Unified Reaction Valley Approach Research Articles

A stunning example for a spontaneous reaction with a complex mechanism: the vinylidene–acetylene cycloaddition reaction

The chelotropic addition reaction (1): singlet vinylidene + acetylene → methylenecyclopropene (MCP), was investigated using different levels of theory (B3LYP, CASSCF, CCSD(T), G2M) and different basis sets (6-31G(d,p), 6-311G(d,p), 6-311++G(3df,3pd), cc-pVTZ). The concerted reaction is spontaneous at room temperature (activation enthalpy of 3 kcal mol−1) and strongly exothermic (ΔE = −64 kcal mol−1; ΔH(298) = −59 kcal mol−1). Analysis of the reaction mechanism with the help of the Unified Reaction Valley approach reveals a complicated sequence of structural and electronic changes, which can be best described by partitioning the mechanism into seven phases: (1) van der Waals, (2) electrophilic attack, (3) biradical, (4) allene, (5) carbene, (6) ring closure, and (7) MCP formation phase. In the transient regions from one phase to the next, structures are located that possess properties of hidden transition states (TSs) or hidden intermediates, i.e. by variation of the electronic nature or the environment of the reaction complex, real TSs and/or real intermediates can be generated. There is indication that a given sequence of reaction phases is fixed for a wide variation in the electronic nature of the reaction complex and that other than just orbital symmetry principles play a decisive role for the reaction mechanism.

From Molecular Vibrations to Bonding, Chemical Reactions, and Reaction Mechanism

The vibrational motions of a molecule in its equilibrium or during a chemical reaction provide a wealth of information about its structure, stability, and reactivity. This information is hidden in measured vibrational frequencies and intensities, however can be unraveled by utilizing quantum chemical tools and applying the Cal-X methods in form Vib-Cal-X. Vib-Cal-X uses the measured frequencies, complements them to a complete set of 3N-L values (N number of atoms; L number of translations and rotations), derives experimentally based force constants, and converts them into local mode stretching, bending, and torsional force constants associated with the internal coordinates describing the geometry of the molecule. This is done by utilizing the adiabatic vibrational mode concept, which is based on a decomposition of delocalized normal vibrational modes into adiabatic internal coordinate modes (AICoMs) needed to describe bonding or changes in bonding. AICoM force constants relate to the intrinsic bond dissociation energy (IBDE) of a bond and, accordingly, are excellent descriptors for bond order and bond strength. It is shown that bond dissociation energies, bond lengths, or bond densities are not directly related to the bond strength because they also depend on other quantities than just the bond strength: the bond dissociation energy on the stabilization energies of the fragments, the bond length on the compressibility limit distance between the atoms, the bond stretching frequency on the atom masses, etc. The bond stretching force constants however lead directly to bond order and bond strength as has been demonstrated for the bonds in typical organic molecules. Using this insight, the generalized vibrational frequencies of reacting molecules are used to obtain insight into the chemical processes of bond breaking and forming. An elementary chemical reaction based on these processes is characterized by a curved reaction path. Path curvature is a prerequisite for chemical change and directly related to the changes in the stretching force constants as they respond to the bond polarizing power of a reaction partner. The features of the path curvature can be used to partition the reaction path and by this the reaction mechanism in terms of reaction phases. A reaction phase is characterized by an elementary structural change of the reaction complex leading to a chemically meaningful transient structure that can convert into a real transition state or intermediate upon changing the environmental conditions or the electronic structure (substituents, etc.) of the reaction complex. A unified approach to the study of reaction mechanism (URVA: Unified Reaction Valley Approach) is discussed that is based extensively on the analysis of vibrational modes and that is aimed at detailed understanding of chemical reactions with the goal of controlling them. Keywords: Cal-X methods, vibrational frequency, bond strength, chemical bond, adiabatic internal Coordinate mode (AICoM), unified reaction valley approach (URVA), reaction path curvature, reaction path, Reaction Mechanism, Vib-Cal-X, Quantum chemical tools, Vibrational Force Constants, Fermi resonance, Mossbauer spectroscopy, Overtone Spectroscopy, Bond Energy (BE), Bond Dissociation Energy (BDE), NMR Spin-Spin Coupling Constant, Reaction Path Hamiltonian, Electron Density Analysis, Analysis of Coriolis Couplings, Vibrational spectroscopy, Scalar curvature K(s), Diels-Alder reaction, Woodward-Hoffmann rules

The mechanism of a barrierless reaction: hidden transition state and hidden intermediates in the reaction of methylene with ethene

