1.ENCUT【待完善】

DFT calculations rarely use a completely converged plane-wave basis, but that convergence is usually unnecessary.

   However, incomplete basis set calculations using different cell sizes require that each calculation use the same Ecut.

Details:

  There is a further truncation of plane wave expansion in plane-wave calculations. Namely, only the reciprocal lattice vectors whose kinetic energy lower than a predefined maximum cutoff energy,are kept in the expansion, while the rest of the coefficients are set to zero.

  Besides reducing the computational load, this truncation【切断】 strategy limits the effects of unit cell orientation on the outcome of the calculation.

2. cusp

  Lack of accuracy comes from cusp in cutoff Coulomb kernel

3. The Pseudopotential Approximation

Frozen core: remove core-electron degrees of freedom.

• Valence electrons see a weaker potential than the full Coulomb potential, replaces electron-nuclear potential.

• Tailor this pseudopotential so that wavefunctions behave ‘properly’ in region of interest【在感兴趣的成键区域】, yet computationally cheap.

(Numerical) Advantages when solving Kohn-Sham eqns.:

• Have to solve for fewer eigenvalues.

• When solving using a basis (especially plane waves),basis size drastically reduced (smaller matrices to diagonalize).

• No Coulomb singularity (cusp in wavefunction) at origin.

Disadvantages:

• Can lose accuracy