Intermolecular potentials clusters

Caldwell J, Dang LX, Kollman PA (1990) Implementation of nonadditive intermolecular potentials by use of molecular-dynamics - development of a water water potential and water ion cluster interactions. J Am Chem Soc 112(25) 9144—9147... 

The virial coefficients B(T), C(T), D(T),... are functions of temperature only. Although these coefficients might be treated simply as empirical fitting parameters, they are actually deeply connected to the theory of intermolecular clustering, as developed by J. E. Mayer (Sidebar 13.5). More specifically, the second virial coefficient B(T) is related to the intermolecular potential for pairs of molecules, the third virial coefficient C(T) to that for triples of molecules, and so forth. For example, knowledge of the intermolecular pair potential V(R) (see Sidebar 2.8) allows B T) to be explicitly evaluated by statistical mechanical methods as... 

Here the number of molecules in the th cluster is n the total number of molecules N, and the number of ways of allocating N molecules to a given partition n,. U, is the cluster formation energy of the cluster j, which consists of n, molecules U, is the sum of each intermolecular potential. S( n, ) is the allocation entropy of partition [21]. 

Figures 5-2 and 5-3. First, the dispersed emission from the cluster

Comparisons have been made between the two analogous molecules CH4 and CF4. In the latter, clusters of molecules are seen via 19F NMR, at various temperatures and pressures,61 in various phases. Intermolecular potentials have been derived and compared for the two molecular species, as a result of gas-phase NMR studies.62... 

Compared to the situation described in earlier reviews, the scope of applications has noticeably widened. In particular, more mixed clusters are now being studied (albeit only binary ones). Also, a few papers have appeared that treat clusters other than bare clusters in a vacuum hydrogen-passivated silicon clusters and ligand-coated gold clusters have been investigated, as well as clusters on supporting surfaces. Studies of molecular clusters, however, which were attempted at the very beginning of the development described earlier, are still quite rare, and are limited to comparatively small cluster sizes. This bears testimony to the additional difficulty of this task, and perhaps also to the lack of reliable intermolecular potentials. 

Most of the other EA applications to molecular clusters the present author is aware of focus on pure or mixed water clusters. This is not too surprising, considering the facts that water is the most important molecule on this planet and that reliable intermolecular potentials are even harder to produce than reliable interatomic potentials. 

So far, our discussion of intermolecular potentials has been limited to pair interactions. In clusters involving more than two monomers the three- and higher-body terms will appear. For example, the total energy of a trimer ABC may be expressed as follows... 

Implementation of Nonadditive Intermolecular Potentials by Use of Molecular Dynamics Development of a Water—Water Potential and Water—Ion Cluster Interactions. 

Classical density functional theory (DFT) [18,19] treats the cluster formation free energy as a functional of the average density distributions of atoms or molecules. The required input information is an intermolecular potential describing the substances at hand. The boundary between the cluster and the surrounding vapor is not anymore considered sharp, and surface active systems can be studied adequately. DFT discussed here is not to be confused with the quantum mechanical density functional theory (discussed below), where the equivalent of the Schrodinger equation is expressed in terms of the electron density. Classical DFT has been used successfully to uncover why and how CNT fails for surface active systems using simple model molecules [20], but it is not practically applicable to real atmospheric clusters if the molecules are not chain-like, the numerical solution of the problem gets too burdensome, unless the whole molecule is treated in terms of an effective potential. 

The numerieal methods which were used in our work were discussed in detail previously [2, 3J and only a general outline will be presented here. The equations of motion were integrated by using a modified public domain program Venus [4]. For an intermolecular potential we have used a potential calculated by Bludsky, Spirko, Herouda, and Hobza [5] (BSHH) who reported ab initio calculations of an Ar-benzene cluster and fitted the results to a potential funetion which is based on pair-wise atom-atom interactions. This is called the BSHH potential. 

Evaluation of the Hartree-Fock dispersion (HFD) model as a practical tool for probing intermolecular potentials of small aromatic clusters Comparison of the HFD and MP2 intermolecular potentials68... 

Both second and third cluster integrals can be calculated in neat forms for the standard intermolecular potential which was introduced in Section 1.3. 

Comparing the calculated function for the second cluster integral with observed values given in Table II, we can determine two parameters X and ft of the intermolecular potential, Eq. 1.28. This potential can be rewritten in the form... 

Fig. 2. Third cluster integral of neon for additive (broken line) and non-additive (full line) intermolecular potentials compared with observed values.

Beu TA, Buck U, Siebers JG, Wheatley RJ. A new intermolecular potential for hydrazine clusters structures and spectra. J Chem Phys 2001 106 6795-6805. 

In addition to the dependence of the intermolecular potential energy surface on monomer vibrational level, the red-shifting of the monomer absorption as a function of the number of rare gas atoms in the cluster has been studied. The band origin for the Vj p =1- 0 vibration in a series of clusters Ar -HF, with 0 < < 5, was measured and compared to the HF vibrational frequency in an Ar matrix ( = oo). The monomer vibrational frequency Vjjp red shifts monotonically, but highly nonlinearly, towards the matrix value as sequential Ar atoms are added. Indeed, roughly 50% of the shift is already accounted for by = 3. 

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