The delocalisation energy of benzene and the non-empirical MO theory

Algebraic expressions for the vertical Delocalisation Energy (DE) of benzene are derived from non-empirical MO theory. For comparison with early work in the π-electron approximation, and ultimately with Hückel theory, the results are formulated in terms of a core resonance integral,β, and π-electronic repulsion integrals. All integral values are inferred from the results ofab initio SCF calculations. Two expressions are derived, which refer to two ways of forming the localised π MOs: one where three pairs of adjacent atomic orbitals are selected from a set of six orthogonalised orbitals; and another where a non-orthogonal set of atomic orbitals is used. The first expression is formally similar to an expression originally derived by Pople from a different point of view and with many approximations. This expression gives too large a magnitude for DE when used with anab initio value ofβ. The second expression gives a result much closer to an empirical value of DE and shows that the main reason for DE being about 50% of 2β rather than 2β is the stabilising effect of overlap in the localised structure, and that the less important factor is the inclusion of electronic repulsion.     

Alternant boron nitride cages: A theoretical study

Heteroatomic cages (B_N/2N_N/2) with borons and nitrogens fully replacing alternant sets of carbons in cages are built graph-theoretically and investigated via the semiempirical MNDO Hamiltonian. The comparison with their parent carbon cages C_N is made in terms both of electronic and of geometric changes. Infinite classes first of octahedral symmetry and second of hexagonal-bipyramidal symmetry fullerenoid cages are considered in detail. The difference in the electronegativities for boron and nitrogen implies the opening of HOMO-LUMO gaps for alternant BN clusters. In general, the borons prefer planar geometry (sp² hybridization) while the nitrogens prefer pyramidalization (sp³ hybridization). © 1997 John Wiley & Sons, Inc.     

Solvatochromic studies on the hydrogen-bond donating and dipolarity/polarizability properties of the polyethylene oxide/silica interface

The polarity of the polyethylene oxide(PEO)/silica interface in 1,2-dichloroethane as solvent is classified by means of linear solvation energy (LSE) relationships . The properties of the bare silica particle surface and the silica/PEO interface is expressed by two terms: the dipolarity/polarizability (π*) of the interface and the hydrogen-bond donating ability (α) of the surface silanols. These terms can be defined by using the Kamlet–Taft solvent parameters α and π* as a reference system. The interfacial polarity parameters α and π* were calculated by means of correlation analyses of the energy of the UV/vis absorption maxima of the surface polarity indicators: di-cyano-bis(1,10-phenanthroline) iron II, bis-4,4′-(N,N-dimethylamino) benzophenone, and 2,6-diphenyl-4-(2,4,6-triphenyl-N-pyridino)phenolate when adsorbed onto the PEO/silica particle surface. The experimental values of the E _T(30) parameter of the PEO/silica interface are compared with independently calculated values employing specific LSE relations derived for well-behaved regular solvents and functionalized silicas. PEO adsorption on silica causes a decrease in the value of the α parameter of the silica surface and an evident increase in the dipolarity/polarizability of the interface. Received: 16 December 1998 Accepted in revised form: 8 January 1999     

Some answers to frequently asked questions about the distortive tendencies of π-electronic system

The paper reviews briefly the various computational strategies, which have been devised by different groups to probe the symmetrizing vs distortive propensities of the π-bonding species of polyenes. All methods point to the same conclusion that the π-bonding components of benzene, allyl, aromatic annulenes and related species have intrinsic distortive tendencies; these species maintain bond-equalized geometries due to the symmetrizing driving force of the corresponding σ frames. Some frequently asked questions, that deal with the compatibility of the π-distortivity scenario with the greater body of experimental data regarding aromatic stability and π-delocalization, are addressed. Many of these questions are immediately answered, once the notion is accepted that delocalized π-systems possess a duality: their π-component is distortive and at the same time resonance stabilized relative to the localized structure with the same geometry. The notion of distortive π-electronic components of polyenes is shown to find a natural place in the wider context of a unified model of electronic delocalization that is valid for both conjugated π- and σ-electronic systems.     

