Activation of the Unreactive Bond in C70 Fullerene toward Diels‐Alder Reaction by Encapsulation of a Lithium Atom

Diels‐Alder cycloaddition reaction is useful for generation of covalent derivatives of fullerenes. Diels‐Alder reactions of C₇₀ and dienes usually take place at the carbon‐carbon bond that has a short bond length in C₇₀, while the bonds with long lengths are generally unreactive. In this paper, we investigated the reactivities of Li⁺@C₇₀ and Li@C₇₀ toward Diels‐Alder reactions with cyclohexadiene by means of density functional theory calculations. We found that the thermodynamic and kinetic reactivities of the fullerene cage are changed significantly after the encapsulation of the lithium ion or atom. The encapsulated lithium ion causes a remarkable decrease of the activation barrier for the cycloaddition reaction, which can be ascribed to the enhanced orbital interaction between cyclohexadiene and the fullerene cage. The unreactive bond with a long length in C₇₀ is activated efficiently after the encapsulation of the lithium atom. According to the activation‐strain model analysis, the improved reactivity of the long bond is associated with the small deformation energy and large interaction energy of the reactants. Unlike conventional Diels‐Alder reactions that proceed through concerted mechanism, the reaction of Li@C₇₀ and cyclohexadiene undergoes an unusual stepwise mechanism because of the open‐shell electronic structure of Li@C₇₀.     

Lanthanide metals in the boron cages: Computational prediction of M@Bn (M = Eu,Gd; n = 38, 40)

Endohedral metalloborofullerenes (EMBFs) are novel boron analogues of the famous endohedral metallofullerenes (EMFs). Many EMBFs have been proposed by theoretical calculations thus far. However, in sharp contrast to EMFs, which trap most of the lanthanides with f electrons inside the cages, the corresponding lanthanide‐based EMBFs have never been reported. In this work, the encapsulation of Eu and Gd in the B₃₈ and B₄₀ fullerenes was studied by means of density functional theory calculations. Our results revealed that Gd@B₃₈(⁹A), Eu@B₄₀(⁸B₂), and Gd@B₄₀(⁷A″) all favor the endohedral configuration, and the electronic structures can be described as Gd³⁺@ , Eu²⁺@ , and Gd³⁺@ with jailed f electron spins. The large binding energies and sizable HOMO–LUMO gaps suggest that they may be achieved experimentally. They feature σ and π double aromaticity, and their excellent stabilities were confirmed by the Born–Oppenheimer molecular dynamics simulations. Finally, the infrared and UV/vis spectra were simulated to assist experimental characterization.     

Comments on the carbon cluster C60 and on its complexes with alkaline elements

We have analyzed in the Hartree–Fock approximation the carbon cluster C₆₀ with a single-zeta [(9,5)/(2,1)] basis set and a double-zeta [(9,5)/(4,2)] basis set, the latter with and without 3d polarization functions. Estimates of the correlation energy correction were obained either using Becke's density functional theory or the Clementi–Chakravorty's electron–pair density approximation. The cluster's positive ion and singly and doubly charged negative ions have also been studied (doublets for C and C and singlet and triplet for C) and computed both with a doublezeta basis set and defferent geometries or a double-zeta plus polarization basis set. The geometries considered include the one obtained by quantum molecular dynamics using the Car–Parrinello approximation and two additional near this minimum. The computed ionization potential and electron affinity are in reasonable agreement with the experiments considering the basis sets adopted. A lithium, a sodium, or a potassium atom or the corresponding positive ions have been placed at the center of the cluster and have been shown to form stable complexes: C₆₀Li⁺, C₆₀Li, C₆₀Na⁺, C₆₀Na, C₆₀K⁺, and C₆₀K. In addition, preliminary data with a calcium atom are reported. Computations on model cluster C₅, C₆, and C₉ are also reported to show that one needs large basis sets, extended use of polarization functions, and correlation corrections for quantitative results, more accurate than ～5 kcal/mol per carbon atom, in the total energy, as in this work.     

