Probing electron correlations in molecules by two-dimensional coherent optical spectroscopy

The nonlinear optical signal generated in phenol by three femtosecond pulses with wavevectors k1, k2, and k3 in the phase-matching direction k1 + k2 - k3 is simulated. This two-dimensional coherent spectroscopy (2DCS) signal has a rich pattern containing information on double-excitation states. The signal vanishes for uncorrelated electrons due to interference among quantum pathways and, thus, provides direct signatures of correlated many-electron wavefunctions. This is illustrated by the very different 2DCS signals predicted by two levels of electronic structure calculations: state-averaged complete active space self-consistent field (SA-CASSCF) and multistate multiconfigurational second-order perturbation theory (MS-CASPT2).     

Probing interactions between core-electron transitions by ultrafast two-dimensional x-ray coherent correlation spectroscopy

Two-dimensional x-ray correlation spectra (2DXCS) obtained by varying two delay periods in a time-resolved coherent all-x-ray four-wave-mixing measurement are simulated for the N 1s and O 1s transitions of aminophenol. The necessary valence and core-excited states are calculated using singly and doubly substituted Kohn-Sham determinants within the equivalent-core approximation. Sum-over-states calculations of the 2DXCS signals of aminophenol isomers illustrate how novel information about electronic states can be extracted from the 2D spectra. Specific signatures of valence and core-excited states are identified in the diagonal and off-diagonal peaks arising from core transitions of the same and different types, respectively.     

Photochemistry of a retinal protonated schiff-base analogue mimicking the opsin shift of bacteriorhodopsin

A retinal Schiff base analogue which artificially mimics the protein-induced red shifting of absorption in bacteriorhodopsin (BR) has been investigated with femtosecond multichannel pump probe spectroscopy. The objective is to determine if the catalysis of retinal internal conversion in the native protein BR, which absorbs at 570 nm, is directly correlated with the protein-induced Stokes shifting of this absorption band otherwise known as the "opsin shift". Results demonstrate that the red shift afforded in the model system does not hasten internal conversion relative to that taking place in a free retinal-protonated Schiff base (RPSB) in methanol solution, and stimulated emission takes place with biexponential kinetics and characteristic timescales of approximately 2 and 10.5 ps. This shows that interactions between the prosthetic group and the protein that lead to the opsin shift in BR are not directly involved in reducing the excited-state lifetime by nearly an order of magnitude. A sub-picosecond phase of spectral evolution, analogues of which are detected in photoexcited retinal proteins and RPSBs in solution, is observed after excitation anywhere within the intense visible absorption band. It consists of a large and discontinuous spectral shift in excited-state absorption and is assigned to electronic relaxation between excited states, a scenario which might also be relevant to those systems as well. Finally, a transient excess bleach component that tunes with the excitation wavelength is detected in the data and tentatively assigned to inhomogeneous broadening in the ground state absorption band. Possible sources of such inhomogeneity and its relevance to native RPSB photochemistry are discussed.     

Vibrational-exciton couplings for the amide I, II, III, and A modes of peptides

The couplings between all amide fundamentals and their overtones and combination vibrational states are calculated. Combined with the level energies reported previously (Hayashi, T.; Zhuang, W.; Mukamel, S. J. Phys. Chem. A 2005, 109, 9747), we obtain a complete effective vibrational Hamiltonian for the entire amide system. Couplings between neighboring peptide units are obtained using the anharmonic vibrational Hamiltonian of glycine dipeptide (GLDP) at the BPW91/6-31G(d,p) level. Electrostatic couplings between non-neighboring units are calculated by the fourth rank transition multipole coupling (TMC) expansion, including 1/R3 (dipole-dipole), 1/R4 (quadrupole-dipole), and 1/R5 (quadrupole-quadrupole and octapole-dipole) interactions. Exciton delocalization length and its variation with frequency in the various amide bands are calculated. The simulated infrared amide I and II absorptions and CD spectra of 24 residue alpha-helical motifs (SPE3) are in good agreement with experiment.     

Optical coherence and theoretical study of the excitation dynamics of a highly symmetric cyclophane-linked oligophenylenevinylene dimer

Optoelectronic properties of a polyphenylenevinylene-based oligomer and its paracylophane-linked dimer are studied using a variety of experimental and theoretical techniques. Despite the symmetrical structure and redshifted absorption of the dimer versus the monomer, an exciton picture is not the most appropriate. Electronic structure calculations establish changes in charge density upon optical excitation and show localized excitations that cannot be accounted for by a simple Frenkel exciton model. Visible frequency pump-probe anisotropy measurements suggest that the dimer should be considered as a three-level system with a fast, approximately 130 fs, internal conversion from the higher to lower energy excited electronic state. Signatures of nuclear relaxation processes are compared for electric field-resolved transient grating and two-dimensional photon echo spectra. These measurements reveal that nuclear relaxation occurs on similar time scales for the monomer and dimer. The connection between the spectral phase of four-wave mixing signals and the time dependent width of a nuclear wave packet is discussed. Semiempirical electronic structure and metropolis Monte Carlo calculations show that the dominant line broadening mechanisms for the monomer and dimer are associated with inter-ring torsional coordinates. Together, the theoretical calculations and electric field-resolved four-wave mixing experiments suggest that while the structure of dimer is more rigid than that of monomer, the difference in their rigidities is not sufficient to slow down excited state relaxation of dimer with respect to the monomer.     

