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 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 dband lies approximately
0.5 eV beneath the Fermilevel. Rhodium and Vanadium posses a fairly
complex structure in the DOS at the Fermilevel, sigma must be small.
The method described in the last section has two shortcomings:

The forces calculated by VASP are a derivative of the free electronic
energy F (see section 9.5).
Therefore the forces can not be used to
obtain the equilibrium groundstate, which corresponds to
an energyminimum of .
Nonetheless the error in the forces is generally small and acceptable.

The parameter must be chosen with great care. If
is too large the energy will converge to the
wrong value even for an infinite kpoint mesh, if
is to small the convergence speed with the number of kpoints
will deteriorate. An optimal choice for for several cases is given
in table 3. The only way to get a good is
by performing several calculations with different kpoint meshes
and different parameters for .
These problems can be solved by adopting a slightly different
functional form for . 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
In contrast to the Gaussian method
the entropy term will be very small
for reasonable values of
(for instance for the values given in table 3).
The
is a simple error estimation for the difference between the
free energy F and the 'physical' energy .
can be increase till this error estimation gets to large.
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