A Linear Scaling Three Dimensional Fragment Method for Large ScaleElectronic Structure Calculations Page: 2 of 12
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In the past decade, we have witnessed an increasing number of experimental investiga-
tions of structural, electronic, and optical properties of ever more complex nanostructures.
This trend calls for a corresponding set of theoretical ab initio calculations on these nanosys-
tems, some of which may contain tens of thousands of atoms. However, due to the O(N3)
computational scaling  of the direct density functional theory (DFT), it can only be ap-
plied to about one to two thousand atoms despite of the ever increasing computer powers
and parallelism . Over the last 15 years, many linear scaling O(N) electronic structure
algorithms have been proposed . A common algorithm is based on localized orbitals. Un-
fortunately, the use of localized orbitals can lead to local minimum in the energy functionals,
causing convergence problem in the calculations . Besides, it is difficult to represent the
local orbitals with planewave basis which is widely used in material science simulation. The
overlaps between neighboring local orbitals also make the code parallelization not so straight
forward. Overall, there is a continue need for new and simple O(N) ab initio methods which
can be used by a wider population in the computational electronic structure community.
In this paper, we present a new O(N) ab initio electronic structure method and use
it to study dipole moments in CdSe quantum dots. This method satisfies the following
criteria for a good modern O(N) algorithm:(1) It is accurate, obtaining essentially the same
results compared to the direct ab initio method; (2) It is simple, which makes it easy to be
implemented from an existing ab initio code; (3) It is trivially parallelizable, which makes
it suitable for large scale computation; (4) It is applicable to any ab initio method, not
restricted to DFT.
Our method is based on the observation that the total energy of a given system can be
split into two parts: the electrostatic energy and the quantum mechanical energy (e.g, the
kinetic energy and exchange correlation energy). While the electrostatic energy is long-range
and must be solved via a global Poisson equation, the computationally expensive quantum
mechanical energy is short-range  and can be solved locally. Our idea is to divide the whole
system into small fragments, calculate the quantum mechanical energies of these fragments,
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Wang, Lin-Wang; Zhao, Zhengji & Meza, Juan. A Linear Scaling Three Dimensional Fragment Method for Large ScaleElectronic Structure Calculations, article, July 26, 2007; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc893490/m1/2/: accessed April 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.