Radial limit of lithium revisited

Configuration interaction (CI) calculations are carried out for the ground state of lithium using a thoroughly optimized basis set of s-type Slater functions. They establish that the radial limit of the nonrelativistic energy of the ground ²S state of lithium is no higher than −7.448666443E_h. Thus, radial correlation accounts for 35.2% of the total correlation energy. The radial CI wave function predicts a significantly more accurate Fermi contact parameter than the Hartree-Fock wave function. However, the imbalanced treatment of electron correlation in the radial CI wave function leads to an excessively diffuse electron density that is worse than that of the Hartree-Fock wave function. © 1997 John Wiley & Sons, Inc.     

Orbital functional theory of linear response and excitation

Orbital functional theory (OFT) is based on a rule that determines a single‐determinant reference state Φ for any exact N‐electron eigenstate Ψ. An OFT model postulates an explicit correlation energy functional E_c of occupied orbital functions {?_i} and occupation numbers {n_i}. The orbital Euler–Lagrange equations are analogous to Kohn–Sham equations, but do not in general contain local potential functions. Time‐dependent Hartree–Fock theory is generalized in OFT to a formally exact linear response theory that includes electronic correlation. In the exchange‐only limit, the theory reduces to the random‐phase approximation of many‐body theory. The formalism determines excitation energies. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Projected BCS Tamm-Dancoff method for molecular electronic structures

A new Tamm–Dancoff method for the ground and excited states of molecular electronic systems is developed. The method begins with a number-projected BCS (PBCS ) wave function and is generated by excitations of particle pairs from the degenerate geminals in the PBCS wave function. A direct optimization of the PBCS wave function is accomplished with successive Bogoliubov transformations so that one-pair excitation terms in the Tamm-Dancoff expansion of the ground state vanish (the generalized Brillouin theorem). The spin-symmetry adapted first- and second-order Tamm–Dancoff bases and matrix elements are calculated by means of the CI expansion of the PBCS wave function with natural orbitals that diagonalize the BCS geminal matrix. Numerical calculations are presented for the H₄ system with D_2h and D_4h conformations and for methylene. The PBCS wave function is not a very good approximation for the ground state, accounting for only about half of the correlation energy. The second-order Tamm–Dancoff correction improves the result as much as the double excitation CI . The Tamm–Dancoff terms consisting of two triplet pairs coupled to a singlet, and those relaxing the constraint imposed on the pairwise excitations in the PBCS wave function are important.     

Difluorenyl carbo‐Benzenes: Synthesis,Electronic Structure,and Two‐Photon Absorption Properties of Hydrocarbon Quadrupolar Chromophores

The synthesis, crystal and electronic structures, and one‐ and two‐photon absorption properties of two quadrupolar fluorenyl‐substituted tetraphenyl carbo‐benzenes are described. These all‐hydrocarbon chromophores, differing in the nature of the linkers between the fluorenyl substituents and the carbo‐benzene core (C?C bonds for 3 a , C?C?C?C expanders for 3 b ), exhibit quasi–superimposable one‐photon absorption (1PA) spectra but different two‐photon absorption (2PA) cross‐sections σ_2PA. Z‐scan measurements (under NIR femtosecond excitation) indeed showed that the C?C expansion results in an approximately twofold increase in the σ_2PA value, from 336 to 656 GM (1 GM=10^?50 cm⁴ s molecule^?1 photon^?1) at λ=800 nm. The first excited states of A_u and A_g symmetry accounting for 1PA and 2PA, respectively, were calculated at the TDDFT level of theory and used for sum‐over‐state estimations of σ_2PA(λ_i), in which λ_i=2 hc/E_i, h is Planck’s constant, c is the speed of light, and E_i is the energy of the 2PA‐allowed transition. The calculated σ_2PA values of 227 GM at 687 nm for 3 a and 349 GM at 708 nm for 3 b are in agreement with the Z‐scan results.     

