Integrated Multiscale Modeling of Molecular Computing Devices

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The main bottleneck in modeling transport in molecular devices is to develop the correct formulation of the problem and efficient algorithms for analyzing the electronic structure and dynamics using, for example, the time-dependent density functional theory. We have divided this task into several steps. The first step is to developing the right mathematical formulation and numerical algorithms for analyzing the electronic structure using density functional theory. The second step is to study time-dependent density functional theory, particularly the far-field boundary conditions. The third step is to study electronic transport in molecular devices. We are now at the end of the ... continued below

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E, Weinan March 29, 2012.

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Description

The main bottleneck in modeling transport in molecular devices is to develop the correct formulation of the problem and efficient algorithms for analyzing the electronic structure and dynamics using, for example, the time-dependent density functional theory. We have divided this task into several steps. The first step is to developing the right mathematical formulation and numerical algorithms for analyzing the electronic structure using density functional theory. The second step is to study time-dependent density functional theory, particularly the far-field boundary conditions. The third step is to study electronic transport in molecular devices. We are now at the end of the first step. Under DOE support, we have made subtantial progress in developing linear scaling and sub-linear scaling algorithms for electronic structure analysis. Although there has been a huge amount of effort in the past on developing linear scaling algorithms, most of the algorithms developed suffer from the lack of robustness and controllable accuracy. We have made the following progress: (1) We have analyzed thoroughly the localization properties of the wave-functions. We have developed a clear understanding of the physical as well as mathematical origin of the decay properties. One important conclusion is that even for metals, one can choose wavefunctions that decay faster than any algebraic power. (2) We have developed algorithms that make use of these localization properties. Our algorithms are based on non-orthogonal formulations of the density functional theory. Our key contribution is to add a localization step into the algorithm. The addition of this localization step makes the algorithm quite robust and much more accurate. Moreover, we can control the accuracy of these algorithms by changing the numerical parameters. (3) We have considerably improved the Fermi operator expansion (FOE) approach. Through pole expansion, we have developed the optimal scaling FOE algorithm.

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  • Report No.: DOE/ER/25587/1
  • Grant Number: FG02-03ER25587
  • DOI: 10.2172/1037453 | External Link
  • Office of Scientific & Technical Information Report Number: 1037453
  • Archival Resource Key: ark:/67531/metadc835422

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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  • March 29, 2012

Added to The UNT Digital Library

  • May 19, 2016, 3:16 p.m.

Description Last Updated

  • Nov. 29, 2016, 3:59 p.m.

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E, Weinan. Integrated Multiscale Modeling of Molecular Computing Devices, report, March 29, 2012; United States. (digital.library.unt.edu/ark:/67531/metadc835422/: accessed November 19, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.