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.

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.

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.

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.

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.

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.

Harmonic electron correlation operator.

An appealing way to model electron correlation within the single determinant wave function formalism is through the expectation value of a linear two-electron operator. For practical reasons, it is desirable for such an operator to be universal, i.e., not depend on the positions and types of nuclei in a molecule. We show how a perturbation theory applied to a hookium atom provides for a particular form of a correlation operator, hence called the harmonic correlation operator. The correlation operator approach is compared and contrasted to the traditional ways to describe electron correlation. To investigate the two-electron approximation of this operator, we apply it to many-electron hookium systems. To investigate the harmonic approximation, we apply it to the small atomic systems. Directions of future research are also discussed.

Semiclassical electron correlation operator.

The concept of the correlation operator, introduced 10 years ago as a possible method to model the electron correlation effects with single determinant wave functions [Rassolov, J. Chem. Phys. 110, 3672 (1999)], is revisited. We derive a semiclassical limit of the correlation operator in weakly correlated systems and give its coordinate space representation. Application of this operator to the atomic systems, such as computations of energies of the neutral atoms, energies of the cations, and spin states energy gaps, demonstrates capabilities and limitations of this concept.

Stable long-time semiclassical description of zero-point energy in high-dimensional molecular systems.

Semiclassical implementation of the quantum trajectory formalism [J. Chem. Phys. 120, 1181 (2004)] is further developed to give a stable long-time description of zero-point energy in anharmonic systems of high dimensionality. The method is based on a numerically cheap linearized quantum force approach; stabilizing terms compensating for the linearization errors are added into the time-evolution equations for the classical and nonclassical components of the momentum operator. The wave function normalization and energy are rigorously conserved. Numerical tests are performed for model systems of up to 40 degrees of freedom.

Geminal model chemistry. IV. Variational and size consistent pure spin states.

We present a computationally inexpensive method that yields ground state wave functions of pure spin symmetry. The method is variational and rigorously size consistent, free from adjustable parameters, and has a favorable scaling with system size. It is based on the recently introduced partially spin restricted geminal wave functions with limited spin contamination. Computations of a bond breaking, a transition metal compound, and a symmetric hydrogen cluster confirm the properties of this method.

Geminal model chemistry III: Partial spin restriction.

The authors define an ab initio electronic structure model that uses partial spin restriction. It is an intermediate case between the so-called spin-restricted and spin-unrestricted formulations, which are popular in electronic structure methodology. Partial spin restriction arises naturally when the wave function is represented as an antisymmetrized product of two-electron functions, as it is done in generalized valence bond and antisymmetrized product of strongly orthogonal geminal theories. The authors show that the new model is size consistent, and it improves the description of transition metal compounds.

Advances in methods and algorithms in a modern quantum chemistry program package.

Advances in theory and algorithms for electronic structure calculations must be incorporated into program packages to enable them to become routinely used by the broader chemical community. This work reviews advances made over the past five years or so that constitute the major improvements contained in a new release of the Q-Chem quantum chemistry package, together with illustrative timings and applications. Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.

Semiclassical nonadiabatic dynamics based on quantum trajectories for the O(3P,1D) + H2 system.

The O(3P,1D) + H2 --> OH + H reaction is studied using trajectory dynamics within the approximate quantum potential approach. Calculations of the wave-packet reaction probabilities are performed for four coupled electronic states for total angular momentum J = 0 using a mixed coordinate/polar representation of the wave function. Semiclassical dynamics is based on a single set of trajectories evolving on an effective potential-energy surface and in the presence of the approximate quantum potential. Population functions associated with each trajectory are computed for each electronic state. The effective surface is a linear combination of the electronic states with the contributions of individual components defined by their time-dependent average populations. The wave-packet reaction probabilities are in good agreement with the quantum-mechanical results. Intersystem crossing is found to have negligible effect on reaction probabilities summed over final electronic states.

Quantum trajectory dynamics in arbitrary coordinates.

The quantum trajectory approach is generalized to arbitrary coordinate systems, including curvilinear coordinates. This allows one to perform an approximate quantum trajectory propagation, which scales favorably with system size, in the same framework as standard quantum wave packet dynamics. The trajectory formulation is implemented in Jacobi coordinates for a nonrotating triatomic molecule. Wave packet reaction probabilities are computed for the O(3P) + H2 --> OH + H reaction using the approximate quantum potential. The latter is defined by the nonclassical component of the momentum operator expanded in terms of linear and exponential functions. Unlike earlier implementations with linear functions, the introduction of the exponential function provides an accurate description of asymptotic dynamics for this system and gives good agreement of approximate reaction probabilities with accurate quantum calculations.

Semiclassical nonadiabatic dynamics using a mixed wave-function representation.

Nonadiabatic effects in quantum dynamics are described using a mixed polar/coordinate space representation of the wave function. The polar part evolves on dynamically determined potential surfaces that have diabatic and adiabatic potentials as limiting cases of weak localized and strong extended diabatic couplings. The coordinate space part, generalized to a matrix form, describes transitions between the surfaces. Choice of the effective potentials for the polar part and partitioning of the wave function enables one to represent the total wave function in terms of smooth components that can be accurately propagated semiclassically using the approximate quantum potential and small basis sets. Examples are given for two-state one-dimensional problems that model chemical reactions that demonstrate the capabilities of the method for various regimes of nonadiabatic dynamics.

Modified quantum trajectory dynamics using a mixed wave function representation.

Dynamics of quantum trajectories provides an efficient framework for description of various quantum effects in large systems, but it is unstable near the wave function density nodes where the quantum potential becomes singular. A mixed coordinate space/polar representation of the wave function is used to circumvent this problem. The resulting modified trajectory dynamics associated with the polar representation is nonsingular and smooth. The interference structure and the nodes of the wave function density are described, in principle, exactly in the coordinate representation. The approximate version of this approach is consistent with the semiclassical linearized quantum force method [S. Garashchuk and V. A. Rassolov, J. Chem. Phys. 120, 1181 (2004)]. This approach is exact for general wave functions with the density nodes in a locally quadratic potential.

Bohmian dynamics on subspaces using linearized quantum force.

In the de Broglie-Bohm formulation of quantum mechanics the time-dependent Schrodinger equation is solved in terms of quantum trajectories evolving under the influence of quantum and classical potentials. For a practical implementation that scales favorably with system size and is accurate for semiclassical systems, we use approximate quantum potentials. Recently, we have shown that optimization of the nonclassical component of the momentum operator in terms of fitting functions leads to the energy-conserving approximate quantum potential. In particular, linear fitting functions give the exact time evolution of a Gaussian wave packet in a locally quadratic potential and can describe the dominant quantum-mechanical effects in the semiclassical scattering problems of nuclear dynamics. In this paper we formulate the Bohmian dynamics on subspaces and define the energy-conserving approximate quantum potential in terms of optimized nonclassical momentum, extended to include the domain boundary functions. This generalization allows a better description of the non-Gaussian wave packets and general potentials in terms of simple fitting functions. The optimization is performed independently for each domain and each dimension. For linear fitting functions optimal parameters are expressed in terms of the first and second moments of the trajectory distribution. Examples are given for one-dimensional anharmonic systems and for the collinear hydrogen exchange reaction.