Carbon–sulfur chains: A high‐resolution infrared and quantum‐chemical study of C3S and SC7S

In the course of a 5 μm high‐resolution infrared study of laser ablation products from carbon–sulfur targets, the ν₁ vibrational mode region of linear C₃S has been studied continuously from 2046 to 2065 cm^?1. Besides the prominent vibrational fundamental, the region was found to feature the , and even hot bands, the latter two of which were observed for the first time. Owing to the high signal‐to‐noise ratio obtained, the ν₁ mode of S could also be observed in natural abundance for the first time at high spectral resolution in the infrared. At 2061 cm^?1, hidden inside the branch of the C₃S ν₁ fundamental mode, a weak new band is observed which exhibits very tight line spacing and stems from a heavy both carbon and sulfur containing carrier. On the basis of high‐level quantum‐chemical calculations of selected carbon–sulfur chains and other carbon‐rich cumulenes, this feature is attributed to the ν₅ vibrational fundamental of linear SC₇S, which stands for the first gas‐phase spectroscopic detection of this long cumulenic chain.     

Catalytic action of Mn‐superoxide dismutase in scavenging superoxide radical anion by double hydrogen abstraction from dihydrolipoic acid: A theoretical study

The mechanism of scavenging superoxide radical anion ( ) by dihydrolipoic acid (diLA) in absence and presence of the enzyme Manganese‐superoxide dismutase (Mn‐SOD) has been investigated using density functional theory. Mn‐SOD was modelled by a complex of a manganese cation (Mn²⁺) bonded to three similar molecules having a histidine ring each and a water molecule. It has been shown that the scavenging mechanism involves double hydrogen abstraction by from different pairs of neighboring sites of diLA. It has been found that diLA alone cannot scavenge superoxide radical anions efficiently as the barrier energies involved in the reactions are very high. However, in presence of Mn‐SOD, owing to its catalytic action, the corresponding reactions become barrierless due to which superoxide radical anions would be scavenged highly efficiently. H₂O₂ formed from superoxide radical anion due to double hydrogen abstraction from diLA is scavenged by diLA alone barrierlessly without involving Mn‐SOD or any other catalyst.     

Theoretical investigation of geometry and stability of small lithium‐iodide LinI (n = 2–6) clusters

We present theoretical investigation of the structural characteristics and stabilities of neutral and positively charged Li_nI (n = 2‐6) species. The structural isomers were found by using a randomized algorithm to search for minima structures, followed by B3LYP optimizations; the single‐point RCCSD(T)/cc‐pwCVTZ(‐PP) calculations were performed in order to compute relative energies, binding energies per atom, adiabatic and vertical ionization energies, and dissociation energies. Stability was compared to the pure lithium clusters; there is a typical odd‐even alternation; iodine doped clusters are more stable than pure lithium clusters. Lithium “cage” transfers its valence electron to the iodine atom to form neutral and cationic clusters. An electron departures the lithium cage upon ionization. An important reason for the larger stability of closed‐shell species is the existence of the HOMO 3c/2e natural bond orbitals. © 2013 Wiley Periodicals, Inc.     

Simulated annealing‐based optimal control over tunneling process through SDWP and Eckart barrier: A momentum basis representation

For a reaction to proceed via tunneling mechanism, it is essential that the reactants will cross the potential barrier (E_P), where its initial energy (E₀) is below the potential barrier E_P. Tunneling probability τ is defined as the probability of having momentum higher than k_m, where . In the momentum basis representation, τ can be directly calculated by integrating from the limit k_m to infinity, where is the wave function in the momentum space. Instead of the continuous basis, if we chose momentum grid space, τ can be expressed as . Our target here is to increase this τ by applying a polychromatic field, so that the reaction rate can be enhanced. By applying Simulated Annealing technique we have designed some polychromatic electric fields, spatially symmetric and asymmetric type, which enhances the tunneling rate in symmetric double well system and Eckart barrier confined in an infinite well.     

The nature of the chemical bond in borazine (B3N3H6), boroxine (B3O3H3), carborazine (B2N2C2H6), and related species

The bonding problem in borazine (B₃N₃H₆), boroxine (B₃O₃H₃), and carborazine (B₂N₂C₂H₆) is successfully addressed through the consideration of the excited states of the constituent fragments, namely BH( ), NH( ), and CH( ). We propose the participation of resonant structures for all three species that help to explain the experimental findings. A discussion on the chemical pattern of the parental molecule benzene (C₆H₆) helps to make coherent the whole bonding analysis on the titled species.     

