Chapter

Many-Electron Densities and Reduced Density Matrices

Part of the series Mathematical and Computational Chemistry pp 165-181

Natural Orbital Functional Theory

  • S. GoedeckerAffiliated withDépartement de recherche fondamentale sur la matière condensée, SP2M/NM, CEA-Grenoble
  • , C. J. UmrigarAffiliated withCornell Theory Center

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Abstract

One of the central problems of solid state physics and quantum chemistry is to find an accurate and computationally affordable method for the description of electronic correlation. The most accurate methods available today, e.g. the configuration interaction (CI) method [1] or the coupled cluster (CC) method [1], are computationally too expensive to be applied to large systems. Quantum Monte Carlo approaches [2] require considerable human input and the computational cost of reducing the statistical error to an acceptable level for large systems, particularly those with deep core electrons, is considerable. On the other hand, straightforward implementations of the density functional formalism [3] have only a cubic scaling with respect to system size and consequently have been applied to systems with more than 100 atoms. Recent work on O(N) methods [4] will lead to a linear scaling with respect to system size that will allow for the application of density functional schemes to systems with thousands of atoms. This is the main reason for the popularity of density functional methods even though all practical density functional schemes make an approximation for the unknown exchange-correlation energy functional that cannot be systematically improved.