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. Klepeis Lawrence Livermore National Laboratory Livermore, CA 94551 ABSTRACT The purpose of this paper is to provide an introduction for non-experts to first-principles electronic structure methods that are widely used in the field of condensed-matter physics, including applications to actinide materials. The methods I describe are based on density functional theory (DFT) within the local density approximation (LDA) and generalized gradient approximations (GGAs). In addition to explaining the meaning of this terminology I also describe the underlying theory itself in some detail in order to enable a better understanding of the relative strengths and weaknesses of the methods. I briefly mention some particular numerical implementations of DFT, including the linear muffin-tin orbital (LMTO), linear augmented plane wave (LAPW), and pseudopotential methods, as well as general methodologies that go beyond DFT and specifically address some of the weaknesses of the theory. The last third of the paper is devoted to a description of a few selected applications that illustrate the ideas discussed in the first two-thirds, including quantum molecular dynamics (QMD) simulations and applications to surfaces, impurities, and defects. I conclude by addressing the current controversy regarding magnetic DFT calculations for actinide materials. Throughout this paper particular emphasis is placed on providing the appropriate background to enable the nonexpert to gain a better appreciation of the application of first-principles electronic structure methods to the study of actinide and other materials. INTRODUCTION First-principles electronic structure methods are quantum mechanical methods for numerically solving the Schrödinger (nonrelativistic) or Dirac (relativistic) equation for systems of electrons
HΨ (r ) = EΨ (r )
(1)
Equation (1) is simply the time-independent Schrödinger equation. The term “first-principles” 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 in order 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 method 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 I will discuss some of them in this paper. Another aspect, which could also be viewed as a limitation, is that first-principles 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
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paper will be devoted to a somewhat technic
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