsive materials and possess wide range of applications.

Ferrocene Orientation Determined Intramolecular Interactions Using Energy Decomposition Analysis

Two very different quantum mechanically based energy decomposition analyses (EDA) schemes are employed to study the dominant energy differences between the eclipsed and staggered ferrocene conformers. One is the extended transition state (ETS) based on the Amsterdam Density Functional (ADF) package and the other is natural EDA (NEDA) based in the General Atomic and Molecular Electronic Structure System (GAMESS) package. It reveals that in addition to the model (theory and basis set), the fragmentation channels more significantly affect the interaction energy terms (ΔE) between the conformers. It is discovered that such an interaction energy can be absorbed into the pre-partitioned fragment channels so that to affect the interaction energies in a particular conformer of Fc. To avoid this, the present study employs a complete fragment channel—the fragments of ferrocene are individual neutral atoms. It therefore discovers that the major difference between the ferrocene conformers is due to the quantum mechanical Pauli repulsive energy and orbital attractive energy, leading to the eclipsed ferrocene the energy preferred structure. The NEDA scheme further indicates that the sum of attractive (negative) polarization (POL) and charge transfer (CL) energies prefers the eclipsed ferrocene. The repulsive (positive) deformation (DEF) energy, which is dominated by the cyclopentadienyle (Cp) rings, prefers the staggered ferrocene. Again, the cancellation results in a small energy residue in favour of the eclipsed ferrocene, in agreement with the ETS scheme. Further Natural Bond Orbital (NBO) analysis indicates that all NBO energies, total Lewis (no Fe) and lone pair (LP) deletion all prefer the eclipsed Fc conformer. The most significant energy preferring the eclipsed ferrocene without cancellation is the interactions between the donor lone pairs (LP) of the Fe atom and the acceptor antibond (BD*) NBOs of all C–C and C–H bonds in the ligand, LP(Fe)-BD*(C–C & C–H), which strongly stabilizes the eclipsed (D_5h) conformation by −457.6 kcal·mol⁻¹.

Ferrocene analogues of sandwich M(CrB₆H₆)₂: a theoretical investigation

The stability and electronic structures of the new sandwich compounds M(CrB6H6)2 (M = Cr, Mn(+), Fe(2+)) are investigated by density functional theory. All the investigated sandwich complexes are in D(6d) symmetry and all of them are thermodynamically stable according to the large HOMO-LUMO gap, binding energy, vertical ionization potential and vertical electron affinity analyses, as well as Fe(C5H5)2 and Cr(C6H6)2, following the 18-electron principle. The natural bond orbital, detailed molecular orbitals and adaptive natural density partitioning analyses suggest that the spd-π interaction plays an important role in the sandwich compounds. This work challenges the traditional chemical bonding of the inorganic metal compound, investigates first the bonding style of the d atom orbital interacting with the π MO which was formed by p-d atomic orbitals, and indicates that the metal-doped borane ring can also be an ideal type π-electron donor ligand to stabilize the transition metal.

Molecular seesaw: a three-way motion and motion-induced surface modification

We introduce a three-way molecular motion which can be a suitable switching system in future molecule-based nanocircuits. A real-space investigation revealed that vinylferrocene adsorbs site-specifically on the Ge(100) surface and then shows a reversible tilting motion, similar to a seesaw. Unlike conventional molecular motions, it not only has three stable switching states at room temperature but also shows a motion-induced surface-structure modification, allowing surface-mediated signal transmission. Demonstrated STM-tip influence on the motion allows the feasibility of tip-induced manipulation.

Ab initio study of structural and magnetic properties of TM(n)(ferrocene)(n+1) (TM = Sc, Ti, V, Mn) sandwich clusters and nanowires (n = infinity)

Structural and magnetic properties of multidecker sandwich clusters TM(n)(ferrocene)(n+1) [TM = V, Ti, Sc, Mn, ferrocene=FeCp(2), n = 1-3] and corresponding one-dimensional sandwich nanowires (n = infinity) are studied by means of gradient-corrected density functional theory. The TM(n)(FeCp(2))(n+1) clusters are highly stable polyferrocene-like sandwich structures due to strong Fe-Cp interaction. The total magnetic moment of TM(n)(FeCp(2))(n+1) (TM = V, Ti, Mn) increases linearly with the size n. More strikingly, Ti(n)(FeCp(2))(n+1) and V(n)(FeCp(2))(n+1) (n = 1-3) exhibit high magnetic moments 4, 8, 12 mu(B) and 1, 6, 11 mu(B), respectively. In contrast, Sc(n)(FeCp(2))(n+1) clusters are paramagnetic. The [TM(FeCp(2))](infinity) sandwich nanowires are ferromagnetic semiconductors whose band gap is 0.361, 0.506, 0.51, and 1.310 eV, respectively, for TM = Ti, Sc, V, and Mn. Among the four sandwich nanowires, [V(FeCp(2))](infinity) nanowire possesses the highest magnetic moment (5 mu(B)) per unit cell.

