Stability Trends in disubstituted Cobaltocenium Based on the Analysis of the Machine Learning Models.

Cobaltocenium derivatives have shown great potential as components of anion exchange membranes in fuel cells because they exhibit excellent thermal and alkaline stability under operating conditions while allowing for high anion mobility. The properties of the cobaltocenium-anion complexes can be chemically tuned through the substituent groups on the cyclopentadienyl (Cp) rings of the cation CoCp2+. However, the synthesis and characterization of the full range of possible derivatives are very challenging and time-consuming, and while the computational tools can greatly expedite this process, full screening of the electronic structure at a high level of theory is still computationally intensive. Therefore, in this work, we consider the machine learning (ML) modeling as a tool of predicting stability of disubstituted [CoCp2]OH complexes measured by their bond-dissociation energy (BDE). The relevant process here is the dissociation of the cobaltocenium-hydroxide complex into fragments [CoCpY']OH and CpY, where Y and Y' each represent one out of 42 substituent groups of experimental interest. In agreement with the previous ML study of 120 mono- and selected disubstituted species [Wetthasinghe et al. J. Chem. Phys. A (2022) 126], our analysis of the data set expanded to all possible disubstituted cobaltoceniums, points to the highest occupied and lowest unoccupied molecular orbitals, along with the Hirshfeld charge on the singly substituted benzene, to be the key features predicting the BDE of the unseen complexes. Based on the examination of the outliers, the acidity of substituents ((CO)NH2 in our case) is found to be of special significance for the cobaltocenium stability and for the model development. Moreover, we demonstrate that upon the data set refinement, the conventional ML models are capable of predicting the BDE close to 1 kcal/mol based on the properties of just the fragments, thereby greatly reducing the total number of species and of the computational time of each calculation. Such fragment-based "combinatorial" approach to the BDE modeling is noteworthy, since the geometry optimization of complexes in solution is conceptually challenging and computationally demanding, even when leveraging high-performance computing resources.

Breaking the photoswitch speed limit.

The forthcoming generation of materials, including artificial muscles, recyclable and healable systems, photochromic heterogeneous catalysts, or tailorable supercapacitors, relies on the fundamental concept of rapid switching between two or more discrete forms in the solid state. Herein, we report a breakthrough in the "speed limit" of photochromic molecules on the example of sterically-demanding spiropyran derivatives through their integration within solvent-free confined space, allowing for engineering of the photoresponsive moiety environment and tailoring their photoisomerization rates. The presented conceptual approach realized through construction of the spiropyran environment results in ~1000 times switching enhancement even in the solid state compared to its behavior in solution, setting a record in the field of photochromic compounds. Moreover, integration of two distinct photochromic moieties in the same framework provided access to a dynamic range of rates as well as complementary switching in the material's optical profile, uncovering a previously inaccessible pathway for interstate rapid photoisomerization.

Theoretical Examination of the Hydroxide Transport in Cobaltocenium-Containing Polyelectrolytes.

Polymers incorporating cobaltocenium groups have received attention as promising components of anion-exchange membranes (AEMs), exhibiting a good balance of chemical stability and high ionic conductivity. In this work, we analyze the hydroxide diffusion in the presence of cobaltocenium cations in an aqueous environment based on the molecular dynamics of model systems confined in one dimension to mimic the AEM channels. In order to describe the proton hopping mechanism, the forces are obtained from the electronic structure computed at the density-functional tight-binding level. We find that the hydroxide diffusion depends on the channel size, modulation of the electrostatic interactions by the solvation shell, and its rearrangement ability. Hydroxide diffusion proceeds via both the vehicular and structural diffusion mechanisms with the latter playing a larger role at low diffusion coefficients. The highest diffusion coefficient is observed under moderate water densities (around half the density of liquid water) when there are enough water molecules to form the solvation shell, reducing the electrostatic interaction between ions, yet there is enough space for the water rearrangements during the proton hopping. The effects of cobaltocenium separation, orientation, chemical modifications, and the role of nuclear quantum effects are also discussed.

Factorized Electron-Nuclear Dynamics with an Effective Complex Potential.

