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In the same spirit of the CarParrinello dynamics, at each ionic move, eq. 5.22, the parameters are optimized using eq. 2.31. This has allowed us to relax the wavefunction to the energy minimum during the ionic dynamics .
We call this technique Generalized Langevin Dynamics using Quantum Monte Carlo noisy forces(GLQ).
In order to simulate finite temperature systems using the GQL dynamics some control parameters has to be fixed for an efficient scheme.
Let us imagine that we want to simulate a system at given temperature
and density
. First of all we have to choose the friction tensor. Two choices are possible: the first one is to work with the friction as small as possible, compatibly with the QMC noise, in order not to affect dynamic properties; the second choice is to choose the friction in such a way to achieve the maximum convergence speed. In this thesis we did not investigate dynamical properties and so we opted for the second choice.
Second, we have to determine the two parameters
and
see eq. 2.33 and 5.22.
We have chosen
as big as possible to have a stable optimization. Instead
has been chosen enough small to allow the Hessian optimization to follow the ionic dynamics. This can be easily checked controlling if the forces 2.11 are zero within a given accuracy. For example for a system of
hydrogen atoms we have used a time step
of the order of
for a temperature around
. For higher temperature in order to maintain the same precision between ionic dynamics and optimization of parameters the time step
is roughly rescaled as
in such a way to maintain the same mean ionic step
.
Moreover to have a stable minimization not all parameters have to be changed at each ionic step but only the most relevant, see the forthcoming section 5.4.3.
Thanks to GLQ technique we were able to simulate reasonably large systems, by using highly correlated wavefunctions with many parameters (see figure 5.1) and with essentially a single processor machine.
Figure 5.1:
Ionic dynamics of 54 hydrogen atoms using GLQ, with a time step
, starting from a BCC lattice. The trial wavefunction contains 2920 variational parameters and we have optimized 300 of them at each step. In the inset the maximum deviation
of the forces acting on the variational parameters is shown.

Subsections
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Claudio Attaccalite
20051107