Philicity indices within the spin-polarized density-functional theory framework

The electrophilicity index is analyzed within the framework of spin-polarized density-functional theory. In this context, constrained philicities, omega(N) identical with (mu(N))(2)(2eta(NN)), are introduced in order to define the capability of a system to acquire or donate electrons in a process at constant spin number. The spin-philicity/spin-donicity indices, omega(S)(+/-) identical with (mu(S) (+/-))(2)(2eta(SS)), are examined and rationalized here as the philicity of a given system to change its spin-polarization state, as being defined through the spin potential mu(S) and spin hardness eta(SS) for a process at constant number of electrons. The local extension of these indices has been also outlined and numerical results have been discussed on the analysis of the electrophilic nature of some simple carbene systems both in the singlet and triplet states.     

Spin-polarized conceptual density functional theory study of the regioselectivity in ring closures of radicals

The regioselectivity of ring-forming radical reactions is investigated within the framework of the so-called spin-polarized conceptual density functional theory. Two different types of cyclizations were studied. First, a series of model reactions of alkyl- and acyl-substituted radicals were investigated. Next, attention was focused on the radical cascade cyclizations of N-alkenyl-2-aziridinylmethyl radicals (a three-step mechanism). In both of these reactions, the approaching radical (carbon or nitrogen centered) adds to a carbon-carbon double bond within the same molecule to form a radical ring compound. In this process, the number of electrons is changing from a local point of view (a charge transfer occurs from one part of the molecule to another one) at constant global spin number Ns (both the reactant and the product ring compound are in the doublet state). It is shown that the experimentally observed regioselectivities for these ring-closure steps can be predicted using the spin-polarized Fukui functions for radical attack, f0NN(r).     

Catalytic effect of molecular iodine in Diels–Alder reaction: a density functional theory study

We explore here the feasibility of employing molecular iodine as Lewis acid catalyst for Diels–Alder (DA) reaction using conceptual density functional theory (DFT) based reactivity indices and transition state analysis at the DFT (B3LYP)/6-31G(d) level of theory. Catalytic effect of iodine is probed using reactivity indices considering six different substituents for the diene at the 2-position and five different substituents at the 1-position of the olefinic dienophile. Comparison of HOMO diene–LUMO dienophile gap between the catalyzed and uncatalyzed processes confirms catalytic effect of iodine in DA reaction. Mechanistic details of both the uncatalyzed and the iodine catalyzed processes is achieved through transition state analysis for four possible stereoisomeric reactive channels with respect to isoprene–acrolein model reaction. A significant cutback in activation barrier is observed in presence of iodine. Influence of iodine on regioselectivity of the reaction and asynchronicity of bond formation is analyzed using local version of the HSAB principle and philicity index.     

Electron localizability indicator for correlated wavefunctions. III: singlet and triplet pairs

The electron pair density can be decomposed into the symmetric and antisymmetric parts. The antisymmetric component is connected with the probability that two electrons are coupled to a triplet. On the basis of triplet-coupled electrons the electron localizability indicator is defined, describing the correlation of motion of electrons forming a triplet pair. In case of spin-polarized systems the electron localizability indicator for triplet pairs combines the two spin channels together into a single functional.     

PHOTOCHEMISTRY OF CONJUGATED POLYACETYLENES: [2+2] PHOTOCYCLOADDITION OF l-PHENYL-l,3,5-HEXATRIYNES WITH SOME OLEFINS

Abstract— Irradiation of 1-phenyl-1,3,5-hexatriynes with various olefins in methylene chloride yields [2 + 2] type 1:1 photoadducts. The photoreaction proceeds through a triplet excited state and shows site selectivity and regioselectivity. Olefins with electron-withdrawing substituents, such as dimethyl fumarate, fumaronitrile, acrylonitrile, methyl acrylatc, and styrene, are more reactive than electron-rich olefins, suggesting that the triplet excited states of 1-phenyl-1,3,5-hexatriynes have a nucleophilic radical character.     

