Introduction to first-principles electronic structure methods: Application to actinide materials
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Introduction to first-principles electronic structure methods: Application to actinide materials John E. Klepeisa) Lawrence Livermore National Laboratory, Livermore, California 94551 (Received 22 April 2006; accepted 2 August 2006)
This paper provides an introduction for non-experts to first-principles electronic structure methods that are widely used in condensed-matter physics. Particular emphasis is placed on giving the appropriate background information needed to better appreciate the use of these methods to study actinide and other materials. Specifically, the underlying theory is described in sufficient detail to enable an understanding of the relative strengths and weaknesses of the methods. In addition, the meaning of commonly used terminology is explained, including density functional theory (DFT), local density approximation (LDA), and generalized gradient approximation (GGA), as well as linear muffin-tin orbital (LMTO), linear augmented plane wave (LAPW), and pseudopotential methods. Methodologies that extend the basic theory to address specific limitations are also briefly discussed. Finally, a few illustrative applications are presented, including quantum molecular dynamics (QMD) simulations and studies of surfaces, impurities, and defects. The paper concludes by addressing the current controversy regarding magnetic calculations for actinide materials.
I. INTRODUCTION
First-principles electronic structure methods are quantum mechanical methods for numerically solving the Schrödinger (nonrelativistic) or Dirac (relativistic) equation for systems of electrons H⌿共r兲 = E⌿共r兲 .
(1)
Equation (1) is the time-independent Schrödinger equation. The term “first-principles” simply means that there is no empirical fitting, or equivalently, no adjustable parameters. The term “ab initio” is sometimes used instead and means the same thing. This aspect of the methodology is important for it to be predictive. In other words, when applied to a new system it is not necessary to make any adjustments but rather there is an expectation that the
methods will be applicable. Another important quality that makes first-principles methods predictive is that they are accurate. In the present context that means they have been well tested against experiment. Naturally these methods do have limitations and some of them will be discussed in this paper. Another characteristic, which could also be viewed as a limitation, is that firstprinciples methods are very computationally expensive. In condensed-matter physics the term first-principles usually refers to a method that is based on density functional theory (DFT). The first two-thirds of this paper will be devoted to an overview of DFT. It is important to understand a few technical details to better appreciate the application of these methods. Some of the material that will be discussed in this paper can be found in greater detail in a recent book written by Richard Martin.1 No attempt has been made to provide a comprehensive set of references to the literature but instea
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