Interpretation of unusual absorption bandwidths and resonance Raman intensities in excited state mixed valence

Excited state mixed valence (ESMV) occurs in molecules in which the ground state has a symmetrical charge distribution but the excited state possesses two or more interchangeably equivalent sites that have different formal oxidation states. Although mixed valence excited states are relatively common in both organic and inorganic molecules, their properties have only recently been explored, primarily because their spectroscopic features are usually overlapped or obscured by other transitions in the molecule. The mixed valence excited state absorption bands of 2,3-di-p-anisyl-2,3-diazabicyclo[2.2.2]octane radical cation are well-separated from others in the absorption spectrum and are particularly well-suited for detailed analysis using the ESMV model. Excited state coupling splits the absorption band into two components. The lower energy component is broader and more intense than the higher energy component. The absorption bandwidths are caused by progressions in totally symmetric modes, and the difference in bandwidths is caused by the coordinate dependence of the excited state coupling. The Raman intensities obtained in resonance with the high and low energy components differ significantly from those expected based on the oscillator strengths of the bands. This unexpected observation is a result of the excited state coupling and is explained by both the averaging of the transition dipole moment orientation over all angles for the two types of spectroscopies and the coordinate-dependent coupling. The absorption spectrum is fit using a coupled two-state model in which both symmetric and asymmetric coordinates are included. The physical meaning of the observed resonance Raman intensity trends is discussed along with the origin of the coordinate-dependent coupling. The well-separated mixed valence excited state spectroscopic components enable detailed electronic and resonance Raman data to be obtained from which the model can be more fully developed and tested.     

Classical curves via one-vertex maps

One-vertex maps (a type of dessin d’enfant) give a uniform characterization of certain well-known algebraic curves, including those of Klein, Wiman, Accola–Maclachlan and Kulkarni. The characterization depends on a new classification of one-vertex (dually, one-face or unicellular) maps according to the size of the group of map automorphisms. We use an equivalence relation appropriate for studying the faithful action of the absolute Galois group on dessins, although we do not pursue that line of inquiry here.     

Strategic response to pollution taxes in supply chain networks: Dynamic,spatial, and organizational dimensions

This paper presents a model of the strategic behavior of firms operating in a spatial supply chain network. The manufacturing and retailing firms engage in an oligopolistic, noncooperative game by sharing customer demand such that a firm’s decisions impact the product prices, which in turn result in changes in all other firms’ decisions. Each firm’s payoff is to maximize its own profit and we show that, in response to such changes in prices and to exogenous environmental taxes, the manufacturing firms may strategically alter a variety of choices such as ’make-buy’ decisions with respect to intermediate inputs, spatial distribution of production, product shipment patterns and inventory management, environmental tax payment vs recycling decisions, and timing of all such choices to sustainably manage the profit and the environmental regulations. An important implication is that effects of a tax depends on the oligopolistic game structure. With respect to methods, we show that this dynamic game can be represented as a set of differential variational inequalities (DVIs) that motivate a computationally efficient nonlinear complementarity (NCP) approach that enables the full exploitation of above-mentioned salient features. We also provide a numerical example that confirms the utility of our proposed framework and shows substantial strategic reaction can be expected to a tax on pollution stocks.     

Modelling toolkit to assist with introducing a stepped care system design in mental health care

We describe a modelling toolkit that was developed with the aim of assisting those responsible for introducing stepped care systems to local mental health services in the UK. The toolkit was pre-populated with real patient flow data collected from four sites that piloted the stepped care system design. Two analytical models were developed and coded as part of the toolkit to provide insights concerning workload, patient throughput, and changes in waiting times and waiting list size. An interface was built to allow users to specify their own stepped care system and input their own estimates or data of service demands and capacities at different steps. Despite the challenges and limitations, the use of modelling to inform the design of new service configurations is an important step in the right direction and we would recommend this as a reasonable way forward.     

Synthesis, coordination studies and redox properties of a novel ditertiary phosphine bearing two ferrocenyl groups

The new ferrocenyl substituted ditertiary phosphine {FcCH₂N(CH₂PPh₂)CH₂}₂ [Fc = (η⁵-C₅H₄)Fe(η⁵-C₅H₅)] (1) was prepared, in 72% yield, by Mannich based condensation of the known bis secondary amine {FcCH₂N(H)CH₂}₂ with 2 equiv. of Ph₂PCH₂OH in CH₃OH. Phosphine 1 readily coordinates to various transition-metal centres including Mo⁰, Ru^II, Rh^I, Pd^II, Pt^II and Au^I to afford the heterometallic complexes {RuCl₂(p-cym)}₂(1) (2), (AuCl)₂(1) (3), cis-PtCl₂(1) (4), cis-PdCl₂(1) (5), cis-Mo(CO)₄(1) (6), trans,trans-{Pd(CH₃)Cl(1)}₂ (7) and trans,trans-{Rh(CO)Cl(1)}₂ (8). In complexes 2, 3, 7 and 8 ligand 1 displays a P,P′-bridging mode whilst for 4-6 a P,P′-chelating mode is observed. All new compounds have been fully characterised by spectroscopic and analytical methods. Furthermore the structures of 1, 2 · 2CH₂Cl₂, 3 · CH₂Cl₂, 4 · CH₂Cl₂, 6 · 0.5CHCl₃ and 8 have been elucidated by single crystal X-ray crystallography. Electrochemical measurements have been undertaken, and their redox chemistry discussed, on both noncomplexed ligand 1 and representative compounds containing this new ditertiary phosphine.