A proposed modification of CBS-4M model chemistry for application to molecules of increasing molecular size

 In order to calculate more accurately the enthalpies of formation, ΔH _f°(298 K), for large molecules using the CBS-4M method, a new formulation of the empirical higher-level correction to the energy is proposed: ΔE=a|S|² _{i i} I _{i i} +b(n _α+n _β)+cΔ<S ²>+Σn _i d _{i .} The new methodology (CBS-4MB) applied to a set of 114 molecules of different size significantly decreases the mean absolute deviation from 3.78 to 2.06 kcal/mol. Received: 7 February 2001 / Accepted: 5 April 2001 / Published online: 13 June 2001     

The Features of Interaction of Bis(4, 6‐di‐tert‐butyl‐N‐(2, 6‐diisopropylphenyl)‐o‐amidophenolato)tin(IV) with Bromine and Iodine

The oxidation of tin(IV) bis‐amidophenolate (APiPr)₂Sn · THF ( I ) by bromine and iodine leads to the formation of monoradical mixed‐ligand complexes (APiPr)(ISQiPr)SnBr · THF ( II ) and (APiPr)(ISQiPr)SnI · THF ( III ) or diradical complexes (ISQiPr)₂SnBr₂ ( IV ) and (ISQiPr)₂SnI₂ ( V ), respectively [APiPr = dianion 4, 6‐di‐tert‐butyl‐N‐(2, 6‐diisopropylphenyl)‐o‐amidophenolate; ISQiPr = radical‐anion 4, 6‐di‐tert‐butyl‐N‐(2, 6‐diisopropylphenyl)‐o‐iminobenzosemiquinone], depending on the molar ratio of reagents (2:1 or 1:1). According to EPR data for compounds II and III , the unpaired electron is delocalized between both organic ligands. The EPR spectrum of IV in toluene matrix at 130 K is typical for diradical species with S = 1 with parameters D = 530 G, E = 105 G. The mixed‐ligand complexes II and III are unstable and undergo to symmetrization leading to formation of IV or V . The molecular structures of IV and V are determined by X‐ray analysis.     

A new algorithm for solving large inhomogeneous linear system of algebraic equations

An algorithm based on a small matrix approach to the solution of a system of inhomogeneous linear algebraic equations is developed and tested in this short communication. The solution is assumed to lie in an initial subspace and the dimension of the subspace is augmented iteratively by adding the component of the correction vector obtained from the Jacobi scheme on the coefficient matrix A (A^TA, if the matrix A is nondefinite) that is orthogonal to the subspace. If the dimension of the subspace becomes inconveniently large, the iterative scheme can be restarted. The scheme is applicable to both symmetric and nonsymmetric matrices. The small matrix is symmetric (nonsymmetric), if the coefficient matrix is symmetric (nonsymmetric). The scheme has rapid convergence even for large nonsymmetric sparse systems.     

Differential Pulse Polarography for a First‐Order EC Process and Its Diagnostic Parameters

Theoretical expressions for differential pulse polarography (DPP) for a reversible electron transfer coupled with an irreversible follow‐up first‐order chemical reaction (E_rC_i) is derived approximately. The peaks as given by the current expressions are analyzed in terms of several parameters such as a ratio of anodic‐to‐cathodic peak‐currents (i_p^a/i_p^c), a separation of peak‐potentials (E_p^c?E_p^a), and a ratio of anodic‐to‐cathodic half‐peak‐widths (W_1/2^a/W_1/2^c) in order to characterize the E_rC_i process and distinguish it from other types of electrode processes. The anodic peak is found to be more susceptible to the post kinetics than the cathodic peak. The new parameter of W_1/2^a/W_1/2^c ratio is much more sensitive to the post kinetics than the peak separation (E_p^c?E_p^a). The peak current ratio (i_p^a/i_p^c) and the peak‐width ratio (W_1/2^a/W_1/2^c) have comparable sensitivities to the kinetics. Hence, W_1/2^a/W_1/2^c ratio is a better diagnostic parameters than (E_p^c?E_p^a) which has a poor sensitivity. This phenomenon is different from cyclic voltammetry (CV) in which E_p^c?E_p^a is as sensitive as i_p^a/i_p^c. The new criteria for EC with DPV is tested and successfully applied to several Co(III) complex systems, including coenzyme B₁₂. The homogeneous rate constant (k) for the follow‐up step is estimated from the measurements of the experimental values of the parameters. The present treatment is valid quantitatively at lower values of k, yielding relatively larger errors for higher k values (k>10 s^?1).     

