The Sphere Optimization Technique

The Sphere optimization technique is related to the saddle method described in 

Method Path minimization Path maximization Hyperplane minimization Hypersphere minimization Global minimization Points moved 

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The sphere optimization technique is related to the saddle method described in Section 2.2, and involves a. sequence of constrained optimizations on hyperspheres with increasingly larger radii, using the reactant (or product) geometry as a constant expansion point (Figure 9). The lowest-energy point on each successive hypersphere thus traces out a low-energy path on the PES. 

Variational one-center restoration. In the variational technique of one-center restoration (VOCR) [79, 80], the proper behavior of the four-component molecular spinors in the core regions of heavy atoms can be restored as an expansion in spherical harmonics inside the sphere with a restoration radius, Rvoa, that should not be smaller than the matching radius, Rc, used at the RECP generation. The outer parts of spinors are treated as frozen after the RECP calculation of a considered molecule. This method enables one to combine the advantages of two well-developed approaches, molecular RECP calculation in a gaussian basis set and atomic-type one-center calculation in numerical basis functions, in the most optimal way. This technique is considered theoretically in [80] and some results concerning the efficiency of the one-center reexpansion of orbitals on another atom can be found in [75]. 

Kinetics of Selenium Adsorption. Zhang and Sparks 4G) examined selenate and selenite adsorption and desorption on goethite using pressure jump relaxation techniques. Selenate produced a single relaxation, that was interpreted as outer-sphere complexation with surface protonation based on fitting to the triple layer model. The forward rate constant was 10 L mol s Selenite adsorption was proposed to occur via two steps, an initial outer-sphere complex and subsequent replacement of a water molecule by formation of inner-sphere complexes of both HSeOj and SeOj, based on optimized fits using the triple layer model. The model optimized fit for the pK, of the surface species was approximately 8.7. Forward rate constants for the first step were on the order of 10 L -mor -s for HSeOj and 10 L -mor -s for SeOj. Forward rate constants for the formation of the inner-sphere complexes were 100 and 13 s respectively for HSeOj and SeOj. Agreement between the equilibrium constant obtained from batch and kinetic studies was taken as confirmation of the proposed reactions. 

Meanwhile, cation - crown complexes were fully optimized by ab initio QM techniques in the gas phase, allowing to investigate the effect of electronic reorganization (mainly charge transfer + polarization effects) on the recognition properties/15,161 QM/MM hybrid methods which combine a QM representation of the ion coordination sphere with a MM representation of the more remote species, have been tested on 18C6/ cation complexes/17, 18] Typical applications of "computational approaches in supramolecular chemistry" up to 1994 can be found in ref. [191 There are also reviews on more specialized fields like calixarenes/20,21]... 

Use resource optimization when you need to come up with solution ideas that provide higher value than those in existence today—or when you need to refine and optimize a specific solution design. The key is to make sure you list as many resources as possible within and outside your immediate system or sphere of focus. After this, you can use any number of idea-generation techniques to figure out how your available resources can be applied to your inventive problem. 

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