Unveiling the Nature of Chemical Bonds in Real Space.

Recent advent of diverse chemical entities necessitates a re-evaluation of chemical bond concepts, underscoring the importance of experimental evidence. Our prior study introduced a general methodology, termed Core Differential Fourier Synthesis (CDFS), for mapping the distribution of valence electron density (VED) in crystalline substances within real space. In this study, we directly compare the VED distributions obtained through CDFS with those derived from high-accuracy theoretical calculation using long-range corrected density functional theory, which quantitatively reproduces accurate orbital energies. This comparison serves to demonstrate the precision of the CDFS in replicating complex details. The VED patterns observed experimentally exhibited detailed structures and phases of wave functions indicative of sp3 hybrid orbitals, closely aligning with theoretical predictions. This alignment underscores the utility of our approach in gathering quantum chemical data experimentally, a crucial step for discussing the chemical properties, such as reaction mechanisms.

Total and orbital density-based analyses of molecules revealing long-range interaction regions.

Total and orbital electron densities of molecules are explored for the effect of the long-range correction (LC) for density functional theory (DFT) exchange functionals by comparing to the effect of the ab initio coupled cluster singles and doubles (CCSD) method. Calculating the LC effect on the total electron densities shows that the LC stabilizes the electrons around the long-range interaction regions of kinetic energy density, which are assumed to be electrons other than free electrons and self-interacting electrons, while the CCSD method stabilizes the electrons in the long-range interaction regions in the vertical molecular planes. As a more precise test, the LC effect on orbital densities are compared to the CCSD effect on Dyson orbital densities. Surprisingly, these effects are similar for the unoccupied orbitals, indicating that the LC covers the effects required to reproduce the CCSD Dyson unoccupied orbitals. For exploring the discrepancies between these effects on the occupied orbitals, the photoionization cross sections are calculated as a direct test for the shapes of the HOMOs to investigate the differences between these effects on the occupied orbitals. Consequently, the LC clearly produces the canonical HOMOs close to the CCSD Dyson and experimental ones, except for the HOMO of benzene molecule that mixes with the HOMO - 1 for the CCSD Dyson orbitals. This indicates that the orbital analyses using the photoionization cross sections are available as a direct test for the quality of DFT functionals.

Reactive orbital energy theory serving a theoretical foundation for the electronic theory of organic chemistry.

It is established that the reactive orbital energy theory (ROET) theoretically reproduces the rule-based electronic theory diagrams of organic chemistry by a comparative study on the charge transfer natures of typical organic carbon-carbon and carbon-heteroatom bond formation reactions: aldol, Mannich, α-aminooxylation, and isogyric reactions. The ROET, which is an expansion of the reaction electronic theories (e.g., the frontier orbital theory) in terms of orbital energies, elucidates the reactive orbitals driving reactions and the charge transferability indices of the reactions. Performing the ROET analyses of these reactions shows that the charge transfer directions given in the rule-based diagrams of the electronic theory are reproduced even for the functional groups of charge transfer destinations in all but only two processes for 38 reaction processes. The ROET analyses also make clear the detailed orbital-based pictures of these bond formation reactions: that is, the use of the out-of-plane antibonding π orbitals in acidic conditions (enol-mode) and in-plane antibonding π orbitals in basic conditions (enolate-mode), which explain the experimentally assumed mechanisms such as the π-bond formations in acidic conditions and σ-bond formations at α-carbons in basic conditions. Furthermore, the ROET analyses explicate that the methyl group initially accepts electrons and then donates them to the bond formations in the target reactions. It is, consequently, suggested that the ROET serves a theoretical foundation for the electronic theory of organic chemistry.

Water-oxidation mechanism of cobalt phosphate co-catalyst in artificial photosynthesis: a theoretical study.

The initial water-oxidation reaction mechanism of the hydrated cobalt phosphate (CoPi) co-catalyst, which is consistent with conventional experimental findings, is investigated for O-O bond and OOH formation in this study. Theoretical calculations of hydrated CoPi cluster models, which are validated by vibrational spectrum calculations, elucidate the roles of phosphate as a source of oxygen and deliverer of protons, both of which result in the spontaneous formation of an O-O bond after the release of two electrons and two protons. The calculations also show that OOH formation proceeds subsequently depending on the spin electronic states of the hydrated CoPi surface, and O2 formation then spontaneously progresses after the release of two electrons and two protons. By theoretically tracing these processes, the initial water-oxidation reaction mechanism of the hydrated CoPi co-catalyst is proposed.

