2/23/2015PHY 752 Spring 2015 -- Lecture 171 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 17: Reading: Chapter 10 in MPM Ingredients.

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Presentation transcript:

2/23/2015PHY 752 Spring Lecture 171 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 17: Reading: Chapter 10 in MPM Ingredients of electronic structure calculations 1.Plane wave basis sets 2.Evaluation of matrix elements 3.Construction of pseudopotentials

2/23/2015PHY 752 Spring Lecture 172

2/23/2015PHY 752 Spring Lecture 173 Some practical considerations in electronic structure calculations

2/23/2015PHY 752 Spring Lecture 174 Kohn-Sham equations (assuming “local” potential)

2/23/2015PHY 752 Spring Lecture 175 Digression on evaluation of the Fourier transform of the effective potential

2/23/2015PHY 752 Spring Lecture 176 Digression on evaluation of the Fourier transform of the effective potential

2/23/2015PHY 752 Spring Lecture 177 Examples of convergence of Fourier transforms:

2/23/2015PHY 752 Spring Lecture 178 Convergence of plane wave expansions

2/23/2015PHY 752 Spring Lecture 179 Some practical tricks Fourier space representation of density can be determined by inverse FFT

2/23/2015PHY 752 Spring Lecture 1710 FFT grid size Enclosing parallelepiped

2/23/2015PHY 752 Spring Lecture 1711 FFT equations

2/23/2015PHY 752 Spring Lecture 1712 How can we construct a pseudopotential? Norm-conserving pseudopotentials

2/23/2015PHY 752 Spring Lecture 1713 r (Bohr) rV(r) (Bohr * Ry Self-consistent full potential for C Local pseudopotential for C

2/23/2015PHY 752 Spring Lecture 1714 Construction methods used in ATOMPAW code

2/23/2015PHY 752 Spring Lecture 1715

2/23/2015PHY 752 Spring Lecture 1716 Properties of pseudopotential and corresponding pseudo- wavefunctions  Correct logarithmic derivatives at energy E and at nearby energies

2/23/2015PHY 752 Spring Lecture 1717 Construction energy E (Ry) L[P]

2/23/2015PHY 752 Spring Lecture 1718 The construction ensures that  PS and AE have same log derivatives near E  What about other partial waves? (Non-local contributions to pseudopotential)