Raman K. Singh

Reaction energetics on long-range corrected density functional theory: Diels–Alder reactions

The possibility of quantitative reaction analysis on the orbital energies of long‐range corrected density functional theory (LC‐DFT) is presented. First, we calculated the Diels–Alder reaction enthalpies that have been poorly given by conventional functionals including B3LYP functional. As a result, it is found that the long‐range correction drastically improves the reaction enthalpies. The barrier height energies were also computed for these reactions. Consequently, we found that dispersion correlation correction is also crucial to give accurate barrier height energies. It is, therefore, concluded that both long‐range exchange interactions and dispersion correlations are essentially required in conventional functionals to investigate Diels–Alder reactions quantitatively. After confirming that LC‐DFT accurately reproduces the orbital energies of the reactant and product molecules of the Diels–Alder reactions, the global hardness responses, the halves of highest occupied molecular orbital (HOMO)‐lowest unoccupied molecular orbital (LUMO) energy gaps, along the intrinsic reaction coordinates of two Diels–Alder reactions were computed. We noticed that LC‐DFT results satisfy the maximum hardness rule for overall reaction paths while conventional functionals violate this rule on the reaction pathways. Furthermore, our results also show that the HOMO‐LUMO gap variations are close to the reaction enthalpies for these Diels–Alder reactions. Based on these results, we foresee quantitative reaction analysis on the orbital energies.

Reactivity index based on orbital energies.

This study shows that the chemical reactivities depend on the orbital energy gaps contributing to the reactions. In the process where a reaction only makes progress through charge transfer with the minimal structural transformation of the reactant, the orbital energy gap gradient (OEGG) between the electron‐donating and electron‐accepting orbitals is proven to be very low. Using this relation, a normalized reaction diagram is constructed by plotting the normalized orbital energy gap with respect to the normalized intrinsic reaction coordinate. Application of this reaction diagram to 43 fundamental reactions showed that the majority of the forward reactions provide small OEGGs in the initial stages, and therefore, the initial processes of the forward reactions are supposed to proceed only through charge transfer. Conversely, more than 60% of the backward reactions are found to give large OEGGs implying very slow reactions associated with considerable structural transformations. Focusing on the anti‐activation‐energy reactions, in which the forward reactions have higher barriers than those of the backward ones, most of these reactions are shown to give large OEGGs for the backward reactions. It is also found that the reactions providing large OEGGs in the forward directions inconsistent with the reaction rate constants are classified into SN2, symmetric, and methyl radical reactions. Interestingly, several large‐OEGG reactions are experimentally established to get around the optimum pathways. This indicates that the reactions can take significantly different pathways from the optimum ones provided no charge transfer proceeds spontaneously without the structural transformations of the reactants.

On low-lying excited states of extended nanographenes

Low‐lying excited states of planarly extended nanographenes are investigated using the long‐range corrected (LC) density functional theory (DFT) and the spin‐flip (SF) time‐dependent density functional theory (TDDFT) by exploring the long‐range exchange and double‐excitation correlation effects on the excitation energies, band gaps, and exciton binding energies. Optimizing the geometries of the nanographenes indicates that the long‐range exchange interaction significantly improves the CC bond lengths and amplify their bond length alternations with overall shortening the bond lengths. The calculated TDDFT excitation energies show that long‐range exchange interaction is crucial to provide accurate excitation energies of small nanographenes and dominate the exciton binding energies in the excited states of nanographenes. It is, however, also found that the present long‐range correction may cause the overestimation of the excitation energy for the infinitely wide graphene due to the discrepancy between the calculated band gaps and vertical ionization potential (IP) minus electron affinity (EA) values. Contrasting to the long‐range exchange effects, the SF‐TDDFT calculations show that the double‐excitation correlation effects are negligible in the low‐lying excitations of nanographenes, although this effect is large in the lowest excitation of benzene molecule. It is, therefore, concluded that long‐range exchange interactions should be incorporated in TDDFT calculations to quantitatively investigate the excited states of graphenes, although TDDFT using a present LC functional may provide a considerable excitation energy for the infinitely wide graphene mainly due to the discrepancy between the calculated band gaps and IP–EA values.

