On the limits of highest-occupied molecular orbital driven reactions: the frontier effective-for-reaction molecular orbital concept

We carried out Hartree-Fock (HF) and density functional theory calculations for 61 compounds, the conjugated bases of carboxylic acids, phenols, and alcohols, and analyzed their acid-base behavior using molecular orbital (MO) energies and their dependence on solvent effects. Despite the well-known correlation between highest-occupied MO (HOMO) energies and pKa, we observed that HOMO energies are inadequate to describe the acid-base behavior of these compounds. Therefore, we established a criterion to identify the best frontier MO for describing pKa values and also to understand why the HOMO approach fails. The MO that fits our criterion provided very good correlations with pKa values, much better than those obtained by HOMO energies. Since they are the frontier molecular orbitals that drive the acid-base reactions in each compound, they were called frontier effective-for-reaction MOs, or FERMOs. By use of the FERMO concept, the reactions that are HOMO driven, and those that are not, can be better explained, independently from the calculation method used, as both HF and Kohn-Sham methodologies lead to the same FERMO.     

Mechanism of the forbidden [3s,5s]-sigmatropic shift: orbital symmetry influences stepwise mechanisms involving diradical intermediates

The mechanisms of [3s,5s]-sigmatropic shifts of octa-1,3,7-triene and 7-methylenenona-1,3,8-triene have been elaborated using B3LYP and BPW91 density functional theory and CASPT2 methods. These orbital symmetry forbidden rearrangements are stepwise, involving diradical intermediates. A comparison with several [3,3]-sigmatropic shifts of substituted hexadienes and of [5,5]-sigmatropic shifts that are allowed, but nevertheless follow stepwise paths, shows that the activation barrier for the disallowed [3,5] shift is significantly larger than that for the stepwise reactions that are orbital symmetry allowed. Cyclic diradicals that have an aromatic circuit of electrons including the two radical centers and conjugated pi or sigma bonds are stabilized as compared to cyclic diradicals with an antiaromatic circuit of electrons. This applies to the transition states leading to and from the diradicals and influences the activation energies of stepwise sigmatropic shifts. The magnitudes of these effects are small but will have a significant influence on the rates of competing processes. This series of calculations has been used to assess the relative capabilities of the two functionals. We find that BPW91 underestimates the endothermicity of diradical formation and the barrier to diradical formation whereas B3LYP overestimates these quantities.     

A cornucopia of cycloadducts: theoretical predictions of the mechanisms and products of the reactions of cyclopentadiene with cycloheptatriene

The potential cycloaddition reactions between cyclopentadiene and cycloheptatriene have been explored theoretically. B3LYP/6-31G was used to locate the transition states, intermediates, and products for concerted pathways and stepwise pathways passing through diradical intermediates. Interconversions of various cycloadducts through sigmatropic shifts were also explored. CASPT2/6-31G single point calculations were employed to obtain independent activation energy estimates. MM3 was also used to compute reaction energetics. Several bispericyclic cycloadditions in which two cycloadducts are linked by a sigmatropic shift have been identified. B3LYP predicts, in line with frontier molecular orbital predictions, that the [6+4] cycloaddition is the favored concerted pathway, but an alternative [4+2] pathway is very close in energy. By contrast, CASPT2 predicts that a [4+2] cycloaddition is the preferred pathway. B3LYP predicts that the lowest energy path to many of the cycloadducts will involve diradical intermediates, whereas CASPT2 predicts that each of the products of orbital symmetry allowed reactions will be reached most readily by closed shell processes-concerted cycloadditions and sigmatropic shift rearrangements of cycloadducts.     

Molecular orbital study of anthracene photo-oxidation

The light stimulated interaction of anthracene and oxygen was studied by the MO (molecular orbital) method. Using the principle of orbital symmetry conservation, the interactions anthracene-oxygen in the ground and first excited states and in various geometric arrangements were classified as symmetry allowed or forbidden. The results indicate that the photo-oxidation of anthracene is catalysed by transition metals.     

Reactivity of molecular oxygen on the surface of ionic crystals

A possibility of multiplicity change for ground‐state molecular oxygen adsorbed on the surface of regular and doped broad‐gap ionic crystals was considered in the framework of cluster approximation by using SCF MO LCAO quantum chemical methods [semiempirical INDO approximation and ab initio calculation with the 6‐311G** basis set taking into account the correlation effects on the level of second‐order Meller–Plesset perturbation theory (MP2)]. The formation energetics of cyclic products of addition reactions of dioxygen in different multiplet states to furan and cis‐butadiene in the gas phase and on the surface of ionic crystals was considered. (These reactions are typical for the O₂ singlet state in the gas phase.) It is shown that the presence of sites with high effective charge on the crystal surface can result in a situation not requiring, as in the gas phase, multiplicity change in the transition of a system from an initial to the final state, which can significantly affect the kinetic parameters of the reactions. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Ab initio molecular orbital calculations on the transition state for the addition of a methyl radical to vinyl monomers