Natural reaction orbitals for characterizing electron transfer responsive to nuclear coordinate displacement.

The natural reaction orbital (NRO) is proposed as a new concept for analyzing chemical reactions from the viewpoint of the electronic theory. The pair of the occupied and virtual NROs that characterize electron transfer responsive to nuclear coordinate displacement along the reaction path is automatically extracted from the solution of the coupled-perturbed self-consistent-field (CPSCF) equation for the perturbation of the nuclear displacement. The NRO-based reaction analysis method is applied to several reactions. As a result, it is found that the sum of squares of the singular values, derived from the solution of the CPSCF equation, gives sharp peaks around the transition state structures and at the shoulders of the potential energy curve. The peaks around the transition states suggest a new physical meaning of transition state from the viewpoint of the electronic theory. Furthermore, the double peaks reveal the asynchronous processes of reactions, which are not always shown in potential energy analyses. Since the NRO-based reaction analysis method is universal and robust for describing reaction mechanisms from an electronic theory viewpoint, it is expected to lead to universal reaction analyses based on the electronic theory.

Reply to the 'Comment on "Theoretical investigations on hydrogen peroxide decomposition in aquo"' by W. H. Koppenol, Phys. Chem. Chem. Phys., 2021, 23, DOI: 10.1039/D1CP03545B.

Following the comment article by Koppenol (W. H. Koppenol, Phys. Chem. Chem. Phys., 2021, 23, DOI: 10.1039/D1CP03545B), the H2O2 decomposition reaction mechanism based on the production of a de facto monovalent iron ion hydration complex, which is theoretically proposed in T. Tsuneda and T. Taketsugu, Phys. Chem. Chem. Phys., 2018, 20, 24992-24999, is reviewed from the standpoint of chemical kinetics. As a result, it is found that this decomposition mechanism is strongly supported by comparing the Gibbs energies of formation in consideration of the O-O bond dissociation of H2O2 for de facto monovalent iron, ferrous, and ferric ion complexes.

Density Functional Theory as a Data Science.

The development of density functional theory (DFT) functionals and physical corrections are reviewed focusing on the physical meanings and the semiempirical parameters from the viewpoint of data science. This review shows that DFT exchange-correlation functionals have been developed under many strict physical conditions with minimizing the number of the semiempirical parameters, except for some recent functionals. Major physical corrections for exchange-correlation function- als are also shown to have clear physical meanings independent of the functionals, though they inevitably require minimum semiempirical parameters dependent on the functionals combined. We, therefore, interpret that DFT functionals with physical corrections are the most sophisticated target functions that are physically legitimated, even from the viewpoint of data science.

Synthesis and Synthetic Application of Chloro- and Bromofuroxans.

Furoxans are potentially useful heteroaromatic units in pharmaceuticals and agrichemicals. However, the applications for furoxan-based compounds have been hampered due to the underdevelopment of their synthetic methods. Herein, we report a new synthetic approach for the synthesis of chloro- and bromofuroxans. The starting materials were dichloro- and dibromofuroxans, and the substituents were directly introduced to the furoxan ring in a modular fashion. The synthesized monohalofuroxans served as substrates for the installation of a second substituent to prepare further functionalized furoxans.

Theoretical investigations on geometrical and electronic structures of silver clusters.

Geometrical structures and ground and excited states of silver clusters are theoretically investigated using long-range corrected (LC) density functional theory (DFT) calculations. The discrepancy between HOMO-LUMO gaps and the vertical ionization potential minus vertical electron affinity values, which should be the same values, is explored to reveal the significance of long-range exchange effects on the electronic states of metal clusters. The difference between HOMO-LUMO gaps and HOMO-LUMO excitation energies, which is called "exciton binding energy," is also tested. As a result, it is found that the long-range exchange effects are requisite in DFT calculations to quantitatively investigate the ground and excited states of metal clusters. © 2018 Wiley Periodicals, Inc.

On principal features of organic electrolyte molecules in lithium ion battery performance.

