Unified Reaction Valley Approach Research Articles

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.

URVA and Local Mode Analysis of an Iridium Pincer Complex Efficiently Catalyzing the Hydrogenation of Carbon Dioxide

The catalytic effects of iridium pincer complexes for the hydrogenation of carbon dioxide were investigated with the Unified Reaction Valley Approach (URVA), exploring the reaction mechanism along the reaction path traced out by the reacting species on the potential energy surface. Further details were obtained with the Local Mode Analysis performed at all stationary points, complemented by the Natural Bond Orbital and Bader’s Quantum Atoms in Molecules analyses. Each of the five reaction paths forming the catalytic cycle were calculated at the DFT level complemented with DLPNO-CCSD(T) single point calculations at the stationary points. For comparison, the non-catalytic reaction was also investigated. URVA curvature profiles identified all important chemical events taking place in the non-catalyzed reaction and in the five reactions forming the catalytic cycle, and their contribution to the activation energy was disclosed. The non-catalytic reaction has a large unfavorable activation energy of 76.3 kcal/mol, predominately caused by HH bond cleave in the H2 reactant. As shown by our study, the main function of the iridium pincer catalyst is to split up the one–step non-catalytic reaction into an energy efficient multistep cycle, where HH bond cleavage is replaced by the cleavage of a weaker IrH bond with a small contribution to the activation energy. The dissociation of the final product from the catalyst requires the cleavage of an IrO bond, which is also weak, and contributes only to a minor extent to the activation energy. This, in summary, leads to the substantial lowering of the overall activation barrier by about 50 kcal/mol for the catalyzed reaction. We hope that this study inspires the community to add URVA to their repertoire for the investigation of catalysis reactions.

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 of 15 ruthenium(II) nitrile 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 L; 12 compounds originally synthesized by Loftus et al. [J. Phys. Chem. C 123, 10291-10299 (2019)] and three new complexes. We utilized local vibrational force constants derived from the local mode theory as a quantitative measure of bond strength complemented with the topological analysis of the electron density and the natural bond orbital analysis. Loftus et al. suggested that nitrile dissociation occurs after light induced singlet-triplet transition of the original complexes and they used as a measure of nitrile release efficiency quantum yields for ligand exchange in water. They observed larger quantum yields for complexes with smaller singlet-triplet energy gaps. The major goal of this work was to assess how the Ru-NC and Ru-L bond strengths in these 15 compounds relate to and explain the experimental data of Loftus et al., particularly focusing on the question whether there is a direct correlation between Ru-NC bond strength and measured quantum yield. Our study provides the interesting result that the compounds with the highest quantum yields also have the strongest Ru-NC bonds suggesting that breaking the Ru-NC bond is not the driving force for the delivery process rather than the change of the metal framework as revealed by first results of a unified reaction valley approach investigation of the mechanism. Compounds with the highest quantum yield show larger electronic structure changes upon singlet-triplet excitation, i.e., larger changes in bond strength, covalency, and difference between the singlet and triplet HOMOs, with exception of the compound 12. In summary, this work provides new insights into the interplay of local properties and experimental quantum yields forming in synergy a useful tool for fine tuning of existing and future design of new nitrile releasing ruthenium compounds. We hope that this work will bring theoretical and experimental studies closer together and serves as an incubator for future collaboration between computational chemists and their experimental colleagues.

A Closer Look at the Isomerization of 5-Androstene-3,17-Dione to 4-Androstene-3,17-Dione in Ketosteroid Isomerase

We report a comprehensive investigation of the 5-androstene-3,17-dione to 4-androstene-3,17-dione isomerization in Ketosteroid Isomerase, gas phase and aqueous solution, applying as tools the Unified Reaction Valley Approach (URVA) and the Local Vibrational Mode Analysis. Conformational changes of the steroid rings are monitored via Cremer-Pople puckering coordinates. URVA identifies simultaneous breakage of the C[Formula: see text]–H bond and O–H bond formation with the catalytic acid, leading to an intermediate with the acid positioned over ring [Formula: see text] as the major chemical events of the first reaction step. Via a barrier-less shift, a second intermediate is formed with the acid being positioned over ring [Formula: see text]. Then, according to URVA, breakage of the intermediate O–H bond, the formation of the new C[Formula: see text]–H bond accompanied by a double bond shift in rings [Formula: see text] and [Formula: see text] forms the major chemical events of the second reaction step, which is facilitated by favorable ring puckering. Reactions in protein and gas phase have comparable activation enthalpies, whereas the barrier in aqueous solution is higher, confirming that the major task of the enzyme pocket is to shield the migrating hydrogen atom and the catalyzing acid from interactions with solvent molecules diluting the catalytic power. We do not find exceptional H-bonding with Asp99 and Tyr14, excluding their catalytic activity. There is no strong hydrogen bonding in the TS, which could account for lowering the activation barrier. Our study provides a clear picture of the isomerization process, which will also inspire similar investigations of other important enzymatic reactions.