Reduced local energy as a criterion for the accuracy of approximate Hartree–Fock wave functions. Application to H2O and CH4

The reduced local energy E_L of Rothstein and co-workers is discussed as a criterion for the local accuracy of approximate wave functions. The behavior of E_L for different approximation levels is discussed. It is shown that, for particular classes of wave functions, fluctuations of E_L reflect local inaccuracies of the wave function as compared to certain convergence limits. The applicability of this criterion is illustrated with approximate Hartree–Fock wave functions for water and methane.     

Boron as a Powerful Reductant: Synthesis of a Stable Boron‐Centered Radical‐Anion Radical‐Cation Pair

Despite the fundamental importance of radical‐anion radical‐cation pairs in single‐electron transfer (SET) reactions, such species are still very rare and transient in nature. Since diborenes have highly electron‐rich B? B double bonds, which makes them strong neutral reductants, we envisaged a possible realization of a boron‐centered radical‐anion radical‐cation pair by SET from a diborene to a borole species, which are known to form stable radical anions upon one‐electron reduction. However, since the reduction potentials of all know diborenes (E_1/2=?1.05/?1.55 V) were not sufficiently negative to reduce MesBC₄Ph₄ (E_1/2=?1.69 V), a suitable diborene, IiPr?(iPr)B?B(iPr)?IiPr, was tailor‐made to comply with these requirements. With a halfwave potential of E_1/2=?1.95 V, this diborene ranks amongst the most powerful neutral organic reductants known and readily reacted with MesBC₄Ph₄ by SET to afford a stable boron‐centered radical‐anion radical‐cation pair.     

Electronegativity Scaled as a Average Attracting Energy of Valence‐Shell Electrons in a Ground‐State Free Atom

The total capability of an atom attracting valence electrons can be measured by the sum of ionization energies of valence electron in a ground‐state free atom plus its electron affinity called Total Attracting Energy, TAE = Σn_iE_i + EA, where, E_i is the ionization energy of the ith valence‐shell electron in a ground‐state free atom, n_i is the number of valence‐shell electron bearing energy E_i, and EA is the electron affinity. And the electronegativity χ_CL is proportional to the average of TAE, AAE = TAE_av, divided by Σn_i, the number of atomic valence‐shell electrons. χ_CL = 0.1813 TAE_av = 0.1813 AAE = 0.1813 TAE/Σn_i, = 0.1813 (Σn_iE_I + EA)/Σn_i. Further, the atomic valence orbital electronegativity can be also obtained from the TAE value of an atom. Some discussions were made on several special aspects such as scale of rare gases, comparisons with Pauling's and Allen's scales, etc.     

Ab initio SCF calculations on [V10O28]6−: A benchmark for the classical calculation and processing of molecular integrals on large Gaussian basis sets

A vector efficient implementation of the McMurchie and Davidson algorithm for the calculation of one- and two-electron molecular integrals is presented, as available in the Cray version of the ASTERIX program system. The implementation and performance of a vector-oriented strategy for the generation and processing of the P supermatrix is also discussed. This program system has been applied to the ab initio SCF computation of the ground-state wave function for the [V₁₀O₂₈]^6? ion, with a basis set of triple-zeta quality for the valence shell of oxygen generating 1404 GTOS and 574 CGTOS for the complete system. The performance and the bottlenecks of the integral calculation are discussed as a function of the integral classes. Two-dimensional maps of the electrostatic potential are presented for this molecule and compared to experimental information about proton fixation.     