The chelotropic addition reaction of singlet methylene to ethene yielding cyclopropane (reaction 1) was investigated with the help of the Unified Reaction Valley approach (URVA) using different levels of theory (B3LYP, MP2, MP4, CCSD(T), G3) and two basis sets (6-31G(d,p), 6-311++G(3df,3pd)). At all levels of theory, reaction (1) proceeds without barrier and transition state (TS). Nevertheless, reaction (1) possesses a distinct mechanism comprising four different reaction phases: (i) a van der Waals phase, in which the stereochemistry of the reaction is decided; (ii) an electrophilic attack phase, in which charge is transferred from ethene to methylene to establish a weak bonding interaction between the reaction partners typical of those encountered in TSs of CC bond forming reactions; (iii) a nucleophilic attack phase, in which charge transfer between methylene and ethene is reverted and a trimethylene biradical structure is formed; (iv) a ring closure phase, in which the trimethylene structure closes to the three-membered ring. The URVA analysis identifies a hidden TS and two hidden intermediates at the transitions from one phase to the next. If methylene is replaced by difluorocarbene (reaction 2) or germylene (reaction 3), the 4-phase mechanism is retained, however the hidden TS and one of the hidden intermediates are converted into a real TS and a real intermediate thus establishing 2-step mechanisms with strongly different energy profiles along the reaction path.

Mechanism of the Diels−Alder Reaction Studied with the United Reaction Valley Approach: Mechanistic Differences between Symmetry-Allowed and Symmetry-Forbidden Reactions

The unified reaction valley approach (URVA) was used to investigate the mechanism of the reaction between ethene and 1,3-butadiene. The reaction valley was explored using different methods (Hartree...

Mechanism and Dynamics of Organic Reactions: 1,2‐H Shift in Methylchlorocarbene

AbstractFor Abstract see ChemInform Abstract in Full Text.

Mechanism and dynamics of organic reactions: 1,2‐H shift in methylchlorocarbene

AbstractThe unified reaction valley approach (URVA) was used to investigate the mechanism of the rearrangement of methylchlorocarbene to chloroethene [reaction(1)] in the gas phase with special emphasis on the role of H tunneling. The reaction valley of (1) was explored using different methods (HF, MP2 and DFT/B3LYP) and different basis sets [6–31G(d), 6–31G(d,p) and cc‐pVTZ]. Results were analyzed characterizing normal modes, reaction path vector and curvature vector in terms of generalized adiabatic modes associated with internal parameters that are used to describe the reaction complex. For reaction (1), H tunneling plays a significant role even at room temperature, but does not explain the strongly curved Arrhenius correlations observed experimentally. The probability of H tunneling can be directly related to the curvature of the reaction path and the associated curvature couplings. The reaction is preceeded in the forward and reverse direction by energy‐consuming conformational changes that prepare the reactant for the actual 1,2‐H shift, which requires only little energy. The effective energy needed for CH bond breaking is just 6 kcal mol−1 for (1). The gas‐phase and the solution‐phase mechanisms of (1) differ considerably, which is reflected by the activation enthalpies: 11.4 (gas, calculated) and 4.3 kcal mol−1 (solution, measured). Stabilizing interactions with solvent molecules take place in the latter case and reduce the importance of H tunneling. The non‐linearity of the measured Arrhenius correlations most likely results from bimolecular reactions of the carbene becoming more important at lower temperatures. Copyright © 2002 John Wiley & Sons, Ltd.

The mechanism of the reaction FH + H2C=CH2→H3C–CFH2. Investigation of hidden intermediates with the unified reaction valley approach

The unified reaction valley approach (URVA) is used to investigate the mechanism of the reaction H2CCH2 + FH → H3C–CH2F (reaction I) at different levels of theory (HF, MP2 and CCSD(T)) with different basis sets (6-31G(d,p), 6-311 + + G(3df,3dp) and cc-pVTZ). URVA is based on the reaction path Hamiltonian, the intrinsic reaction coordinate, and the characterization of normal modes, reaction path vector and curvature vector in terms of generalized adiabatic modes associated with internal parameters that are used to describe the reaction complex. In addition, URVA combines the investigation of the harmonic reaction valley with the analysis of attractive and repulsive forces exerted on the nuclei by analyzing the changes of the electron density distribution along the reaction path. It is shown that reaction I involves two different chemical processes: (a) the simultaneous FH bond cleavage and CH bond formation leading to an intermediate structure with ion-pair character and (b) the formation of a CF bond and, by this, the final product. The properties of the reaction complex suggest the possibility that a hidden intermediate formed in process (a), which upon a change in the reaction conditions (environment, substitution pattern) can convert into a real intermediate (in solution: solvated ion pairs). Using the results of the URVA analysis of reaction I predictions with regard to the occurrence of hidden intermediates in related addition/cycloaddition reactions are made.