Orbital interactions energy separation

Orbital interaction energies are limited to a, ft and 0. The Fock matrix orbital interactions are limited to a, jl and 0, depending on whether the Htj interaction is, respectively i,i, adjacent, or further-removed. The value of ft does not vary smoothly with the separation of the orbitals, although logically it should decrease continuously to zero as the separation increases. 

Orbital interaction energies are calculated and vary smoothly with geometry. The EHM Fock matrix orbital interactions //, are calculated in a way that depends on the distance apart of the orbitals, so their values vary smoothly with orbital separation. 

Increased a donation by itself cannot cause X-H bond rupture BD is responsible for this task. Sorting out these two components is important in understanding (T-bond activation, and the BD component, bd of the total M-Hj orbital interaction energy can be separated from [Pg.346]

Frori tier Orbital theory supplies an additional asstim piion to ih is calculation. It considers on ly the interactions between the h ighest occupied molecular orbital (HOMO) and the lowest unoccupied rn olecular orbital (I.UMO). These orbitals h ave th e sin a 1 lest energy separation, lead in g to a sin all den oin in a tor in th e Klopinan -.Salem ct uation, fhe Hronticr orbitals are generally diffuse, so the numerator in the equation has large terms. 

AEis the interaction energy q and qg are charges on atoms A and B, separated by Rab, on different molecules, r and s are molecular orbitals on the two different molecules, p and v label the atomic orbitals that contribute to these molecular orbitals, with coefficients Cjjj. and Cyg. Hj y is the matrix element between atomic orbitals p and V, which is a measure of the energy of their interaction, roughly proportional to their overlap. The energies of the molecular orbitals are and e. ... 

An important contribution for the endo selectivity in the carho-Diels-Alder reaction is the second-order orbital interaction [1], However, no bonds are formed in the product for this interaction. For the BF3-catalyzed reaction of acrolein with butadiene the overlap population between Cl and C6 is only 0.018 in the NC-transi-tion state [6], which is substantially smaller than the interaction between C3 and O (0.031). It is also notable that the C3-0 bond distance, 2.588 A, is significant shorter than the C1-C6 bond length (2.96 A), of which the latter is the one formed experimentally. The NC-transition-state structure can also lead to formation of vinyldihydropyran, i.e. a hetero-Diels-Alder reaction has proceeded. The potential energy surface at the NC-transition-state structure is extremely flat and structure NCA (Fig. 8.6) lies on the surface-separating reactants from product [6]. 

Multiple M=P bonding in (OC)5M=PR becomes evident with ADF s bond energy analysis in terms of electrostatic interactions, Pauli repulsion, and orbital interactions from which the a,Ti-separation is obtained using a symmetry decomposition scheme [21]. For singlet (OC)5Cr=PR, which has a BDEst of 40.5 kcal/mol, the a- and n-components are 62.4 and 40.9 kcal/mol, respectively. 

As is apparent from the above definitions, each of these effective matrices depend on basis sets and molecular orbitals of both fragments. It is also important to observe that these matrices possess a correct asymptotic behavior as at large interfragment distances they become the usual overlap and Fock matrices of the separate fragments, while the paired secular systems uncouple and converge to the separate Roothaan equations for the single monomers. Finally, as it is usual in a supermolecular approach, the interaction energy is expressed as... 

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