How to Obtain a Consistent Set of Various Calculated Properties for van der Waals Clusters

The main advantage of theoretical study of a molecular cluster is the fact that a nearly complete set of consistent cluster properties can be generated. The quality of the evaluated properties depends on the theoretical level used; some properties require higher-level treatment. The following steps must be performed:

3.3.4.1 Potential Energy Surface (P.E.S.)

The aim is not only to localize all the minima and saddle points of the P.E.S. but also to correctly describe regions far from the minima. Clearly, several dozen points are required even for a small molecular cluster. Detailed investigation of the P.E.S. is very tedious but without its knowledge one cannot evaluate a (nearly) complete consistent set of various properties of the cluster under study. One-electron properties are evaluated for global and local minima. The classical search for all the minima on the P.E.S. (i.e., based on chemical intuition) is limited to small clusters having not more than 10-15 atoms. For larger clusters, some objective method must be used; the quenching method [26] can be recommended.

3.3.4.2 Stabilization Energy

The stabilization energy for the global minimum or for global and nearest local minima should be investigated more carefully. The stabilization energy is more sensitive to the quality of the theoretical description than the other properties of a cluster.

3.3.4.3 Empirical Potential

The most important property of a cluster is the respective intermolecular potential. The importance of theoretical determination of the intermolecular potential is increased by the fact that its evaluation using various experimental characteristics is tedious and not sufficiently accurate. The main advantage of the theoretical procedure is the fact that it can be applied to any type of molecular cluster. The analytical form of the potential should be sufficiently flexible and should contain a maneagable number of adjustable parameters.

3.3.4.4 Vibration Frequencies

Let us begin with a statement saying that a harmonic oscillator is described by a parabolic potential energy, while an anharmonic oscillator is characterized by a nonpara-bolic dependence. The use of the harmonic approximation for molecular clusters - and especially for floppy clusters - is limited; therefore, for biological systems it represent a poor approximation. The vibrational energy levels of the cluster should be obtained by solving the vibrational Schrodinger equation, which requires knowledge of the intermolecular potential. In this way, anharmonic frequencies are generated. The calculation of intermolecular vibrational frequencies is topical for two reasons: a) vibrational frequencies (in contrast, e.g., to the structure or stabilization energy) are observable; b) vibrational frequencies directly probe the quality of the intermolecular potential.

3.3.4.5 Computer Experiments

The structure of higher clusters at temperature T can be determined by molecular dynamics (MD); here again, the knowledge of the respective intermolecular potential is essential. Furthermore, when performing MD calculations the thermodynamic characteristics of cluster formation can also be obtained. This step is extremely important; it must be kept in mind that the global minimum localized on the P.E.S. at 0 K can be less favorable at higher temperatures. This is due to the different role which entropy plays for various structures of the cluster under study.

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