The transition state region in nonsynchronous concerted reactions

The critical and vanishing points of the reaction force F(ξ) = -dV(ξ)/dξ yield five important coordinates (ξ_R, ξ_R^* , ξ_TS, ξ_P^* , ξ_P) along the intrinsic reaction coordinate (IRC) for a given concerted reaction or reaction step. These points partition the IRC into three well-defined regions, reactants (ξ_R→ξ_R^* ), transition state (ξ_R^* →ξ_P^* ), and products (ξ_P^* →ξ_P), with traditional roles of mostly structural changes associated with the reactants and products regions and mostly electronic activity associated with the transition state (TS) region. Following the evolution of chemical bonding along the IRC using formal descriptors of synchronicity, reaction electron flux, Wiberg bond orders, and their derivatives (or, more precisely, the intensity of the electron activity) unambiguously indicates that for nonsynchronous reactions, electron activity transcends the TS region and takes place well into the reactants and products regions. Under these circumstances, an extension of the TS region toward the reactants and products regions may occur.

A combined QTAIM/IRI topological analysis of the effect of axial/equatorial positions of NH2 and CN substituents in the [(PY5Me2)MoO]+ complex

By means of the Interaction Region Indicator (IRI) and Quantum Theory of Atoms in Molecules (QTAIM), the influence exerted by NH₂ (amino) and CN (cyano) as electron donor and electron acceptor substituent groups, respectively, located at para-positions of axial and equatorial pyridine rings of derivatized complexes coming from the [(PY₅Me₂)MoO]⁺ complex during the hydrogen molecular release in the gas phase was analyzed. In any case, a H-H covalent bond is forming at the transition state, with a strengthening of the electron density of 5.5% when the substituent group involved is NH₂ at the para-position of the axial pyridine ring. However, there was no difference between NH₂ and CN when these substituent groups are located at the para-positions of the equatorial pyridine rings. The topological properties of electron densities from the QTAIM are not perturbed by the electron donor and electron acceptor nature of the substituents, even when these substituent groups are located at the axial or equatorial pyridine rings of the Mo-based complex.

A deeper analysis of the role of synchronicity on the Bell-Evans-Polanyi plot in multibond chemical reactions: a path-dependent reaction force constant

The role of the degree of synchronicity in the formation of the new single-bonds in a large set of 1,3-dipolar cycloadditions and its relation in the fulfilment of the classical Bell-Evans-Polanyi principle and Hammond-Leffler postulate are deeply investigated. Our results confirm that asynchronicity is an important path-dependent factor to be taken into account: (i) the Bell-Evans-Polanyi is fulfilled as the degree of (a)synchronicity is quite the same, and a linear relationship between reorganisation energy and asynchronicity is found; (ii) the asynchronicity is the origin of deviations of this classical principle of chemical reactivity since any decrease of the energy barrier is due to an increase of asynchronicity at the same exothermicity; and (iii) the less exothermic the reaction is, the more asynchronous the mechanism is, at the same energy barrier. Thus, this implies that TS imbalance decreases the reorganisation energy, consequently affecting the reaction exothermicity as well.

The density polarization reveals directions of electron displacements due to the substituent effect: Analysis performed on a metal-organic Mo-Oxo catalyst

Some Mo-oxo complexes bearing pyridine rings have the capability for dihydrogen production from water. However, energy barrier and overall energy vary depending on the effect exerted by several substituent groups located at different positions around one or more pyridine rings which are ligands of these compounds. Based on the Karunadasa and coworkers investigation where the para-position was experimentally tested in compounds derivatised from the 2,6-bis[1,1-bis(2-pyridil)ethyl]-pyridine oxo-molybdenum complex synthesized (Karunadasa et al., Nature, 2010, 464, 1329), we tested the combined effect of electron-withdrawing and electron-donating groups simulated as perturbations represented by point-charges. Then, we used the density polarization concept, δρ(r), a local reactivity descriptor corresponding to the partially integrated linear response function, χ(r, r') (a non-local reactivity descriptor), which is able to reveal different displacements of π-electrons on molecular structures. We perturbed the para-positions in the pentadentate ligand 2,6-bis[1,1-bis(2-pyridil)ethyl]-pyridine in the Mo-based complex by means of point-charges. They were located in three different configurations of the organic ligand (trans, geminal, and cis) which could help to explain energy barriers and overall energy of reactions catalyzed by this type of Mo-complexes. Our results indicate that the trans configuration of point-charges induces the most amount of fraction of electron shifted on the complex. A Mo-based complex bearing the same trans configuration for electron-withdrawing and electron-donating substituent groups (cyano and amino, respectively), leads to a kinetically more favorable H₂ release than the cis or geminal configuration of the substituent groups aforementioned.