Pseudo Jahn–Teller origin tracking for symmetry breaking in halogenabenzene: How can a bird fly?

The cyclic iodabenzene molecule (CH)₅I was first introduced and characterized as planar configuration and zwitterionic valence structure by Glukhovtsev in 1991. Recently, it caused researchers' great interest due to the theoretical discovery of a stable bird‐like structure by Hoffmann et al. in 2017 which has similar electronic structure and charge distribution as well‐known Meisenheimer complex C₆H. Inspired by this, we continue to tell the halogenabenzene story by revealing the origin of the bird‐like structure and understanding how the electronic behavior affects the geometrical symmetry for a molecule. By combining the Pseudo Jahn–Teller effect (PJTE) theory with the ab initio calculations for halogenabenzenes (CH)₅X (X = F, Cl, Br, I) and C₆H, it is illustrated that the vibronic coupling of ¹A₁ ground state and ¹B₁ excited states with C_2v planar structure along the out‐of‐plane b₁ distortion triggers the symmetry breaking of planar configuration to form a preferred bird‐like structure. This interpretation can be also applied to explain their different stabilization energies by analyzing numerically the energy gaps of coupled electronic states and PJTE vibronic coupling parameters. Taking use of the PJTE formulation above, we also tracked the origin of restoring to be planar for (CH)₅X²⁺ cation, as well as their isoelectronic species (CH)₅O⁺ and (CH)₅N, and suggests an effective strategy to stabilize the planar configuration for halogenabenzenes.     

A theoretical study on the stability difference of the borane and carborane C2Bn−2Hn (5 ≤ n ≤ 7) clusters

In order to study the electronic structure and structural stability of borane and carborane C₂B_n?2H_n (5 ≤ n ≤ 7) clusters, especially the stability difference between the borane and carborane C₂B₃H₅. The frontier orbital energy levels of the borane and carborane C₂B_n?2H_n (5 ≤ n ≤ 7) clusters are calculated at CCSD(T)/aug‐cc‐pVXZ//B3LYP/def2‐TZVPP level. The results are further analyzed by qualitative frontier orbital method based on the cap–ring interaction. The results reveal that: (1) the larger E_gap(HOMO‐LUMO energy gap) of carborane C₂B_n?2H_n (5 ≤ n ≤ 7) clusters than borane (5 ≤ n ≤ 7) clusters originates from the more effective cap–ring orbital overlap of carborane C₂B_n?2H_n (5 ≤ n ≤ 7) clusters than that of borane (5 ≤ n ≤ 7) clusters; (2) the smallest E_gap of the borane results from the highest energy level of the ring symmetry‐adapted linear combination orbital of cluster; and (3) the largest E_gap of the carborane C₂B₃H₅ is induced by the most effective cap–ring orbital interaction of C₂B₃H₅ cluster. © 2014 Wiley Periodicals, Inc.     

Topological defects on the energy spectra of diatomic molecules embedded with shifted Deng–Fan oscillator potential under AB flux field

A study on the effect of point like global monopole topological defects on the energy eigenvalues of the diatomic molecules $H_2$, $LiH$, $CO$, $HCl$ embedded with Shifted Deng–Fan Oscillator Potential under the influence of Aharonov–Bohm flux field has been made here. Asymptotic Iteration Method (AIM) is used to find out the bound state solutions for arbitrary $l$ states by solving the non-relativistic Schrödinger equation. A Pekeris-type approximation has been used to approximate the centrifugal barrier term. It is observed that, energy levels of the diatomic molecules is significantly affected by the global effects of the point like global monopole, flux field and effective potential field.     

Prediction of the pH‐rate profile for dimethyl sulfide oxidation by hydrogen peroxide: The role of elusive H3O2+ Ion

Experimental kinetics of sulfide oxidation by hydrogen peroxide presents a pH‐dependent profile. In this article, it was carried out a detailed study of the mechanism and kinetics of dimethyl sulfide (DMS) oxidation by H₂O₂ in neutral, acid, and basic aqueous medium using ab initio calculations. The results point out that DMS oxidation in neutral aqueous medium occurs through its direct reaction with H₂O₂. In acid medium, cluster‐continuum model calculations shows that cluster is the best representation of the very reactive species. In basic medium, there is formation of the species. However, the pathway involving this species has high free energy barrier, making this pathway unfeasible. The theoretical pH‐rate profile is in good agreement with the experimental observations. © 2013 Wiley Periodicals, Inc.     

