Describing Polytopal Rearrangements of Fluxional Molecules with Curvilinear Coordinates Derived from Normal Vibrational Modes: A Conceptual Extension of Cremer-Pople Puckering Coordinates

Homoleptic hexa- and penta-coordinated gallium(I) amide complexes of ruthenium and molybdenum

Reaction of neutral olefin complexes of ruthenium and molybdenum with GaTMP (TMP = 2,2,6,6-tetramethylpiperidinyl) by substitution leads to the formation of respective five- and six-coordinated homoleptic products. [Ru(GaTMP)5] (1) and [Mo(GaTMP)6] (2) were isolated and characterized. Core structure geometries were analyzed using continuous shape measure, and the complexes were subjected to DFT calculations unveiling competing π-interactions between the transition metal center and the amido substituent with the unoccupied pπ orbitals of the gallium.

"Polytopal Rearrangement Model of Stereoisomerization" and Its Potential as the Basis for a Systematic Model of All Stereoisomerism

The term "polytopal rearrangement" describes any shape changing process operating on a coordination "polyhedron"-the solid figure defined by the positions of the ligand atoms directly attached to the central atom of a coordination entity. Developed in the latter third of the last century, the polytopal rearrangement model of stereoisomerization is a general mathematical approach for analyzing and accommodating the complexity of such processes for any coordination number. The motivation for the model was principally to deal with the complexity, such as Berry pseudorotation in pentavalent phosphorus species, arising from rearrangements in inorganic coordination complexes of higher coordination numbers. The model is also applicable to lower coordination centers, for example, thermal "inversion" at nitrogen in NH3 and amines. We present the history of the model focusing on its essential features, and review some of the more subtle aspects addressed in recent literature. We then introduce a more detailed and rigorous modern approach for describing such processes using an assembly of existing concepts, with the addition of formally described terminology and representations. In our outlook, we contend that the rigorous and exhaustive application of the principles of the polytopal rearrangement model, when combined with torsional isomerism, will provide a basis for a mathematically complete, general, and systematic classification for all stereoisomerism and stereoisomerization. This is essential for comprehensively mapping chemical structure and reaction spaces.

Chiral-at-Metal Racemization Unraveled for MX2 (a-chel)2 by means of a Computational Analysis of MoO2 (acnac)2

Octahedral chiral-at-metal complexes MX2 (a-chel)2 (a-chel=asymmetric chelate) can rearrange their ligands by four mechanisms known as the Bailar (B), Ray-Dutt (RD), Conte-Hippler (CH), and Dhimba-Muller-Lammertsma (DML) twists. Racemization involves their interconnections, which were computed for MoO2 (acnac)2 (acnac=β-ketoiminate) using density functional theory at ωB97x-D with the 6-31G(d,p) and 6-311G(2d,p) basis sets and LANL2DZ for molybdenum. Racemizing the cis(NN) isomer, being the global energy minimum with trans oriented imine groups, is a three step process (DML-CH-DML) that requires 17.4 kcal/mol, while all three cis isomers (cis(NN), cis(NO), and cis(OO)) interconvert at ≤17.9 kcal/mol. The B and RD twists are energetically not competitive and neither are the trans isomers. The interconnection of all enantiomeric minima and transition structures is summarized in a graph that also visualizes valley ridge inflection points for two of the three CH twists. Geometrical features of the minima and twists are given. Lastly, the influence of N-substitution on the favored racemization pathway is evaluated. The present comprehensive study serves as a template for designing chiral-at-metal MX2 (a-chel)2 catalysts that may retain their chiral integrity.

Potential Energy Surfaces Sampled in Cremer-Pople Coordinates and Represented by Common Force Field Functionals for Small Cyclic Molecules

The complex conformations of the cyclic moieties impact the physical and chemical properties of molecules. In this work, we chose 22 molecules of four-, five-, and six-membered rings and performed a thorough conformational sampling using Cremer-Pople coordinates. With consideration of symmetries, we obtained a total of 1504 conformational structures for four-membered, 5576 for five-membered, and 13509 for six-membered rings. All well-known and many less well-known conformers for each molecule were identified. We represented the potential energy surfaces (PESs) by fitting the data to common analytical force field (FF) functional forms. We found that the general features of PESs can be described by the essential FF functional forms; however, the accuracy of representation can be improved remarkably by including the torsion-bond and torsion-angle coupling terms. The best fit yields R-squared (R²) values close to 1.0 and mean absolute errors in energy less than 0.3 kcal/mol.

