Phase equilibria and critical properties of carbon dioxide obtained by molecular dynamics simulations

Gibbs Ensemble:
A new algorithm for the Gibbs ensemble molecular dynamics method was constructed (see
section 6.2 on page 56). The algorithm is based on the Nosé-Hoover non-Hamiltonian equations
of motion. It was shown that states de�ned by the Gibbs ensemble partition function are
sampled (see section 6.2.4 on page 70 and previous pages).
The molecular dynamics algorithm is more complicated than the Monte Carlo method. However,
the complexity does not increase from atoms to larger molecules, whereas the Monte Carlo
method has to be extended to sample additional degrees of freedom. Further advantages are
that time averages are obtained, time correlation functions can be calculated and the single
step transfer could be replaced by an exchange trajectory.
An accurate ab initio CO2 pair potential was used to validate the algorithm. The critical values
were in good agreement with the experimental critical point. The molecular results will be the
�rst published data of the Gibbs ensemble molecular dynamics method with one exchange
molecule. It was shown that the exchange length is proportional to the density of the liquid
phase. Therefore, the same method could even be used for solid phases.
The new Gibbs ensemble molecular dynamics algorithm could be easily extended to larger
molecules by extending the exchange algorithm or to smaller systems like Car-Parrinello molecular
dynamics by adding Nosé-Hoover chains. The non-Hamiltonian approach gives a high
�exibility for the construction of equations of motion in the future.
It would be interesting to check the algorithm with di�erent potentials under various conditions
such as large molecules, solid phases or the triple point. It should be possible to get the triple
point by using three subsystems for the liquid, vapor and solid phases.
Critical Properties:
The properties of supercritical CO2 in the vicinity of the critical point were studied by di�erent
methods. Several critical phenomena known from experiments could be reproduced.
To get a better insight into the critical region and the correlation length in the vicinity of
the critical point, the calculation of more isotherms is necessary. So far, the microcanonical
ensemble was used to calculate the time correlation. The results could be improved by using a
canonical ensemble.