View source for Bloch-Siegert shift

'''CONQUEST''' is a [[linear function|linear]] scaling, or O(N), [[density functional theory]] (DFT) electronic structure code.<ref name='Bowler2002'>{{cite journal | doi=10.1088/0953-8984/14/11/303 | author=D. R. Bowler, T. Miyazaki and M. J. Gillan | title=Recent progress in linear-scaling ab initio electronic structure techniques | journal=J. Phys. Condens. Matter | volume=14 | pages=2781 | year=2002}}</ref><ref name='Bowler2006'>{{cite journal | author=D. R. Bowler, R. Choudhury, M. J. Gillan and T. Miyazaki | title=Recent progress with large-scale ab initio calculations: The CONQUEST code | journal=Physica Status Solidi | volume=243 | pages=989 | year=}}</ref> 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 (quantum chemistry)|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 [[Germanium|Ge]] on [[Silicon|Si(001)]], containing over 20,000 [[atoms]].<ref name='Miyazaki2008'>{{cite journal | doi=10.1143/JPSJ.77.123706 | author=T. Miyazaki, D. R. Bowler, M. J. Gillan and T. Ohno | title=The energetics of hut-cluster self-assembly in Ge/Si(001) from linear-scaling DFT calculations | journal=J. Phys. Soc. Japan | volume=77 | pages=123706 | year=2008}}</ref> 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.

==Methodology==
Instead of solving for the Kohn-Sham eigenstates as normal DFT codes do, CONQUEST solves for the one particle density matrix, <math>\rho(\mathbf{r},\mathbf{r}^\prime)</math>.  To make the problem computationally tractable, the density matrix is written in separable form:<br />
<math>\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)</math>,
where <math>\phi_{i\alpha}(\mathbf{r})</math> is a ''support function'' centred on atom ''i'' (with support functions on the same atom notated by <math>\alpha</math>) and <math>K_{i\alpha j\beta}</math> is the density matrix in the basis of the support functions.<ref name='Hern95'>{{cite journal | doi=10.1103/PhysRevB.51.10157 | author=E. Hernandez and M. J. Gillan | title=Self-consistent first-principles technique with linear scaling | journal=Phys. Rev. B | volume=51 | pages=10157 | year=1995}}</ref>  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<br />
• Find self-consistency between charge density and potential<br />
• 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: <math>K_{ij} = 0, |\mathbf{R}_i - \mathbf{R}_j| > R_c</math>.  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 Nanotechnology]], [[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.

== See also ==

* [[Density functional theory]]
* [[Quantum chemistry computer programs]]

== External links ==
* [http://www.conquest.ucl.ac.uk/ CONQUEST official website]
* [http://www.nims.go.jp/ National Institute for Materials Science website]
* [http://www.london-nano.com/ London Centre for Nanotechnology website]

== References ==

{{reflist}}

{{DEFAULTSORT:Conquest}}
[[Category:Computational chemistry software]]
[[Category:Physics software]]
[[Category:Density functional theory]]