We present a quantum dynamics approach for molecular systems based on wave function factorization into components describing the light and heavy particles, such as electrons and nuclei. The dynamics of the nuclear subsystem can be viewed as motion of the trajectories defined in the nuclear subspace, evolving according to the average nuclear momentum of the full wave function. The probability density flow between the nuclear and electronic subsystems is facilitated by the imaginary potential, derived to ensure a physically meaningful normalization of the electronic wave function for each configuration of the nuclei, and conservation of the probability density associated with each trajectory in the Lagrangian frame of reference. The imaginary potential, defined in the nuclear subspace, depends on the momentum variance in the nuclear coordinates averaged over the electronic component of the wave function. An effective real potential, driving the dynamics of the nuclear subsystem, is defined to minimize motion of the electronic wave function in the nuclear degrees of freedom. Illustration and the analysis of the formalism are given for a two-dimensional model system of vibrationally nonadiabatic dynamics.

Synthesis and Chemistry of Ammonioethenyl and Phosphonioethenyl Ligands in Zwitterionic Dirhenium Carbonyl Complexes.

New zwitterionic dirhenium carbonyl complexes containing ammonioethenyl and phosphonioethenyl ligands have been synthesized and studied. The reaction of Re2(CO)10 with C2H2 and Me3NO yielded the dirhenium complex Re2(CO)9(NMe3) (6) and the new zwitterionic complex Re2(CO)9[η1-E-2-CH═CH(NMe3)] (7). Compound 6 was characterized structurally and was found to have a NMe3 ligand in an equatorial coordination site cis to a long Re-Re single bond, Re-Re = 3.0938(2) Å. Compound 7 can be obtained from the reaction of 6 with ethyne (C2H2) formally by the insertion of ethyne into the Re-N bond to the NMe3 ligand. Compound 7 contains a 2-trimethylammonioethenyl ligand, -CH═CH(+NMe3), that is formally a zwitterion having a positive charge on the nitrogen atom and a negative charge on the terminal carbon atom. When coordinated to rhenium by the terminal ethenyl carbon atom, the negative charge on the -CH═CH(+NMe3) carbon atom is formally transferred to the rhenium atom. The reaction of Re2(CO)10 with C2H2 and NEt3 in the presence of Me3NO yielded the new dirhenium complex Re2(CO)9[η1-E-2-CH═CH(NEt3)] (8) together with some 6 and 7. Compound 8 is structurally similar to 7, but it contains a NEt3 group in the ammonioethenyl ligand in the place of the NMe3 group in 7. Reactions of 7 with PMePh2 and PPh3 yielded the zwitterionic 2-arylphosphonioethenyl-coordinated dirhenium carbonyl complexes, Re2(CO)9[η1-E-2-CH═CH(PPh2Me)] (9a) and Re2(CO)9[η1-E-2-CH═CH(PPh3)] (9b), and the zwitterionic 1-phosphonioethenyl ligand in the dirhenium carbonyl complexes, Re2(CO)9[η1-1-C(PPh2Me)(═CH2)] (10a), Re2(CO)8[µ-η2-1-C(PPh2Me)(═CH2)] (11a), and Re2(CO)8[[µ-η2-1-C(PPh3)(CH2)] (11b). Compound 10a was converted to 11a and the new compound Re2(CO)7(µ-H)[µ-η2-1-(CH2C)P(Ph)(Me)(o-C6H4)], (12) by decarbonylation using Me3NO. Compound 12 contains an ortho-metalated phenyl ring. The new products 6,7, 8, 9b, 10a, 11a, 11b and 12 were characterized structurally by single-crystal X-ray diffraction analyses.

Experimental and Theoretical Examination of the Kinetic Isotope Effect in Cytochrome P450 Decarboxylase OleT.