The validities of centrifugal sudden approximations in chemical reaction dynamics

In this review article, we discuss and analyze the validities of centrifugal sudden (CS) approximations in chemical reactions, with emphasis on the recent progress in the comparison studies of close‐coupling and CS approximations in chemical dynamics both adiabatically and nonadiabatically. All these relevant studies are performed using the time‐dependent wave packet approach, focusing on several typical and benchmark chemical reactions, for example, the triatomic adiabatic ion–molecule reactions of Ne + , He + HeH⁺, O⁺ + H₂, O⁺ + D₂, and O⁺ + HD, the triatomic nonadiabatic reactions of N + NH and O + N₂, and the tetraatomic and polyatomic adiabatic reactions of H₂ + D₂ and H + CHD₃. © 2015 Wiley Periodicals, Inc.     

Geometric and electronic structures of silicon fluorides (N = 4 – 6) and potential energy surfaces for dissociation reactions → SiF4 + F– and → + F–

The geometric and electronic structures of a series of silicon fluorides (n = 4 ? 6) were computationally studied with the aid of density functional theory (DFT) method with B3LYP and M06‐2X functionals and coupled cluster (CCSD and CCSD(T)) methods with 6‐311++G(d,p) basis set. The nature of the Si‐F bonds in these compounds was analyzed in the framework of the natural bond orbital theory and natural resonance theory. Energy characteristics (heats of reactions and energy barriers) of the dissociation reactions → SiF₄ + F^– and → + F^– were calculated using the DFT and CCSD methods. The potential energy surface of elimination of a fluoride anion from has a specific topology with valley‐ridge inflection points corresponding to bifurcations of the minimal energy reaction path. © 2016 Wiley Periodicals, Inc.     

Theoretical prediction of the optical rotation of chiral molecules in ordered media: A computational study of (Ra)‐1,3‐dimethylallene, (2R)‐2‐methyloxirane,and (2R)‐N‐methyloxaziridine

A theoretical procedure has been developed and implemented to calculate the optical rotation of chiral molecules in ordered phase via origin‐independent diagonal components , of the optical activity tensor and origin‐independent components , for , of the mixed electric dipole‐electric quadrupole polarizability. Origin independence was achieved by referring these tensors to the principal axis system of the electric dipole dynamic polarizability at the same laser frequency ω. The approach has been applied, allowing for alternative quantum mechanical methods based on different gauges, to estimate near Hartree–Fock values for three chiral molecules, (2R)‐N‐methyloxaziridine C₂NOH₅, (2R)‐2‐methyloxirane (also referred to as propylene oxide) C₃OH₆, and ( )‐1,3‐dimethylallene C₅H₈, at two frequencies. The theoretical predictions can be useful for an attempt at measuring correspondent experimental values in crystal phase. © 2015 Wiley Periodicals, Inc.     

Unexpected properties of non‐autoionizing doubly excited states of the H2 molecule

We present accurate calculations of the non‐autoionizing and doubly excited states of the H₂ molecule using full configuration interaction with Hartree–Fock molecular orbitals and Heitler–London atomic orbitals. We consider the united atom configurations from He(2p2p) up to He(2p8g) and dissociation products from H₂(2p + 2p) up to H₂(2p + 6?). Born–Oppenheimer calculations are carried out with extended and optimized Slater‐type orbitals for a total of 40 states, 10 for each symmetry, covering the internuclear distances from the united atom to dissociation, which, for some states, is reached beyond 100 a₀. Occurrences of repulsive states cleanly interlaced between bound states with many vibrational levels are reported. Some of the potential minima are deep enough to accommodate many vibrational levels (up to 50). Noteworthy large equilibrium minima, like R_eq = 46.0 a₀ in the state dissociating as (2p + 6h) and with 18 vibrational levels. The occurrence of vertical excitations from the singly excited manifolds is analyzed. Several states present double minima generated by avoided crossings, some with a strong ionic character. © 2016 Wiley Periodicals, Inc.     

