Minimal Substitution

Hazard and Risk Analysis Consideration should be given to identifying process hazards as early as possible in the process equipment design, so that measures can be taken to reduce or eliminate the hazards. Inherently safer design strategies, such as minimize, substitute, moderate, and simplify, should be implemented. 

External fields are introduced in the relativistic free-particle operator hy the minimal substitutions (17). One should at this point carefully note that the principle of minimal electromagnetic coupling requires the specification of particle charge. This becomes particularly important for the Dirac equation which describes not only the electron, but also its antiparticle, the positron. We are interested in electrons and therefore choose q = — 1 in atomic units which gives the Hamiltonian... 

Using the right-hand side of the identity for minimal substitution (17) gives the Hamiltonian... 

The insight provided by studying 8-oxo-guanine, and the ability to substitute DNA with a nucleobase that could be selectively oxidized by a low-potential complex, prompted us to search for other minimally substituted, redox-active nucleobases [92]. We therefore developed a library of nucleobases that were investigated using density functional theory (DFT) [93, 94] calculations self-consistently coupled to the conductorlike solvation model (COSMO) [95, 96]. The case of oxidation of nucleobases, particularly guanine. 

Elimination reactions are a useful method for the preparation of alkenes, provided that certain limitations are recognized. One problem is the competition between substitution and elimination. The majority of eliminations are done under conditions that favor the E2 mechanism. In these cases, steric hindrance can be used to slow the competing SN2 pathway. Tertiary substrates and most secondary substrates give good yields of the elimination product when treated with strong bases. Sterically hindered bases can be employed with primary substrates to minimize substitution. 

The peculiarity of the pentalene molecule resides in its central bond which connects nonalternant atoms (a perturbed [8]annulene), its completely conjugated and alternating w bond periphery, and its apparent antiaromatic nature. The transannular bond conveys planarity to the structure without contributing to its stabilization. Consequently, pentalene is expected to be highly reactive since, in a sense, it has ground state properties customarily found in excited states. The many early attempts to synthesize pentalene have been reviewed224-226 and will not be considered per se here. Suffice it to say that the lability of minimally substituted pentalenes ultimately required the implementation of rather specific reaction conditions for their successful synthesis (vide infra). 

After a brief historical recapitulation, the substantial body of experimental and theoretical work on these thermal epimerization reactions reported over the past 40 years is summarized. Of primary concern here are examples of stereomutations involving monocyclic, stereochemically unconstricted and minimally substituted molecules. Experimental studies of more heavily substituted cyclopropanes attempts to generate trimethylene diradical intermediates from pyrazolines " and the fascinating and still incompletely understood thermal chemistry of bicyclo[2.1.0]pentanes, 2-methylenebi-cyclop.l.OJpentanes", bicyclo[3.1.0]hex-2-enes and related reactions such as the pyrolysis of cyclopropane at 1200 °C to give products such as cyclopentadiene and toluene are neglected, in spite of obvious mechanistic interrelationships. 

In general, the cyclodehydrative potential of DDPP is particularly impressive. For example, high conversions of minimally-substituted 1,2-, 1,4-, and 1,5-diols to the epoxides (70-92%), tetrahydrofurans (95-99%), and tetrahydropyrans (85%), respectively, are noteworthy (25). 

P. R. L. Malenfant, M. Jayaraman and J. M. J. Frdchet, Dendrimer-supported ohgothiophene synthesis aliphatic ether dendrimers in the preparation of ohgothiophenes with minimal substitution, Chem. Mater., 11, 3420-3422... 

The perturbation Hamiltonian contains the magnetic perturbation which enter the Hamiltonian via minimal substitution of the linear momentum operator... 

The presence of a magnetic field-external, or from a nuclear spin-can be incorporated by minimal substitution for the electron momentum operator. 

As it has been shown previously [21 ], at the ZORA level the magnetic perturbation operators are the same no matter if the minimal substitution is made in the Dirac Hamiltonian before... 

There are at least four conceptually distinct ways in which orbital magnetism can appear in a physical system. One is the presence of external magnetic fields B(r), whose vector potential A(r) enters the Hamiltonian via the usual minimal substitution in the kinetic energy... 

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