Ab initio molecular orbital calculations have been performed on the transition state for the addition of methyl radical to twelve vinyl monomers using the SV 3–21G basis set. A linear relationship has been found between the calculated energies of activation and previously calculated energies of reaction. This supports the assumption of an Evans-Polanyi type rule in previous work which attempted to correlate reactivity with calculated energies of reaction. The activation energies obtained for methyl addition to butadiene and styrene were calculated to be negative. This is caused by errors introduced by a number of sources, viz. basis set superposition error, spin contamination and zero point energy. These errors are discussed. Previous authors have reported reasonable agreement between calculated activation energies at SV3–21G and experimental values for methyl addition to ethylene, this work suggests that this agreement was coincidental and results from the fortuitous cancellation of errors. The nature of the transition state for these radical addition reactions is discussed and the limitations of the SV3–21G basis set are highlighted. The theoretical prediction of activation energies for radical addition reactions would require much larger calculations, beyond the computational means of most research laboratories.     

Molecular orbital electronegativity

The molecular orbital electronegativities of a representative set of free radicals of Be, BC, N and O have been calculated for the first time using the transition operator method within the semi-empirical CNDO LCAO MO theory. The significance of the effect of delocalization on electronegativity is discussed.     

Theoretical studies on the ene reaction mechanisms of propene and cyclopropene with ethylene and cyclopropene: concerted or stepwise

The potential energy surfaces of the ene reactions of propene and cyclopropene with ethylene and cyclopropene were studied by ab initio molecular orbital (MO) methods. The reaction mechanisms were analyzed by CiLC method on the basis of CASSCF MOs. The concerted and stepwise reaction pathways of the ene reaction of propene with ethylene as the parent reaction were located. The energy barrier of the stepwise process is about 4 kcal/mol lower than that of the concerted one. The other reactions can be found only the stepwise mechanism. Although the endo-type reaction of propene with cyclopropene, where cyclopropene is the enophile, probably occurs through a one-step process, the mechanism is divided into the CC bond formations and the hydrogen migration as a stepwise reaction. The CiLC-IRC analysis of the concerted process of propene with ethylene shows the different patterns of the electronic state variation for the CC bond formation/breaking and the hydrogen migration.     

[2+2]环加成反应机理的理论研究

[2+2]环加成反应是有机化学中非常重要的一类反应,其机理的研究一直是实验和理论工作者关注的课题之一。本文从理论的角度综述了三类[2+2]环加成反应的反应机理,即简单烯烃或炔烃参与的环加成反应、累积双键体系参与的环加成反应以及稀土钍化合物参与的环加成反应, 得出对于简单的烯烃或炔烃之间的环加成反应一般是按双自由基机理进行,而其他两类反应主要按协同或两性离子方式进行,并且从前线分子轨道作用理论角度分析了产生不同反应机理的原因。     

The electronic structure and conformation of dimethylaminobenzonitrile

Ab initio molecular orbital (MO) computations on the closed shell singlet ground state ofN, N-dimethylaminobenzonitrile (DMABN) are reported. Fully optimized structures of several conformers of DMABN were calculated at the HF/6-31G level of theory. Our results indicate that for each of these conformations the minimum energy structure has a trigonal (sp² hybridized] amino nitrogen. The most stable DMABN conformer was found to be planar with its methyl groups eclipsed. The Koopmans ionization potentials and dipole moments of the various ground state conformers are compared. The implications for dynamical models of twisted-intramolecular charge transfer (TICT) are discussed. Moreover, the use of qualitative MO theory arguments provides an interpretation of the computational results in a simple orbital interaction framework.A. Mellon Foundation Fellow (1989–1992).Operated for the U.S. Department of Energy by Battelle Memorial Institute under Contract DE-AC06-76RLO 1830.     

Second hyperpolarizability (gamma) of singlet diradical system: dependence of gamma on the diradical character

The dependence of the second hyperpolarizability (gamma) on the diradical character (y) for singlet diradical systems is investigated using a model compound, the p-quinodimethane (PQM) molecule with different both-end carbon-carbon (C-C) bond lengths, by several ab initio molecular orbital and density functional theory methods. The diradical character based on UHF calculations indicates that at equilibrium geometry PQM is in a singlet ground state and primarily exhibits a quinoid structure, whereas the diradical character increases when increasing both-end C-C bond lengths. At the highest level of approximation, that is, using the UCCSD(T) method with the 6-31G+diffuse p (zeta = 0.0523) basis set, the longitudinal static gamma of PQM presents a maximum value for intermediate diradical character (y approximately 0.5) while the gamma values are larger for intermediate and large diradical character (y approximately 0.5-0.7) than for small diradical character (y < 0.2). This feature suggests that the gamma values of singlet diradical systems in the intermediate and somewhat strong correlation regimes are significantly enhanced as compared to those in the weak correlation regime. These results are substantiated by a complementary study of the variation in gamma upon twisted ethylene.     