The lithium (Li) complexes of organic electrolyte solvents are theoretically investigated using the long-range correction for density functional theory in order to figure out the cause for the high performance of cyclic carbonate electrolytes in lithium ion batteries (LIBs). Calculations of the Li complexes with ethylene carbonate solvent molecules prove that ten ligand molecules should be incorporated to obtain near-degenerate four- and five-coordination optimum structures and dramatically improved orbital energies. The geometry optimizations of the Li complexes with thirteen types of organic solvent molecules give four-coordination neutral and five-coordination cation complexes for many solvent molecules. The five-coordination Li complexes are considered to use Berry pseudorotation to approach the electrodes from the Li atom. The calculated Koopmans, vertical and adiabatic ionization potentials and electron affinities show that near-degeneracy and structural deformation effects play significant roles in the electronic states of the Li complexes. Mulliken charge and dipole moment analyses indicate that the Li complexes of cyclic carbonates construct a deep electric double layer near electrodes due to the electron-donating ability of the ligand molecules. Molecular orbital analyses also explain that the Li complexes of cyclic carbonates easily construct a solid electrolyte interface, which contributes to Li ion conductance, by localizing the accepted electron to one ligand molecule. In conclusion, the Li complexes of cyclic carbonates have three main features: preference of five-coordination structures, high electron-donating ability of ligand molecules, and localization of the accepted electron to one ligand molecule.

Roles of silver nanoclusters in surface-enhanced Raman spectroscopy.

The cause for the huge enhancement factors of surface-enhanced Raman spectroscopy (SERS) by the addition of small silver nanoclusters is theoretically investigated by focusing on the difference between resonance Raman activity and surface plasmon effects. First, the resonance and off-resonance Raman spectra are calculated using the incident light wavenumbers of the low-lying charge transfer excitations for the surface (S) and vertex (V) complexes of the pyridine molecule attaching to three small silver nanoclusters: Ag5, Ag10, and Ag20. As a result, it is found that the incident radiation dramatically increases the resonance Raman activities with the enhancement factors up to 1012. This indicates that the resonance Raman effects are dominant in the enhancement factors of SERS, at least when to use small silver clusters. It is also found that the resonance Raman spectra significantly depend on the adsorption sites given in S or V complexes, and on the inclusion or exclusion of the long-range correction for density functional theory, irrespective of the size of the silver clusters. The electromagnetic field enhancement effects called "surface plasmon effects" are also examined for the Ag20 cluster to confirm this conclusion. Consequently, the enhancement in the electric field is roughly evaluated as less than one for the static polarizability of this small cluster. It is, therefore, concluded that the resonance Raman activity effect is dominant in the huge SERS enhancement factors for, at least, small silver nanoclusters.

Theoretical investigations on hydrogen peroxide decomposition in aquo.

Hydrogen peroxide (H2O2) decomposition mechanisms in the absence and presence of iron ions in aqueous solution, which contain no OH radical formation, are theoretically determined. Calculating the oxygen-oxygen bond dissociation energies of H2O2, we confirmed that OH radical formation requires spin-forbidden transitions. Instead, we tested an H2O2 dimer-based decomposition mechanism and found that this mechanism provides reasonable barrier heights of 52-62 kcal mol-1, which are close to the experimental activation energy. We next calculated the oxygen-oxygen bond dissociation of H2O2 coordinating to the iron ion hydration complex in order to explore H2O2 decomposition in the presence of iron ions. Surprisingly, we found that a monovalent iron ion complex provides no reaction barrier to dissociate H2O2, in contrast to the ferrous (Fe2+) and ferric (Fe3+) ion complexes with accompanying very high barriers. Following this result, we determined the subsequent oxygen formation mechanism of the monovalent iron ion complex and found that this mechanism needs a hydrogen bond network around H2O2 to proceed at room temperature. We, therefore, conclude that H2O2 decomposition in the presence of iron ions is driven by electron transfer to the iron ion hydration complex and proceeds by hydrogen transfers in the hydrogen bond network around H2O2.

Diagrams for comprehensive molecular orbital-based chemical reaction analyses: reactive orbital energy diagrams.

