EXTREME-SCALE QUANTUM SIMULATIONS

• Introduction
• Quantum molecular dynamics (QMD): slide; notes on QMD summary, QMD equation, adiabatic approximation
• Density functional theory (DFT): slide; note
• Exchange-correlation functional: slide
• Pseudopotentials: slide; slide on projector-augmented wave method by Azarang; do-it-yourself PAW by Hiroyuki, see also T. Sugahara et al., Numerical procedures for generating ultrasoft pseudopotentials, Phys. Rep. Kumamoto Univ. 12, 279 (2006); notes on norm-conserving pseudopotential, nonlocal pseudopotential, fully-nonlocal pseudopotential, real-space operation of nonlocal pseudopotential
• Representation & solution: slide on plane waves & real-space grids; notes on plane-wave basis and supercell; note on Pulay charge mixing; notes on conjugate-gradient (CG) method, CG electronic-state solver, CG DFT solver, 2D electron example and multigrid preconditioned CG
• Linear scaling QMD: slide; notes on divide-&-conquer (DC) DFT: origin of DC-DFT, parallel DC-DFT, DC-DFT data structures, DC-DFT algorithm, DC forces, lean divide-&-conquer (LDC) DFT; note on Fermi-operator expansion; note on local orbital minimization; notes on density matrix minimization (DMM): density-matrix idempotency, orthogonal DMM, nonorthogonal DMM, real-space DMM; note on filter diagonalization; note on Green's function (GF) approches: Pade via Lanczos, cf., Bethe lattice; note on block-diagonal divide-&-conquer matrix diagonalization; notes on embedded-cluster boundary condition (BC): embedded-cluster BC, orbital BC, multiple scattering, surface GF; note on density matrix renormalization group (DMRG)
• Time-dependent density functional theory (TDDFT): summary; fundamentals; field theory of exchange-correlation potential
• Nonadiabatic quantum molecular dynamics (NAQMD): slide; notes on fewest-switch surface hopping, linear-response time-dependent Kohn-Sham equations; linear-response time-dependent density functional theory (LR-TDDFT), many-body wave function, range-separated exact-exchange functional, excited-state forces, excitation-energy balance sheet
• Parallelization: slide; molecular dynamics machines; Beowulf clusters; Pre-Beowulf parallel computing; parallel quantum dynamics; shift-collapse (SC) algorithm
• Advanced QMD: note on real-space DFT (Hasegawa et al., SC11) by Xiangyu; density materix renormalization group (DMRG) by Yongqian; neural-network force fields (NNFF) by Prof. Kohei Shimamura (Kobe Univ., Japan); note on NNFF papers by Yuan, Shichun & Size; Harris functional by Ben; mutual information, renormalization group & neural network by Kyle; quantum chemistry using quantum computing by Guoqing & Yuzi
• Miscellaneous lectures:
  • Unitary time propagation
  • Closed-time path integral
  • Functional derivative
  • Quantum dynamical computation of electric conductivity
  • Second quantization
  • Hartree-Fock approximation
  • Time-dependent perturbation
  • Fourier transform of step function
  • Atomic wave functions: Laplacian in spherical coordinates; Schrodinger equation for spherically symmetric potentials; Numerical integration of radial wave function; Kohn-Sham potential; logarithmic derivative
  • Nonorthogonal orbitals
  • Lanczos method: slide; supplementary note; note on Lanczos tridiagonalization
  • Singular value decomposition (SVD)
  • Software version control by Lindsay Bassman
  • Slurm workload manager by Kuang Liu