Competition between diradical stepwise and concerted mechanisms in chalcogeno-Diels-Alder reactions: a density functional study

The chalcogeno-Diels-Alder reactions of H(2)C=X (X = S, Se, Te) with butadiene, with trans,trans- and cis,trans-2,4-hexadiene, as well as of ethylene with thio-, seleno-, and telluroacrolein and reactions of thioformaldehyde with thioacrolein are examined theoretically. The B3LYP exchange-correlation functional with the 6-31G(d) and LanL2DZ(d) basis sets is employed. Stepwise diradical and concerted pathways are considered for all reactants. A modified concerted mechanism via a pre-reaction complex followed by a concerted transition state is studied for thioformaldehyde reacting with thioacrolein. The stepwise diradical pathways are predicted to be energetically less favorable than the concerted pathways for all cases considered. Even the sterically hindered reaction between selenoformaldehyde and cis,trans-2,4-hexadiene prefers a concerted path. It is a considerable challenge to reverse this energy preference for the concerted reaction given that both electronic and steric factors act to increase or decrease the activation energies of the concerted and diradical stepwise paths in the same way. A modified concerted mechanism operates for reagents with very small HOMO-LUMO gaps such as thioformaldehyde and thioacrolein. This mechanism is completely synchronous, with a vanishingly small barrier.     

The Nature of Chemical Bonds from PNOF5 Calculations

Natural orbital functional theory (NOFT) is used for the first time in the analysis of different types of chemical bonds. Concretely, the Piris natural orbital functional PNOF5 is used. It provides a localization scheme that yields an orbital picture which agrees very well with the empirical valence shell electron pair repulsion theory (VSEPR) and Bent’s rule, as well as with other theoretical pictures provided by valence bond (VB) or linear combination of atomic orbitals–molecular orbital (LCAO‐MO) methods. In this context, PNOF5 provides a novel tool for chemical bond analysis. In this work, PNOF5 is applied to selected molecules that have ionic, polar covalent, covalent, multiple (σ and π), 3c–2e, and 3c–4e bonds.     

Study of the electronic structure of molecules. XV. Comments on the molecular orbital valency state and on the molecular orbital energies

The valency state (vs) concept is analyzed in the Hartree–Fock approximation. A valency state “standard” is defined for atoms at infinite separation. A molecular orbital valency state (Movs) is defined from a partitioning technique (bond energy analysis) previously introduced for the Hartree–Fock molecular wave functions. The Movs for a given atom in a molecule is much higher in energy than the vs and its energy varies from molecule to molecule depending on the exact field of the surrounding atoms. The examples selected in the discussion are the CH₄ CH₃F, CH₂F₂, CHF₃ and CF₄ molecules. An analysis of the orbital energies is then given in terms of the bond energy. The importance of the rearrangement effects following ionization of inner shell electrons (simulation of ESCA type experiments) is illustrated with computations of the positive ion for methane and its fluoroderivatives. It is concluded that rearrangement following ionization from inner shells is as important as rearrangements following ionization from valency electrons. A direct consequence is that the orbital energies should not be equated to the inner shell ionization potentials. The computation of such ionization potentials agrees to about 99.5% with ESCA data, when the energy of both the neutral and ionic species are computed; the use of the orbital energies limits this agreement to about 95%.     

The 1deltag dioxygen ene reaction with propene: a density functional and multireference perturbation theory mechanistic study