Using a combination of experimental studies, theory, simulation, and modeling, we investigate the hydrogen atom transfer (HAT) reaction by the high-valent ferryl cytochrome P450 (CYP) intermediate known as Compound I, a species that is central to innumerable and important detoxification and biosynthetic reactions. The P450 decarboxylase known as OleT converts fatty acids, a sustainable biological feedstock, into terminal alkenes and thus is of high interest as a potential means to produce fungible biofuels. Previous experimental work has established the intermediacy of Compound I in the C─C scission reaction catalyzed by OleT and an unprecedented ability to monitor the HAT process in the presence of bound fatty acid substrates. Here, we leverage the kinetic simplicity of the OleT system to measure the activation barriers for CYP HAT and the temperature dependence of the substrate 2H kinetic isotope effect. Notably, neither measurement has been previously accessible for a CYP to date. Theoretical analysis alludes to the significance of substrate fatty acid coordination for generating the hydrogen donor/acceptor configurations that are most conducive for HAT to occur. The analysis of the two-dimensional potential energy surface, based on multireference electronic wave functions, illustrates the uncoupled character of the hydrogen motion. Quantum dynamics calculations along the hydrogen reaction path demonstrate that hydrogen tunneling is essential to qualitatively capture the experimental isotope effect, its temperature dependence, and appropriate activation energies. Overall, a more fundamental understanding of the OleT reaction coordinate contributes to the development of biomimetic catalysts for controlled C─H bond activation, an outstanding current challenge for (bio)synthetic chemistry.

Modeling the Ligand Effect on the Structure of CYP 450 Within the Density Functional Theory.

An improved understanding of the P450 structure is relevant to the development of biomimetic catalysts and inhibitors for controlled CH-bond activation, an outstanding challenge of synthetic chemistry. Motivated by the experimental findings of an unusually short Fe-S bond of 2.18 Šfor the wild-type (WT) OleT P450 decarboxylase relative to a cysteine pocket mutant form (A369P), a computational model that captures the effect of the thiolate axial ligand on the iron-sulfur distance is presented. With the computational efficiency and streamlined analysis in mind, this model combines a cluster representation of the enzyme─40-110 atoms, depending on the heme and ligand truncation level─with a density functional theory (DFT) description of the electronic structure (ES) and is calibrated against the experimental data. The optimized Fe-S distances show a difference of 0.25 Šbetween the low and high spin states, in agreement with the crystallographic structures of the OleT WT and mutant forms. We speculate that this difference is attributable to the packing of the ligand; the mutant is bulkier due to an alanine-to-proline replacement, meaning that it is excluded from the energetically favored low-spin minimum because of steric constraints. The presence of pure spin-state pairs and the intersection of the low/high spin states for the enzyme model is indicative of the limitations of single-reference ES methods in such systems and emphasizes the significance of using the proper state when modeling the hydrogen atom transfer (HAT) reaction catalyzed by OleT. At the same time, the correct characterization of both the short and long Fe-S bonds within a small DFT-based model of 42 atoms paves the way for quantum dynamics modeling of the HAT step, which initiates the OleT decarboxylation reaction.

Stability Analysis of Substituted Cobaltocenium [Bis(cyclopentadienyl)cobalt(III)] Employing Chemistry-Informed Neural Networks.

Cationic cobaltocenium derivatives are promising components of the anion exchange membranes because of their excellent thermal and alkaline stability under the operating conditions of a fuel cell. Here, we present an efficient modeling approach to assessing the chemical stability of substituted cobaltocenium CoCp2+, based on the computed electronic structure enhanced by machine learning techniques. Within the aqueous environment, the positive charge of the metal cation is balanced by the hydroxide anion through formation of the CoCp2+OH- complexes, whose dissociation is studied within the implicit solvent employing the density functional theory. The data set of about 118 the CoCp2+OH- complexes based on 42 substituent groups characterized by a range of electron-donating (ED) and electron-withdrawing (EW) properties is constructed and analyzed. Given 12 carefully chosen chemistry-informed descriptors of the complexes and relevant fragments, the stability of the complexes is found to strongly correlate with the energies of the highest occupied and lowest unoccupied molecular orbitals, modulated by a switching function of the Hirshfeld charge. The latter is used as a measure of the electron-withdrawing-donating character of the substituents. On the basis of this observation from the conventional regression analysis, two fully connected, feed-forward neural network (FNN) models with different unit structures, called the chemistry-informed (CINN) and the quadratic (QNN) neural networks, together with a support vector regression (SVR) model are developed. Both deep neural network models predict the bond dissociation energies of the cobaltocenium complexes with mean relative errors less than 10.56% and average absolute errors less than 1.63 kcal/mol, superior to the conventional regression and the SVR model prediction. The results show the potential of QNN to efficiently capture more complex relationships. The concept of incorporating the domain (chemical) knowledge/insight into the neural network structure paves the way to applications of machine learning techniques with small data sets, ultimately leading to better predictive models compared to the classical machine learning method SVR and conventional regression analysis.

