Sequential decay involving multiple continua

We have utilized the Green's function method to derive an explicit solution for the problem of sequential decay involving multiple continua with constant coupling between adjacent continua. This model system is applicable for theoretical studies of dynamics of photodissociation, predissociation and electronic quenching of polyatomic molecules.     

Integral-equation theories and Mayer-sampling Monte Carlo: a tandem approach for computing virial coefficients of simple fluids

Mayer-sampling Monte Carlo (MSMC) has enabled computation of higher-order virial coefficients than previously possible for a variety of potential models, but it is not required for computation of the entire virial coefficient for models that are spherically symmetric: approximations that result from the hypernetted-chain (HNC) or Percus–Yevick (PY) integral-equation theories in conjunction with the compressibility equation (c) or virial equation (v) can be computed quickly by fast Fourier transforms. For the fourth and fifth virial coefficients of the Lennard–Jones potential (with parameters σ and ε), we demonstrate that the corrections to each of the four approximations (HNC(c), HNC(v), PY(c), and PY(v)) are faster to compute to a desired precision by MSMC than the full coefficient itself, with the exception of the PY(v) correction at fifth order, and that the optimal decomposition with regard to precision can be identified using a fraction of the steps required to obtain precise virial coefficients. At reduced temperatures kT/ε greater than 4, the PY(c) correction is fastest to compute by MSMC at both fourth and fifth orders. For lower temperatures, the HNC(v) decomposition is most efficient at fourth order, while the HNC(c) decomposition is most efficient at fifth order. These results are specific to the Lennard–Jones potential, but the method for determining the optimal decomposition is applicable to any spherically symmetric potential.     

Two-dimensional vibrational lineshapes of amide III, II, I and A bands in a helical peptide

An effective exciton Hamiltonian for all amide bands is used to calculate the absorption and photon echo spectra of a 17 residue helical peptide (YKKKH17). The cross peak bandshapes are sensitive to the inter-band couplings. Fluctuations of the local amide frequencies of the all amide fundamental and their overtone and combination states are calculated using the multipole electric field induced by environment employing the electrostatic DFT map of N-methyl acetamide. 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 a 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.     

On the location of chain-ends in rapidly crystallized poly(ethylene terephthalate)

Phenylmercurated poly(ethylene terephthalate) (PET) chain-ends are obtainable through the transesterification of PET by phenylmercury hydroxide or acetate in solution in nitrobenzene at 165 ± 10°C. The reaction results in an average of one mercury atom per chain. The phenylmercuration may be followed by infrared or x-ray fluorescence. Reaction with concentrated HCI Affords the elucidation of some structural parameters of the resultant partially crystalline tagged PET, through analyses of changes in viscosity and molecular weight, in percent crystallinity, and in the amount of mercury in the system. The chain-ends are almost completely excluded from the stem region of the PET crystal with no more than 2% remaining. The chain-ends are distributed unevenly throughout the amorphous phase. This is corroborated by sharp decreases in scattered intensity of small-angle x-ray measurements. Two models for the distribution of chain-ends in the amorphous phase are considered. The one in which the ends are pushed farthest from the crystal surface and concentrate halfway between crystallites is tentatively adopted. Analysis of the HCI hydrolysis kinetics and products leads to the following picture concerning the fold tightness and position. About one out of five folds extends significantly into the amorphous matter where it is mingled with cilia, tie molecules, and unattached molecules. Random scission throughout such an amorphous mass should lead to a preponderance of cleaved molecules whose length should be four to five times the lenght of the crystalline stem region, as is indeed observed.     

Monitoring molecular vibronic coherences in a bichromophoric molecule by ultrafast X-ray spectroscopy

The role of quantum-mechanical coherences in the elementary photophysics of functional optoelectronic molecular materials is currently under active study. Designing and controlling stable coherences arising from concerted vibronic dynamics in organic chromophores is the key for numerous applications. Here, we present fundamental insight into the energy transfer properties of a rigid synthetic heterodimer that has been experimentally engineered to study coherences. Quantum non-adiabatic excited state simulations are used to compute X-ray Raman signals, which are able to sensitively monitor the coherence evolution. Our results verify their vibronic nature, that survives multiple conical intersection passages for several hundred femtoseconds at room temperature. Despite the contributions of highly heterogeneous evolution pathways, the coherences are unambiguously visualized by the experimentally accessible X-ray signals. They offer direct information on the dynamics of electronic and structural degrees of freedom, paving the way for detailed coherence measurements in functional organic materials.

Coherences during the non-adiabatic dynamics of a bichromophoric molecules are probed via stimulated X-ray Raman signals. They survive for several hundred femtoseconds, despite highly heterogeneous contributions across the molecular sampling space.     

Efficient fluoride-selective fluorescent host: experiment and theory

A new naphthalene derivative containing a urea group at the 1,8-position of naphthalene was synthesized and showed a unique absorption and fluorescence peak with fluoride ion. Calculations suggested that a new peak was attributed to the increased anionic character of urea nitrogen due to the strongly charged hydrogen bonding between fluoride and amide protons of the urea. The fluoride selectivity among halides (F(-), Cl(-), Br(-)) comes from the fact that the fluoride approaches much closer to the amide protons than other halides and resides in the cavity with fast dynamics. The nature of electronic transitions that were analyzed from the calculations by the collective electronic oscillator method also supports the anionic nature of the complex between host and fluoride.     

Collective solvent coordinates for the infrared spectrum of HOD in D2O based on an ab initio electrostatic map

An ab initio MP2 vibrational Hamiltonian of HOD in an external electrostatic potential parametrized by the electric field and its gradient-tensor is constructed. By combining it with the fluctuating electric field induced by the D(2)O solvent obtained from molecular dynamics simulations, we calculate the infrared absorption of the O-H stretch. The resulting solvent shift and infrared line shape for three force fields (TIP4P, SPC/E, and SW) are in good agreement with the experiment. A collective coordinate response for the solvent effect is constructed by identifying the main electrostatic field and gradient components contributing to the line shape. This allows a realistic stochastic Liouville equation simulation of the line shapes which is not restricted to Gaussian frequency fluctuations.     

Transport and percolation in disordered systems—A self-consistent time-local approach

A new self-consistent equation for the transport of excitations in disordered systems, which forms the basis for a new class of time-domain coherent potential approximations, is developed. As an example, we calculate the probability of remaining in the original site G₀(t) as well as the second moment of the distribution of excitations r²(t) for a random mixture of donors which satisfy a master equation with short-range transition rates. A percolation-type transition is observed and its characteristics are analyzed both above and below the transition point.Alfred P. Sloan fellow, Camille and Henry Dreyfus teacher-scholar.     

A discrete time markovian inventory model for perishable commodities

In this paper, we analyze a Markovian inventory model for perishable commodities, in which the arrivals of items into the system as well as the demands for these items are assumed to be discrete r.v.'s having a common support {0, 1,…}. Each item in the system is classified into one of N age categories. New items arriving in the system are placed into the first age category. Items of age category j, j = 1,…, N-l, which have not been removed by demand during a day, are placed into age category j+1 at the beginning of the next day. Items of age N, which have not been removed by demand, are registered as outdates. Results concerning the characteristics of such a model are derived for the case of two and three age categories.