Probing the role of the linker in ferrocene-ATP conjugates: monitoring protein kinase catalyzed phosphorylations electrochemically

The synthesis and electrochemical properties of ferrocene conjugates are presented for the purpose of investigating adenosine 5′‐[γ‐ferrocenoylalkyl] triphosphate ( 1 a – 4 a , ferrocene (Fc)–ATP) as co‐substrates for phosphorylation reactions. Compounds 1 a – 4 a were synthesized, purified by HPLC, and characterized by NMR spectroscopy and mass spectrometry. In solution, all Fc–ATP bioconjugates exhibit a reversible one‐electron redox process with a half‐wave potential (E_1/2) in the 390–430 mV range, peak separations (ΔE_p) in the 40–70 mV range, and the peak current ratio (i_pa/i_pc) near unity. The peptide‐modified surface Glu‐Gly‐Ile‐Tyr‐Asp‐Val‐Pro was used to study the sarcoma‐related protein (Src) kinase activity by employing the Fc–ATP bioconjugates as co‐substrates. Subsequent kinase‐catalyzed transfer of the γ‐Fc‐phosphate group to the tyrosine residues of the surface‐bound peptides was characterized by a formal potential (E^o) ≈390 mV (vs. Ag/AgCl). The Fc‐coverage, estimated by time‐of‐flight secondary‐ion mass spectrometry (TOF‐SIMS) and cyclic voltammetry (CV), suggested validity of Fc–ATP conjugates as kinase co‐substrates. Depending on the length of the alkyl spacer of the Fc–ATP conjugate, different current densities were obtained, pointing to a direct correlation between the two. Molecular modeling revealed that the structural constraint imposed by the short alkyl spacer ( 1 a ) causes a steric congestion and negatively affects the outcome of phosphorylation reaction. An optimal analytical response was obtained with the Fc–ATP conjugates with linker lengths longer than six CH₂ groups.     

Configurations conducive to the formation of intramolecular excimers in poly(N‐vinyl carbazole) and its copolymers

The ratios of the intensity of excimer and monomer emissions, denoted I_E/I_M, in poly(N‐vinyl carbazole) and copolymers of N‐vinyl carbazole and methyl methacrylate were measured with steady‐state fluorescence. Measurements were performed in dilute solutions of several fluid solvents at 25 °C and in a solid matrix of poly(methyl methacrylate) at room temperature. The values of I_E/I_M depended on the nature of the solvent, the emission wavelength, and the copolymer composition. Molecular dynamics simulations were performed for diastereoisomers of 2,4‐di(N‐carbazolyl)pentane and for isotactic and syndiotactic trichromophoric copolymer fragments to assist in the identification of the thermally accessible conformations capable of forming intramolecular excimers and the configurational relationship of the carbazole units in these complexes. Nearest neighbor carbazole groups made the dominant contribution to the excimers. Excimers were more likely in isotactic sequences than in syndiotactic sequences, as was also the case for the low‐energy excimer arising from the complete overlap of two carbazole units. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1272–1281, 2001     

E5M7+ (E=C–Pb,M=Li–Cs): A Source of Viable Star‐Shaped Clusters

Herein we report the systematic exploration of the potential energy surfaces of a series of clusters with formula E₅M₇⁺ (E=C‐Pb and M=Li‐Cs). Fifteen of these combinations adopt a D_5h three‐dimensional seven‐pointed star‐like structure in a singlet state, where M atoms interact electrostatically with the E₅ ring. The determining factors in the relative preference of having the D_5h structure over the most competitive isomer or vice‐versa are analyzed. These star‐shaped systems satisfy the 4n+2 Hückel's rule and exhibit a strong diatropic (σ and π) response to an external magnetic field.     

Thermodynamic Calculation in Elimination of Water Pollutants at Hydro‐geo‐chemical Barriers

Thermodynamic saturation coefficients (K_s) and transformation indices (I_t) can be used to evaluate the possibility of forming hydro‐geo‐chemical precipitation barriers and assess the solid phase (rock) stability in aquifers. Calculations are made on the basis of data on water pH, E_h, conductivity (x) and some relevant ion concentrations. The dependencies of K₂ and I_t on water pH and E_h values can be expressed graphically to estimate the barriers parameters. Barrier generation leads to a decrease in concentrations of pollutants due mainly to precipitation, co‐precipitation and/or sorption processes. Using the diagram K_s, I_t= f (pH, E_h), supplemented with representative data on concentrations of pollutants before and after the barrier, the elimination and migration of pollutants can be roughly evaluated (predicted) only on the basis of determining pH and E_h values of water and concentrations of ions participating in the barrier formation. The proposed method is applied to assess the migration and elimination of pollutants (U, ²²⁶Ra, β‐emitters, SO₄²) in Bulgarian uranium mine surroundings.     