Syntheses,structures, and properties of two mononuclear cobalt(III) azido complexes containing a tetradentate N-donor Schiff base as end-capping ligand

Two hexacoordinated mononuclear Co(III) compounds of the type cis-[Co(L)(N₃)₂] X [1, X = ClO₄; 2, X = PF₆; L = N,N′-(bis(pyridine-2-yl)benzylidine)-1,4-butanediamine] have been synthesized and characterized by physicochemical and spectroscopic methods. The crystal structures of complexes 1 and 2 both have distorted octahedral geometry with two terminal azides in mutual cis orientations. In the crystalline state, two mononuclear units of 1 are associated by weak C–H…π interactions to produce a dimeric unit, which packs through C–H…O hydrogen bonds and π…π interactions leading to a 2-D continuum. The mononuclear units in 2 are engaged in weak cooperative intermolecular C–H…π interactions and multiple C–H…F hydrogen bonds giving rise to a 3-D network structure. These diamagnetic compounds are redox active and show luminescence in DMF solutions.     

Preparation and nonlinear optical properties of two acrylate polymers bearing different long conjugated pendants

Two new acrylate monomers containing different long π-election conjugation bridge structure, 4′-[(N,N-diethylacrylate) amino], 4-(pyridine-4-vinyl) stilbene (DAS) and 4′-[(N,N-diethylacrylate) amino], 4-(pyridine-4-vinyl) azobenzene (DAA), were synthesized and their copolymers with methyl methacrylate (MMA) were prepared by free radical polymerization method. Their structures and properties of these copolymers were characterized and evaluated by FTIR, ¹H-NMR, UV spectra, GPC and Z-scan technique with 8 ns pulses at 532 nm wavelength. The relationship between their structures and properties was investigated. The results show that the structure of these resultant copolymers can be effectively tuned by simply varying the feed ratio and these copolymers exhibit good solubility and large third-order nonlinear optical properties. The large third-order nonlinear optical properties are mainly attributed to the substituted NLO-chromophore with long D-π-A conjugated structure. Simultaneously, it is found that poly (DAA-co-MMA) with N=N double bond as conjugation bridge has larger third-order nonlinear optical susceptibility than poly (DAS-co-MMA) with C=C double bond as conjugation bridge owing to more effective π electron conjugation effect.     

Molecular structures and reactivities of 1,3-diphthalimidobenzene derivatives

X-ray diffraction analysis of 4,6-di(morpholin-4-yl) and 4,6-di(2,2,2-trifluoroethoxy) derivatives of 1,3-diphthalimidobenzene, which are potent reagents in the synthesis of heterocyclic polymers, was carried out. The conjugation between the π-systems of the benzene ring and of the phthalimide and morpholine substituents is distorted due to the rotation of the substituents about the C(Ar)−N bonds. The AMI calculations demonstrated that the hydrogen atoms of the methylene groups are “acidic”, which is favorable for condensation reactions. Steric hindrances to intramolecular condensation were estimated. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1155–1161, June, 1998.     

Approximate symmetry-breaking in the independent particle model of monocyclic completely conjugated polyenes

We examine the singlet stability of symmetry adapted, restricted Hartree-Fock (RHF) solutions and the implied symmetry breaking for various planar, π-electron systems with conjugated double bonds as described by the semiempirical Pariser-Parr-Pople Hamiltonian. In particular, we explore the energy and charge- density waves (CDWs) in various real and hypothetical structures that result by a systematic deformation of the nuclear framework: we start with a highly symmetric cyclic polyene C _N H _N having a nondegenerate ground state (N = 2n = 4ν + 2, ν = 1, 2,...), whose sites form a regular N-gon (D _Nh point group), and proceed to structures with lower symmetry (D _6h , D _3h , D _2h point groups), or with only the planar symmetry of the conjugated π-electron system (C _1h ). The objective of this study is to explore the phenomenon that could be referred to as a breaking of an approximate symmetry or an implied symmetry breaking.     

