Linear combinations of fragment

We shall now illustrate how this approach, designated the Linear Combination of Fragment Configurations (LCFC) approach, can be applied to diverse chemical problems. 

The dynamic linear combination of fragment confi ia-tions method. - Even-even intermolecular multicentric reactions. - The problem of correlation imposed barriers. -Reactivity trends of thermal cycloadditions. - Reactivity trends of singlet photochemical cycloadditions. - Miscellaneous intermolecular multicentric reactions. - tc + o addi-tion reactions. - Even-odd multicentric intermolecular reactions. - Potential energy surfaces for odd-odd multicentric intermolecular reactions. - Even-even intermolecular bicen-tric reactions. - Even-odd intermolecular bicentric reactions. 

The charge decomposition analysis based on linear combination of fragment molecular orbitals is proved to be very useful tool for studying interaction between molecular fragments in terms of donation, back-donation and polarization. 

Control over the a, and production of the desired superposition states can be achieved by several routes. One nice way is to utilize the reactants from an earlier photodissociation step, altering the af by any of a number of coherent control scenarios [2] for this piereactive step. Consider then preparing n, 0) via a prereactive stage in which an adduct AB, made up of a structureless atom A and the molecular fragment B, is photodissociated. The AB is assumed to be initially in a pure state of energy Eg and the photodissociation is carried out with a coherent source. Under these circumstances photodissociation produces B in a linear combination of internal states. For... 

The major orbital interactions of the /i-vinylidene ligand in binuclear complexes are with (i) an unperturbed nxy orbital of the Rh2 fragment, (ii) a bonding linear combination of the Rh2 n y and C p orbitals, and (iii) a bonding linear combination of the Rh2 a orbitals. The small rotation (0° -14°) which is often found between the CR2 and the CM2 planes serves to optimize these orbital overlaps. 

Our starting point is the decomposition of the normal modes of a larger system into those of independently computed fragments [12], An exact decomposition is possible if the number of the nuclei of the fragments equals those of the supersystem, and provided all normal modes are considered, which means rotations and translations must be included in the treatment. In order to avoid the otherwise ubiquitous mass factors, it is convenient to use the matrix L which gives the transformation between the mass-weighted excursions of the nuclei a and the normal modes Qp, rather than Lx. The elements of the two matrices are related by Laip = /mJtLxai p [59], A normal mode Lsp of the system S can be written as linear combination of the normal modes Lf, Lf, Lcr of the independent subunits A, B, C - - with the numbers NA, NB, Nc - of nuclei ... 

In this case the combination of fragments with flexible and rigid molecular chains in linear chains can help to synthesise elastomers and plas-tomers with a higher thermostability. 

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