Energy bond distance deformation

The above models consider only one spatial variable which is the bonding distance. It is clear that, for a molecule anything more complex than diatomic, many parameters are needed to define even approximately the potential energy surface. The enormous advances in computational chemistry during the last few years have allowed quantum mechanical calculations on fairly large size molecules. The first attempt to apply quantum mechanics on deformed polymer chains was made... 

The deformation energy will be larger if the monomer geometry is substantially different in the complex than in the free monomer. We have encountered this in studies of HCO" (van Mourik and Dunning Jr.). Although the C-H bond is weak (the equilibrium bond dissociation energy, D, is approximately 8.2 kcal/mol (Berkowitz, private communication), the addition of H to CO has a pronounced effect on the CO distance. The CO distance in HCO" is calculated [CCSD(T)/aug-cc-pVQZ]tobe 1.2403 A, while it is 1.1318 A in a free CO molecule. 

For a fixed deformation energy V Do,Dq)-V(PQ), this equation represents an equipotential hyperellipsoidal surface with principal axes along the eigenvectors As an example, consider the bond-stretching deformations of a symmetric I3 fragment with distance deformations d and di-... 

In equation (1) the first five terms comprise the internal energies [25]. The first two terms account for bond and angle deformations using a harmonic approximation, where Kf, and are the bond stretching force constant and the equilibrium bond distance, and Kg and the bond angle stretch... 

Hardness of a material is a measure of its ability to resist deformation [1,2]. The upper limit of the hardness is determined by the rigidity of the crystal structure upon isostatic pressure. This theoretical hardness is proportional to the reciprocal value of the bulk modulus, B. From the Hooke s law B — dafde cr is the applied stress and e the resulting elastic strain) and from the relationship between the stress (a force) and the first derivative of the binding energy, E, with bond distance, a, at the equilibrium position oq, a — (d b/dfl)o, one obtains [3]... 

The following features are collected C=C and H-H bond lengths (in A), H "ti and H - o distances (in A, from H-atom to the mid-point of C=C or H-H bond), electron transfer (in milielectrons) from the proton acceptor to the proton donating moiety, the binding energy (BSSE and the deformation energy as a result of complexation are taken into account) (Reprinted from Ref [5] with kind permission of The American Chemical Society)... 

Two types of deformation may be imagined to excite the energy wells. First, the 109° bond angle is opened (ideally) to 180°. Second, the carbon-carbon bond distance is elongated from 1.54 A to some larger value. Mark (65) assumed that stretching the C—C bond to 2.54 A was required to cause the bond to fail. 

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