next up previous contents
Next: Real space Up: Discussion of the methods Previous: Discussion of the methods

Density functional theory / Local Density Approximation

One of the greatest advantage of density functional schemes under the local density approximation is their reliance on the charge density as the fundamental variable, which greatly simplifies the amount of calculation required. However they consistently underpredict bandgaps (this is to some extent compensated by the use of clusters, see Section 3.7.3 below), and as a ground state theory they are restricted in their application to excited state problems. Various methods have been used to try and overcome this, notably constrained relaxation techniques to determine saddle points (see Section 6). In addition since the wavefunction eigenvalues are a computational tool and do not directly link to experimental eigenvalues, physical interpretation of these states is somewhat dangerous (although there is normally qualitative agreement between the two). Current work suggests Slater transition methods may provide a way of quantitatively relating the two [42].

Density functional theory under the local density approximation is well known for overbinding of molecules such as O2, but can be greatly improved through the use of gradient corrections. AIMPRO actually does better than the standard DFT result, shown in Table 3.1. These results support the conclusion that we are obtaining good structural and vibrational data, but need to improve the accuracy of our total energies. However the magnitude of such errors normally decreases with system size. The local density approximation is good for smoothly varying systems, so given that other DFT/LDA calculations on oxygen/silicon structures have also had trouble with total energies (see, for example, Chapter 5), it suggests that part of the problem of innacurate total energies could be due to the local density approximation.

Table: Properties of the O2 molecule. AIMPRO values are obtained using the standard basis set described elsewhere in the thesis, i.e. six Gaussian fitting functions on each O atom for charge density, 24 for wavefunction, with three more Gaussian functions on the bond centre for charge density and two for the wavefunction. All non-AIMPRO values from [43].
Source Binding O stretch Bond Length
  Energy (eV) mode (cm-1) (a.u.)
AIMPRO, spin      
averaged 8.79 1565 2.28
polarised 6.41 1581 2.28
Experiment 5.23 1580 2.28
Quoted DFT 7.54 1610 2.31
Hartree Fock 1.43 2000 2.18

next up previous contents
Next: Real space Up: Discussion of the methods Previous: Discussion of the methods
Chris Ewels