Density functional calculations of NMR shielding tensors for paramagnetic systems with arbitrary spin multiplicity: validation on 3d metallocenes

The calculation of nuclear shieldings for paramagnetic molecules has been implemented in the ReSpect program, which allows the use of modern density functional methods with accurate treatments of spin-orbit effects for all relevant terms up to order Omicron(alpha4) in the fine structure constant. Compared to previous implementations, the methodology has been extended to compounds of arbitrary spin multiplicity. Effects of zero-field splittings in high-spin systems are approximately accounted for. Validation of the new implementation is carried out for the 13C and 1H NMR signal shifts of the 3d metallocenes 4VCp2, 3CrCp2, 2MnCp2, 6MnCp2, 2CoCp2, and 3NiCp2. Zero-field splitting effects on isotropic shifts tend to be small or negligible. Agreement with experimental isotropic shifts is already good with the BP86 gradient-corrected functional and is further improved by admixture of Hartree-Fock exchange in hybrid functionals. Decomposition of the shieldings confirms the dominant importance of the Fermi-contact shifts, but contributions from spin-orbit dependent terms are frequently also non-negligible. Agreement with 13C NMR shift tensors from solid-state experiments is of similar quality as for isotropic shifts.

Substitution effect on the geometry and electronic structure of the ferrocene

The substitution effects on the geometry and the electronic structure of the ferrocene are systematically and comparatively studied using the density functional theory. It is found that -NH(2) and -OH substituents exert different influence on the geometry from -CH(3), -SiH(3), -PH(2), and -SH substituents. The topological analysis shows that all the C-C bonds in a-g are typical opened-shell interactions while the Fe-C bonds are typical closed-shell interactions. NBO analysis indicates that the cooperated interaction of d --> pi* and feedback pi --> d + 4s enhances the Fe-ligand interaction. The energy partitioning analysis demonstrates that the substituents with the second row elements lead to stronger iron-ligand interactions than those with the third row elements. The molecular electrostatic potential predicts that the electrophiles are expected to attack preferably the N, O, P, or S atoms in Fer-NH(2), Fer-OH, Fer-PH(2), and Fer-SH, and attack the ring C atoms in Fer-SiH(3) and Fer-CH(3). In turn, the nucleophiles are supposed to interact predominantly by attacking the hydrogen atoms. The simulated theoretical excitation spectra show that the maximum absorption peaks are red-shifted when the substituents going from second row elements to the third row elements.

The Equilibrium Structure of Ferrocene

The molecular structures of ferrocene in the eclipsed (equilibrium) and staggered (saddle-point) conformations have been determined by full geometry optimizations at the levels of second-order Møller-Plesset (MP2) theory, coupled-cluster singles-and-doubles (CCSD) theory, and CCSD theory with a perturbative triples correction [CCSD(T)] in a TZV2P+f basis set. Existing experimental results are reviewed. The agreement between the CCSD(T) results and experiment is in all cases excellent; the calculated structure parameters and the barrier to internal rotation of the ligand rings differ from the most accurate experimental values by less than two estimated standard deviations. The CCSD(T) calculations for single-configuration-dominated transition metal complexes such as ferrocene thus appear to have an accuracy comparable to that observed for molecules containing only first- and second-row atoms, and to be of a quality similar to that obtained experimentally. A comparison with previous DFT results indicates that the B3LYP model gives overall the best DFT results, with a deviation of around 2 pm for the metal-carbon distance and smaller errors for the cyclopentadienyl rings.

Intramolecular rearrangements in six-coordinate ruthenium and iron dihydrides

Molecular orbital calculations at the ab initio level are used to study polytopal rearrangements in H2Ru(PH3)4 and H2Fe(CO)4 as models of 18-electron, octahedral metal dihydrides. It is found that, in both cases, the transition state for these rearrangements is a dihydrogen species. For H2Fe(CO)4, this is a square pyramidal complex where the H2 ligand occupies an apical position and is rotated by 45 degrees from its original orientation. This is precisely analogous to the transition state for Fe-olefin rotation in (olefin)Fe(CO)4 complexes and has a very similar electronic origin. Another transition state very close in energy is found wherein the basic coordination geometry is a trigonal bipyramid and the H2 ligand is coordinated in the axial position. For H2Ru(PH3)4, the former stationary point lies at a much higher energy and the latter clearly serves as the transition state for hydride exchange. The reason for this difference is discussed along with the roles of electron correlation in the two compounds.