Advances in Chemical Physics, Vol. 115 by Ilya Prigogine, Stuart A. Rice

By Ilya Prigogine, Stuart A. Rice

This sequence of volumes represents learn relative to advances in chemical physics. Edited through Nobel Prize winner Ilya Prigogine, quantity a hundred and fifteen is a different topical stand-alone two-volume paintings in a sequence.

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137. 28 DAVID J. WALES ET AL. D. Master Equation Dynamics The interwell dynamics of a complex PES represents a set of coupled differential equations that we solve using the master equation [ 153,1541. The first applications to clusters were made by Kunz and co-workers [57,58,155,156]. Since then the method has been pursued by our group [ 16,149,157-1601 and a number of others [ 17,59,63,71,140,148,151, 16 1,1621. Let P ( t ) be a vector whose components, P , ( t ) ( l 5 i 5 nmin), are the probabilities of the cluster residing in a potential well corresponding to minimum i at time t.

W and W have the same ) u(i),respectively, eigenvalues, hi, and their normalized eigenvectors, u ( ~and are related by u ( ~=) Su('), where S is the diagonal matrix Sii = Hence, individual components of the eigenvectors are related by u j i ) = iiji)@. The solution of Eq. 39) is then [153,154] R. where iik) is component m of u b ) . Apart from the zero eigenvalue, all the hJ are negative [153]. We adopt the convention of labeling the eigenvalues and eigenvectors in decreasing order according to the value of A,, so that hl = 0, and hJ < 0 for 2 < j 5 nm,*.

8. 486 for LJ75. The two pathways differ in a number of ways. First, the LJ75 path is longer, more complicated and higher in energy. Second, at its highest points the LJ3* pathway passes through disordered structures [ 130,2141, whereas all the minima along the LJ75 pathway are ordered. Indeed, a quasi-fivefold axis is retained throughout the pathway, as has also been observed in MD simulations of a decahedral to icosahedral transition in gold [215,216] and in LJ55 [218]. 44 DAVID J. WALES ET AL.

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