Dimer method

In most cases, none ofthe following were observed ( )-head-to-head dimers, head-to-tail dimers, or trimers. High regio- and stereo-selectivities set this method apart from Rh(I)-catalyzed dimerization methods. 

V"-Boc-7Va -Z-L,L-diaminosuberic acid co-tert-butyl ester or bis(7V"-Boc)-L,L-diaminosuberic acid synthesized by the mixed Kolbe electrolytic carboxylative dimerization method was successfully utilized in the synthesis of nonreducible bicyclic analogues of somatostatin1491 or hematoregulatory peptide (pGlu-Glu-Asp)2-Dsu-(Lys)2, respectively.[50]... 

The three initial points are different enough that the dimer searches converge to separate saddle points. In general the strategy for the Dimer method is to try many different initial configurations aroimd a minimum, in order to find the saddle points that lead out of that minimum basin. 

Figure 6 The calculation of the effectiveforce in the Dimer method. A pair of images, spaced apart by a small distance, on the order q/ 0.1A is rotated to minimize the energy. This gives the direction of the lowest frequency normal mode. The component of the force in the direction of the dimer is then inverted and the minimization of this effectiveforce leads to convergence to a saddle point. No reference is made to the final state.

Figure 7 Application of the dimer method to a two-dimensional test problem. Three different starting points are generated in the reactant region by taking extrema along a high temperature dynamical trajectory. From each one of these, the dimer isjirst translated only in the direction of the lowest mode, but once the dimer is out of the convex region a full optimization of the effective force is carried oat at each step (thus the kink in two of the paths). Each one of the three starting p>oints leads to a different saddle point in this case.

Figure 9 Thefrequency at which the various saddle points for the surface island transitions (illustrated in figure 8) are found with the Dimer method. The lowest saddle points are found with the highestjrequency. Also shown are the number of iterations required to go from the intial state to the saddle point to within a force tolerance of0.001 eV/AFor the more practical 0.01 eV/A tolerance, the average number offeree evaluations was a little under 300. The error bars show the standard deviation.

Using a different dimerization method, namely phenolic oxidation, chiral substrates react in a more stereoselective manner than under reductive conditions. The choice of oxidizing reagent may drastically affect the stereochemical outcome of the reaction. Thus, when potassium hexacyanoferrate(III) is used (17 )-l,2,3,4-tetrahydro-6-methoxy-l,2-dimethyl-7-isoquino-linol couples to give a mixture of atropisomers 3 in 38 % yield and with a d.r. (M)I(P) of 45 553,4. Only one single atropisomer, namely (A/)-3, is formed, in a 66% yield by anodic oxidation, which is attributed to electrode surface effects3. 

LSKMC) method [81], the search for saddle points in the vicinity of a given local minimum by the dimer method was used [82], For the found new local minima, the rate constants of transitions are calculated based on the TST... 

The limitations of this theory are (1) the applicability of harmonic transition state theory (which is rarely an issue for the kind of accuracies typically required in geochemical/mineralogical problems), and (2) the sparsity of transition states the dimer method, as presently formulated, finds any transition state. If many of these are not of interest, as might be the case for diffusion barriers on the water side of the mineral-water interface, the method would be impractical. This points out another advantage to the multiresolution approach keeping the extra degrees of freedom of atoms in a region where one could get by with a continuum approach would, for example, require a reformulation of the dimer method. 

The high consumption of electricity in electrochemical processes stimulated research on purely chemical dimerization methods ... 

A. Heyden, A. T. Bell, and F. J. Keil, Efficient methods for finding transition states in chemical reactions comparison of improved dimer method and partitioned rational function optimization method, Journal of Chemical Physics, vol. 123, p. 224101, 2005. 

Baker J (1986) An algorithm for the location of transition states. J Comp Chem 7 385-395 Henkelman G, Jdnsson H (1999) A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J Chem Phys 111 7010-7022 Hanggi P, Talkner P, Borkovec M (1990) Reaction-rate theory fifty years after Kramers. Rev Mod Phys 62 251-341... 

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