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9.4.3 Improved functional form for f - method of Methfessel and Paxton

 

Sigma (eV)
Aluminium 1.0
Lithium 0.4
Tellurium 0.8
Copper, Palladium 0.4
Vanadium 0.2
Rhodium 0.2
Potassium 0.3
Table 3:   Typical convenient settings for sigma for different metals: Aluminium posses a extremely simple DOS, Lithium and Tellurium are also simple nearly free electron metals, therefore sigma might be large. For Copper sigma is restricted by the fact that the d-band lies approximately 0.5 eV beneath the Fermi-level. Rhodium and Vanadium posses a fairly complex structure in the DOS at the Fermi-level, sigma must be small.

The method described in the last section has two shortcomings:

These problems can be solved by adopting a slightly different functional form for tex2html_wrap_inline4957 . This is possible expending the step function in an complete orthonormal set of functions (method of Methfessel and Paxton [33]). The Gaussian function is only the first approximation (N=0) to the step function, further successive approximations (N=1,2,...) are easily obtained. In similarity to the Gaussian method, the energy has to be replaced by a generalized free energy functional

displaymath1860

In contrast to the Gaussian method the entropy term tex2html_wrap_inline5003 will be very small for reasonable values of tex2html_wrap_inline4971 (for instance for the values given in table 3). The tex2html_wrap_inline5003 is a simple error estimation for the difference between the free energy F and the 'physical' energy tex2html_wrap_inline4985 . tex2html_wrap_inline4971 can be increase till this error estimation gets to large.


next up previous contents
Next: 9.5 Forces Up: 9.4 Partial occupanciesdifferent Previous: 9.4.2 Finite temperature approaches

MASTER USER VASP
Mon Mar 29 10:38:29 MEST 1999