Improved Predictor–Corrector Integrators For Evaluating Reaction Path Curvature

Reaction mechanism - explored with the unified reaction valley approach

One of the ultimate goals of chemistry is to understand and manipulate chemical reactions, which implies the ability to monitor the reaction and its underlying mechanism at an atomic scale. In this article, we introduce the Unified Reaction Valley Approach (URVA) as a tool for elucidating reaction mechanisms, complementing existing computational procedures. URVA combines the concept of the potential energy surface with vibrational spectroscopy and describes a chemical reaction via the reaction path and the surrounding reaction valley traced out by the reacting species on the potential energy surface on their way from the entrance to the exit channel, where the products are located. The key feature of URVA is the focus on the curving of the reaction path. Moving along the reaction path, any electronic structure change of the reacting species is registered by a change in the normal vibrational modes spanning the reaction valley and their coupling with the path, which recovers the curvature of the reaction path. This leads to a unique curvature profile for each chemical reaction, with curvature minima reflecting minimal change and curvature maxima indicating the location of important chemical events such as bond breaking/formation, charge polarization and transfer, rehybridization, etc. A decomposition of the path curvature into internal coordinate components or other coordinates of relevance for the reaction under consideration, provides comprehensive insight into the origin of the chemical changes taking place. After giving an overview of current experimental and computational efforts to gain insight into the mechanism of a chemical reaction and presenting the theoretical background of URVA, we illustrate how URVA works for three diverse processes, (i) [1,3] hydrogen transfer reactions; (ii) α-keto-amino inhibitor for SARS-CoV-2 Mpro; (iii) Rh-catalyzed cyanation. We hope that this article will inspire our computational colleagues to add URVA to their repertoire and will serve as an incubator for new reaction mechanisms to be studied in collaboration with our experimental experts in the field.

Mechanistic Details of the Sharpless Epoxidation of Allylic Alcohols—A Combined URVA and Local Mode Study

In this work, we investigated the catalytic effects of a Sharpless dimeric titanium (IV)–tartrate–diester catalyst on the epoxidation of allylalcohol with methyl–hydroperoxide considering four different orientations of the reacting species coordinated at the titanium atom (reactions R1–R4) as well as a model for the non-catalyzed reaction (reaction R0). As major analysis tools, we applied the URVA (Unified Reaction Valley Approach) and LMA (Local Mode Analysis), both being based on vibrational spectroscopy and complemented by a QTAIM analysis of the electron density calculated at the DFT level of theory. The energetics of each reaction were recalculated at the DLPNO-CCSD(T) level of theory. The URVA curvature profiles identified the important chemical events of all five reactions as peroxide OO bond cleavage taking place before the TS (i.e., accounting for the energy barrier) and epoxide CO bond formation together with rehybridization of the carbon atoms of the targeted CC double bond after the TS. The energy decomposition into reaction phase contribution phases showed that the major effect of the catalyst is the weakening of the OO bond to be broken and replacement of OH bond breakage in the non-catalyzed reaction by an energetically more favorable TiO bond breakage. LMA performed at all stationary points rounded up the investigation (i) quantifying OO bond weakening of the oxidizing peroxide upon coordination at the metal atom, (ii) showing that a more synchronous formation of the new CO epoxide bonds correlates with smaller bond strength differences between these bonds, and (iii) elucidating the different roles of the three TiO bonds formed between catalyst and reactants and their interplay as orchestrated by the Sharpless catalyst. We hope that this article will inspire the computational community to use URVA complemented with LMA in the future as an efficient mechanistic tool for the optimization and fine-tuning of current Sharpless catalysts and for the design new of catalysts for epoxidation reactions.

Bonding in Nitrile Photo-dissociating Ruthenium Drug Candidates --A Local Vibrational Mode Study

In this work, we investigated bonding features 15 ruthenium complexes of the type [Ru(tpy)(L)-(CH3CN)]n+, containing the tridentate tpy ligand (tpy = 2,2':6',2'--terpyridine) and various bidentate ancillary ligands, 12 compounds originally synthesized by Loftus et al. (J. Phys. Chem. C 123, 10291-10299 (2019)) complemented with three additional complexes. The main focus of our work was to relate these local features to the experimental data of Loftus et al. which assess the efficiency of nitrile release in an indirect way via observed quantum yields for ruthenium water association after nitrile release. As a tool to quantitatively assess Ru-NC and Ru-L bonding we utilized the local vibrational mode analysis complemented by the topological analysis of the electron density and the natural bond orbital analysis. Interestingly, the stronger Ru-NC bonds have the greater observed quantum yields, leading to the conclusion that the observed quantum yields are a result of a complex interplay of several processes excluding a direct relationship between QY and Ru-NC or Ru-L bond strengths. We identified the ST splitting as one of the key players and not the Ru-NC bond strength, as one may have thought. In summary, this work has presented a modern computational tool set for the investigation of bonding features applied to nitrile photo-dissociating ruthenium drug candidates forming a valuable basis for future design and fine tuning of nitrile releasing ruthenium compounds, as well as for the understanding of how local properties affect overall experimental outcomes.