Quantum control of electron‐proton symmetry breaking in dissociative ionization of H2 by intense laser pulses

Forward and backward electron/proton ionization/dissociation spectra from one‐dimensional non‐Born‐Oppenheimer H₂ molecule exposed to ultrashort intense laser pulses ( W/cm², λ = 800 nm) have been computed by numerically solving the time‐dependent Schrödinger equation. The resulting above‐threshold ionization and above‐threshold dissociation spectra exhibit the characteristic forward‐backward asymmetry and sensitivity to the carrier‐envelope phase (CEP), particularly for high energies. A general framework for understanding CEP effects in the asymmetry of dissociative ionization of H₂ has been established. It is found that the symmetry breaking of electron‐proton distribution with π periodic modulation occurs for all CEPs except for ( integer) and the largest asymmetry coming from the CEP of . At least one of the electron and proton distributions is asymmetric when measured simultaneously. Inspection of the nuclear and electron wave packet dynamics provides further information about the relative contribution of the gerade and ungerade states of to the dissociation channel and the time delay of electrons in asymmetric ionization. © 2014 Wiley Periodicals, Inc.     

How Alkali Cations Catalyze Aromatic Diels‐Alder Reactions

We have quantum chemically studied alkali cation‐catalyzed aromatic Diels‐Alder reactions between benzene and acetylene forming barrelene using relativistic, dispersion‐corrected density functional theory. The alkali cation‐catalyzed aromatic Diels‐Alder reactions are accelerated by up to 5 orders of magnitude relative to the uncatalyzed reaction and the reaction barrier increases along the series Li⁺ < Na⁺ < K⁺ < Rb⁺ < Cs⁺ < none. Our detailed activation strain and molecular‐orbital bonding analyses reveal that the alkali cations lower the aromatic Diels‐Alder reaction barrier by reducing the Pauli repulsion between the closed‐shell filled orbitals of the dienophile and the aromatic diene. We argue that such Pauli mechanism behind Lewis‐acid catalysis is a more general phenomenon. Also, our results may be of direct importance for a more complete understanding of the network of competing mechanisms towards the formation of polycyclic aromatic hydrocarbons (PAHs) in an astrochemical context.     

Dealing with the shifted and inverted Tietz–Hua oscillator potential using the J‐matrix method

The tridiagonal J‐matrix approach has been used to calculate the low and moderately high‐lying eigenvalues of the rotating shifted Tietz–Hua (RSTH) oscillator potential. The radial Schrödinger equation is solved efficiently by means of the diagonalization of the full Hamiltonian matrix, with the Laguerre or oscillator basis. Ro–vibrational bound state energies for 11 diatomic systems, namely , , , NO, CO, , , , , , and NO⁺, are calculated with high accuracy. Some of the energy states for molecules are reported here for the first time. The results of the last four molecules have been introduced for the first time using the oscillator basis. Higher accuracy is achieved by calculating the energy corresponding to the poles of the S‐matrix in the complex energy plane using the J‐matrix method. Furthermore, the bound states and the resonance energies for the newly proposed inverted Tietz–Hua IRSTH‐potential are calculated for the H₂‐molecule with scaled depth. A detailed analysis of variation of eigenvalues with n, quantum numbers is made. Results are compared with literature data, wherever possible. © 2015 Wiley Periodicals, Inc.     

The reactivity enhancement in Diels–Alder cycloaddition of 1,3-diene by cation encapsulation to C60: a computational insight

The origin of the experimentally known preference for [6,6] bonds in cycloaddition reactions involving C₆₀ has been computationally explored. To this end, we examined the reactions of 1,3-dienes with fullerene (C₆₀) in the context of an approach to open a large orifice on the fullerene framework by using the activation model of reactivity in combination with the energy analysis method. In this study, the effect of the alkali metal of Li⁺, Na⁺, and K⁺ as an encapsulated element was investigated on the kinetic and thermodynamic behaviors of the Diels–Alder (DA) process. Our calculations indicated that encapsulated Na⁺ and K⁺ cations are located close to the center of the C₆₀ molecule; however, encapsulated Li⁺ is displaced from the center, which leads to a higher reactivity for Li⁺@C₆₀ in DA cycloaddition reaction in the gas phase. Also, benzene as a non-polar solvent affects the DA reactions greater than water as a polar solvent. Different analyses show that solvent changes the catalysis reaction performance, in which a greater efficiency was obtained for K⁺ in the solvent in comparison with other alkali ions because of a facilitated mechanism of electron transfer.