Ion fractions of matrix elements and impurities in GaAs bombarded by O2+ primary ions

Summary Useful ion yields Y of secondary ion mass spectrometry (SIMS) analyses were measured for GaAs bombarded with O ₂ ⁺ primary ions at normal incidence. The useful ion yields of several analytes were found to decrease with increasing ionisation potentialE _i of the analytes far less drastically than reported in the literature. For valuesE _i lower than 8 eV only a slight decrease of Y with increasing ionisation potential is observed. The saturation of the useful ion yields at lower values of the ionisation potential is interpreted to result from very high ion fractions. If an ion fraction of unity is assumed for Ga the ion fractions of impurities withE _i lower than 8 eV would exceed 40%. For analytes withE _i higher than 8 eV the ion fraction decreases rapidly with increasing ionisation potential. A value of 8×10^–4 is estimated for the matrix element As (E _i= 9.81 eV).

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Ionenausbeuten von Matrixelementen und Dotierstoffen in GaAs unter O ₂ ⁺ -Primärionenbeschuß

     

Microemulsion polymerization of styrene stabilized by sodium dodecyl sulfate and short‐chain alcohols

Styrene microemulsion polymerizations with different short‐chain alcohols [n‐C_iH_2i+1OH (C_iOH), where i = 4, 5, or 6] as the cosurfactant were investigated. Sodium dodecyl sulfate and sodium persulfate (SPS) were used as the surfactant and initiator, respectively. The desorption of free radicals out of latex particles played an important role in the polymerization kinetics. An Arrhenius expression for the radical desorption rate coefficient was obtained from the polymerizations at temperatures of 50–70 °C. The polymerization kinetics were not very sensitive to the alkyl chain length of alcohols compared with the temperature effect. The maximal polymerization rate in decreasing order was C₆OH > C₄OH > C₅OH. This was related to the differences in the water solubility of C_iOH and the structure of the oil–water interface. The feasibility of using a water‐insoluble dye to study the particle nucleation mechanisms was also evaluated. The parameters chosen for the study of the particle nucleation mechanisms include the cosurfactant type (C_iOH), the SPS concentration, and the initiator type (oil‐soluble 2,2′‐azobisisobutyronitrile versus water‐soluble SPS). © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3199–3210, 2001     

Theoretical Investigation into Electronic Structures and Charge Transfer Properties of π‐Conjugated System with Different Combinations of Thiophene and Vinyl/Butadiene

A series of combinations of thiophene and vinyl/butadiene were investigated by ab initio and DFT methods to explore their electronic structures and charge transfer properties. The results show that increasing thiophene ring and vinyl number is a rational strategy to raise the HOMO energy levels and lower the LUMO energy levels. Moving the vinyl from the periphery to the core has the slight effect on the HOMO and LUMO energy levels. Furthermore, replacing the middle vinyl and end‐capped vinyl of 3b (T5V4) with the butadiene can lower LUMO energy levels and then facilitate the electron injection. Above all, the close hole and electron reorganization energies (λ_h and λ_e) are observed from these compounds. However, the λ_es are smaller than their respective λ_hs in some compounds, which is relatively rare in organic materials. Especially, the promising ambipolar material 3c (T5B4) is recommended theoretically for possessing the equivalent minimum λ_h (0.24 eV) and λ_e (0.24 eV). The absorption wavelengths exhibit red shifts with the increasing of the thiophene ring and the vinyl number under the same configuration, which correspond to the reverse order of ΔE_H‐L and E_g. The linear relationships are found between experimental lowest singlet excited energies (E_exp) with theoretical values ΔE_H‐L and E_g.