Reactive orbital energy diagrams are presented as a tool for comprehensively performing orbital-based reaction analyses. The diagrams rest on the reactive orbital energy theory, which is the expansion of conceptual density functional theory (DFT) to an orbital energy-based theory. The orbital energies on the intrinsic reaction coordinates of fundamental reactions are calculated by long-range corrected DFT, which is confirmed to provide accurate orbital energies of small molecules, combining with a van der Waals (vdW) correlation functional, in order to examine the vdW effect on the orbital energies. By analysing the reactions based on the reactive orbital energy theory using these accurate orbital energies, it is found that vdW interactions significantly affect the orbital energies in the initial reaction processes and that more than 70% of reactions are determined to be initially driven by charge transfer, while the remaining structural deformation (dynamics)-driven reactions are classified into identity, cyclization and ring-opening, unimolecular dissociation, and H2 reactions. The reactive orbital energy diagrams, which are constructed using these results, reveal that reactions progress so as to delocalize the occupied reactive orbitals, which are determined as contributing orbitals and are usually not HOMOs, by hybridizing the unoccupied reactive orbitals, which are usually not LUMOs. These diagrams also raise questions about conventional orbital-based diagrams such as frontier molecular orbital diagrams, even for the well-established interpretation of Diels-Alder reactions.

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. © 2017 Wiley Periodicals, Inc.

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. © 2016 Wiley Periodicals, Inc.

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 SN 2, 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.

Self-interaction corrections in density functional theory.

Self-interaction corrections for Kohn-Sham density functional theory are reviewed for their physical meanings, formulations, and applications. The self-interaction corrections get rid of the self-interaction error, which is the sum of the Coulomb and exchange self-interactions that remains because of the use of an approximate exchange functional. The most frequently used self-interaction correction is the Perdew-Zunger correction. However, this correction leads to instabilities in the electronic state calculations of molecules. To avoid these instabilities, several self-interaction corrections have been developed on the basis of the characteristic behaviors of self-interacting electrons, which have no two-electron interactions. These include the von Weizsäcker kinetic energy and long-range (far-from-nucleus) asymptotic correction. Applications of self-interaction corrections have shown that the self-interaction error has a serious effect on the states of core electrons, but it has a smaller than expected effect on valence electrons. This finding is supported by the fact that the distribution of self-interacting electrons indicates that they are near atomic nuclei rather than in chemical bonds.

Singlet Fission as the Gateway to Triplet Generation in Heavy Atom-Free Organic Molecules.

Triplet generations in heavy atom-free organic molecules are primarily revealed to proceed through singlet fissions (SFs) by investigating the contributions of SFs and intersystem crossings to the generation rates. The spin-flip long-range corrected time-dependent density functional theory calculations on 11 organic molecules known for triplet generation under photoirradiation are performed. The correlation between the descriptors for SF and the experimental singlet-to-triplet conversion rates strongly supports the predominance of SF progressions in all these molecules, corroborated by experimental observations of their triplet-triplet annihilations. Based on these findings, we propose updated conditions for SF progression: There is a high-absorption singlet state just above the triplet-triplet excitation of the chromophore dimer, or the singlet (triplet-triplet) excitation itself is responsible for photoabsorption. To the best of our knowledge, all organic molecules known for rapid triplet state generation fulfill these conditions.

Singlet fission initiating organic photosensitizations.

The feasibility of singlet fission (SF) in organic photosensitizers is investigated through spin-flip long-range corrected time-dependent density functional theory. This study focuses on four major organic photosensitizer molecules: benzophenone, boron-dipyrromethene, methylene blue, and rose bengal. Calculations demonstrate that all these molecules possess moderate [Formula: see text]-stacking energies and closely-lying singlet (S) and quintet (triplet-triplet, TT) excitations, satisfying the essential conditions for SF: (1) Near-degenerate low-lying S and (TT) excitations with a significant S-T energy gap, and (2) Moderate [Formula: see text]-stacking energy of chromophores, slightly higher than solvation energy, enabling dissociation for triplet-state chromophore generation. Moreover, based on the El-Sayed rule, intersystem crossing is found to simultaneously proceed at very slow rates in all these photosensitizers. This is attributed to the fact that the lowest singlet excitation of the monomers partly involves [Formula: see text] transitions alongside the main [Formula: see text] transitions. The proposed mechanisms are strongly substantiated by comparisons with experimental studies.

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.