BF3–Catalyzed Diels–Alder Reaction between Butadiene and Methyl Acrylate in Aqueous Solution—An URVA and Local Vibrational Mode Study

In this study we investigate the Diels–Alder reaction between methyl acrylate and butadiene, which is catalyzed by BF3 Lewis acid in explicit water solution, using URVA and Local Mode Analysis as major tools complemented with NBO, electron density and ring puckering analyses. We considered four different starting orientations of methyl acrylate and butadiene, which led to 16 DA reactions in total. In order to isolate the catalytic effects of the BF3 catalyst and those of the water environment and exploring how these effects are synchronized, we systematically compared the non-catalyzed reaction in gas phase and aqueous solution with the catalyzed reaction in gas phase and aqueous solution. Gas phase studies were performed at the B3LYP/6-311+G(2d,p) level of theory and studies in aqueous solution were performed utilizing a QM/MM approach at the B3LYP/6-311+G(2d,p)/AMBER level of theory. The URVA results revealed reaction path curvature profiles with an overall similar pattern for all 16 reactions showing the same sequence of CC single bond formation for all of them. In contrast to the parent DA reaction with symmetric substrates causing a synchronous bond formation process, here, first the new CC single bond on the CH2 side of methyl acrylate is formed followed by the CC bond at the ester side. As for the parent DA reaction, both bond formation events occur after the TS, i.e., they do not contribute to the energy barrier. What determines the barrier is the preparation process for CC bond formation, including the approach diene and dienophile, CC bond length changes and, in particular, rehybridization of the carbon atoms involved in the formation of the cyclohexene ring. This process is modified by both the BF3 catalyst and the water environment, where both work in a hand-in-hand fashion leading to the lowest energy barrier of 9.06 kcal/mol found for the catalyzed reaction R1 in aqueous solution compared to the highest energy barrier of 20.68 kcal/mol found for the non-catalyzed reaction R1 in the gas phase. The major effect of the BF3 catalyst is the increased mutual polarization and the increased charge transfer between methyl acrylate and butadiene, facilitating the approach of diene and dienophile and the pyramidalization of the CC atoms involved in the ring formation, which leads to a lowering of the activation energy. The catalytic effect of water solution is threefold. The polar environment leads also to increased polarization and charge transfer between the reacting species, similar as in the case of the BF3 catalyst, although to a smaller extend. More important is the formation of hydrogen bonds with the reaction complex, which are stronger for the TS than for the reactant, thus stabilizing the TS which leads to a further reduction of the activation energy. As shown by the ring puckering analysis, the third effect of water is space confinement of the reacting partners, conserving the boat form of the six-member ring from the entrance to the exit reaction channel. In summary, URVA combined with LMA has led to a clearer picture on how both BF3 catalyst and aqueous environment in a synchronized effort lower the reaction barrier. These new insights will serve to further fine-tune the DA reaction of methyl acrylate and butadiene and DA reactions in general.

Unusual Intramolecular Motion of ReH92- in K2ReH9 Crystal: Circle Dance and Three-Arm Turnstile Mechanisms Revealed by Computational Studies

The nonahydridorhenate dianion ReH₉^2- is a unique rhenium polyhydride complex due to its remarkably high coordination number; however, its detailed polytopal rearrangement process in either solution or crystal is so far unclear. In this work, our quantum chemical calculations have identified two previously unreported fluxional mechanisms for the ReH₉^2- dianion in the K₂ReH₉ crystal: three-arm turnstile rotation and circle dance mechanism. These two polytopal rearrangements in the crystal offer an alternative interpretation to the pulse and wide-line NMR spectra (Farrar et al. J. Chem. Phys. 1969, 51, 3595). The previously postulated hindered rotation of the whole ReH₉^2- dianion in K₂ReH₉ (White et al. J. Chem. Soc., Faraday Trans. 2 1972, 68, 1414) turns out to be a combination of the above-mentioned two elementary fluxional processes. In addition, our calculations have confirmed the Muetterties' D_3h⇌C_4v rearrangement as the intramolecular motion for the ReH₉^2- dianion in solution.