On the formation of CN bonds in Titan's atmosphere-a unified reaction valley approach study

In this work, we investigated the formation of protonated hydrogen cyanide HCNH⁺ and methylene amine cation CH[Formula: see text] (both identified in Titan's upper atmosphere) from three different pathways which stem from the interaction between CH₄ and N⁺(³P). As a mechanistic tool, we used the Unified Reaction Valley Approach (URVA) complemented with the Local Mode Analysis (LMA) assessing the strength of the CN bonds formed in these reactions. Our URVA studies could provide a comprehensive overview on bond formation/cleavage processes relevant to the specific mechanism of eight reactions R1- R8 that occur across the three pathways. In addition, we could explain the formation of CH[Formula: see text] and the appearance of HCNH⁺ and CHNH[Formula: see text] along these paths. Although only smaller molecules are involved in these reactions including isomerization, hydrogen atom abstraction, and hydrogen molecule capture, we found a number of interesting features, such as roaming in reaction R3 or the primary interaction of H₂ with the carbon atom in HCNH⁺ in reaction R8 followed by migration of one of the H₂ hydrogen atoms to the nitrogen which is more cost effective than breaking the HH bond first; a feature often found in catalysis. In all cases, charge transfer between carbon and nitrogen could be identified as a driving force for the CN bond formation. As revealed by LMA, the CN bonds formed in reactions R1-R8 cover a broad bond strength range from very weak to very strong, with the CN bond in protonated hydrogen cyanide HCNH⁺ identified as the strongest of all molecules investigated in this work. Our study demonstrates the large potential of both URVA and LMA to shed new light into these extraterrestrial reactions to help better understand prebiotic processes as well as develop guidelines for future investigations involving areas of complex interstellar chemistry. In particular, the formation of CN bonds as a precursor to the extraterrestrial formation of amino acids will be the focus of future investigations. Formation of CN bonds in Titan's atmosphere visualized via the reaction path curvature.

Structural Transitions in Glassy Atactic Polystyrene Using Transition-State Theory

Transition pathways on the energy landscape of atactic polystyrene (aPS) glassy specimens are probed below its glass-transition temperature. Each of these transitions is considered an elementary structural relaxation event, whose corresponding rate constant is calculated by applying multidimensional transition-state theory. Initially, a wide spectrum of first-order saddle points surrounding local minima on the energy landscape is discovered by a stabilized hybrid eigenmode-following method. Then, (minimal-energy) “reaction paths” to the adjacent minima are constructed by a quadratic descent method. The heights of the free energy, the potential energy, and the entropy barriers are estimated for every connected triplet of transition state and minima. The resulting distribution of free energy barriers is asymmetric and extremely broad, extending to very high barrier heights (over 50 k_BT); the corresponding distribution of rate constants extends over 30 orders of magnitude, with well-defined peaks at the time scales corresponding to the subglass relaxations of polystyrene. Analysis of the curvature along the reaction paths reveals a multitude of different rearrangement mechanisms; some of them bearing multiple distinct phases. Finally, connections to theoretical models of the glass phenomenology allows for the prediction, based on first-principles, of the “ideal” glass-transition temperature entering the Vogel–Fulcher–Tammann (VFT) equation describing the super-Arrhenius temperature dependence of glassy dynamics. Our predictions of the time scales of the subglass relaxations and the VFT temperature are in favorable agreement with available experimental literature data for systems of similar molecular weight under the same conditions.

Theoretical Insights into [NHC]Au(I) Catalyzed Hydroalkoxylation of Allenes: A Unified Reaction Valley Approach Study

Hydroxylation is an effective approach for the synthesis of carbon-oxygen bonds and allylic ethers. The [NHC]Au(I) catalyzed intermolecular hydroalkoxylation of allene was studied at the DFT and Coupled Cluster level of theory. Using the Unified Reaction Valley Approach (URVA), we carry out a comprehensive mechanistic analysis of [NHC]Au(I)-catalyzed and noncatalyzed reactions. The URVA study of several possible reaction pathways reveal that the [NHC]Au(I) catalyst enables the hydroalkoxylation reaction to occur via a two step mechanism based upon the Au ability to switch between π- and σ-complexation. The first step of the mechanism involves the formation of a CO bond after the transition state with no energy penalty. Following the CO bond breakage, the OH bond breaks and CH bond forms during the second step of the mechanism, as the catalyst transforms into the more stable π-Au complex. The URVA results were complemented with local vibrational mode analysis to provide measures of intrinsic bond strength for Au(I)-allene interactions of all stationary points, and NBO analysis was applied in order to observe charge transfer events along the reaction pathway. Overall, the π-Au C═C interactions of the products are stronger than those of the reactants adding to their exothermicity. Our work on the hydroxylation of allene provides new insights for the design of effective reaction pathways to produce allylic ethers and also unravels new strategies to form C-O bonds by activation of C═C bonds.

