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Abstract
A possible procedure for calculating the molecular electronic states in mesoscopic inhomogeneous structures is explained based on the results of simulations on different spatial scales. Electrostatic potential is discussed as an essential factor to connect the electronic characteristics of different scales. The procedure is demonstrated by applying the results of hierarchical simulations on the structural formula of a polyelectrolyte (Nafion, a DuPont trademark) molecule to the electronic state calculations for a hydronium ion in a hydrated Nafion membrane via the mesoscopic structure of the membrane. The mesoscopic simulation method adopted here is dissipative particle dynamics (DPD), which is a coarse graining simulation method with dissipative and randomly fluctuating force terms. A mixed basis function method is introduced for electronic state calculations in inhomogeneous fields as a combination of Gaussian basis functions and shape functions of the finite element method (FEM) for expressing electronic wavefunctions. The procedure of the multi-scale simulation represents a practical example of ones reproducing electronic structural information within a mesoscopic inhomogeneous structure.
Acknowledgements
The author is grateful to Dr S. Yamamoto and Mr S. Yamakawa for their enthusiastic collaboration.
Notes
†A fundamental characteristic of macroscopic systems is that the system has a large degree of freedom and irreversibility. In the present text, only the problem of large degree of freedom is discussed, focusing on the multi-scale simulation procedure at different spatial scales. The term “long-range timescale” has meaning in a system with irreversibility, because the correlation of motion on a short-range time-scale will be smeared out for motions in a system having a large degree of freedom.