Shape-constrained searches

In the context of density functional theory (DFT), the shape function can be considered to be the fundamental variable in the Levy-constrained search [5],... 

The paper of Parr and Bartolotti is prescient in many ways [1], It defines the shape function and describes its meaning. It notes the previously stated link to Levy s constrained search. It establishes the importance of the shape function in resolving ambiguous functional derivatives in the DFT approach to chemical reactivity—the subdiscipline of DFT that Parr has recently begun to call chemical DFT [6-9]. Indeed, until the recent resurgence of interest in the shape function, the Parr-Bartolotti paper was usually cited because of its elegant and incisive analysis of the electronic chemical potential [10],... 

Analysis of the shape of the orienting potential, which constrains the preferred orientation of the effective axis of internal rotation of the tethered nitroxide, revealed the presence of two different conformations of the spin-label moiety. In order to explain these results, the quantum chemical procedure was utilized. The spin-label moiety in the polymer system was reduced to 4-acetamido-2,2,6,6-tetramethylpiperidine-l-yloxyl (II) (spin label plus tether). The molecule was subjected to a search for stable confonn-ers, which resulted in the two minima corresponding to the structures Da and nb." ... 

As discussed in detail elsewhere [12], the dipole magnitude and direction parameters are constrained by the x-ray structure of the RC [13] to lie within rather narrow choices of ranges. All aspects of the AF spectrum in Fig. 2 were fit simultaneously (magnitude, shape, shift, X> and field dependence). A simulated annealing fitting algorithm was implemented to insure a systematic search of parameter space [12]. 

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