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.

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.

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.

New mechanistic insights into the Claisen rearrangement of chorismate – a Unified Reaction Valley Approach study

ABSTRACTThe Bacillus subtilis chorismate mutase catalysed Claisen rearrangement of chorismate to prephenate is one of the few pericyclic processes in biology, and as such provides a rare opportunity for understanding how Nature promotes such rearrangements so successfully. The major focus of this work is on (i) Exploring the hypothesis that the mechanism of the chorismate rearrangement is the same in the gas phase, in the aqueous solution and in the enzyme; (ii) Investigating current suggestions that the enzyme lowers the barrier via transition state stabilisation rather than via space confinement; and (iii) A comparison of Nature's way of catalysing the reaction with a gold(I) catalysed chorismate rearrangement. Based the Unified Reaction Valley Approach (URVA), for the first time, a detailed one-to-one comparison of the rearrangement in the gas phase, in the aqueous solution and in the enzyme is presented. URVA confirms that the actual chemical process of CO bond breaking and CC bond forming is the same for all media and unravels the unique catalytic function of the enzyme as a combination of shortening the process of positioning the enolpyruvyl side chain over the cyclohexadienyl ring by space confinement in concert with facilitating CO cleavage by enhanced charge polarisation. The transition state does not play a signifiant role for the rearrangement. In contrast, the gold catalyst changes the chemical process. The rearrangement is split into two steps by switching between Au[I]-π and Au[I]-σ complexation, thus avoiding the energy consuming CO breakage in the first step. Suggestions are made for metalloenzyme analogues combining both strategies.

Gold(I)-assisted catalysis – a comprehensive view on the [3,3]-sigmatropic rearrangement of allyl acetate

ABSTRACTThe unified reaction valley approach (URVA) combined with the local mode, ring puckering and electron density analysis is applied to elucidate the mechanistic differences of the non-catalysed and the Au[I]-N-heterocyclic carbene (NHC)-catalysed [3,3]-sigmatropic rearrangement of allyl acetate. Using a dual-level approach (DFT and DLPNO-CCSD(T)), the influence of solvation, counter-ions, bulky and electron withdrawing/donating substituents as well as the exchange of the Au[I]-NHC with a Au[I]-phosphine catalyst is investigated. The catalyst breaks up the rearrangement into two steps by switching between Au[I]–π and Au[I]–σ complexation, thus avoiding the energy-consuming CO cleavage in the first step. Based on local stretching force constants ka(C=C), we derive for the first time a quantitative measure of the π-acidity of the Au[I] catalyst; in all catalysed reactions, the bond order n(C=C) drops from 2 to 1.65. The ring puckering analysis clarifies that all reactions start and end via a six-membered ring with a boat form. All Au[I]–σ-complex intermediates show a considerable admixture of the chair form. The non-catalysed [3,3]-sigmatropic rearrangement goes through a maximum of charge separation between the allyl and acetate units at the transition state, while all catalysed reactions proceed via a minimum of charge separation reached in the region of the Au[I]–σ-complex.

A Reaction Valley Investigation of the Cycloaddition of 1,3-Dipoles with the Dipolarophiles Ethene and Acetylene: Solution of a Mechanistic Puzzle.

The reaction mechanism of the cycloaddition of 10 1,3-dipoles with the two dipolarphiles ethene and acetylene is investigated and compared using the Unified Reaction Valley Approach in a new form, which is based on a dual-level strategy, an accurate description of the reaction valley far out into the van der Waals region, and a comparative analysis of the electronic properties of the reaction complex. A detailed one-to-one comparison of 20 different 1,3-dipolar cycloadditions is performed, and unknown mechanistic features are revealed. There are significant differences in the reaction mechanisms for the two dipolarophiles that result from the van der Waals complex formation in the entrance channel of the cycloadditions. Hydrogen bonding between the 1,3-dipoles and acetylene is generally stronger, which leads to higher reaction barriers in the acetylene case, but which also facilitates to overcome the problem of a reduced charge transfer from 1,3-dipole to acetylene. Mechanistic differences are found in the prechemical and chemical reaction regions with regard to reactant orientation, preparation for the reaction, charge transfer, charge polarization, rehybridization, and bond formation. It is shown that similarities in the reaction barriers as determined by CCSD(T)-F12/aug-cc-pVTZ calculations result from a fortuitous cancellation of different electronic effects. In general, a caveat must be made with regard to oversimplified descriptions of the reaction mechanism based on orbital theory or energy decomposition schemes.

