Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

Pseudopotential methods in condensed matter applications

The effects of uniaxial stress on the pressure-induced α → ω transition in pure titanium (Ti) are investigated by means of angle dispersive X-ray diffraction in a diamond-anvil cell. Experiments under four different pressure environments reveal that: (1) the onset of the transition depends on the pressure medium used, going from 4.9 GPa (no pressure medium) to 10.5 GPa (argon pressure medium); (2) the α and ω phases coexist over a rather large pressure range, which depends on the pressure medium employed; (3) the hysteresis and quenchability of the ω phase is affected by differences in the sample pressure environment; and (4) a short-term laser heating of Ti lowers the α → ω transition pressure. Possible transition mechanisms are discussed in the light of the present results, which clearly demonstrate the influence of uniaxial stress in the α → ω transition.

Pressure-induced α → ω transition in titanium metal: a systematic study of the effects of uniaxial stress

Lattice dynamics of body-centered cubic (bcc) Vb-VIb group transition metals (TM), and B1-type monocarbides and mononitrides of IIIb-VIb transition metals are studied by means of first-principles density functional perturbation theory, ultra soft pseudopotentials, and generalized gradient approximation to the exchange-correlation functional. Ground state parameters of transition metals and their compounds are correctly reproduced with the generated ultrasoft pseudopotentials. The calculated phonon spectra of the bcc metals are in excellent agreement with results of inelastic neutron scattering experiments. We show that the superconductivity of transition metal carbides (TMC) and transition metal nitrides (TMN) is related to peculiarities of the phonon spectra, and the anomalies of the spectra are connected to the number of valence electrons in crystals. The calculated electron-phonon interaction constants for TM, TMC, and TMN are in excellent agreement with experimentally determined values. Phonon spectra for a number of monocarbides and mononitrides of transition metals within the cubic NaCl- and hexagonal WC-type structures are predicted. Ideal stoichiometric B1 crystals of ScC, YC, and VC are predicted to be dynamically stable and superconducting materials. We also conclude that YN is a semiconductor.

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Phonon related properties of transition metals, their carbides, and nitrides: A first-principles study

On the effect of alloy composition on martensite start temperatures and latent heats in Ni–Ti-based shape memory alloys

The vibrational frequencies of selected normal modes can be obtained entirely from first principles with use of frozen phonon calculations which involve the precise evaluation of crystal total energy as a function of lattice displacement. The calculations allow a detailed analysis of the microscopic mechanisms causing phonon anomalies and soft-mode phase transitions. Successful calculations for Zr, Nb, and Mo have been made with use of both tight-binding and pseudopotential methods.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=8713&context=rtd

Vibrational frequencies and structural properties of transition metals via total-energy calculations

The total energy for Si with various lattice distortions has been calculated using a first-principles linear-combination-of-atomic-orbitals method. The physical properties derived from these calculations include not only the equilibrium lattice constant, cohesive energy, and bulk modulus, but also the internal strain parameter and several phonon frequencies including anharmonic terms. For all these properties there is good agreement with experiment. The frozen-core approximation was tested and found to be valid for Si in a large region about the equilibrium lattice position.

Total-energy calculations for Si with a first-principles linear-combination-of-atomic-orbitals method

A nesting feature in the Fermi surface of ordered, equiatomic NiTi is reported, and related to observed premartensitic'' phenomena.

Electronic origin of the intermediate phase of NiTi

First-principles pseudopotential band-structure calculations were performed for fcc La and revealed a small but sharp nesting feature of the Fermi surface. In order to investigate the relationship between this nesting and possible phonon anomalies, the phonon-dispersion curves were calculated. Along the (xixixi) direction a sharp dip in the transverse branch was found at xi = 0.42 in agreement with recent low-temperature neutron scattering experiments. Calculations at 14% smaller volume (corresponding to a pressure of 50 kbar) indicate that the frequencies of the phonons along the transverse (xixixi) branch decrease with pressure because of the increased magnitude of the electron-phonon matrix elements. This result helps to explain the unusual negative thermal expansion, the dramatic increase of the superconducting transition temperature, and the observed structural transition near 50 kbar.

Anomalous lattice dynamics of fcc lanthanum.

We have used a first principles linear combination of atomic orbitals (LCAO) method to calculate the total ground state energy for crystals of Si, Nb and Mo involving lattice distortions. From these calculations the equilibrium lattice constant, cohesive energy, and bulk modulus as well as the vibrational frequencies for selected phonons were determined.

W. Weber

Papers

Vibrational frequencies and structural properties of transition metals via total-energy calculations

Total-energy calculations for Si with a first-principles linear-combination-of-atomic-orbitals method

Electronic origin of the intermediate phase of NiTi

Anomalous lattice dynamics of fcc lanthanum.

Vibrational frequencies via frozen phonons