1,3-Dipolar Cycloadditions by a Unified Perspective Based on Conceptual and Thermodynamics Models of Chemical Reactivity

The main aim in the present report is to gain a deeper understanding of typical 1,3-dipolar cycloadditions by means of three chemical reactivity models in a unified perspective: conceptual density functional theory, distortion/interaction, and reaction force analysis. The focus is to explore the information provided by each reactivity model and how they complement or reinforce each other. Our results showed that the Bell-Evans-Polanyi (BEP) relationship is fulfilled, which is consistent with the Hammond-Leffler postulate. The electronic chemical potential based analysis classifies the reactions as HOMO-, HOMO/LUMO-, and LUMO-controlled reactions as the activation energy increases. It seems likely that HOMO-controlled reaction shifts into LUMO-controlled one as the transition state (TS) position does from early into late. Therefore, the transition from HOMO- (and early TS) into LUMO-controlled (and late TS) is paid by shifting the overall energy change into an endothermic direction, thus supporting the fulfillment of the BEP principle. While thermodynamic models unveil that the distortion or structural rearrangements mainly drive the activation barriers rather than interaction or electronic rearrangements in accord with the distortion/interaction and reaction force analysis, respectively. It is also found that both models are consistent when energy associated with structural and electronic reordering from reaction force analysis is respectively confronted with destabilizing (distortion and Pauli repulsion) and stabilizing (electrostatic and orbital interactions) contributions from the distortion/interaction model, which, on the other hand, increases as low activation barrier and high exothermicity are converted into the high barrier and low exothermicity along with the BEP relation. Finally, the reaction force constant reveals that all 1,3-dipolar cycloaddition reactions proceed by a synchronous single-step mechanism, unveiling that the degree of synchronicity is quite the same in all reactions, confirming the statement that BEP is fulfilled for similar reactions proceeding by a quite alike degree of synchronicity.

KID Procedure Applied on the [(PY5Me2)MoO]+ Complex

The KID (Koopmans in DFT) protocol usually applies in organic molecules of the closed-shell type. We used the KID procedure on an open-shell Mo-based system for the first time to choose the most suitable density functional to compute global and local reactivity descriptors obtained from the conceptual density-functional theory (DFT). From a set of 18 density functionals, spread from the second until the fourth rung of Jacob's ladder: BLYP, BP86, B97-D, MN12-L, MN15-L, M06-L, M11-L, CAM-B3LYP, PBE0, B3LYP, N12-SX, M06-2X, MN15, MN12-SX, ωB97X-D, M11, LC-ωHPBE, and APFD, we concluded that CAM-B3LYP provides the best outcome, and in the second place, M06-2X. Because the vertical first ionization potential and vertical first electron affinity in the ground state (gs) are defined as follows I = E _gs(N - 1) - E _gs(N) and A = E _gs(N) - E _gs(N + 1), where E _gs(N - 1), E _gs(N), and E _gs(N + 1) correspond to energies of the system bearing N, N + 1, and N - 1 electrons, along with Koopmans' theorem (KT) given by I ≈ -ε_HOMO (ε_HOMO, highest occupied molecular orbital energy) and A ≈ -ε_LUMO (ε_LUMO, lowest unoccupied molecular orbital energy), the deviation from the KT was performed by the use of the index, such that J _I = |E _gs(N - 1) - E _gs(N) + ε_HOMO| and J _A = |E _gs(N) - E _gs(N + 1) + ε_LUMO|, which are absolute deviations from the perspective of I and A, respectively. Furthermore, the ε_SOMO (SOMO: singly-occupied molecular orbital energy) leads us to another index given by |ΔSL| = |ε_SOMO - ε_LUMO|. Therefore, J _HL and |ΔSL| are indexes defined to evaluate the quality of the KT when employed within the context of quantum chemical calculations based on DFT and not the Hartree-Fock theory. We propose the index that could be more suitable to choose the most proper density functional because the J _HL and |ΔSL| are independent indexes.

Double-Ring Epimerization in the Biosynthesis of Clavulanic Acid

All reaction steps during the biosynthesis of suicidal clavulanic acid (coformulated with β-lactam antibiotics and used to fight bacterial infections) are known, except for the crucial 3S,5S → 3R,5R double epimerization needed to produce a biologically active stereoisomer, for which mechanistic hypothesis is subject to debate. In this work, we provide evidence for a reaction channel for the double inversion of configuration that involves a total of six reaction steps. When mediated by an enzyme with a terminal S-H bond, this highly complex reaction is spontaneous in the absence of solvents. Polarizable continuum models introduce reaction barriers in aqueous environments because of the strong destabilization of the first transition state. Molecular geometries and electronic structures in both cases indicate that solvent-free spontaneity and aqueous medium barriers are both firmly rooted in a substantial reorganization of the electron density right at the onset of the reaction, mostly involving a cyclic evolution/involution of large regions of π delocalization used to stabilize the excess charge left after the initial proton abstraction.

Tautomers of homophthalic anhydride in the ground and excited electronic states: analysis through energy, hardness and vibrational signatures

The keto-enol tautomerisation in homophthalic anhydride (HA) is investigated in the ground (S₀) and excited (S₁) electronic states. The keto form with a dicarbonyl structure is found to be the most stable form in S₀ and enol form with a monocarbonyl structure in S₁ indicating an excited state intramolecular proton transfer (ESIPT) process. The computed results show consistency with the change in basis sets and methods of calculations. Apart from the two tautomers, transition states are also identified. The barrier to interconversion is found to reduce substantially in S₁. Internal reaction coordinate (IRC) calculations confirm the pathway of interconversion between the two forms in S₀ and S₁. The observed FT-IR spectra corroborate well with our computed spectra. The appearance of two strong lines around 1800 cm^-1 confirms the lowest energy structure to be the keto tautomer with a dicarbonyl form in S₀. Our computations corroborate well with the crystal structure data for an analogous molecule. Electron distribution in HOMO and LUMO indicate the excitation process as π → π^* in nature. The qualitative chemical concepts like hardness and electrophilicity are calculated to estimate the stability of the tautomers. The energy and hardness profiles with the variation of IRC are opposite to each other, verifying the principle of maximum hardness.