Rational Design in Catalysis: A Mechanistic Study of β-Hydride Eliminations in Gold(I) and Gold(III) Complexes Based on Features of the Reaction Valley.

β-Hydride eliminations for ethylgold(III) dichloride complexes are identified as reactions with an unusually long prechemical stage corresponding to the conformational preparation of the reaction complex and spanning six phases. The prechemical process is characterized by a geared rotation of the L-Au-L group (L = Cl) driving methyl group rotation and causing a repositioning of the ligands. This requires more than 28 kcal/mol of the total barrier of 34.0 kcal/mol, according to the unified reaction valley approach, which also determines that the energy requirements of the actual chemical process leading to the β-elimination product are only about 5.5 kcal/mol. A detailed mechanistic analysis was used as a basis for a rational design of substrates (via substituents on the ethyl group) and/or ligands, which can significantly reduce the reaction barrier. This strategy takes advantage of either a higher trans activity of the ligands or a tuned electronic demand of the ethyl group. The β-hydride elimination of gold(I) was found to suffer from strong Coulomb and exchange repulsion when a positively charged hydrogen atom enforces a coordination position in a d(10)-configured gold atom, thus triggering an unassisted σ-π Au(I)-C conversion.

Extraordinary Mechanism of the Diels-Alder Reaction: Investigation of Stereochemistry, Charge Transfer, Charge Polarization, and Biradicaloid Formation.

The Diels-Alder reaction between 1,3-butadiene and ethene is investigated from far-out in the entrance channel to the very last step in the exit channel thus passing two bifurcation points and extending the range of the reaction valley studied with URVA (Unified Reaction Valley Approach) by 300% compared to previous studies. For the first time, the pre- and postchemical steps of the reaction are analyzed at the same level of theory as the actual chemical processes utilizing the path curvature and its decomposition into internal coordinate or curvilinear coordinate components. A first smaller charge transfer to the dienophile facilitates the rotation of gauche butadiene into its cis form. The actual chemical processes are initiated by a second larger charge transfer to the dienophile that facilitates pyramidalization of the reacting carbon centers, bond equalization, and biradicaloid formation of the reactants. The transition state is aromatically stabilized and moved by five path units into the entrance channel in line with the Hammond-Leffler postulate. The pseudorotation of the boat form into the halfchair of cyclohexene is analyzed. Predictions are made for the Diels-Alder reaction based on a 11-phase mechanism obtained by the URVA analysis.

A New Method for Describing the Mechanism of a Chemical Reaction Based on the Unified Reaction Valley Approach.

The unified reaction valley approach (URVA) used for a detailed mechanistic analysis of chemical reactions is improved in three different ways: (i) Direction and curvature of path are analyzed in terms of internal coordinate components that no longer depend on local vibrational modes. In this way, the path analysis is no longer sensitive to path instabilities associated with the occurrences of imaginary frequencies. (ii) The use of third order terms of the energy for a local description of the reaction valley allows an extension of the URVA analysis into the pre- and postchemical regions of the reaction path, which are typically characterized by flat energy regions. (iii) Configurational and conformational processes of the reaction complex are made transparent even in cases where these imply energy changes far less than a kcal/mol by exploiting the topology of the potential energy surface. As examples, the rhodium-catalyzed methanol carbonization, the Diels-Alder reaction between 1,3-butadiene and ethene, and the rearrangement of HCN to CNH are discussed.

Solving the Pericyclic-Pseudopericyclic Puzzle in the Ring-Closure Reactions of 1,2,4,6-Heptatetraene Derivatives.

The ongoing controversy whether cyclization reactions of conjugated allenes or ketenes follow a pericyclic or a pseudopericyclic mechanism has triggered dozens of investigations, which have led to new valuable synthetic routes. In this work, the mechanism of 10 representative cyclization reactions of hepta-1,2,4,6-tetraenes with different terminal groups is investigated utilizing the unified reaction valley approach that registers all electronic structure changes of the target molecule along the entire reaction pathway. A clear differentiation between a purely pericyclic and a purely pseudopericyclic mechanism is established. Additionally, it is found that, by using suitable functional groups, a pericyclic mechanism can be converted into a pseudopericyclic one, which is associated with a steady decrease of the reaction barrier and a continuous change from one mechanism to the other. The energetics of the reaction are confirmed by coupled cluster calculations of the CCSD(T) type. The mechanistic insight gained is used to design new pseudopericyclic reactions with low or no barrier, which will open new synthetic avenues.

