Computational investigation of the photoinduced homolytic dissociation of water in the pyridine-water complex / Xiaojun Liu;Andrzej L. Sobolewski;Raffaele Borrelli;Wolfgang Domcke. -In: PHYSICAL CHEMISTRY CHEMICAL PHYSICS. -ISSN 1463-ISSN -9076. -15(2013, pp. 5957-5966. Original Citation:Computational investigation of the photoinduced homolytic dissociation of water in the pyridine-water complex AbstractThe photochemistry of the hydrogen-bonded pyridine-water complex has been investigated with ab initio computational methods. Vertical excitation energies,

A method is proposed to construct a new extended KP hierarchy, which includes two types of KP equation with self-consistent sources and admits reductions to k-constrained KP hierarchy and to Gelfand-Dickey hierarchy with sources. It provides a general way to construct soliton equations with sources and their Lax representations.Comment: Published in Phys. Lett. A, 13 page

In blockchain networks adopting the proof-of-work schemes, the monetary incentive is introduced by the Nakamoto consensus protocol to guide the behaviors of the full nodes (i.e., block miners) in the process of maintaining the consensus about the blockchain state. The block miners have to devote their computation power measured in hash rate in a crypto-puzzle solving competition to win the reward of publishing (a.k.a., mining) new blocks. Due to the exponentially increasing difficulty of the crypto-puzzle, individual block miners tends to join mining pools, i.e., the coalitions of miners, in order to reduce the income variance and earn stable profits. In this paper, we study the dynamics of mining pool selection in a blockchain network, where mining pools may choose arbitrary block mining strategies. We identify the hash rate and the block propagation delay as two major factors determining the outcomes of mining competition, and then model the strategy evolution of the individual miners as an evolutionary game. We provide the theoretical analysis of the evolutionary stability for the pool selection dynamics in a case study of two mining pools. The numerical simulations provide the evidence to support our theoretical discoveries as well as demonstrating the stability in the evolution of miners' strategies in a general case.

A new multicomponent CKP hierarchy and solutionsA combination of dressing method and variation of constants as well as a formula for constructing the eigenfunction is used to solve the extended KP hierarchy, which is a hierarchy with one more series of time flow and based on the symmetry constraint of KP hierarchy. Similarly, extended mKP hierarchy is formulated and its zero-curvature form, Lax representation, and reductions are presented. Via gauge transformation, it is easy to transform dressing solutions of extended KP hierarchy to the solutions of extended mKP hierarchy. Wronskian solutions of extended KP and extended mKP hierarchies are constructed explicitly.

It has recently been shown that low-lying dark charge-separated singlet excited states of nπ* and ππ* character exist in the hydrogen-bonded pyridine-water complex in addition to the familiar nπ* and ππ* excited states of the pyridine chromophore. The former have been shown to promote the transfer of a proton from water to pyridine, resulting in the pyridinyl-hydroxyl radical pair. In the present work, the potential-energy surfaces of the triplet excited states of the pyridine-water complex have been explored with the same ab initio electronic-structure methods (ADC(2), CASPT2). Minimum-energy reaction paths for excited-state H atom transfer, energy surfaces in the vicinity of the barrier for H atom transfer, as well as multistate surface crossings have been characterized. The photochemical reaction mechanisms on the singlet and triplet potential-energy surfaces are compared, and their relevance for photoinduced water oxidation with the pyridine chromophore are discussed.

The hydrogen-bonded acridine-water complex is considered as a model system for the exploration of photochemical reactions which can lead to the splitting of water into H(•) and OH(•) radicals. The vertical excitation energies of the lowest singlet and triplet excited states of the complex were calculated with the CASSCF/CASPT2 and ADC(2) ab initio electronic-structure methods. In addition to the well-known excited states of the acridine chromophore, excited states of charge-transfer character were identified, in which an electron is transferred from the p orbital of the H2O molecule to the π* orbital of acridine. The low-energy barriers which separate these reactive charge-transfer states from the spectroscopic states of the acridine-water complex have been characterized by the calculation of two-dimensional relaxed potential-energy surfaces as functions of the H atom-transfer coordinate and the donor (O)-acceptor (N) distance. When populated, these charge-transfer states drive the transfer of a proton from the water molecule to acridine, which results in the acridinyl-hydroxyl biradical. The same computational methods were employed to explore the photochemistry of the (N-hydrogenated) acridinyl radical. The latter possesses low-lying (about 3.0 eV) ππ* excited states with appreciable oscillator strengths in addition to a low-lying dark ππ* excited state. The bound potential-energy functions of the ππ* excited states are predissociated by the potential-energy function of an excited state of πσ* character which is repulsive with respect to the NH stretching coordinate. The dissociation threshold of the πσ* state is about 2.7 eV and thus below the excitation energies of the bright ππ* states. The conical intersections of the πσ* state with the ππ* excited states and with the electronic ground state provide a mechanism for the direct and fast photodetachment of the H atom from the acridinyl radical. These computational results indicate that the H2O molecule in the acidine-H2O complex can be dissociated into H(•) and OH(•) radicals by the absorption of two visible/ultraviolet photons.

A Wronskian formulation is presented for the Boussinesq equation, which involves a broad set of sufficient conditions consisting of linear partial differential equations. The representative systems of the differential equations in the sufficient conditions are explicitly solved. The obtained solution formulae provide us with a comprehensive approach to construct exact and explicit solutions to the Boussinesq equation, by which solitons, negatons, positons and complexitons are computed for the Boussinesq equation.

A method is proposed in this paper to construct a new extended q-deformed KP (q-KP) hiearchy and its Lax representation. This new extended q-KP hierarchy contains two types of q-deformed KP equation with self-consistent sources, and its two kinds of reductions give the q-deformed Gelfand-Dickey hierarchy with self-consistent sources and the constrained q-deformed KP hierarchy, which include two types of q-deformed KdV equation with sources and two types of q-deformed Boussinesq equation with sources. All of these results reduce to the classical ones when q goes to 1. This provides a general way to construct (2+1)-and (1+1)-dimensional q-deformed soliton equations with sources and their Lax representations.