Comparison of photoelectron transfer in solution and the solid state for two intervalence radical cations

[structure: see text] The optical diffuse reflectance and solution spectra of two bis-hydrazine radical cationic intervalence compounds have been compared. The results are consistent with an ion-pairing increase and an "effective polarity" in these crystals that is not far from that of acetonitrile or other polar solvents.     

Decision-dependent probabilities in stochastic programs with recourse

Stochastic programming with recourse usually assumes uncertainty to be exogenous. Our work presents modelling and application of decision-dependent uncertainty in mathematical programming including a taxonomy of stochastic programming recourse models with decision-dependent uncertainty. The work includes several ways of incorporating direct or indirect manipulation of underlying probability distributions through decision variables in two-stage stochastic programming problems. Two-stage models are formulated where prior probabilities are distorted through an affine transformation or combined using a convex combination of several probability distributions. Additionally, we present models where the parameters of the probability distribution are first-stage decision variables. The probability distributions are either incorporated in the model using the exact expression or by using a rational approximation. Test instances for each formulation are solved with a commercial solver, BARON, using selective branching.     

A branch-and-bound method for discretely-constrained mathematical programs with equilibrium constraints

We present a branch-and-bound algorithm for discretely-constrained mathematical programs with equilibrium constraints (DC-MPEC). This is a class of bilevel programs with an integer program in the upper-level and a complementarity problem in the lower-level. The algorithm builds on the work by Gabriel et al. (Journal of the Operational Research Society 61(9):1404–1419, 2010) and uses Benders decomposition to form a master problem and a subproblem. The new dynamic partition scheme that we present ensures that the algorithm converges to the global optimum. Partitioning is done to overcome the non-convexity of the Benders subproblem. In addition Lagrangean relaxation provides bounds that enable fathoming in the branching tree and warm-starting the Benders algorithm. Numerical tests show significantly reduced solution times compared to the original algorithm. When the lower level problem is stochastic our algorithm can easily be further decomposed using scenario decomposition. This is demonstrated on a realistic case.     

Efficient computation of Lyapunov functions for nonlinear systems by integrating numerical solutions

Nonlinear Dynamics - A strict Lyapunov function for an equilibrium of a dynamical system asserts its asymptotic stability and gives a lower bound on its basin of attraction. For nonlinear systems,...     

Excited-state mixed-valence distortions in a diisopropyl diphenyl hydrazine cation

Excited-state mixed valence (ESMV) occurs in the 1,2-diphenyl-1,2-diisopropyl hydrazine radical cation, a molecule in which the ground state has a symmetrical charge distribution localized primarily on the hydrazine, but the phenyl to hydrazine charge-transfer excited state has two interchangeably equivalent phenyl groups that have different formal oxidation states. Electronic absorption and resonance Raman spectra are presented. The neighboring orbital model is employed to interpret the absorption spectrum and coupling. Resonance Raman spectroscopy is used to determine the excited-state distortions. The frequencies of the enhanced modes from the resonance Raman spectra are used together with the time-dependent theory of spectroscopy to fit the two observed absorption bands that have resolved vibronic structure. The origins of the vibronic structure and relationships with the neighboring orbital model are discussed.     

Photochemical charge separation within aromatic hydrazines and the effect of excited-state intervalence in dihydrazines

Photolysis into the longest wavelength absorption band of 2-tert-butyl-2,3-diazabicyclo[2.2.2]oct-3-yl hydrazine (Hy) substituted naphthalenes causes aryl group reduction electron transfer to give (+)Hy-Ar(-). Electrooptical absorption measurements characterize the charge separation properties from these bands. Emission studies demonstrate that the separation between absorption and emission maxima for symmetrically disubstituted compounds is smaller than that for monosubstituted compounds, which is attributed to excited-state intervalence. The excited-state diabatic surfaces may be described as a Hy(+)-NA(- )-Hy(0), Hy(0)-NA(-)-Hy(+) pair, for which electronic interaction produces a double minimum that qualitatively resembles that in the ground state of the disubstituted intervalence radical cations.     