Broadly tunable dual-wavelength light source for coherent anti-Stokes Raman scattering microscopy

The signal and idler beams from a picosecond, synchronously pumped optical parametric oscillator (OPO) provide the two colors necessary for coherent anti-Stokes Raman scattering (CARS) microscopy. The OPO provides a continuously tunable frequency difference between the two beams over a broad range of Raman shifts (100-3700 cm(-1)) by varying the temperature of a single nonlinear crystal. The near-infrared output (900-1300 nm) allows for deep penetration into thick samples and reduced nonlinear photodamage. Applications of this light source to in vivo cell and ex vivo tissue imaging are demonstrated.     

Weak exciton scattering in molecular nanotubes revealed by double-quantum two-dimensional electronic spectroscopy

The two-exciton manifold of a double-wall cylindrical molecular aggregate is studied using a coherent third order optical technique. Experiments reveal the anharmonic character of the exciton bands. Atomistic simulations of the exciton-exciton scattering show that the excitons can be treated as weakly coupled hard-core bosons. The weak coupling stems from the extended exciton delocalization made possible by the nanotube geometry.     

Scale-dependent Macroscopic Balance Equations Governing Transport Through Porous Media: Theory and Observations

A theory is developed providing a rational framework for spatial scale- dependent fluid’s flow and heat transfer, and mass of a component migrating with it through porous media. Introducing the assumption of a non-Brownian type motion and referring to asymptotic expansion in powers of a small defined parameter, we develop a novel approach associated with macroscopic balance equations obtained by averaging over a Representative Elementary Volume (REV). We prove that these equations can be decomposed into a primary part that refers to the REV length scale and a secondary part valid at a length scale smaller than that of the corresponding REV length. Further to our previous development, we obtain two general forms of the primary and secondary macroscopic balance equations. One is based on the assumption that the advective flux of the extensive quantity is dominant over that of the dispersive flux, whereas the other disregards this assumption. Moreover we also introduce the primary and secondary macroscopic forms for the fluid heat- transfer equation. Considering a Newtonian fluid, the resulting primary Navier–Stokes equation can vary from a nonlinear wave equation to a drag-dominant equation at the fluid–solid interface (Darcy’s law). The secondary momentum balance equation describes a wave equation governing the concurrent propagation of the intensive momentum and the dispersive momentum flux, deviating from their corresponding average terms. The primary macroscopic fluid heat-transfer equation accounts for advective and dispersive heat fluxes and the secondary macroscopic heat-transfer equation involves the simultaneous advection of heat deviating from its corresponding intensive average quantity. The primary macroscopic solute mass balance equation accounts for advection and hydrodynamic dispersion. The secondary macroscopic component mass balance equation is in the form of pure advection governing migration of the deviation from the average component concentration. At this stage, we focus on establishing the viability of the developed theory. We do this by arguing that field observations of motion at small spatial scales are coherent with the hyperbolic characteristics of the secondary balance equations. Field observations under natural gradient flow conditions show excessive high concentration (average of 50 mg/L) of colloids under land irrigated by sewage effluents. We argue that this displacement of condensed colloidal parcels manifests the theoretical findings for the smaller spatial scale. Further evidence show the accumulation of particles moving behind the front of an emitted shockwave. We consider this as an experimental proof reinforcing the argument that colloidal migration is subject to the action of a shockwave in the fluid and pure advection transport, governed by the respective suggested hyperbolic macroscopic balance equations of fluid momentum and component mass at the smaller spatial scale.     

Applications of bulk queues to group testing models with incomplete identification

A population of items is said to be “group-testable”, (i) if the items can be classified as “good” and “bad”, and (ii) if it is possible to carry out a simultaneous test on a batch of items with two possible outcomes: “Success” (indicating that all items in the batch are good) or “failure” (indicating a contaminated batch). In this paper, we assume that the items to be tested arrive at the group-testing centre according to a Poisson process and are served (i.e., group-tested) in batches by one server. The service time distribution is general but it depends on the batch size being tested. These assumptions give rise to the bulk queueing model M/G^(m,M)/1, where m and M(>m) are the decision variables where each batch size can be between m and M. We develop the generating function for the steady-state probabilities of the embedded Markov chain. We then consider a more realistic finite state version of the problem where the testing centre has a finite capacity and present an expected profit objective function. We compute the optimal values of the decision variables (m, M) that maximize the expected profit. For a special case of the problem, we determine the optimal decision explicitly in terms of the Lambert function.     

Acidity and alkylation of 4-phenyl-3,5-dihydroxypyrazole and its derivatives. C versus O and N alkylation

4-Phenyl-3,5-dihydroxypyrazole is a relatively strong acid, with a pKa of 3.70. The effect of substitution, both in the phenyl ring and on the heterocyclic ring, on the acidity was studied. Electron attracting groups on the phenyl group enhance the acidity. Selective replacement by an alkyl group of one or two of the heterocyclic hydrogens lowers the acidity. Meerwein reagent, as well as methyl iodide bring about alkylation on carbon, whereas diazomethane and diethyl sulfate do not. Michael addition proceeds through both carbon and nitrogen.