Palladium(II) complexes with 1-allyl-3-(2-pyridyl)thiourea: Synthesis and spectroscopic characterization

New Pd(II) complexes with 1-allyl-3-(2-pyridyl)thiourea (APTU) of the formulas [Pd(C₉H₁₁N₃S)Cl₂] (I) and [Pd(C₉H₁₁N₃S)₂]Cl₂ (II) were obtained and examined by UV-Vis, IR, and 1H NMR spectroscopy. The conditions for the complexation reactions were optimized. The instability constants and molar absorption coefficients of these complexes were calculated. Comparison of the characteristic bands in the UV-Vis and IR spectra of the complexes and free APTU revealed that the ligand in both complexes is coordinated to the metal atom in the thione form in the bidentate chelating mode through the S atom of the thiourea group and the pyridine N atom. In the UV-Vis spectra of the complexes, the charge transfer bands (π → π* Py) and n → π* (C=N_Py), (C=S) experience hypsochromic shifts by 450–470 cm⁻¹ caused by the coordination of APTU to the metal ion, which gives rise to ligand-metal charge-transfer bands (C=N_Py → Pd, n → π* (C=S)) and (SPd). The protons in the 6-, 4-, and 3-positions of the pyridine ring and the thiourea NH proton in the chelate ring are most sensitive to the complexation.     

Atomic ionization potentials and electron affinities with relativistic and mass corrections

Relativistic corrections to ionization potentials (IPs) and electron affinities (EAs) of atoms with an atomic number Z≤54 are examined based on the first-order perturbation theory with an approximate Schr?dinger form of the Dirac-Coulomb-Breit Hamiltonian. Using a Hartree-Fock (HF) wave function from the numerical HF method as the unperturbed function, both the LS-non-splitting and fine-structure corrections are evaluated together with the normal and specific mass corrections. The LS-non-splitting corrections are found to be important for IPs and EAs of transition metal atoms. The fine-structure corrections are generally larger in magnitude than the LS-non-splitting corrections for the atoms of groups 13–18 with Z≥31, and can never be neglected. Comparison of the IPs and EAs presented here and experimental IPs and EAs gives an estimation of the electron correlation correction for these properties. For some light atoms, the estimated values agree with the results directly obtained from correlated calculations. Received: 28 January 1997 / Accepted: 4 March 1997     

The calculation of electron localization and delocalization indices at the Hartree–Fock, density functional and post-Hartree–Fock levels of theory

 Localization, λ(A), and delocalization indices, δ(A,B), as defined in the atoms in molecules theory, are a convenient tool for the analysis of molecular electronic structure from an electron-pair perspective. These indices can be calculated at any level of theory, provided that first- and second-order electron densities are available. In particular, calculations at the Hartree–Fock (HF) and configuration interaction (CI) levels have been previously reported for many molecules. However, λ(A) and δ(A,B) cannot be calculated exactly in the framework of Kohn–Sham (KS) density functional theory (DFT), where the electron-pair density is not defined. As a practical workaround, one can derive a HF-like electron-pair density from the KS orbitals and calculate approximate localization and delocalization indices at the DFT level. Recently, several calculations using this approach have been reported. Here we present HF, CI and approximate DFT calculations of λ(A) and δ(A,B) values for a number of molecules. Furthermore, we also perform approximate CI calculations using the HF formalism to obtain the electron-pair density. In general, the approximate DFT and CI results are closer to the HF results than to the CI ones. Indeed, the approximate calculations take into account Coulomb electron correlation effects on the first-order electron density but not on the electron-pair density. In summary, approximate DFT and CI localization and delocalization indices are easy to calculate and can be useful in the analysis of molecular electronic structure; however, one should take into account that this approximation increases systematically the delocalization between covalently bonded atoms, with respect to the exact CI results. Received: 13 February 2002 / Accepted: 24 April 2002 / Published online: 18 June 2002     

Molecular structure and Bader's theory

 It is shown that a supposed catastrophe of Bader's theory of atoms in molecules, suggested by Cassam-chena? and Jayatilaka [Theor Chem Acc (2001) 105: 213] is merely a consequence of the approximate character of the adiabatic Born–Oppenheimer theory of molecular structure, and that nonadiabatic approaches could be in accordance with Bader's ideas. Received: 4 April 2001 / Accepted: 5 September 2001 / Published online: 3 June 2002     

