Abstract. Linear scaling methods, or O(N ) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N , in contrast to standard approaches which scale with the cube of the number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. The theory behind the locality of electronic structure is described and related to physical properties of systems to be modelled, along with a survey of recent developments in real-space methods which are important for efficient use of high performance computers. The linear scaling methods proposed to date can be divided into seven different areas, and the applicability, efficiency and advantages of the methods proposed in these areas is then discussed. The applications of linear scaling methods, as well as the implementations available as computer programs, are considered. Finally, the prospects for and the challenges facing linear scaling methods are discussed.

[1] Peatlands are widely regarded as a significant source of atmospheric CH 4 , a potent greenhouse gas. At present, most of the information on environmental emissions of CH 4 comes from infrequent, temporally discontinuous ground-based flux measurements. Enormous efforts have been made to extrapolate measured emission rates to establish seasonal or annual averages using relevant biogeochemical factors, such as water table positions or peat temperatures, by assuming that the flux was stationary during a substantial nonsampling period. However, this assumption has not been explicitly verified, and little is known about the continuous variation of the CH 4 flux in a timescale of individual flux measurement. In this study, we show an abrupt change in the CH 4 emission rate associated with falling atmospheric pressure. We found that the CH 4 flux can change by 2 orders of magnitude within a matter of tens of minutes owing to the release of free-phase CH 4 triggered by a drop in air pressure. The contribution of the ebullition to the total CH 4 flux during the measurements was significant (50-64%). These results clearly indicated that field campaigns must be designed to cover this rapid temporal variability caused by ebullition, which may be especially important in intemperate weather. Process-based CH 4 emission models should also be modified to include air pressure as a key factor for the control of ebullient CH 4 release from peatland.

An overview of the CONQUEST linear scaling density functional theory (DFT) code is given, focusing particularly on the scaling behaviour on modern high-performance computing platforms. We demonstrate that essentially perfect linear scaling and weak parallel scaling (with fixed number of atoms per processor core) can be achieved, and that DFT calculations on millions of atoms are now possible.

Within the framework of the density functional theory, we calculate the electronic structure of α-(BEDT-TTF)2I3 at 8 K and room temperature at ambient pressure and with uniaxial strain along the a-and b-axes. We confirm the existence of anisotropic Dirac cone dispersion near the chemical potential. We also extract the orthogonal tight-binding parameters to analyze physical properties. An investigation of the electronic structure near the chemical potential clarifies that effects of uniaxial strain along the a-axis is different from that along the b-axis. The carrier densities show T 2 dependence at low temperatures, which may explain the experimental findings not only qualitatively but also quantitatively.

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