# Workshops

## Linear-scaling ab initio calculations: applications and future directions

### Organisers

- Chris-Kriton Skylaris
*(University of Southampton, United Kingdom)* - Peter Haynes
*(Imperial College London, United Kingdom)* - Jean-Luc Fattebert
*(Lawrence Livermore National Research Laboratory, USA)* - David R. Bowler
*(University College London, United Kingdom)* - Mike Gillan
*(Department of Physics and Astronomy, University College London, United Kingdom)*

### Supports

The CCP9 network of the EPSRC (UK) encourages participation of UK academics to workshops related to electronic structure theory by covering part of their expenses.

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### Description

The study of properties and of processes in materials, frequently hinges upon understanding phenomena which originate at the atomic level. In such cases the accurate description of the interactions between large numbers of atoms is critical and in turn requires the accurate description of the electrons which play a crucial role in the bonding of atoms into molecules, surfaces and solids. This can only be achieved by solving the equations of quantum mechanics. These equations are too complicated to solve exactly; however their solutions can be approximated by computational techniques. The most accurate but also most computationally demanding are the ab initio techniques which do not use any empirical adjustable parameters. Amongst them, the Density Functional Theory (DFT) formulation of quantum mechanics stands out as an excellent compromise between accuracy and computational efficiency. However, the applicability of ab initio techniques is severely limited by poor scaling: the computational effort needed to perform an ab initio calculation increases with (at least) the third power of the number of atoms, N. This cubic-scaling bottleneck limits the number of atoms we can study to a few hundred at most, even on parallel supercomputers.

To overcome this length-scale limitation, a number of researchers worldwide have been pioneering the development of a novel class of ab initio methods with linear-scaling or Order N" (O(N)) computational cost which nevertheless retain the same high level of accuracy as the conventional approaches. While physically motivated, such methods have proved particularly hard to develop as they introduce highly non-trivial localisation constraints. Nevertheless, many major obstacles have been overcome and a number of O(N) methods (SIESTA, CONQUEST, ONETEP, etc.) for ground state DFT calculations on systems with a gap (e.g. molecules, semiconductors and insulators) are now available and have reached a state of maturity that allows them to be used to study "real" materials. The particular focus of this workshop is therefore to look forward to what can be achieved in the next few years. Our aim is twofold:

(1) As O(N) methods are currently extending the applicability of DFT calculations to problems involving biomolecules and nanostructures they are leading to completely new levels of understanding of these systems. This CECAM meeting will give us the opportunity to make an appraisal of such large-scale simulations and their potential to connect more directly to experiments.

(2) We also want to examine the options for extending linear-scaling to problems that cannot be treated by ground-state DFT but require other, more complex approaches. These include methods for treating metallic systems, excited states and wavefunction-based theories for including electronic correlation. Finding ways to transform these methods to linear-scaling cost, and hence extent their applicability to the nano-scale, is the next big challenge that the community of developers of large-scale electronic structure methods is beginning to face. We hope that this workshop will stimulate these major new O(N) methodological developments by bringing together the leading groups in the development of O(N) DFT methods with the leading groups in the development of metal and excited-state or wavefunction-based methods.

Strong emphasis during the workshop will be given to discussion in order to promote the exchange of ideas between different communities (Physics, Chemistry, Materials Science, Biochemistry) which are all interested in large-scale applications with ab initio accuracy but are approaching them from different perspectives.

### References

1) D. Alfe and M. J. Gillan. Linear-scaling quantum Monte Carlo with non-orthogonal localized orbitals. J. Phys.: Condens. Matter, 16:L305, 2004.

2) D. R. Bowler, T. Miyazaki, and M. J. Gillan. Recent progress in linear scaling ab initio electronic structure techniques. J. Phys.: Condens. Matter, 14:2781, 2002.

3) M. Brandbyge, J.-L. Mozos, P. Ordejon, J. Taylor, and Stokbro K. Density-functional method for nonequilibrium electron transport. J. Chem. Phys., 65:165401, 2002.

