Chaotic scattering and the n-bounce resonance in solitary-wave interactions

We present a new and complete analysis of the n-bounce resonance and chaotic scattering in solitary-wave collisions. In these phenomena, the speed at which a wave exits a collision depends in a complicated fractal way on its input speed. We present a new asymptotic analysis of collective-coordinate ordinary differential equations (ODEs), reduced models that reproduce the dynamics of these systems. We reduce the ODEs to discrete-time iterated separatrix maps and obtain new quantitative results unraveling the fractal structure of the scattering behavior. These phenomena have been observed repeatedly in many solitary-wave systems over 25 years.     

Evidence for significant through-space and through-bond electronic coupling in the 1,4-diphenylcyclohexane-1,4-diyl radical cation gained by absorption spectroscopy and DFT calculations

Photoinduced single-electron-transfer promoted oxidation of 2,5-diphenyl-1,5-hexadiene by using N-methylquinolinium tetrafluoroborate/biphenyl co-sensitization takes place with the formation of an intense electronic absorption band at 476 nm, which is attributed to the 1,4-diphenylcyclohexane-1,4-diyl radical cation. The absorption maximum (lambda(ob)) of this transient occurs at a longer wavelength than is expected for either the cumyl radical or the cumyl cation components. Substitution at the para positions of the phenyl groups in this radical cation by CH(3)O, CH(3), F, Cl, and Br leads to an increasingly larger redshift of lambda(ob). A comparison of the rho value, which was obtained from a Hammett plot of the electronic transition energies of the radical cations versus sigma(+), with that for the cumyl cation shows that the substituent effects on the transition energies for the 1,4-diarylcyclohexane-1,4-diyl radical cations are approximately one half of the substituent effects on the transition energies of the cumyl cation. The observed substituent-induced redshifts of lambda(ob) and the reduced sensitivity of lambda(ob) to substituent changes are in accordance with the proposal that significant through-space and -bond electronic interactions exist between the cumyl radical and the cumyl cation moieties of the 1,4-diphenylcyclohexane-1,4-diyl radical cation. This proposal gains strong support from the results of density functional theory (DFT) calculations. Moreover, the results of time-dependent DFT calculations indicate that the absorption band at 476 nm for the 1,4-diphenylcyclohexane-1,4-diyl radical cation corresponds to a SOMO-3 --> SOMO transition.     

Dinuclear palladium-azido complexes containing thiophene derivatives: reactivity toward organic isocyanides and isothiocyanates

Cyclopalladated tetranuclear Pd(II) complexes, [Pd2(micro-Cl)2(Y)]2 (Y = L1 or L2; H2L1 = di(2-pyridyl)-2,2'-bithiophene; H2L2 = 5,5'-di(2-pyridyl)-2,2':5',2'-terthiophene), containing two pyridyl-alpha, alpha'-disubstituted derivatives of thiophene were prepared. Treating these products with PR3 and subsequently with NaN3 produced the dinuclear Pd-azido complexes [(PR3)2(N3)Pd-Y-Pd(N3)(PR3)2] (Y = L1 or L2) or a cyclometallated complex [(PR3)(N3)Pd-Y'-Pd(N3)(PR3)] (Y' = C,N-L2). Reactions of these Pd-azido complexes with CN-Ar (Ar = 2,6-Me(2)C(6)H(3), 2,6-i-Pr(2)C(6)H(3)) or R-NCS (R = i-Pr, Et, allyl) led to the complexes containing end-on carbodiimido groups [(PMe3)2(N[double bond]C[double bond]N-Ar)Pd-Y-Pd(N[double bond]C[double bond]N-Ar)(PMe3)2] or S-coordinated tetrazole-thiolato groups {(PMe3)2[CN4(R)]S-Pd-Y-Pd-S[CN4)(R)](PMe3)2}. Interestingly, when treated with elemental sulfur, the carbodiimido complexes transformed into the cyclometallated derivatives, [(PMe3)(N[double bond]C[double bond]N-Ar)Pd-Y'-Pd(N[double bond]C[double bond]N-Ar)(PMe3)] (Y' = C,N-L1, C,N-L2). We also report the preparation of linear, thienylene-bridged dinuclear Pd complexes [L2(N3)Pd-X(or X')-Pd(N3)L2] (L = PMe3 or PMe2Ph; H2X = 2,2'-bithiophene or H2X' = 2,2':5',2'-terthiophene) and their reactivity toward organic isocyanide and isothiocyanates.     

An analytical approach for computing Franck‐Condon integrals of harmonic oscillators with arbitrary dimensions

We have developed an analytical approach for computing Franck‐Condon integrals (FCIs) of harmonic oscillators (HOs) with arbitrary dimensions in which the mode‐mixing Duschinsky effect is taken into account. A general formula of FCIs of HOs was obtained and was applied to study the photoelectron spectroscopy of vinyl alcohol and ovalene (C₃₂H₁₄). The equilibrium geometries, harmonic vibrational frequencies and normal modes of vinyl alcohol, ovalene, and their cations were computed at the B3LYP/aug‐cc‐pVTZ or the B3LYP/6‐31G(d) level, from which Franck‐Condon factors were calculated and photoelectron spectra were simulated. The adiabatic ionization energies of vinyl alcohol were also computed by extrapolating the CCSD(T) energies to the complete basis set limit with aug‐cc‐pVXZ (X = D, T, Q, 5). The simulated photoelectron spectra of both vinyl alcohol and ovalene are in agreement with the experiments. The computed adiabatic ionization energies of syn‐ and anti‐vinyl alcohol are in consistent with the experiment within 0.008 eV and 0.014 eV, respectively. We show, for the first time, that the analytical approach of computing FCIs is also efficient and promising for the studies of vibronic spectra of macrosystems. © 2012 Wiley Periodicals, Inc.     

Dynamic combinatorial discovery of a [2]-catenane and its guest-induced conversion into a molecular square host

A simple water-soluble naphthalenedithiol building block is converted quantitatively into a series of octameric [2]-catenanes, composed of two interlocked molecular squares. When this mixture is re-equilibrated in the presence of an adamantyl ammonium guest, the catenanes disassemble into their macrocyclic components that bind the guest with nanomolar affinity in water.