Correlation between the Stability of Substituted Cobaltocenium and Molecular Descriptors.

Metallocenium cations, used as a component in an anion exchange membrane of a fuel cell, demonstrate excellent thermal and alkaline stability, which can be improved by the chemical modification of the cyclopentadienyl rings with substituent groups. In this work, the relation between the bond dissociation energy (BDE) of the cobaltocenium (CoCp2+) derivatives, used as a measure of the cation stability, and chemistry-informed descriptors obtained from the electronic structural calculations is established. The analysis of 12 molecular descriptors for 118 derivatives reveals a nonlinear dependence of the BDE on the electron donating-withdrawing character of the substituent groups coupled to the energy of the frontier molecular orbitals. A chemistry-informed feed-forward neural network trained using k-fold cross-validation over the modest data set is able to predict the BDE from the molecular descriptors with the mean absolute error of about 1 kcal/mol. The theoretical analysis suggests some promising modifications of cobaltocenium for experimental research. The results demonstrate that even for modest data sets the incorporation of the chemistry knowledge into the neural network architecture, e.g., through mindful selection and screening of the descriptors and their interactions, paves the way to gain new insight into molecular properties.

Local Measure of Quantum Effects in Quantum Dynamics.

The Madelung-de Broglie-Bohm formulation of the Schrödinger equation casts the time-evolution of a wave function as dynamics of an ensemble of quantum, or Bohmian, trajectories, interacting via the nonlocal quantum potential. This trajectory perspective gives insight into the quantumness (or classicality) of a given system due to clear partitioning of the energy into classical and quantum components. Here, we propose a system-independent measure of the quantumness of dynamics, based on the energy time-change, referred to as "quantum power". This measure is local in the coordinate space. Based on applications to model chemical systems, we argue that during the transition from the quantum to classical regime, defined as compression of quantization, the quantum features in dynamics do not "disappear" but are pushed forward in time. This feature may be used to gauge the validity of the semiclassical and other approximate dynamics approaches in applications to anharmonic systems.

Large transition state stabilization from a weak hydrogen bond.

A series of molecular rotors was designed to study and measure the rate accelerating effects of an intramolecular hydrogen bond. The rotors form a weak neutral O-H⋯O[double bond, length as m-dash]C hydrogen bond in the planar transition state (TS) of the bond rotation process. The rotational barrier of the hydrogen bonding rotors was dramatically lower (9.9 kcal mol-1) than control rotors which could not form hydrogen bonds. The magnitude of the stabilization was significantly larger than predicted based on the independently measured strength of a similar O-H⋯O[double bond, length as m-dash]C hydrogen bond (1.5 kcal mol-1). The origins of the large transition state stabilization were studied via experimental substituent effect and computational perturbation analyses. Energy decomposition analysis of the hydrogen bonding interaction revealed a significant reduction in the repulsive component of the hydrogen bonding interaction. The rigid framework of the molecular rotors positions and preorganizes the interacting groups in the transition state. This study demonstrates that with proper design a single hydrogen bond can lead to a TS stabilization that is greater than the intrinsic interaction energy, which has applications in catalyst design and in the study of enzyme mechanisms.

Quantum Trajectory Dynamics Based on Local Approximations to the Quantum Potential and Force.

