Global minimum Subject

The authors noted that state of 14 should be subject to Jahn-Teller distortion. At the HF/6-31G level they found a local minimum at Cs symmetry that was 89.1 kcal/mol higher than the global minimum (15). However, after corrections were made the transition structure connecting this min-immn to 15 was found to have lower energy and the authors concluded that there is no evidence for 14 as a distinct species. 

The problem of finding a global minimum in parameter fitting is partly due to a disparity in the relative size of the components of the kinetic rate constant and partly to the inherent problems of fitting sums of exponential terms to data. Perhaps there is no solution and we will always be troubled by this issue. However, now that the data is available and the need for better fitting procedures is before us, there is an incentive to improve parameter optimization routines to reduce the subjectivity present in these procedures. Then again, subjectivity in this type of data-fitting may well be inevitable. 

This problem can be solved using a quadratic programming algorithm, which finds the global minimum of a quadratic function subject to a set of linear constraints (39) practically it is done with the program PDQPRO (Probability Distribution by Quadratic PROgramming) (23). 

A method to solve the problem is to determine in the Fourier space the connection between the logarithm of refractive index values and the amplitude reflection and transmission coefficients, represented as complex wavelength-dependent functions. The global minimum of thus obtained dependence is then determined. The solution is an inhomogeneous layer, further transformed into a two-material system and subsequently subjected to a new procedure of fine optimization. 

Interest in the family of water clusters for n = 20 stems from the fact that one of the families of minima is the dodecahedron which has been proposed as a model for inclusion compounds and constitutes a budding block of type I ice clathrate (we will discuss this in detail in O section The First Few Water Cages ) The structure of (H2O)20 has been the subject of debate due to the existence of various major families of minima which are energetically in close proximity and the disagreement as to which was the global minimum (Fanourgakis et al. 2004). 

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