DFT++ minicourse:

C = Y*inv(sqrtm(Y^O(Y))); n = f*diag_outerproduct(I(C),I(C)); phi = -(4.0*pi)*Linv(O(n)); E_LDA = -0.5*f*Tr(C^L(C))+ ... J(n)^(V_ion+O(J(exc(n)))+0.5*O(phi));	==>

Over the course of two days, modern software design techniques will make it possible for each participant to build a fully functional density-functional theory code from scratch. The course is ideal for those who would like to better understand the inner workings of such software or who anticipate developing software for new techniques in the future.

Although the exercises and examples will be based on density-functional theory, the design principles are general and applicable to other techniques such as GW calculations.

Familiarity with matlab/octave is not required, but will be useful.

Participation limited to 20.

Syllabus

1. Expressive software ---
   • DFT++ algebraic language: analoque of Dirac notation for density-functional theory
   • Solution of Poisson's equation in a single line of code
   • Object orientation in linear algebra context
   • High performance computing (cache and register optimization) with octave
2. Spectral methods ---
   • Plane wave represenation of DFT++ operators
   • Implementation: solution of Poisson's equation, Ewald energies
3. Variational solution of Kohn-Sham equations ---
   • Energy functional and derivative within DFT++
   • Preconditioned conjugate gradient minimization
   • Implementation: DFT solution of three-dimensional quantum dot (shell structure, etc.)
   • Implementation: DFT solution of hydrogen molecule (bond length, energy and vibrational frequency)
4. Optimizations required for solid state calculations ---
   • Isotropic spectral representations (mapping "plane-wave sphere" to "FFT box")
   • Pseudopotentials
   • Implementation: DFT calculation of solid germanium (bond densities, cohesive energy)