The quantum nature of nuclei often affects molecular structure and properties, which are associated with the motion of protons and other light nuclei at low temperature. However, incorporation of the nuclear quantum effects into theoretical studies of large molecular systems is an outstanding challenge in theoretical chemistry. In this paper, the de Broglie-Bohm formulation of the time-dependent Schrödinger equation is used as a framework for the development of approximate quantum corrections to the dynamics of a trajectory ensemble, representing a time-dependent wave function. Specifically, the trajectory-centered local Least Square Fit (L-LSF) to the trajectory attributes is introduced, formally analyzed and illustrated on model potentials, typically used to benchmark approximate and semiclassical dynamics methods. The L-LSF method improves the dynamics accuracy, compared to the globally defined approximations, developed previously, and is shown to converge to the exact (generally impractical for large systems) limit of quantum dynamics.

OH Radical as a Probe of the Spin Polarizability in 1- and 2-Naphthol.

The relative yields for addition of the OH radical at the various positions of 1- and 2-naphthol provide a measure of the spin polarizability in the naphthols. The observed yields show that addition occurs predominantly at the naphthol positions that are conjugated with the OH substituent. They also show that the electronic structures of the naphthols are significantly affected by a concerted interaction between the OH substituent and the unsubstituted ring and that this effect is somewhat greater when the OH substituent is adjacent to the naphthol bridge. The yields for addition at the different naphthol positions correlate with the local spin polarizabilities at reactive carbons in the naphthol. The spin polarizability may be a general property governing the reactivity of closed-shell molecules with radicals.

Synthesis and Reactivity of Electronically Unsaturated Dirhenium Carbonyl Compounds Containing Bridging Gold-Carbene Groups.

The electronically unsaturated compounds Re2(CO)8[µ-Au(NHC)](µ-Ph), 1, and Re2(CO)8[µ-Au(NHC)]2, 2, were obtained from the reaction of Re2(CO)8[µ-η2-C(H)═C(H)Bun](µ-H) with MeAu(NHC), NHC = 1,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene. Compound 1 was converted to the new compound Re2(CO)8[µ-Au(NHC)](µ-H), 3, by reaction with H2. Addition of CO to 3 yielded the new compound Re2(CO)9[Au(NHC)](µ-H), 4, which contains a terminally coordinated Au(NHC) group on one of the rhenium atoms, and the hydrido ligand was shifted to bridge the Re-Au bond. The mechanism of the formation of 4 was established by DFT computational analyses. Compound 3 also reacted with C2H2 by an addition with insertion into the Re-H bonds to yield the compound Re2(CO)8[µ-Au(NHC)](µ-C2H3), 5, which contains a σ-π coordinated, bridging C2H3 ligand. The stereochemistry of the insertion was found to proceed preferentially with a cis- (syn-) stereochemistry. Compound 1 reacted with HCl to yield Re2(CO)8[µ-Ph](µ-H), 6, and ClAu(NHC) by selective removal of the bridging Au(NHC) group. All new compounds were characterized by single-crystal X-ray diffraction analyses.

Binuclear Aromatic C-H Bond Activation at a Dirhenium Site.

The electronically unsaturated dirhenium complex [Re2(CO)8(µ-H)(µ-Ph)] (1) has been found to exhibit aromatic C-H activation upon reaction with N,N-diethylaniline, naphthalene, and even [D6]benzene to yield the compounds [Re2(CO)8(µ-H)(µ-η(1)-NEt2C6H4)] (2), [Re2(CO)8(µ-H)(µ-η(2)-1,2-C10H7)] (3), and [D6]-1, respectively, in good yields. The mechanism has been elucidated by using DFT computational analyses, and involves a binuclear C-H bond-activation process.

Estimation of the Ground State Energy of an Atomic Solid by Employing Quantum Trajectory Dynamics with Friction.

Evolution with energy dissipation can be used to obtain the ground state of a quantum-mechanical system. This dissipation is introduced in the quantum trajectory framework by adding an empirical friction force to the equations of motion for the trajectories, which, as an ensemble, represent a wave function. The quantum effects in dynamics are incorporated via the quantum force derived from the properties of this ensemble. For scalability to large systems, the quantum force is computed approximately yet with sufficient accuracy to describe the strongly anharmonic ground state of solid (4)He represented by a simulation cell of 180 atoms.

