The Nosé-Hoover chain thermostat is defined by specifying three
parameters: A target kinetic energy, a frequency, and a chain length.
For the ions, given the target temperature 
,
the target kinetic energy is just
, where g is the number of degrees of freedom involved in a
common thermostat. For example, if there is one thermostat on the
entire ionic system, then 
, where 
is
the number of constraints to which the atoms are subject. The frequency
for the ionic thermostat should be chosen to be some characteristic
frequency of the ionic system for which one wishes to insure equilibration.
In water, for example, one could choose the O-H bond vibrational frequency.
(Having a precise value for this frequency is not important, as one only
wishes to insure that the thermostat will couple to the mode of interest.)
The choice of chain length is not
terribly important as it only determines how many extra thermostats
there will be to absorb energy from the system. Usually a
chain length of 4 is sufficient to insure effective equilibration.
Longer chains may be used in situations where heating or cooling
effects are more dramatic.
For the electrons, the target kinetic energy is not usually
known a priori
as it is for the ions. However, by performing a short run without
thermostats, one can determine a value about which the
electron kinetic energy `naturally' fluctuates and take this as the
target value. While the precise value is not important, a little
experience goes a long way, as a choice that is either too small
or too large can cause spurious damping of the ions or departures
from the Born-Oppenheimer surface, respectively. A good choice for the
frequency of the electron thermostat can be made based on
, the maximum frequency in the phonon
spectrum. The frequency of the electron thermostat should be
at least 2-3 times this value to avoid coupling between the ions
and the electron thermostats. As an example, for silicon, the
highest frequency in the phonon spectrum is 0.003 a.u., so a
good choice for the electron thermostat frequency is 0.01 a.u.
The chain length of the electron thermostat can be chosen in
the same way as for the ions. 4 is usually sufficient, however
longer chains may be used if serious heating is expected. In addition,
the electron thermostats have an extra parameter that scales the
number of dynamical degrees of freedom for the electrons.
(
, where 
is the desired electron
kinetic energy and 
is the number of dynamical degrees of
freedom for the electrons - see Eq.(3.4) in Ref.[3]).
The default value is the true number of dynamical degrees of
freedom 
, where p=2 for
orthonormality constraints and p=1 for norm constraints.
When this number is very large, it may not be possible to
integrate the electron chain thermostats stably using a frequency
above that top of the phonon spectrum. Should this be the case
in your problem, then the number of dynamical degrees of freedom
should be scaled to some smaller number such that the
system can once again be integrated stably. This parameter
has no other effect that to change the relative time scales
between the first element of the electron thermostat chain
and the other elements of the chain.
In addition to the basic parameters defining the chains themselves,
one needs to specify two more parameters related to the
integration of the thermostatted equations of motion.
The first is the order 
of the Suzuki integrator. Experience
shows that the choice 
is sufficient for most
applications. Finally, one must specify the number of times
the Suzuki integrator will be applied in a given update.
This is the parameter
which determines the basic Suzuki time step
= 
, where 
is the
time step being used in the MD run. 
or 3
is usually large enough to give stable integration. If more
stable integration is required, try 
or make
larger.