Dispersion interaction of conjugated molecules: One- and many-electron models

A scheme for calculating van der Waals constants C₆, C₈, and C₁₀ in terms of the full configuration interaction for π-shells is suggested. The required imaginary frequency dynamic polarizabilities are also investigated with one-electron schemes. The variational perturbation theory of the Hartree-Fock method considerably exaggerates the constant C_2l the conjugated variant of perturbation theory is preferable. The additive scheme for estimating the Σ-contribution allows one to calculate the energy of dispersion attraction in real conjugated systems, as demonstrated by semiempirical estimates of evaporation heat in butadiene, benzene, naphthalene, and phenylacetylene. Translated fromZhurnal Strukturnoi Khimii, Vol. 38, No. 6, pp. 1029–1037, November–December, 1997. Original article submitted December 14, 1996.     

Study of correlation holes. I. Number–sum rules and infinite system

The correlation holes in a finite system of any size are known to satisfy integral number–sum rules directly related to the N-representability of the reduced density matrices. In regard to infinite systems, the same rules are known to be satisfied in the electron gas. It is shown that the number–sum rules are not generally satisfied in any infinite system, and that this happens independently of the kind of boundary conditions assumed in the N → ∞ limit. A violation is explicitly found within the alternant molecular orbital formalism. The apparent paradox is explained in terms of surface effects (end effects in a linear system), which are present in a large, but finite system. In other words the N-representability does not imply the number–sum rules. In the N → ∞ limit the rules are satisfied only in physical systems having short-range correlation.     

Spectrum of states in icosahedral structures of the electronic configuration gn (N = 1–7). 1. Invariant expansion for integrals and energies

The energy spectrum of the states that appear in structures of icosahedral (I,I_h symmetry with open electronic shells g^N (dim g = 4; N = 1–7) is reported. The energies are obtained in terms of integral invariants (reduced matrix elements of electron-electron interaction) H^k (g, g). The latter are analogs of the Slater-Condon parameters F^k(l,l) for atoms with the l^N electronic configuration. A similar representation is proposed for the integrals mm’≨’) of electron-electron interaction on the 4-fold degenerate g orbitals in the “standard” representation. The relation between the terms of the g^N(I,I_h) configuration and the parent states of the orthogonal group O⁺(4) is discussed. Translated fromZhurnal Strukturnoi Khimii, Vol. 38, No. 1, pp. 3–13, January–February, 1997.     

Syntheses,structures, and properties of two binuclear cadmium(II) iodides containing a bis(tridentate) Schiff base/tetradentate tripodal amine: control of coordination numbers by varying ligand matrices

Two binuclear cadmium(II) iodide compounds of the types [Cd₂(L1)(I)₄] (1) and [(L2)Cd(μ-I)CdI₃] (2) [L1 = N,N′-(bis(pyridine-2-yl)formylidene)triethylenetetramine and L2 = tris(2-aminoethyl)amine] are synthesized and characterized. X-ray structural study shows that each cadmium(II) in 1 has a distorted square pyramidal geometry with a CdN₃I₂ chromophore and that L1 behaves as a binucleating bis(tridentate) ligand bridging the metal centers with iodides remaining as terminals. In 2, one cadmium(II) adopts a distorted tetrahedral geometry with a CdI₄ chromophore surrounded by four iodides, while the other has a distorted trigonal bipyramidal environment with CdN₄I chromophore bound by four N atoms of L2 and one bridging iodide. Weak C–H···π interactions in 1 result in an infinite 1D chain; however, such weak non-covalent interactions are absent in 2. The Schiff base complex, 1, shows high-energy intraligand ¹(π–π*) fluorescence in DMF solution at room temperature, whereas compound 2 containing tripodal amine is fluorescent-inactive.     

Is tetramethyleneethane a ground state triplet?

