Linear Scaling DFT Calculations with Numerical Atomic Orbitals
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Linear Scaling DFT Calculations with Numerical Atomic Orbitals P. Ordejón1, E. Artacho2, R. Cachau3, J. Gale4, A. García5, J. Junquera2, J. Kohanoff6, M. Machado7, D. Sanchez-Portal7, J. M. Soler2 and R. Weht8 1 Institut de Ciència de Materials de Barcelona, CSIC Campus de la UAB, Bellaterra 08193, Barcelona, Spain 2 Departamento de Física de Materia Condensada, C-III, Universidad Autónoma de Madrid 28049 Madrid, Spain 3 Advanced Biomedical Computing Center, National Cancer Institute, SAIC, Frederick 21702, Maryland, USA 4 Imperial College Exhibition Road, London SW7 2AY, United Kingdom 5 Departamento de Física Aplicada II, Universidad del País Vasco Apartado 644, 48080 Bilbao, Spain 6 School of Mathematics and Physics, The Queen´s University of Belfast Belfast BT7 1NN, Northern Ireland, United Kingdom 7 Departamento de Física de Materiales, Universidad del País Vasco Apartado 1072, 20080 San Sebastián, Spain. 8 Departamento de Física, CNEA. Avda. General Paz y Constituyentes, 1650 San Martín, Argentina.
ABSTRACT We have recently developed a method to perform Density Functional Theory calculations in systems with a very large number of atoms, which is based on the use of numerical atomic orbitals as basis sets. The method incorporates Order-N techniques both in the calculation of the Kohn-Sham hamiltonian matrix elements and in the solution of the wave functions, which make the CPU time and memory to scale linearly with the number of atoms, allowing calculations in very large system. In this work, we present results on several test systems to show that the approach and the basis sets used with our method are able to provide an accuracy similar to that of other standard DFT techniques. INTRODUCTION Our ability to compute the properties of condensed matter systems from first principles has matured to the point that these calculations have become a key part of our current understanding of many fields in physics, chemistry, materials sciences and most recently geology and biology. One of the barriers encountered in reaching this situation was the scaling of the computational effort with system size, which in the most favorable cases, like Density Functional Theory [1,2], scale at least as the cube of the number of atoms or electrons in the system. This makes it very difficult to reach system sizes larger than a very few hundreds of atoms, and is therefore an important obstacle to the study of complex materials. However, during the last decade, a number of ideas appeared, suggesting the possibility to reduce the computational cost to linear scaling, by using physically motivated approximations. A number of practical schemes were proposed, and their accuracy characterized quite systematically [3,4]. These so-called Order-N methods AA9.6.1
have matured since these first proposals, and now constitute a viable route for studying systems with unprecedented size. Linear scaling methods make explicit use of the locality properties of electronic systems: the insensitivity of the properties of a region to perturbations suffici
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