Full vs Partial Market Coverage with Minimum Quality Standards

The consequences of the adoption of quality standards on the extent of market coverage is investigated by modelling a game between regulator and low-quality firm in a vertically differentiated duopoly. The game has a unique equilibrium in the most part of the parameter range. There exists a non-negligible range where the game has no equilibrium in pure strategies. This result questions the feasibility of MQS regulation when firms endogenously determine market coverage

An ab initio multiple cloning approach for the simulation of photoinduced dynamics in conjugated molecules

We present a new implementation of the Ab Initio Multiple Cloning (AIMC) method, which is applied for non-adiabatic excited-state molecular dynamics simulations of photoinduced processes in conjugated molecules. Within our framework, the multidimensional wave-function is decomposed into a superposition of a number of Gaussian coherent states guided by Ehrenfest trajectories that are suited to clone and swap their electronic amplitudes throughout the simulation. New generalized cloning criteria are defined and tested. Because of sharp changes of the electronic states, which are common for conjugated polymers, the electronic parts of the Gaussian coherent states are represented in the Time Dependent Diabatic Basis (TDDB). The input to these simulations in terms of the excited-state energies, gradients and non-adiabatic couplings, is calculated on-the-fly using the Collective Electron Oscillator (CEO) approach. As a test case, we consider the photoinduced unidirectional electronic and vibrational energy transfer between two- and three-ring linear poly(phenylene ethynylene) units linked by meta-substitution. The effects of the cloning procedure on electronic and vibrational coherence, relaxation and unidirectional energy transfer between dendritic branches are discussed

Photoinduced non-adiabatic energy transfer pathways in dendrimer building blocks

The efficiency of the intramolecular energy transfer in light harvesting dendrimers is determined by their well-defined architecture with high degree of order. After photoexcitation, through-space and through-bond energy transfer mechanisms can take place, involving vectorial exciton migration among different chromophores within dendrimer highly branched structures. Their inherent intramolecular energy gradient depends on how the multiple chromophoric units have been assembled, subject to their inter-connects, spatial distances, and orientations. Herein, we compare the photoinduced nonadiabatic molecular dynamics simulations performed on a set of different combinations of a chain of linked dendrimer building blocks composed of two-, three-, and four-ring linear polyphenylene chromophoric units. The calculations are performed with the recently developed ab initio multiple cloning-time dependent diabatic basis implementation of the Multiconfigurational Ehrenfest (MCE) approach. Despite differences in short time relaxation pathways and different initial exciton localization, at longer time scales, electronic relaxation rates and exciton final redistributions are very similar for all combinations. Unlike the systems composed of two building blocks, considered previously, for the larger 3 block systems here we observe that bifurcation of the wave function accounted by cloning is important. In all the systems considered in this work, at the time scale of few hundreds of femtoseconds, cloning enhances the electronic energy relaxation by ∼13% compared to that of the MCE method without cloning. Thus, accurate description of quantum effects is essential for understanding of the energy exchange in dendrimers both at short and long time scales

Vibronic Quantum Beating between Electronic Excited States in a Heterodimer

Energy transfer in multichromophoric molecules can be affected by coherences that are induced by the electronic and vibrational couplings between chromophore units. Coherent electron-vibrational dynamics can persist at the subpicosecond time scale even at room temperature. Furthermore, wave-like localized-delocalized motions of the electronic wave function can be modulated by vibrations that actively participate in the intermolecular energy transfer process. Herein, nonadiabatic excited state molecular dynamics simulations have been performed on a rigid synthetic heterodimer that has been proposed as a simplified model for investigating the role and mechanism of coherent energy transfer in multichromophoric systems. Both surface hopping (SH) and Ehrenfest approaches (EHR) have been considered. After photoexcitation of the system at room temperature, EHR simulations reveal an ultrafast beating of electronic populations between the two lowest electronic states. These oscillations are not observed at low temperature and have vibrational origins. Furthermore, they cannot be reproduced using SH approach. This periodic behavior of electronic populations induces oscillations in the spatial localization of the electronic transition density between monomers. Vibrations whose frequencies are near-resonant with energy difference between the two lowest electronic excited states are in the range of the electronic population beating, and they are the ones that contribute the most to the coherent dynamics of these electronic transitions

Nonadiabatic Excited-State Molecular Dynamics Methodologies: Comparison and Convergence

Direct atomistic simulation of nonadiabatic molecular dynamics is a challenging goal that allows important insights into fundamental physical phenomena. A variety of frameworks, ranging from fully quantum treatment of nuclei to semiclassical and mixed quantum–classical approaches, were developed. These algorithms are then coupled to specific electronic structure techniques. Such diversity and lack of standardized implementation make it difficult to compare the performance of different methodologies when treating realistic systems. Here, we compare three popular methods for large chromophores: Ehrenfest, surface hopping, and multiconfigurational Ehrenfest with ab initio multiple cloning (MCE-AIMC). These approaches are implemented in the NEXMD software, which features a common computational chemistry model. The resulting comparisons reveal the method performance for population relaxation and coherent vibronic dynamics. Finally, we study the numerical convergence of MCE-AIMC algorithms by considering the number of trajectories, cloning thresholds, and Gaussian wavepacket width. Our results provide helpful reference data for selecting an optimal methodology for simulating excited-state molecular dynamics