By Ilya Prigogine, Stuart A. Rice
This sequence of volumes represents examine relative to advances in chemical physics. Edited via Nobel Prize winner Ilya Prigogine, quantity one hundred fifteen is a different topical stand-alone two-volume paintings in a sequence.
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Extra resources for Advances in Chemical Physics, Vol. 115
This situation is partly the result of competition between two distinct types of overlayer. In the first type, the anti-Mackay overlayer, atoms are added to the faces and vertices of the underlying 13-atom ENERGY LANDSCAPES: FROM CLUSTERS TO BIOMOLECULES 43 icosahedron (giving rise, for example, to the double icosahedron, 19A). In the second type, the Mackay overlayer atoms are added to the edges and vertices. The completion of the Mackay overlayer leads to the next Mackay icosahedron. LJ31 is the first size for which a cluster with the Mackay overlayer is the global minimum .
33) where El is the potential energy of minimum i . V , is the geometric mean vibrational frequency, K is the number of vibrational degrees of freedom, and p = l / k T . For a cluster, K = 3N - 6 but for a bulk system K = 3N - 3. We have ignored the rotational and translational degrees of freedom since we generally consider systems with zero linear and angular momentum. Although the harmonic approximation usually gives a qualitatively correct picture, to obtain accurate thermodynamic properties one needs to have a good anharmonic expression for Q, or Z,.
The issue of sampling is further discussed in the following section with reference to thermodynamic properties. C. Thermodynamics from the Superposition Approach The superposition method extends Stillinger and Weber's division of the PES into catchment basins for each minimum to calculate thermodynamic properties. In this approach the configurational part of the phase space integral in the definition of the density of states, Q ( E ) ,or partition function, Z ( T ) ,is divided into separate integrals for each minimum, giving R(E) = c L ?