Full-potential electronic structure method. Energy and force calculations with density functional and dynamical mean field theory
The book describes the electron structure theory and its applications within the implementation by using the computer code for relativistic spin-polarized tests (RSPt). The book is divided into fifteen chapters. The introductory Chapter 1 presents a brief information on linear muffin-tin orbital (LMTO) methods together with the units used in this book. The main goals are described and the full-potential linear muffin-tin orbital (FP-LMTO) method is introduced. Chapter 2 gives basic ideas and formulas of the density functional theory (DFT) based on an approximation of the energy functional. The authors present early attempts to solve the many-particle problem. Central concepts of DFT, namely exchange and correlation hole, exchange and correlation energy, are discussed. The authors also consider the Kohn-Sham equation based on mapping the many-particle problem onto a system of non-interacting particles with the same ground state density as the original many-particle system. The very brief Chapter 3 examines the periodicity and general symmetry of a crystal by illustrating the theory with a cubic material. Chapter 4 introduces the electronic structure theory of solids. Here the authors describe the evaluation of electron density, density of states and calculation of energy bands. Moreover, various types of integration of reciprocal space are discussed. Chapter 5 presents different muffin-tin methods, in particular the LMTO method which includes linearization of the radial part of wave function, the ``head'' and ``tails'' of basis functions, and also some structure constants. The authors also introduce here the atomic sphere approximation (ASA) and make a comparison between the Korringa-Kohn-Rostoker method and the LMTO method. Chapter 6 describes in detail how the full-potential methodology can treat the non-spherical electron density and potentials expanded in MT-regions and interstitial region. The authors discuss how the RSPt solves the full-potential problem of a solid using LMTO as basis functions. The chapter highlights also how to calculate matrix elements of the Hamiltonian and overlap and to construct a potential form of a calculated charge density. Chapter 7 shows why the common approximation to the exchange and correlation energy of DFT is insufficient for certain materials. The application of dynamical mean field theory (DMFT) to solve this problem and details of its implementation in the FP-LMTO method are presented with proper examples of DMFT calculations. The short Chapters 8 and 9 are respectively devoted to the FP-LMTO method, numerical implementation (diagonalization, fast Fourier transforms and parallelization), and details of how to obtain the FP-LMTO code via INTERNET and to install this code. Chapter 10 gives numerical examples of calculations of total energy, equation of state properties, and Hellman-Feynman forces. The computation of phonons from the first principles is presented for fcc Al and bcc U. In Chapter 11 an analysis of chemical binding of materials is carried out by introducing concepts like the crystal orbital overlap population. Numerical results describe the transition of metals, lanthanides, actinides and refractory materials. It is shown how to use the RSPt tools for sp-banded materials, transition metals, f-electron systems and few intermetallic compounds. The calculations of mixed valence materials are conducted by using the Kimbal-Filicov model. The concluding chapters are devoted to the calculation of properties of elastic material. Chapter 12 discusses the theory of magnetism (in particular, of nano-objects) focusing on spin and orbital moments and magnetic anisotropy. Numerical examples are present for bulk and for surfaces, and particular symmetry aspects of relativistic one-electron theory and of magnetism are described. Chapter 13 presents a phenomenological theory of optical material properties based on the first principles with special emphasis on the implementation of the FP-LMTO method by using numerical examples of semiconductors and metals. Interband and intraband transitions are discussed as magneto-optical effects. The authors also examine why the simple dipole approximation combined with the scissors operator could give good results. Moreover, they present a general background theory for the considered types of excitation spectra and give examples of calculated spectra. Chapter 13 ends with a description of the theory of X-ray magnetic circular dichroism and its calculation by using the FP-LMTO method. Finally, brief Chapters 14 and 15 present respectively a database of electronic structures with a method in data-mining technology, and possible future developments of the FP-LMTO method. In total, the book presents a very interesting attempt to create a powerful electronic database of physical properties (in this case -- electronic ones). The computer software RSPt may be useful to students, post-graduate students, their teachers and researchers working in modern chemistry, physics and material sciences.
scientific article; zbMATH DE number 5782046