This study aims to determine whether a balance between concerted and non-concerted pathways exists, and in particular to ascertain the possible role of diradical/zwitterion or peroxirane intermediates. Three non-concerted pathways, via 1) diradical or 2) peroxirane intermediates, and 3) by means of hydrogen-abstraction/radical recoupling, plus one concerted pathway (4), are explored. The intermediates and transition structures (TS) are optimized at the DFT(MPW1K), DFT(B3LYP) and CASSCF levels of theory. The latter optimizations are followed by multireference perturbative CASPT2 energy calculations. (1) The polar diradical forms from the separate reactants by surmounting a barrier (deltaE(++)(MPW1K)=12, deltaE++(B3LYP)=14, and deltaE(++)(CASPT2)=16 kcal mol(-1) and can back-dissociate through the same TS, with barriers of 11 (MPW1K) and 8 kcal mol(-1) (B3LYP and CASPT2). The diradical to hydroperoxide transformation is easy at all levels (deltaE(++)(MPW1K)<4, deltaE(++)(B3LYP)=1 and deltaE(++)(CASPT2)=1 kcal mol(-1)). (2) Peroxirane is attainable only by passing through the diradical intermediate, and not directly, due to the nature of the critical points involved. It is located higher in energy than the diradical by 12 kcal mol(-1), at all theory levels. The energy barrier for the diradical to cis-peroxirane transformation (deltaE(++)=14-16 kcal mol(-1)) is much higher than that for the diradical transformation to the hydroperoxide. In addition, peroxirane can very easily back-transform to the diradical (deltaE(++)<3 kcal mol(-1)). Not only the energetics, but also the qualitative features of the energy hypersurface, prevent a pathway connecting the peroxirane to the hydroperoxide at all levels of theory. (3) The last two-step pathway (hydrogen-abstraction by (1)O(2), followed by HOO-allyl radical coupling) is not competitive with the diradical mechanism. (4) A concerted pathway is carefully investigated, and deemed an artifact of restricted DFT calculations. Finally, the possible ene/[pi2+pi2] competition is discussed.     

Adsorption affinity of certain biomolecules onto polymeric resins: Interpretation from molecular orbital theory

Molecular interactions have been studied for adsorption of certain biomolecules in aqueous solutions using two different types of polymeric resins as adsorbents. Molecular modeling study is based on molecular orbital theory. Adsorption affinity expresses as the slope of the linear region of the isotherm for a solute is found to be different for different adsorbents, and this difference can be interpreted from the differences in sorbent surface chemistry and morphological structure. The adsorptive interaction on the polymeric resins computed on the basis of frontier orbital theory seems to correlate well with the experimentally measured adsorption affinity. Electronic states of adsorbent and adsorbate were calculated using the semiempirical molecular orbital (MO) method from which energy of adsorption in aqueous solution was estimated. It was found that charge transfer interaction plays an important role in the adsorption of certain biomolecules on aqueous solution. The experimentally measured enthalpy of adsorption seems to correlate well with the adsorptive interaction energy computed from molecular orbital theory.     

Theoretical Studies on the Mechanism of Photocycloaddition Reaction Between 6 Azauracil and Acetone

The mechanism of photocycloaddition reaction between 6-azauracll and acetone was studied by using semiemptrical SCFMO AMI method. It was found that this reaction is not a concerted one. The calculated results are as follows:(1) A T1 state exciplex is on the T1 state energy surface; (2) T exciplex as a reactant will proceed along the energy surface of T1 state to form a diradical intermediate. The energy barrier of this reaction step is 63. 6 kJ/mol; (3) The T1 state diradical intermediate happens to be close in energy to the ground state intermediate with a similar geometry. Such a situation turns out to be very favorable for an intersystem crossing (jump from the T, state to the ground state) ; (4) The final product will be formed from the ground S0 state intermediate via an energy barrier 88. 2 kJ/mol.     

Molecular orbital study of molecular nitrogen fixation

The model systems of molecular nitrogen fixation [N₂ + H]?, [N₂ + H]⁺, [N₂ + H]^?, [N₂ + H₂], [N₂ + H₂]⁺, and [N₂ + H₂]^? were studied by the semiempirical INDO method. The study was based on the formal analogy between the catalytic reactions and the photochemical, radical, and ionic reactions on the other side. Symmetrical and donor-acceptor properties of necessary catalytic systems were proposed using the dependence of energy characteristics and electron structure on reaction coordinate. On the basis of this MO study we have proposed the appropriate symmetry types of catalysts for each of acceptable models of nitrogen fixation. For one of the proposed systems there was realised a model MO computation with explicit inclusion of atoms of transition metals (Fe, V).     

The chemistry of localized singlet 1,3-diradicals (biradicals): from putative intermediates to persistent species and unusual molecules with a π-single bonded character

Localized singlet diradicals (biradicals) are key intermediates in chemical reactions involving homolytic bond-cleavage and formation processes. The molecular structure and electronic structure had been historically elusive due to the short-lived character of the reactive intermediates. In the last 15 years, a significant development of singlet diradical chemistry was achieved after the pioneering findings of long-lived singlet diradicals. In this tutorial review, the recent development of localized singlet diradical chemistry is summarized and discussed. The following subjects are included (a) the mechanism by which the ground state spin-multiplicity of localized 1,3-diradicals is controlled; (b) the substituent and heteroatom effect on the most stable electronic configuration of the singlet 1,3-diradicals, type-1 versus type-2; (c) the molecular design for the long-lived singlet ground state diradicals; (d) the generation and characterization of the singlet diradicals; and (e) the future prospects.