The electronic spectra of unsaturated hydrocarbons a VESCF-CI treatment

A modified Pariser-Parr method, which allows for the inductive effect of alkyl groups by a VESCF method, has been applied to the calculation of the electronic spectra of a number of hydrocarbons. All singly- and doubly-excited configurations are included in the configuration interaction treatment, except for large molecules for which the configuration interaction matrices are truncated to an order of 110. The red shifts which result from methylation of the polyenes are well calculated. For azulene, the shift to either the red or the blue, depending on the location of the substituent, is also well calculated. The largest deviation between the calculated and experimental transition energies for all of the compounds studied was 1.1 eV, while the standard deviation of all observed transitions for planar compounds was 0.24 eV. The ionization potentials and the singlet-triplet transitions of these compounds were also studied.

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Zusammenfassung Die Spektren einer Reihe von Kohlenwasserstoffen wurden nach einer modifizierten Pariser-Parr-Methode, bei der der induktive Effekt von Alkylgruppen mittels eines VESCF-Verfahrens berücksichtigt wird, berechnet, wobei alle ein- und zweifach angeregten Konfigurationen eingeschlossen wurden außer bei sehr großen Molekülen, wo deren Zahl auf 110 begrenzt wurde. Dabei ergeben sich in schöner Weise die Rotverschiebungen, die bei Methylierung von Polyenen beobachtet werden, desgleichen die Rot- und Violettverschiebungen je nach Ort des Substituenten bei Azulen. Die größten Abweichungen zwischen berechneten und beobachteten Übergangsenergien ist 1,1 eV, die Standardabweichung bei planaren Verbindungen 0,24 eV. Ferner wurden Ionisationspotentiale sowie Sigulett-Triplett-Übergänge der behandelten Verbindungen untersucht.

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Résumé Une méthode Pariser-Parr modifieé, qui tient compte de l'effet inductif des groupes alkyles dans le cadre VESCF, a été employeé pour calculer les spectres électroniques de quelques hydrocarbures. Toutes les configurations mono- et di-excitées sont comprises dans le traitement d'interaction de configurations, excepté pour les grosses molécules; pour ces dernières, l'ordre des matrices d'interaction de configuration a été réduit à 110. Les déplacements versle rouge, après methylation de polyènes, sont bien calculés. Pour l'azulène, les déplacements vers le rouge ou le bleu, suivant le lieu de substitution, sont également bien calculés. La plus grande déviation entre les énergies de transition calculée et expérimentale était de 1.1 eV pour tous les produits étudiés, alors que la déviation standard de toutes les transitions observeés était de 0,24 eV dans les composés planaires. Le potential d'ionisation et les transitions singulet-triplet ont aussi été étudiés.

     

An example of bifurcation to homoclinic orbits

Consider the equation $\text{x}\text{?}\text{? x + x}{}^2\text{= ?λ}{}_1\text{x + λ}{}_2\text{?(t)}\text{where}\text{?(t + 1) = ?(t)}\text{and}\text{λ = (λ}{}_1\text{, λ}{}_2\text{)}$ is small. For λ = 0, there is a homoclinic orbit Γ through zero. For λ ≠ 0 and small, there can be “strange” attractors near Γ. The purpose of this paper is to determine the curves in λ-space of bifurcation to “strange” attractors and to relate this to hyperbolic subharmonic bifurcations.     

Low-energy charge-density excitations in MgB2: Striking interplay between single-particle and collective behavior for large momenta

A sharp feature in the charge-density excitation spectra of single-crystal MgB2, displaying a remarkable cosinelike, periodic energy dispersion with momentum transfer (q) along the c* axis, has been observed for the first time by high-resolution nonresonant inelastic x-ray scattering (NIXS). Time-dependent density-functional theory calculations show that the physics underlying the NIXS data is strong coupling between single-particle and collective degrees of freedom, mediated by large crystal local-field effects. As a result, the small-q collective mode residing in the single-particle excitation gap of the B pi bands reappears periodically in higher Brillouin zones. The NIXS data thus embody a novel signature of the layered electronic structure of MgB2.     

Absence of magnetism in hcp iron-nickel at 11 K

Synchrotron M?ssbauer spectroscopy (SMS) was performed on an hcp-phase alloy of composition Fe92Ni8 at a pressure of 21 GPa and a temperature of 11 K. Density functional theoretical calculations predict antiferromagnetism in both hcp Fe and hcp Fe-Ni. For hcp Fe, these calculations predict no hyperfine magnetic field, consistent with previous experiments. For hcp Fe-Ni, however, substantial hyperfine magnetic fields are predicted, but these were not observed in the SMS spectra. Two possible explanations are suggested. First, small but significant errors in the generalized gradient approximation density functional may lead to an erroneous prediction of magnetic order or of erroneous hyperfine magnetic fields in antiferromagnetic hcp Fe-Ni. Alternately, quantum fluctuations with periods much shorter than the lifetime of the nuclear excited state would prohibit the detection of moments by SMS.     

Synthesis of new amphiphilic dendrons bearing aliphatic hydrocarbon surface sectors and a monocarboxylic or dicarboxylic acid focal point

[structure: see text]. A new series of amphiphilic G1-G3 dendrons containing purely aliphatic hydrocarbon dendritic surface sectors and one or two carboxylic acid group(s) at the focal point was synthesized in good yields. The key branching steps involve diallylation reactions of diethyl malonate or Meldrum's acid. These dendrons are highly soluble in hexane despite having highly polar carboxylic acid groups at the focal point.     

Tuning excited-state electron transfer from an adiabatic to nonadiabatic type in donor-bridge-acceptor systems and the associated energy-transfer process

Through design and synthesis of a new series of dyads I-III composed of 2,3-dimethoxynaphthalene as an electron donor (D) and 2,3-dicyanonaphthalene as an acceptor (A) bridged by n-norbornadiene (n = 1-3) we demonstrate an excellent prototype to switch the excited-state electron-transfer dynamics from an adiabatic to a nonadiabatic process. I reveals a remarkable excitonic effect and undergoes an adiabatic type of electron transfer (ET), resulting in a unique charge-transfer emission, of which the peak wavelength exhibits strong solvatochromism. Conversely, upon exciting the donor moiety, a fast D --> A energy transfer takes place for II (approximately 3 ps) and III (< or =30 ps), followed by a nonadiabatic type, weak coupled electron transfer with a relatively slow ET rate, giving rise to dual emission in polar solvents. Further detailed temperature-dependent studies of the ET rate deduced reaction barriers of 2.7 kcal/mol (for II) and 1.3 kcal/mol (for III) in diethyl ether and CH2Cl2, respectively. The results lead to a deduction of the reaction free energy and reorganization energy for both II (in diethyl ether) and III (in CH2Cl2). Theoretical (for I) and experimental (for II and III) approaches estimate the electronic coupling to be 860, 21.9, and 3.2 cm(-1) for I, II, and III, respectively, supporting the adiabatic versus nonadiabatic switching mechanism.     

On the periodic solutions for both nonlinear differential and difference equations: A unified approach

A direct and unifying scheme for disclosure of periodic wave solutions of both nonlinear differential and difference equations is presented. The scheme is based on Hirota's bilinear form and certain Riemann theta function formulae. The relations between the periodic wave solutions and soliton solutions are rigorously established.