Spectroscopic consequences of a mixed valence excited state: quantitative treatment of a dihydrazine diradical dication

A model for the quantitative treatment of molecular systems possessing mixed valence excited states is introduced and used to explain observed spectroscopic consequences. The specific example studied in this paper is 1,4-bis(2-tert-butyl-2,3-diazabicyclo[2.2.2]oct-3-yl)-2,3,5,6-tetramethylbenzene-1,4-diyl dication. The lowest energy excited state of this molecule arises from a transition from the ground state where one positive charge is associated with each of the hydrazine units, to an excited state where both charges are associated with one of the hydrazine units, that is, a Hy-to-Hy charge transfer. The resulting excited state is a Class II mixed valence molecule. The electronic emission and absorption spectra, and resonance Raman spectra, of this molecule are reported. The lowest energy absorption band is asymmetric with a weak low-energy shoulder and an intense higher energy peak. Emission is observed at low temperature. The details of the absorption and emission spectra are calculated for the coupled surfaces by using the time-dependent theory of spectroscopy. The calculations are carried out in the diabatic basis, but the nuclear kinetic energy is explicitly included and the calculations are exact quantum calculations of the model Hamiltonian. Because the transition involves the transfer of an electron from the hydrazine on one side of the molecule to the hydrazine on the other side and vice versa, the two transitions are antiparallel and the transition dipole moments have opposite signs. Upon transformation to the adiabatic basis, the dipole moment for the transition to the highest energy adiabatic surface is nonzero, but that for the transition to the lowest surface changes sign at the origin. The energy separation between the two components of the absorption spectrum is twice the coupling between the diabatic basis states. The bandwidths of the electronic spectra are caused by progressions in totally symmetric modes as well as progressions in the modes along the coupled coordinate. The totally symmetric modes are modeled as displaced harmonic oscillators; the frequencies and displacements are determined from resonance Raman spectra. The absorption, emission, and Raman spectra are fit simultaneously with one parameter set. The coupling in the excited electronic state H(ab)(ex) is 2000 cm(-1). Excited-state mixed valence is expected to be an important contributor to the electronic spectra of many organic and inorganic compounds. The energy separations and relative intensities enable the excited-state properties to be calculated as shown in this paper, and the spectra provide new information for probing and understanding coupling in mixed valence systems.     

Multi-horizon stochastic programming

Infrastructure-planning models are challenging because of their combination of different time scales: while planning and building the infrastructure involves strategic decisions with time horizons of many years, one needs an operational time scale to get a proper picture of the infrastructure’s performance and profitability. In addition, both the strategic and operational levels are typically subject to significant uncertainty, which has to be taken into account. This combination of uncertainties on two different time scales creates problems for the traditional multistage stochastic-programming formulation of the problem due to the exponential growth in model size. In this paper, we present an alternative formulation of the problem that combines the two time scales, using what we call a multi-horizon approach, and illustrate it on a stylized optimization model. We show that the new approach drastically reduces the model size compared to the traditional formulation and present two real-life applications from energy planning.     

A generalized global optimization formulation of the pooling problem with processing facilities and composite quality constraints

We present a generalized formulation of the pooling problem. Our formulation is different from the standard formulations in explicitly modeling component flows. Modeling the physical components directly, allows easy inclusion of processing facilities that may alter the flow composition. It also allows adding composite quality constraints that cannot be added directly as quality parameters as they do not blend linearly. We provide new test instances motivated by natural gas transport problems at the Norwegian Continental Shelf and give computational results. We show examples of nonlinear composite constraints on quality attributes and give computational results on the effect of adding such constraints to the new set of test instances. The increased flexibility of our formulation comes at the cost of less tight constraints and a performance penalty on existing test cases in literature. The advantage is that it can solve the more general test cases described above. We use GAMS implementations of the various formulations and solve the problems with BARON. We compare the performance of our bilinear formulation in BARON with discretizations solved as a Mixed Integer Linear Program using CPLEX. The discretized versions do not generally perform as well as the continuous model; however, they have better worst-case behavior on the new test cases.