Up: Partial occupancies, different methods
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Typical convenient settings for for different metals:
Aluminium possesses an extremely simple DOS, Lithium and Tellurium
are also simple nearly free electron metals, therefore
might be large. For Copper
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, 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
. This is possible
by expanding the step function in a complete orthonormal set of functions
(method of Methfessel and Paxton ).
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
- The forces calculated by VASP are a derivative of the free electronic
energy F (see section 7.5).
Therefore the forces can not be used to
obtain the equilibrium groundstate, which corresponds to
an energy-minimum 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 k-point mesh, if
is too small the convergence speed with the number of k-points
will deteriorate. An optimal choice for for several cases is given
in table 2. The only way to get a good is
by performing several calculations with different k-point meshes
and different parameters for .
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 2).
is a simple error estimation for the difference between the
free energy and the 'physical' energy
can be increased till this error estimation gets too large.
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