ConQuesT

CONQUEST is a linear scaling, or O(N), density functional theory (DFT) electronic structure code. The code is designed to perform DFT calculations on very large systems containing many thousands of atoms. It can be run at different levels of precision ranging from ab initio tight binding up to full DFT with plane wave accuracy. It has been applied to the study of three-dimensional reconstructions formed by Ge on Si(001), containing over 20,000 atoms. Tests on the UK's national supercomputer HECToR in 2009 demonstrated the capability of the code to perform ground-state calculations on systems of over 1,000,000 atoms.

Instead of solving for the Kohn-Sham eigenstates as normal DFT codes do, CONQUEST solves for the one particle density matrix, ${\displaystyle \rho (\mathbf {r} ,\mathbf {r} ^{\prime })}$. To make the problem computationally tractable, the density matrix is written in separable form:
${\displaystyle \rho (\mathbf {r} ,\mathbf {r} ^{\prime })=\sum _{i\alpha j\beta }\phi _{i\alpha }(\mathbf {r} )K_{i\alpha j\beta }\phi _{j\beta }(\mathbf {r} ^{\prime })}$, where ${\displaystyle \phi _{i\alpha }(\mathbf {r} )}$ is a support function centred on atom i (with support functions on the same atom notated by ${\displaystyle \alpha }$) and ${\displaystyle K_{i\alpha j\beta }}$ is the density matrix in the basis of the support functions. The ground state is found as a series of nested loops:

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