Relationship between orbital energy gaps and excitation energies for long-chain systems.

The difference between the excitation energies and corresponding orbital energy gaps, the exciton binding energy, is investigated based on time‐dependent (TD) density functional theory (DFT) for long‐chain systems: all‐trans polyacetylenes and linear oligoacenes. The optimized geometries of these systems indicate that bond length alternations significantly depend on long‐range exchange interactions. In TDDFT formalism, the exciton binding energy comes from the two‐electron interactions between occupied and unoccupied orbitals through the Coulomb‐exchange‐correlation integral kernels. TDDFT calculations show that the exciton binding energy is significant when long‐range exchange interactions are involved. Spin‐flip (SF) TDDFT calculations are then carried out to clarify double‐excitation effects in these excitation energies. The calculated SF‐TDDFT results indicate that double‐excitation effects significantly contribute to the excitations of long‐chain systems. The discrepancies between the vertical ionization potential minus electron affinity (IP–EA) values and the HOMO–LUMO excitation energies are also evaluated for the infinitely long polyacetylene and oligoacene using the least‐square fits to estimate the exciton binding energy of infinitely long systems. It is found that long‐range exchange interactions are required to give the exciton binding energy of the infinitely long systems. Consequently, it is concluded that long‐range exchange interactions neglected in many DFT calculations play a crucial role in the exciton binding energies of long‐chain systems, while double‐excitation correlation effects are also significant to hold the energy balance of the excitations.

Orbital Energy-Based Reaction Analysis of S N 2 Reactions

An orbital energy-based reaction analysis theory is presented as an extension of the orbital-based conceptual density functional theory. In the orbital energy-based theory, the orbitals contributing to reactions are interpreted to be valence orbitals giving the largest orbital energy variation from reactants to products. Reactions are taken to be electron transfer-driven when they provide small variations for the gaps between the contributing occupied and unoccupied orbital energies on the intrinsic reaction coordinates in the initial processes. The orbital energy-based theory is then applied to the calculations of several S N2 reactions. Using a reaction path search method, the Cl− + CH3I → ClCH3 + I− reaction, for which another reaction path called “roundabout path” is proposed, is found to have a precursor process similar to the roundabout path just before this SN2 reaction process. The orbital energy-based theory indicates that this precursor process is obviously driven by structural change, while the successor SN2 reaction proceeds through electron transfer between the contributing orbitals. Comparing the calculated results of the SN2 reactions in gas phase and in aqueous solution shows that the contributing orbitals significantly depend on solvent effects and these orbitals can be correctly determined by this theory.

Theoretical Investigation of the H2O2-Induced Degradation Mechanism of Hydrated Nafion Membrane via Ether-Linkage Dissociation

A H2O2-induced degradation mechanism is presented for the hydrated Nafion membrane proceeding through the dissociation of the ether linkages of the side chains. Although the durability of proton-exchange membrane fuel cells clearly depends on the degradation rate of the membrane, typically Nafion, the degradation mechanism still has not been resolved. It has often been assumed that the principal mode of degradation involves OH• radicals; in contrast, we show here that a H2O2-induced degradation mechanism is more likely. On the basis of state-of-the-art theoretical calculations and detailed comparison with experimental results, we present such a mechanism for the hydrated Nafion membrane, proceeding through the dissociation of the ether linkage of the side chains, with a relatively low activation energy. In this mechanism, (H2O)λHO3S–CF2–CF2–O–O–H (λ is the hydration number) is obtained as a key degradation fragment. Possible subsequent decomposition-reaction mechanisms are also elucidated for this fragment. The calculated vibrational spectra for the intermediates and products proposed in these mechanisms were found to be consistent with the experimental IR spectra. Further consideration of this H2O2-mediated degradation mechanism could greatly facilitate the search for ways to combat membrane degradation.