Energetics of dioxygen binding into graphene patches with various sizes and shapes

Density functional theory (DFT) calculations were employed to investigate the electronic properties of an H-atom terminated graphene patch (hydrographene) smaller than a rhombic C96H26 structure with zigzag edges. Depending on shapes and sizes of hydrographenes, some hydrographenes have the triplet ground state where unpaired electrons are localized on their zigzag edges. The stability of the triplet spin state is diminished, decreasing the hydrographene sizes. The existence of the localized spin densities allows triplet dioxgen to bind into a hydrographene. According to the DFT calculations, the energetics of the dioxygen bindings is negatively influenced by downsizing hydrographenes, as well as depends on their shapes. The size-and shape-dependences of the dioxygen bindings reflect from the stability of the triplet state of a hydrographene, because its localized unpaired electrons can be utilized to be attached to an unpaired electron of triplet dioxygen.     

Regioselectivity switch achieved in the palladium catalyzed α-arylation of enones by employing the modified Kuwajima-Urabe conditions

A new regioselective approach to the synthesis of α-aryl enones is reported. This represents an important application of the Kuwajima-Urabe protocol toward the synthesis of this simple albeit complex functional array. Several α-aryl enones were synthesized by the palladium catalyzed arylation of triethylsilylenol ethers of enones with high regioselectivity and broad scope, utilizing sterically encumbered electron-rich phosphine ligands to drive the reaction.     

Regio- and sterochemistry of the [2+2]-cycloaddition reaction between enones and alkenes. A DFT study

Calculations at DFT/B3LYP/6-31G+(d,p) level of theory have been performed on the photochemical interaction between enones and alkenes. The photochemical reaction of cyclopentenone with ethyl vinyl ether can be explained assuming the reaction occurs through the triplet excited state of the enone. The interaction between the LSOMO of triplet cyclopentenone and the HOMO of ethyl vinyl ether accounts for the observed stereochemistry. The same behaviour has been observed in the reaction of 3-methylcyclohexenone with 1,1-dimethoxyethene, vinyl acetate, and allene. In the reaction of 3,5,5-trimethylcyclohexenone with methyl cyclobutene-1-carboxylate, the observed regiochemistry can be explained assuming a sensitized reaction able to populate the triplet state of methyl cyclobutene-1-carboxylate. The coupling of the HSOMO of this species with the LUMO of the cyclohexenone derivative account for the observed regiochemistry. Furthermore, the coupling of the radical carbon atoms on the biradical intermediate accounts for the observed stereochemistry. In the reaction of 3-methylcyclohexenone with methyl cyclohexene-1-carboxylate the coupling between the LSOMO of triplet state of 3-methylcyclohexenone and the HOMO of the alkene gave two possible biradical intermediates. The most stable one accounts for the observed regiochemistry. The coupling of the radical carbon atom on the HSOMO and LSOMO of the biradical intermediate accounts for the observed stereochemistry. The coupling between the LSOMO of the triplet state of 3-phenylcyclohexenone and the HOMO of cyclopentene accounts for the observed regiochemistry. The stereochemistry can be explained considering the coupling of the LSOMO and HSOMO in the biradical intermediate.     

Configuration interaction and density functional study of the influence of lithium cation complexation on vertical and adiabatic excitation energies of enones

The changes in the excited state energies of representative cyclic enones (cyclopentenone and cyclohexenone) induced by lithium ion coordination have been examined using ab initio and DFT methods. Quantitative estimates of the vertical triplet state energies were obtained using configuration interaction calculations at the CIS and CIS(D) levels with the 6‐31+G(d) basis. Inclusion of perturbative doubles corrections has a marked effect on the relative energies of the n–π* and π–π* triplet states. At both CI and CIS(D) levels, lithium complexation is predicted to raise the energy of the n–π* triplet state much more than the π–π* triplet. The trends obtained at the CIS(D) level are reproduced using B3LYP/6‐31+G(d) calculations. Adiabatic excitation energies were also computed by carrying out geometry optimization of the triplet states at the B3LYP level. While the separation between the geometry optimized n–π* and π–π* triplet states is very small for the parent enones, the π–π* triplet is clearly favored in the lithium complexes. These results suggest the possibility of reversing the reactive photoexcited state in enones through cation complexation. The conclusions provide a rationale for interesting variations in product distributions observed for enones in cation exchanged zeolites. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1598–1604, 2001     

Theoretical study of the O₂ interaction with a tetrahedral Al₄ cluster

Employing both multireference configuration interaction (MRCI) and density functional theory (DFT) methods, we have studied the interaction of O? with a tetrahedral Al? cluster in the total spin triplet state. For a parallel to the base approach of O? facing an apex of the pyramid, the O? adsorption is hindered by a barrier. Both the MRCI and the DFT calculations show that after a small barrier, there are two local energy minima: a shallow one just above the apex atom and another deeper one below the apex atom. The latter corresponds to dissociative O? adsorption. We discuss the implications of these findings for the understanding of O? adsorption on defect sites of Al surfaces.     