4) M. Buongiorno Nardelli, J.-L. Fattebert, and J. Bernholc. O(n) real-space method for ab initio quantum transport calculations: Applications to carbon nanotube-metal contacts. Phys. Rev.

B, 64:254423, 2001.

5) J.-L. Fattebert and Gygi F. Linear-scaling ¯rst-principles molecular dynamics with plane-waves accuracy. Phys. Rev. B, 73:115124, 2006.

6) Jean-Luc Fattebert and Francois Gygi. Linear scaling First-principles molecular dynamics with controlled accuracy. Comput. Phys. Commun., 162:24, 2004.

7) Stefan Goedecker. Linear scaling electronic structure methods. Rev. Mod. Phys., 71(4):1085, 1999.

8) T. Han M. J., Ozaki and J. Yu. O(N) LDA+U electronic structure calculation method based on the nonorthogonal pseudoatomic orbital basis. Phys. Rev. B, 73:045110, 2006.

9) L. Heady, M. Fenandez-Serra, S. Joyce, A. R. Venkitaraman, E. Artacho, C.-K. Skylaris, Colombi Ciacchi, and M. C. Payne. Novel structural features of CKD inhibition revealed by an

ab initio computational method combined with dynamic simulations. J. Med. Chem., 49:5141, 2006.

10) K. Li, D. R. Bowler, and M. J. Gillan. Tight binding studies of strained Ge/Si(001) growth. Surface Science, 526:356, 2003.

11) Nicola Marzari, David Vanderbilt, and Mike C. Payne. Ensemble density-functional theory for ab initio molecular dynamics of metals and finite-temperature insulators. Phys. Rev. Lett.,

79(7):1337, 1997.

12) T. Miyazaki, D. R. Bowler, R. Choudhury, and M. J. Gillan. Atomic force algorithms in DFT electronic-structure techniques based on local orbitals. J. Chem. Phys., 121:6186, 2004.

13) E. Prodan and W. Kohn. Nearsightedness of electronic matter. Proc. Nat. Acad. Sci.,102(33):11635, 2005.

14) C.-K. Skylaris, P. D. Haynes, A. A. Mostofi, and M. C. Payne. Implementation of linear-scaling plane wave density functional theory on parallel computers. Phys. Stat. Sol. B, 243(5):973,2006.

15) Chris-Kriton Skylaris, Peter D. Haynes, Arash A. Mostofi, and Michael C. Payne. Introducing ONETEP: Linear-scaling density functional simulations on parallel computers. J. Chem. Phys.,

122:084119, 2005.

16) Chris-Kriton Skylaris, Arash A. Mostofi, Peter D. Haynes, Oswaldo Di¶eguez, and Mike C. Payne.

Nonorthogonal generalised Wannier function pseudopotential plane-wave method. Phys. Rev. B, 66:035119, 2002.

17) J. M. Soler, E. Artacho, J. D. Gale, A. Garcia, J. Junquera, P. Ordejon, and D. Sanchez-Portal. The SIESTA method for ab initio order-N materials simulation. J. Phys.: Condens. Matter,

14:2745{2779, 2002.

18) J. E. Subotnik, A. Sodt, and M. Head-Gordon. A near linear-scaling smooth local coupled cluster algorithm for electronic structure. J. Chem. Phys., 125(7):074116, 2006.

19) O. A. von Lilienfeld, I. Tavernelli, U. Roethlisberger, and D. Sebastiani. Performance of optimized atom-centered potentials for weakly bonded systems using density functional theory.

Phys. Rev. B, 71:195119, 2005.

20) V.Weber, A. M. N. Niklasson, and Challacombe M. Higher-order response in O(N) by perturbed projection. J. Chem. Phys., 123:044106, 2005.

21) C. Y. Yam, S. Yokojima, and G. Chen. Localized-density-matrix implementation of time-dependent density-functional theory. J. Chem. Phys., 119(17):8794, 2003.

22) B. Zhou, V. L. Ligneres, and Carter E. A. Improving the orbital-free density functional theory

description of covalent materials. J. Chem. Phys., 122:044103, 2005.