The mechanism of the cycloaddition reaction of 1,3-dipole molecules with acetylene: an investigation with the unified reaction valley approach

The unified reaction valley approach (URVA) is used in connection with a dual-level approach to describe the mechanism of ten different cycloadditions of 1,3- dipoles XYZ (diazonium betaines, nitrilium betaines, azomethines, and nitryl hydride) to acetylene utilizing density functional theory for the URVA calculations and CCSD(T)-F12/aug-cc-pVTZ for the determination of the reaction energetics. The URVA results reveal that the mechanism of the 1,3-dipolar cycloadditions is determined early in the van der Waals range where the mutual orientation of the reactants (resulting from the shape of the enveloping exchange repulsion spheres, electrostatic attraction, and dispersion forces) decides on charge transfer, charge polarization, the formation of radicaloid centers, and the asynchronicity of bond formation. All cycloadditions investigated are driven by charge transfer to the acetylene LUMO irrespective of the electrophilic/nucleophilic character of the 1,3-dipole. However, an insufficient charge transfer typical of an electrophilic 1,3- dipole leads to a higher barrier. Energy transfer and energy dissipation as a result of curvature and Coriolis couplings between vibrational modes lead to an unusual energy exchange between just those bending modes that facilitate the formation of radicaloid centers. The relative magnitude of the reaction barriers and reaction energies is rationalized by determining reactant properties, which are responsible for the mutual polarization of the reactants and the stability of the bonds to be broken or formed.

Improved Predictor-Corrector Integrators For Evaluating Reaction Path Curvature.

The reaction path connects a chemical potential energy landscape and the conceptual descriptions of chemical mechanisms and reactivity. In recent years, a class of predictor-corrector integrators has been developed and shown to provide an excellent compromise between computational efficiency and numerical accuracy. Models based on projected frequencies along the reaction path and coupling matrix elements, such as Reaction Path Hamiltonian (RPH) and Unified Reaction Valley Approach (URVA), require highly accurate integration of the reaction path. In this report, the Euler Predictor-Corrector (EulerPC) and Hessian-based Predictor-Corrector (HPC) methods are shown to be inadequate for studying reaction path curvature, which is a central component of the RPH and URVA models. The source of this apparent failure is explored, and a solution is developed. Importantly, the resulting enhanced EulerPC and HPC integrators do not require more intensive CPU or memory requirements than their predecessors.

Energetics and Mechanism of the Hydrogenation of XHn for Group IV to Group VII Elements X.

High-level ab initio calculations of the NESC/SOC/CCSD(T)/cc-pV5Z type (NESC, Normalized Elimination of the Small Component; SOC, spin-orbit coupling corrections using the Breit-Pauli Hamiltonian) are employed to determine the energetics of the 18 hydrogenation reactions XHn + H2 → XHn+1 + H with X = F, Cl, Br, I, O, S, Se, Te, N, P, As, Sb, Bi, C, Si, Ge, Sn, and Pb. Accurate reaction and activation enthalpies as well as the corresponding free energies are obtained by calculating vibrational, thermochemical, and entropy corrections with a cc-pVTZ basis set. Also calculated are accurate X-H bond dissociation enthalpies at 298 K. The reaction mechanism of all 18 reactions is analyzed using the unified reaction valley approach (URVA) and UMP2/6-31G(d,p) to determine each reaction valley with high accuracy (step size 0.005 to 0.03 amu(1/2) bohr). By analyzing the reaction path curvature, the mechanism can be partitioned into four to six reaction phases, in which the reaction complex XHn···H2 undergoes specific chemical transformations. The fate of the reaction complex is determined at an early stage in the entrance channel. Curvature peaks reflect the strength of the bonds being broken or formed and provide the basis for a quantitative justification of the Hammond-Leffler postulate.

Reaction path Hamiltonian and the unified reaction valley approach

AbstractOne of the major goals of chemistry is to control chemical reactions with the purpose of generating new compounds with useful properties. Control of a chemical reaction implies a detailed understanding of its mechanism as it results from the breaking and forming of chemical bonds. In practice, it is rather difficult to get a detailed mechanistic and dynamical description of even the simplest chemical reactions. This has to do with the fact that apart from reactants, products, and possible stable intermediates, all other molecular forms encountered during a reaction have such a short lifetime that standard experimental means are not sufficient to detect and describe them. Progress in modern laser spectroscopy seems to provide an access to transient species with lifetimes in the pico‐ to femtosecond region; however, computational investigations utilizing state‐of‐the art methods of quantum chemistry, in particular ab initio methods, provide still the major source of knowledge on reaction mechanism and reaction dynamics. The reaction path Hamiltonian model has proven as a powerful tool to derive the dynamics of a chemical reaction by following the reacting species along the reaction path from reactants to products as traced out on the potential energy surface. In this article, the original reaction path Hamiltonian will be reviewed, extensions and applications over the past decades will be summarized, and a new perspective, namely to use it in form of the unified reaction valley approach to derive a deep and systematic insight into the mechanism of a chemical reaction will be introduced. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 531–556 DOI: 10.1002/wcms.65This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods