Preface -- Contents -- PART I Real-Space Finite-Difference Method for First-Principles Calculations -- Chapter 1 Foundations of Methodology -- 1.1 Real-Space Finite-Difference Method -- 1.2 Density-Functional Theory and Kohn-Sham Equation -- 1.3 Finite-Difference Formulas -- 1.4 Real-Space Representation of Kohn-Sham Equation -- 1.5 Norm-Conserving Pseudopotentials -- 1.6 Hellmann-Feynman Forces Acting on Atoms -- Chapter 2 Solvers of the Poisson Equation and Related Techniques -- 2.1 The Real-Space Representation of the Poisson Equation -- 2.2 The Fuzzy Cell Decomposition and Multipole Expansion Technique -- 2.3 Algorithm to Generate the Fuzzy Cell -- 2.4 Illustration for Efficiency of the Fuzzy Cell Decomposition and Multipole Expansion Method -- 2.5 Conjugate-Gradient Method -- 2.6 Conjugate-Gradient Acceleration -- 2.7 Multigrid Method -- Chapter 3 Minimization Procedures of the Energy Functional -- 3.1 Introduction -- 3.2 Approach of Minimizing the Kohn-Sham Energy Functional -- 3.3 Approach of Minimizing the Kohn-Sham Eigenvalues -- 3.4 Multigrid Method for Minimizing the Kohn-Sham Energy Functional -- 3.5 Fermi-Broadening Technique -- 3.6 Approach of Directly Minimizing the Energy Functional -- 3.7 Illustration for Direct Minimization Efficiency -- 3.8 Application of the Direct Minimization: Order-N Calculations for Gold Nanowires -- Chapter 4 Timesaving Double-Grid Technique -- 4.1 Essential Feature of the Timesaving Double-Grid Technique -- 4.2 Illustration of Double-Grid Efficiency -- 4.3 Other Mesh-Refinement Techniques -- Chapter 5 Implementation for Systems under Various Boundary Conditions -- 5.1 Isolated Boundary Condition: Molecules -- 5.2 3D Periodic Boundary Condition: Crystals -- 5.3 (2D Periodic + 1D Isolated) Boundary Condition: Thin Films -- 5.4 (1D Periodic + 2D Isolated) Boundary Condition: Infinite Metallic Wires.

5.5 Twist Boundary Condition: Infinite Helical Carbon Nanotubes -- PART II Electronic Transport through Nanostructures between Semi-Infinite Electrodes -- Chapter 6 Basic Scheme of the Overbridging Boundary-Matching Method -- 6.1 Preliminary Concepts: Ballistic Transport of Electrons and the Landauer Formula -- 6.2 Wave-Function Matching Procedure -- 6.3 Computational Scheme for Generalized Bloch States I. The Generalized Eigenvalue Equation -- 6.4 Computational Scheme for Generalized Bloch States II. The Continued-Fraction Equations -- 6.5 Related Considerations -- 6.6 Application: Sodium Nanowires -- Chapter 7 Inclusion of Norm-Conserving Pseudopotentials -- 7.1 Treatment of Nonlocal Pseudopotentials -- 7.2 Application: Aluminum Nanowire -- Chapter 8 Jellium Electrode Approximation -- 8.1 Generalized Bloch States in Jellium Electrodes -- 8.2 Application: Helical Gold Nanowires -- 8.3 Application: Fullerene Chains -- Chapter 9 Green's Function Formalism and the Overbridging Boundary-Matching Scheme -- 9.1 Preliminary Remarks -- 9.2 Green's Functions in the Discretized Space within the Real-Space Finite-Difference Framework -- 9.3 Green's Function of a Whole System Including the Transition Region and Two Semi-Infinite Electrodes -- 9.4 Green's Function Matching in the Overbridging Boundary-Matching Scheme and Related Topics -- 9.5 Green's Function of a Whole System with a Block-Tridiagonal Hamiltonian Matrix -- Chapter 10 Calculation Method Based on the Lippmann-Schwinger Equation -- 10.1 The Lippmann-Schwinger Equation -- 10.2 Correction of Effective Potentials inside Electrodes at a Finite Bias Voltage -- 10.3 Application: Sodium Nanowire under Finite Bias Voltages -- Appendix A Formulas for Long-Range Potentials under Various Boundary Conditions -- A.1 3D Periodic Boundary Condition -- Ionic pseudopotential -- Hartree potential.

Coulomb energy among the nuclei -- A.2 (2D Periodic + 1D Isolated) Boundary Condition -- Ionic pseudopotential -- Hartree potential -- Coulomb energy among the nuclei -- A.3 (1D Periodic + 2D Isolated) Boundary Condition -- Ionic pseudopotential -- Hartree potential -- Coulomb energy among the nuclei -- A.4 Twist Boundary Condition -- A.5 Uneven 2D Periodic Boundary Condition -- A.6 Uneven 3D Periodic Boundary Condition -- Appendix B Tight-Binding Approach Based on the Overbridging Boundary-Matching Scheme -- B.1 Generalized Bloch States inside Semi-Infinite Crystalline Electrodes -- B.2 Wave-Function Matching Procedure -- B.3 Green's Function Formalism -- Bibliography -- Index.