We have examined a number of possible ways by which tetramethyleneethane (TME) can be a ground state triplet, as claimed by experimental studies, in violation of Ovchinnikov’s theorem for alternant hydrocarbons of equal bond lengths. Model exact π calculations of the low-lying states of TME, 3,4-dimethylenefuran and 3,4-dimethylenepyrrole were carried out using a diagrammatic valence bond approach. The calculations failed to yield a triplet ground state even after (a) tuning of electron correlation, (b) breaking alternancy symmetry, and (c) allowing for geometric distortions. In contrast to earlier studies of fine structure constants in other conjugated systems, the computedD andE values of all the low-lying triplet states of TME for various geometries are at least an order of magnitude different from the experimentally reported values. Incorporation of σ-π mixing by means of UHF MNDO calculations is found to favour a singlet ground state even further. A reinterpretation of the experimental results of TME is therefore suggested to resolve the conflict.     

Sum frequency generation spectroscopic study of the condensation effect of cholesterol on a lipid monolayer

Sum frequency generation (SFG) spectra and surface pressure–molecular area (π–A) isotherms have been obtained for mixed cholesterol–DPPC monolayers with cholesterol mole fractions, x(chol.), from 0 to 1.0, at the air–water interface, under same conditions, at 22 °C. Analysis of the spectra indicated that incorporation of cholesterol into the monolayers at 3 mN m⁻¹ greatly increases the conformational and orientational order of the alkyl chains of DPPC, maximizing these properties at x(chol.)=0.4. Analysis also indicated that order in the mixed monolayers at 15 and 35 mN m⁻¹ is not affected by incorporation of cholesterol. The π–A isotherms measured at 3 mN m⁻¹ for the mixed monolayer with x(chol.)=0.4 have the largest negative deviation of the molecular area relative to those of ideal mixtures (the so-called “condensation effect” of cholesterol), indicating the most thermodynamically stable state. Comparison of results from SFG spectra and π–A isotherms explicitly proved that the condensation effect can be interpreted in terms of conformational and orientational ordering of the alkyl chains of DPPC.     

Spin-projected coupled-cluster theory with single and double excitations

Coupled-cluster (CC) theory including single (S) and double (D) excitations and carried out with a spin-unrestricted Hartree–Fock (UHF) reference wave function is free from S + 1 spin contamination as can be confirmed by an analysis of the expectation value of the spin operator, Ŝ ². Contamination by the S + 2 contaminant can be projected out by an approximate procedure (APCCSD) with a projection operator, P^, represented by the product of the spin annihilation operators ? _{s+ 1} and ?_s+2. The computational cost of such a projection scales with O(M ⁶) (M is the number of basis functions). The APCCSD energy obtained after annihilation of the S + 2 contaminant can be improved by adding triple (T) excitations in a perturbative way, thus leading to APCCSD(T) energies. For the 17 examples studied, the deviation of the UHF-CCSD(T) energies from the corresponding full configuaration interaction values is reduced from 4.0 to 2.3 mhartree on the average as a result of annihilating the S + 2 contaminant in an approximate way. In the case of single-bond cleavage, APCSSD leads to a significant improvement of the energy in the region where the bonding electrons recouple from a closed shell to an open shell singlet electron pair. Received: 13 April 2000 / Accepted: 12 July 2000 / Published online: 24 October 2000     

Molecular and electronic structures and conformational analysis of derivatives of 9-nitroanthracene, anionic σ-complexes

Potassium 10-methoxy-9-nitroanthracenide was studied by X-ray diffraction analysis. The central ring of the anthracene fragment adopts an asymmetrically flattened boat conformation. The bond lengths in the C(Ar)−C(NO₂)−C(Ar) fragment are indicative of the presence of conjugation between the π-systems of the benzene rings and the nitro group owing to a substantial contribution of theaci form to the structure of the nitro group. Quantum-chemical calculations of anionic σ-complexes of 9-nitroanthracene derivatives were performed. In all cases, the central ring adopts two conformations with the pseudoaxial and pseudoequatorial orientations of the substituents at the saturated C(10) atom, respectively. The relative stability of the conformers and the factors determining the stability were considered. The minima on the potential energy surface have a flattened shape in spite of relatively high barriers to the conformational transition (2–4 kcal mol⁻¹). The deviation of the C(Ar)−C(Ar)−C(sp³)−C(Ar) torsion angle from the equilibrium value by ±20° causes an increase in the energy of the anion by less than 1 kcal mol⁻¹. The effect of the substituents on the charge distribution was considered. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 438–443, March, 1998.