» Peacemaker V1.6.2«
General Information:
Peacemaker 1.6.2 is a quantum chemical postprocessing Fortran90 code primarily written in order to carry out
In order to rely on a cluster description of the condensed phase, the two most urgent conditions to be met by the system under investigation are:
a) The system is associated in the condensed phase, i.e. strong intermolecular interactions ensure that clusterlike structures exist at higher densities. This is generally true for most hydrogen-bonded liquids, but should also apply to other strong intermolecular interactions, e.g. the Coulomb interaction in ionic liquids.
b) The cluster structures are representative averages of the structures occuring in the condensed phase, i.e. the cluster set should be understood as a sort of structural average of the molecular liquid. Many examples demonstrate that the inclusion of all relevant cluster motifs (i.e. coordination pattern, topology, etc.) is much more important than the consideration of particular cluster sizes and -geometries. If important cluster motifs are missing from the cluster set, the computed partition function (and thus the thermodynamic quantities) will be an inaccurate approximation to the actual phase under investigation. In a sense the cluster set might thus be vaguely compared to the basis set in a quantum chemical calculation.
The program starts by setting up degree-of-freedom (dof) factorized cluster partition functions, which in the QCE model closely resemble the standard expressions of the rigid-rotor-harmonic-oscillator (RRHO) approximation used in most quantum chemical codes. However, these formulae are modified in two central aspects, namely the volume of free translation entering the translational partition function and the intercluster interaction energy, which enters the electronic partition function. The computation of the actual volume of free translation relies on the excluded volume arising from the molecular volume of the clusters as well as on the actual phase volume, which is calculated out of the molecular partition function. Due to this mutual dependency between volume and partition function an iterative procedure for the self-consistent determination of these quantities has to be introduced. An equivalent dependency is given in case of the volume and the inter cluster interaction, which is approximated in terms of a mean-field potential depending on the cluster size and the actual phase volume, i.e. the model-inherent modifications of the RRHO partition functions lead to the iterative cycle of the QCE procedure. As initial guesses to the iterative cycle the volume of an ideal gas and an uniform population of all clusters are chosen, from which the initial partition functions are obtained. These are employed for the formation of the coefficients of the population polynomial in the next step, whose roots yield possible population distributions of clusters consistent with the fixed monomer particle number of 1 mole. The different population sets together with the initial partition functions are subsequently used for the construction of the volume polynomial coefficients, and the roots of this 3rd degree polynomial yield possible new phase volumes. Both the set of volumes and the set of populations are utilized for test calculations of the Gibbs enthalpy, and the volume/population combination yielding the lowest Gibbs enthalpy is chosen as the physical most sensible basis for the next iteration. This procedure closes the iterative cycle, and after volume convergence (typically to 10-9L) is achieved, the self-conistent partition function may be applied for the calculation of thermodynamic properties at the given p,T point. Such calculations are routinely carried out within a few seconds, which allows the sampling of rather large p,T intervals. As explained above the model contains two adjustable parameters used for the scaling of the excluded cluster volume and the mean-field interaction energy, which have to be specified for a given system. There is current work in progress aiming at the elimination of these parameters from the model or their determination out of cluster properties, respectively, but at the moment the most convenient way to evaluate both factors is a selection procedure implemented in Peacemaker 1.6.2, which determines the most accurate V,T curve with respect to an experimental reference according to a least-squares criterion after a sampling over a predefined parameter interval has been carried out. Following this route, molar densities and entropies for e.g. liquid water are obtained to high accuracy within rather short time scales, and phase transition properties such as boiling points or vaporization entropies are within the scope of the program as well.