The Linearly Scaling three-dimensional fragment (LS3DF) method is an O(N) ab initio electronic structure method for large-scale nano material simulations. It is a divide-and-conquer approach with a novel patching scheme that effectively cancels out the artificial boundary effects, which exist in all divide-and-conquer schemes. This method has made ab initio simulations of thousand-atom nanosystems feasible in a couple of hours, while retaining essentially the same accuracy as the direct calculation methods. The LS3DF method won the 2008 ACM Gordon Bell Prize for algorithm innovation. Our code has reached 442 Tflop/s running on 147,456 processors on the Cray XT5 (Jaguar) at OLCF, and has been run on 163,840 processors on the Blue Gene/P (Intrepid) at ALCF, and has been applied to a system containing 36,000 atoms. In this paper, we will present the recent parallel performance results of this code, and will apply the method to asymmetric CdSe/CdS core/shell nanorods, which have potential applications in electronic devices and solar cells.

# Your search: "author:"Zhao, Zhengji""

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## Scholarly Works (10 results)

Atomic scale surface structure plays an important role indescribing many properties of materials, especially in the case of nanomaterials. One of the most effective techniques for surface structure determination is low-energy electron diffraction (LEED), which can be used in conjunction with optimization to fit simulated LEED intensities to experimental data. This optimization problem has a number of characteristics that make it challenging: it has many local minima, the optimization variables can be either continuous or categorical, the objective function can be discontinuous, there are no exact analytic derivatives (and no derivatives at all for categorical variables), and function evaluations are expensive. In this study, we show how to apply a particular class of optimization methods known as pattern search methods to address these challenges. These methods donot explicitly use derivatives, and are particularly appropriate when categorical variables are present, an important feature that has not been addressed in previous LEED studies. We have found that pattern search methods can produce excellent results, compared to previously used methods, both in terms of performance and locating optimal results.

We present a linear scaling 3 dimensional fragment (LS3DF) method that uses a novel decomposition and patching scheme to do ab initio density functional theory (DFT) calculations for large systems. This method cancels out the artificial boundary effects that arise from the spatial decomposition. As a result, the LS3DF results are essentially the same as the original full-system DFT results with errors smaller than the errors introduced by other sources of numerical approximations. In addition, the resulting computational times are thousands of times smaller than conventional DFT methods, making calculations with 100,000 atom systems possible. The LS3DF method is applicable to insulator and semiconductor systems, which covers a current gap in the DOE's materials science code portfolio for large-scale ab initio simulations.

### A Linear Scaling Three Dimensional Fragment Method for Large Scale Electronic Structure
Calculations

We present a novel linear scaling ab initio total energy electronic structure calculation method, which is simple to implement, easily to parallelize, and produces essentially the same results as the direct ab initio method, while it could be thousands of times faster. Using this method, we have studied the dipole moments of CdSe quantum dots, and found both significant bulk and surface contributions. The bulk dipole contribution cannot simply be estimated from the bulk spontaneous polarization value by a proportional volume factor. Instead it has a geometry dependent screening effect. The dipole moment also produces a strong internal electric field which induces a strong electron hole separation.

A simple method to estimate the atomic degree Hessian matrix of a nanosystem is presented. The estimated Hessian matrix, based on the motif decomposition of the nanosystem, can be used to accelerate ab initio atomic relaxations with speedups of 2 to 4 depending on the size of the system. In addition, the programing implementation for using this method in a standard ab initio package is trivial.

Using atomistic empirical pseudopotentials, we have calculated the electronic structures of CdSe nanowires with a bulged area. The localized state wavefunctions and their binding energies are calculated, and their dependences on the bulged area shape are analyzed. We find that both the binding energy and the wavefunction localization strongly depend on the bulged area shape, with the most compact shape produces the largest binding energy and strongest wavefunction localization. We also find that the top of the valence band state has a weaker localization than the bottom of the conduction band state due to an effective mass anisotropy.