Phenomenological chemical reactivity theory for mobile electrons

We present herein a model to deal with the chemical reactivity, selectivity and site activation concepts of π electron systems derived by merging the classical Coulson–Longuet-Higgins response function theory based on the Hückel molecular orbital (HMO) theory and the conceptual density functional theory. HMO-like expressions for the electronic chemical potential, chemical hardness and softness, including their local counterparts, atomic and bond Fukui functions and non-local response functions are derived. It is shown that sophisticated non-local concepts as site activation may be cast into deeper physical grounds by introducing a simplified version of static response functions. In this way, useful quantities such as self and mutual polarizabilities originally defined through the HMO parameters can be redefined as self and mutual softnesses. The model is illustrated by discussing the classical Hammett free energy relationship describing inductive substituent effects on the reactivity of benzoic acids.     

On the foundations of chemical reactivity theory

In formulating chemical-reactivity theory (CRT) so as to give it a deep foundation in density-functional theory (DFT), Parr, his collaborators, and subsequent workers have introduced reactivity indices as properties of isolated reactants, some of which are in apparent conflict with the underlying DFT. Indices which are first derivatives with respect to electron number are staircase functions of number, making electronegativity equalization problematic. Second derivative indices such as hardness vanish, putting hardness-based principles out of reach. By reformulating CRT within our partition theory, which provides an exact decomposition of a system into its component species, we resolve the conflict. We show that the reactivity of a species depends on its chemical context and define that context. We establish when electronegativity equalization holds and when it fails. We define a generalization of hardness, a hardness matrix containing the self-hardness of the individual species and the mutual hardnesses of the pairs of species of the system, and identify the physical origin of hardness. We introduce a corresponding generalization of the Fukui function as well as of the local and global softnesses and the softness kernel of the earlier formulation. We augment our previous formulation of the partition theory by introducing a model energy function and express the difference between the exact and the model forces on the nuclei in terms of the new reactivity indices. For simplicity, our presentation is limited to time-reversal invariant systems with vanishing spin density; it is straightforward to generalize the theory to finite spin density.     

Time-dependent density-functional theory calculations of triplet-triplet absorption

We present density-functional theory calculations of triplet-triplet absorption by three different approaches based on time-dependent density-functional theory (DFT): unrestricted DFT linear response, open-shell restricted DFT linear response applied to the triplet state, and quadratic response with triplet excitations applied to the ground state. Comparison is also made with corresponding results obtained by Hartree-Fock and multiconfiguration self-consistent-field response theory. Two main conclusions concerning triplet-triplet transitions are drawn in this study: First, the very good agreement between unrestricted and restricted DFT results indicates that spin contamination of the triplet state is not a serious problem when computing triplet-triplet spectra of common organic molecules. Second, DFT response calculations of triplet-triplet transitions can be affected by triplet instability problems, especially for the combination of DFT quadratic response with functionals containing fractional exact Hartree-Fock exchange.     

Halogen‐Bonding Interactions with π Systems: CCSD(T), MP2, and DFT Calculations

Halogen bonding is a noncovalent interaction between a halogen atom and a nucleophilic site. Interactions involving the π electrons of aromatic rings have received, up to now, little attention, despite the large number of systems in which they are present. We report binding energies of the interaction between either NCX or PhX (X=F, Cl, Br, I) and the aromatic benzene system as determined with the coupled cluster with perturbative triple excitations method [CCSD(T)] extrapolated at the complete basis set limit. Results are compared with those obtained by Møller–Plesset perturbation theory to second order (MP2) and density functional theory (DFT) calculations by using some of the most common functionals. Results show the important role of DFT in studying this interaction.