Real space

Calculating everything in realspace means that complex conjugate integrals can be greatly simplified (removing all imaginary terms), and it is much easier to directly interpret wavefunction data, etc. in terms of bonding and anti-bonding orbitals (given the caveat that they are Kohn-Sham wavefunctions, Section 2.4). It removes the need to fill the whole calculational real space with fitting functions, thus large vacuum regions (e.g. seperating molecular species from bulk surfaces) do not increase the size of a calculation; unlike k-space plane wave calculations. In addition it makes it easy to increase the local basis size around key atoms such as defect cores or O atoms where a large basis set is required to accurately model the charge.

In order to accurately model oxygen in silicon a large basis set is required. For real space methods such as this it is easy to locally increase the basis size. However for plane wave calculations the basis is determined for the whole supercell by the cut-off energy of the plane waves. Using bhs pseudopotentials [23] this is typically of the order of 15 Ry for bulk, and 5-12 Ry for surface calculations where the size of the supercell is necessarily larger in order to include a vacuum region [44]. However when including light elements such as carbon, nitrogen or oxygen this figure increases to something over 50 Ry, for example, recent calculations on bulk GaN used a cut-off of 150 Ry [45]. In order to increase the basis locally it is necessary to increase the energy cut-off for the whole calculation, leading to a rapid increase in calculation size. The only way to overcome the computational restriction of this is by changing the pseudo-potential, and using ultra-soft pseudopotentials. These are more slowly varying nearer the core and so are easier to fit. However they have a higher core energy and so are no longer norm-conserving, which leads to errors in self-consistency. In addition, ultra-soft pseudopotentials are less transferable and less able to cope with unusual structures. In the GaN calculation described above the use of ultra-soft pseudopotentials drops the required cut-off energy to 65 Ry. In general, structure converges quicker with cut-off than band structure [44].