CONQUEST
Encyclopedia
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.
. To make the problem computationally tractable, the density matrix is written in separable form:
,
where
is a support function centred on atom i (with support functions on the same atom notated by 
) and 
is the density matrix in the basis of the support functions. The ground state is found as a series of nested loops:
• Minimise the energy with respect to the density matrix for fixed charge density and support functions
• Find self-consistency between charge density and potential
• Minimise the energy with respect to the support functions
The support functions are confined within spheres of given cutoff radius and the density matrix is forced to zero beyond a given range:
. These approximations give linear scaling behaviour, and as the radii are increased tend to the exact result.
, University College London
in the UK and at the Computational Materials Science Centre, National Institute for Materials Science
, Tsukuba, Japan. In the UK, the development team includes Dr. David Bowler, Dr. Veronika Brazdova, Prof. Mike Gillan, Dr. Andrew Horsfield, Mr. Alex Sena and Mr. Lianheng Tong, who are all members of the Thomas Young Centre
; in Japan, the development team includes Dr. Tsuyoshi Miyazaki, Dr. Takahisa Ohno, Dr. Takao Ohtsuka, Dr. Milica Todorovic and Dr. Antonio Torralba.
Previous developers include Ian Bush, Rathin Choudhury, Chris Goringe and Eduardo Hernandez.
Linear function
In mathematics, the term linear function can refer to either of two different but related concepts:* a first-degree polynomial function of one variable;* a map between two vector spaces that preserves vector addition and scalar multiplication....
scaling, or O(N), density functional theory
Density functional theory
Density functional theory is a quantum mechanical modelling method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular atoms, molecules, and the condensed phases. With this theory, the properties of a many-electron system can be determined by...
(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
Plane wave
In the physics of wave propagation, a plane wave is a constant-frequency wave whose wavefronts are infinite parallel planes of constant peak-to-peak amplitude normal to the phase velocity vector....
accuracy. It has been applied to the study of three dimensional reconstructions formed by Ge
Germanium
Germanium is a chemical element with the symbol Ge and atomic number 32. It is a lustrous, hard, grayish-white metalloid in the carbon group, chemically similar to its group neighbors tin and silicon. The isolated element is a semiconductor, with an appearance most similar to elemental silicon....
on Si(001)
Silicon
Silicon is a chemical element with the symbol Si and atomic number 14. A tetravalent metalloid, it is less reactive than its chemical analog carbon, the nonmetal directly above it in the periodic table, but more reactive than germanium, the metalloid directly below it in the table...
, containing over 20,000 atoms. Tests on the UK's national supercomputer HECToR
HECToR
HECToR is a British academic national supercomputer service funded by EPSRC, NERC and BBSRC for the UK academic community. The HECToR service is run by partners including EPCC, STFC and Numerical Algorithms Group ....
in 2009 demonstrated the capability of the code to perform ground-state calculations on systems of over 1,000,000 atoms.
Methodology
Instead of solving for the Kohn-Sham eigenstates as normal DFT codes do, CONQUEST solves for the one particle density matrix,. To make the problem computationally tractable, the density matrix is written in separable form:,where
is a support function centred on atom i (with support functions on the same atom notated by ) and is the density matrix in the basis of the support functions. The ground state is found as a series of nested loops:• Minimise the energy with respect to the density matrix for fixed charge density and support functions
• Find self-consistency between charge density and potential
• Minimise the energy with respect to the support functions
The support functions are confined within spheres of given cutoff radius and the density matrix is forced to zero beyond a given range:
. These approximations give linear scaling behaviour, and as the radii are increased tend to the exact result.Developers
CONQUEST is jointly developed at the Department of Physics and Astronomy and London Centre for NanotechnologyLondon Centre for Nanotechnology
The London Centre for Nanotechnology is a multidisciplinary research centre in physical and biomedical nanotechnology in London, United Kingdom. It brings together two institutions that are world leaders in nanotechnology, University College London and Imperial College London...
, University College London
University College London
University College London is a public research university located in London, United Kingdom and the oldest and largest constituent college of the federal University of London...
in the UK and at the Computational Materials Science Centre, National Institute for Materials Science
National Institute for Materials Science
is an Independent Administrative Institution and one of the largest scientific research centers in Japan.- History :The growth and development of today's scientific research center has passed through several phases in a number of locations:...
, Tsukuba, Japan. In the UK, the development team includes Dr. David Bowler, Dr. Veronika Brazdova, Prof. Mike Gillan, Dr. Andrew Horsfield, Mr. Alex Sena and Mr. Lianheng Tong, who are all members of the Thomas Young Centre
Thomas Young Centre
The Thomas Young Centre is an alliance of London research groups working on the theory and simulation ofmaterials .It is named after the celebrated scientist and polymath Thomas Young , who lived and worked in London and is known in the world of science for a number of important discoveries...
; in Japan, the development team includes Dr. Tsuyoshi Miyazaki, Dr. Takahisa Ohno, Dr. Takao Ohtsuka, Dr. Milica Todorovic and Dr. Antonio Torralba.
Previous developers include Ian Bush, Rathin Choudhury, Chris Goringe and Eduardo Hernandez.