Densely functionalized molecules, methods

Methods that are used to introduce fluorine into a densely functionalized molecule... 

Recently, Chen and coworkers reported an efficient new method to construct a series of densely functionalized 4,5-dihydro-IH-azepine products 41 from the intermolecular reaction of alkyl azides with propargylic esters. In this approach, sequential reaction of vinyl-gold carbenoids 42 with allqrl azides and formation of vinyl imine intermediates 43 may be involved fScheme 4.14). Then a subsequent formal [4+3] cycloaddition with another molecule of vinyl-gold carbenoid 42 afford the desired azepine 41. 

Constraint dynamics is just what it appears to be the equations of motion of the molecules are altered so that their motions are constrained to follow trajectories modified to mclude a constraint or constraints such as constant (total) kinetic energy or constant pressure, where the pressure in a dense adsorbed phase is given by the virial theorem. In statistical mechanics where large numbers of particles are involved, constraints are added by using the method of undetermined multipliers. (This approach to constrained dynamics was presented many years ago for mechanical systems by Gauss.) Suppose one has a constraint g(R, V)=0 that depends upon all the coordinates R=rj,r2...rN and velocities V=Vi,V2,...vn of all N particles in the system. By differentiation with respect to time, this constraint can be rewritten as l dV/dt -i- s = 0 where I and s are functions of R and V only. Gauss principle states that the constrained equations of motion can be written as ... 

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