Kinetic Study of Gas-Phase Reactions of Pyruvic Acid with HO2

Gas-phase reactions between pyruvic acid (PA) and HO₂ radicals were examined using ab initio quantum chemistry and transition state theory. The rate coefficients were determined over a temperature range of 200-400 K including tunneling contributions. Six potential reaction pathways were identified. The two hydrogen abstraction reactions yielding the H₂O₂ product were found to have high barriers. The HO₂ radical was also found to have a catalytic effect on the intramolecular hydrogen transfer reactions occurring by three distinct routes. These hydrogen-shift reactions are very interesting mechanistically although they are highly endothermic. The only reaction that contributes significantly to the consumption of PA is a multistep pathway involving a peroxy-radical intermediate, PA + HO₂ → CH₃COOH + OH + CO₂. This exothermic process has potential atmospheric relevance because it produces an OH radical as a product. Atmospheric models currently have difficulty predicting accurate OH concentrations for certain atmospheric conditions, such as environments free of NOx and the nocturnal boundary layer. Reactions of this sort, although not necessary with PA, may account for a portion of this deficit. The present study helps settle the issue of the relative roles of reaction and photolysis in consumption of PA in the troposphere.

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.

Modeling Hydrogen Release from Water with Borane and Alane Catalysts: A Unified Reaction Valley Approach

The unified reaction valley approach combined with the local vibrational mode and ring puckering analysis is applied to investigate the hydrogen evolution from water in the presence of small hydrides such as BH₃, metal hydrides as AlH₃, and their derivatives. We studied a series of reactions involving BH₃, AlH₃, B₂H₆, Al₂H₆, and AlH₃BH₃ with one- and two-water molecules, considering multiple reaction paths. In addition, the influence of the aqueous medium was examined. A general reaction mechanism was identified for most of the reactions. Those that deviate could be associated with unusually high reaction barriers with no hydrogen release. The charge transfer along the reaction path suggests that a viable hydrogen release is achieved when the catalyst adopts the role of a charge donor during the chemical processes. The puckering analysis showed that twistboat and boat forms are the predominant configurations in the case of an intermediate six-membered ring formation, which influences the activation barrier. The local mode analysis was used as a tool to detect the H-H bond formation as well as to probe catalyst regenerability. Based on the correlation between the activation energy and the change in the charge separation for cleaving O-H and B(Al)-H bonds, two promising subsets of reactions could be identified along with prescriptions for lowering the reaction barrier individually with electron-donating/withdrawing substituents.

Exploring the Mechanism of Catalysis with the Unified Reaction Valley Approach (URVA)—A Review

The unified reaction valley approach (URVA) differs from mainstream mechanistic studies, as it describes a chemical reaction via the reaction path and the surrounding reaction valley on the potential energy surface from the van der Waals region to the transition state and far out into the exit channel, where the products are located. The key feature of URVA is the focus on the curving of the reaction path. Moving along the reaction path, any electronic structure change of the reacting molecules is registered by a change in their normal vibrational modes and their coupling with the path, which recovers the curvature of the reaction path. This leads to a unique curvature profile for each chemical reaction with curvature minima reflecting minimal change and curvature maxima, the location of important chemical events such as bond breaking/forming, charge polarization and transfer, rehybridization, etc. A unique decomposition of the path curvature into internal coordinate components provides comprehensive insights into the origins of the chemical changes taking place. After presenting the theoretical background of URVA, we discuss its application to four diverse catalytic processes: (i) the Rh catalyzed methanol carbonylation—the Monsanto process; (ii) the Sharpless epoxidation of allylic alcohols—transition to heterogenous catalysis; (iii) Au(I) assisted [3,3]-sigmatropic rearrangement of allyl acetate; and (iv) the Bacillus subtilis chorismate mutase catalyzed Claisen rearrangement—and show how URVA leads to a new protocol for fine-tuning of existing catalysts and the design of new efficient and eco-friendly catalysts. At the end of this article the pURVA software is introduced. The overall goal of this article is to introduce to the chemical community a new protocol for fine-tuning existing catalytic reactions while aiding in the design of modern and environmentally friendly catalysts.

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

In this work a new curvilinear coordinate system is presented for the comprehensive description of polytopal rearrangements of N-coordinate compounds (N = 4-7) and systems containing an N-coordinate subunit. It is based on normal vibrational modes and a natural extension of the Cremer-Pople puckering coordinates ( J. Am. Chem. Soc. 1975, 97, 1354) together with the Zou-Izotov-Cremer deformation coordinates ( J. Phys. Chem. A 2011, 115, 8731) for ring structures to N-coordinate systems. We demonstrate that the new curvilinear coordinates are ideal reaction coordinates describing fluxional rearrangement pathways by revisiting the Berry pseudorotation and the lever mechanism in sulfur tetrafluoride, the Berry pseudorotation and two Muetterties' mechanisms in pentavalent compounds, the chimeric pseudorotation in iodine pentafluoride, Bailar and Ray-Dutt twists in hexacoordinate tris-chelates as well as the Bartell mechanism in iodine heptafluoride. The results of our study reveal that this dedicated curvilinear coordinate system can be applied to most coordination compounds opening new ways for the systematic modeling of fluxional processes.