Dynamics in the quantum/classical limit based on selective use of the quantum potential.

A classical limit of quantum dynamics can be defined by compensation of the quantum potential in the time-dependent Schrödinger equation. The quantum potential is a non-local quantity, defined in the trajectory-based form of the Schrödinger equation, due to Madelung, de Broglie, and Bohm, which formally generates the quantum-mechanical features in dynamics. Selective inclusion of the quantum potential for the degrees of freedom deemed "quantum," defines a hybrid quantum/classical dynamics, appropriate for molecular systems comprised of light and heavy nuclei. The wavefunction is associated with all of the nuclei, and the Ehrenfest, or mean-field, averaging of the force acting on the classical degrees of freedom, typical of the mixed quantum/classical methods, is avoided. The hybrid approach is used to examine evolution of light/heavy systems in the harmonic and double-well potentials, using conventional grid-based and approximate quantum-trajectory time propagation. The approximate quantum force is defined on spatial domains, which removes unphysical coupling of the wavefunction fragments corresponding to distinct classical channels or configurations. The quantum potential, associated with the quantum particle, generates forces acting on both quantum and classical particles to describe the backreaction.

SS(p)G: a strongly orthogonal geminal method with relaxed strong orthogonality.

Strong orthogonality is an important constraint placed on geminal wavefunctions in order to make variational minimization tractable. However, strong orthogonality prevents certain, possibly important, excited configurations from contributing to the ground state description of chemical systems. The presented method lifts strong orthogonality constraint from geminal wavefunction by computing a perturbative-like correction to each geminal independently from the corrections to all other geminals. The method is applied to the Singlet-type Strongly orthogonal Geminals variant of the geminal wavefunction. Comparisons of this new SS(p)G method are made to the non-orthogonal AP1roG and the unconstrained Geminal Mean-Field Configuration Interaction method using small atomic and molecular systems. The correction is also compared to Density Matrix Renormalization Group calculations performed on long polyene chains in order to assess its scalability and applicability to large strongly correlated systems. The results of these comparisons demonstrate that although the perturbative correction is small, it may be a necessary first step in the systematic improvement of any strongly orthogonal geminal method.

Facile C-H bond formation by reductive elimination at a dinuclear metal site.

The electronically unsaturated dirhenium complex [Re2(CO)8(µ-AuPPh3)(µ-Ph)] (1) was obtained from the reaction of [Re2(CO)8{µ-η(2)-C(H)=C(H)nBu}(µ-H)] with [Au(PPh3)Ph]. The bridging {AuPPh3} group was replaced by a bridging hydrido ligand to yield the unsaturated dirhenium complex [Re2(CO)8(µ-H)(µ-Ph)] (2) by reaction of 1 with HSnPh3. Compound 2 reductively eliminates benzene upon addition of NCMe at 25 °C. The electronic structure of 2 and the mechanism of the reductive elimination of the benzene molecule in its reaction with NCMe were investigated by DFT computational analyses.

Description of electronic excited states using electron correlation operator.

The electron correlation energy in a chemical system is defined as a difference between the energy of an exact energy for a given Hamiltonian, and a mean-field, or single determinant, approximation to it. A promising way to model electron correlation is through the expectation value of a linear two-electron operator for the Kohn-Sham single determinant wavefunction. For practical reasons, it is desirable for such an operator to be universal, i.e., independent of the positions and types of nuclei in a molecule. The correlation operator models the effect of electron correlation on the interaction energy in a electron pair. We choose an operator expanded in a small number of Gaussians as a model for electron correlation, and test it by computing atomic and molecular adiabatic excited states. The computations are performed within the Δ Self-Consistent Field (ΔSCF) formalism, and are compared to the time-dependent density functional theory model with popular density functionals. The simplest form of the correlation operator contains only one parameter derived from the helium atom ground state correlation energy. The correlation operator approach significantly outperforms other methods in computation of atomic excitation energies. The accuracy of molecular excitation energies computed with the correlation operator is limited by the shortcomings of the ΔSCF methodology in describing excited states.