Organisers

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

Supports

   CECAM

   ESF

CCP9

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.

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.

Scientific Objectives

Linear-scaling methods are now beginning to make an impact in areas such as nanotechnology and biochemistry where traditionally DFT calculations were not applicable due to the large number (thousands) of atoms involved. We believe that a critical review of these applications will be timely as it will provide an understanding of the current and future capabilities of linear-scaling methods, with the following objectives:

• The major applications so far of O(N) DFT (e.g. what types of nanostructures, biomolecules, surfaces, etc.).
• The number of atoms typically involved in these applications.
• The level of accuracy achieved (e.g. has the plane-wave accuracy of traditional cubic-scaling methods been achieved in the applications reported so far).
• The most likely future applications, both in terms of numbers of atoms and in terms of kinds of materials studied.
• The overhead associated with practical O(N) algorithms.
• The system size above which O(N) algorithms become advantageous over traditional approaches and how does this size vary with the atom-density and three-dimensional structure of the material.

The available O(N) methods contain highly sophisticated algorithms that allow for the practical utilisation of the principle of quantum mechanics which Walter Kohn named “Nearsightedness” to achieve O(N) cost. Previous workshops have focused on the techniques for setting up the equations of quantum mechanics in an O(N) framework but have not covered in any detail the “linear-scaling functionals” actually used to solve them. Existing methods often use combinations of these approaches evolved and fine-tuned through years of extensive experimentation. At present there is no general consensus as to their relative advantages and disadvantages in practical applications, their “optimum” implementation (including sparse storage methods for matrices and performance on parallel computers) or their combination. As these important details are often not reported in papers, we feel that there is a strong need to cover this crucial topic in this workshop with the following objectives:

• The practical details of implementation of the various linear-scaling functionals and why some currently available methods have chosen to use combinations of more than one functional.
• Advantages of the implementation of these functionals within the framework of direct energy minimisation as compared to a density mixing framework.
• Their relevant strengths and weaknesses in terms of robustness, parallel performance, speed of convergence, accuracy, general applicability.
• Options for developing linear-scaling functionals with significantly better performance than the currently available variants.

Given the above-mentioned current status of O(N) ground state DFT we feel that the time is ripe now to look to the future. A major aim of the workshop will therefore be to examine the current attempts for linear-scaling or at least reduced scaling in ab initio methods for metallic systems and methods beyond ground-state DFT calculations (e.g. excited states or correlated wavefunction methods). These computational techniques are considered “non-standard” even without any modifications for O(N) cost and clearly our developments in this area are at a nascent stage. We would like to examine the current state-of-the-art in such methods and investigate ways to reformulate them into O(N) frameworks. In the case of the methods for metals our objectives will be:

• The currently most well-established DFT methods for metals and at what stage of development are the current efforts for linear-scaling (or at least reduced-scaling) approaches for metallic systems.
• Theoretical approaches needed to develop robust and accurate O(N) methods for metals.
• How much of the available O(N) technology for insulators can we re-use to develop such methods, and are particular approaches more suitable than others.
• Will we be obliged to always use specific constraints (e.g. finite electronic temperature) in such methods and if so how are these going to affect the accuracy and applicability of our calculations.

In the area of O(N) methods beyond ground-state DFT calculations our workshop will have the following objectives:

• Review the current state of progress in the development of O(N) methods beyond ground state DFT (e.g. quantum Monte Carlo, wavefunction correlation methods such as many-body perturbation theory or variants of configuration interaction).
• Examine if these methods achieve the same high accuracy as their traditional analogues – or even traditional DFT – and if they can offer the same advantages (e.g. reliable estimation of dispersion interactions).
• Find what developments would be needed in order to have these methods in a robust form suitable for applications.
• Investigate if these methods could reach a level of efficiency that could allow them to overtake O(N) DFT in terms of the system sizes that can be studied.

This workshop will bring together the developers of O(N) DFT methods with the developers of metal and excited-state or wavefunction-based methods in order to stimulate major new O(N) methodological developments beyond the realms of ground-state DFT for systems with a gap. Strong emphasis 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

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