Interplay of Rotational and Pseudorotational Motions in Flexible Cyclic Molecules

Solutions to the time-independent nuclear Schrödinger equation associated with the pseudorotational motion of three flexible cyclic molecules are presented and discussed. Structural relaxations related to the pseudorotational motion are described as functions of a pseudorotation angle ϕ which is formulated according to the definition of ring-puckering coordinates originally proposed by Cremer and Pople ( J. Am. Chem. Soc. 1975, 97 (6), 1354-1358). In order to take into account the interplay between pseudorotational and rotational motions, the rovibrational Hamiltonian matrices are formulated for the rotational quantum numbers J = 0 and J = 1. The rovibrational Hamiltonian matrices are constructed and diagonalized using a Python program developed by the authors. Suitable algorithms for (i) the construction of one-dimensional cuts of potential energy surfaces along the pseudorotation angle ϕ and (ii) the assignment of the vibrorotational wave functions (which are needed for the automatic calculation of rotational transition energies J = 0 → J = 1) are described and discussed.

Theoretical Study on Epoxide Ring-opening in CO2/Epoxide Copolymerization Catalyzed by Bifunctional Salen-Type Cobalt(III) Complexes: Influence of Stereoelectronic Factors

Propylene oxide (PO) binding and ring-opening reaction with the bifunctional CO2/epoxide copolymerization catalyst, based on the Co(III)-salcy complex including two quaternary ammonium salts with n-butyl substituents (N+-chains) were investigated by Density Functional Theory (DFT) calculations and compared with the model systems without the N+-chains. The importance of the different possible stereoisomers and the stereoselectivity of these processes for (S)- and (R)-enantiomers of PO were considered. To explore the conformational space for the real catalyst, a complex approach, developed previously was applied. The calculations for the model systems directly demonstrate that PO-ring opening proceeds preferentially in trans catalysts’ configuration and no participation of cis-β isomers is viable; nucleophilic attack at the methylene-carbon atom is preferred over that at methine-carbon atom. For the real bifunctional catalyst, with the (S,S)-configuration of cyclohexane, the results indicate a preference of (R)-PO ring-opening over (S)-PO ring-opening (ca. 6:5). Concerning stereoisomers resulting from the orientation of N+-chains in the real catalyst, different groups of structures participate in the ring-opening reaction for (R)-PO, and different for (S)-PO. The high population of nonreactive complexes of (R)-PO may be the key factor responsible for decreasing the activity of the analyzed catalyst in the epoxide ring-opening reaction.

Describing Polytopal Rearrangement Processes of Octacoordinate Structures. I. Renewed Insights into Fluxionality of the Rhenium Polyhydride Complex ReH5(PPh3)2(Pyridine)

Hydride ligands of transition metal polyhydride complexes with a high coordination number are prone to fluxionality leading to interesting structural dynamics. However, the underlying polytopal rearrangement pathways have been rarely studied. Based on quantum chemical calculations carried out in this work with density functional theory and coupled-cluster theory, two new fluxional mechanisms have been identified for the rhenium polyhydride complex ReH₅(PPh₃)₂(pyridine) to jointly account for two consecutive coalescence events in the variable-temperature NMR spectra upon heating: lateral and basal three-arm turnstile rotation. The frequently cited pseudorotation in ReH₅(PPh₃)₂(pyridine) (Lee et al. Inorg. Chem. 1996, 35, 695) turns out to be a three-step process including two lateral three-arm turnstile steps and one basal turnstile step in between. The new fluxional mechanisms discovered in this work may also exist in other transition metal polyhydrides.

Heavy atom tunnelling on XeF6 pseudorotation

XeF₆ has multiple C_3v equivalent minima due to the Jahn–Teller effect. Through computational means we prove that the rearrangement between isomers occurs through fluorine quantum mechanical tunnelling.