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- 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