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 . 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 . 44 DAVID J. WALES ET AL.