Bond-stretching motion

First of all, we have to take account of every bond-stretching motion. We could write a simple harmonic potential for each bond, as discussed above. For a bond A-B, we would therefore write... 

I The region from 4000 to 2500 cm"1 corresponds to absorptions caused by N-H, C-H, and O-H single-bond stretching motions. N—H and O—H bonds absorb in the 3300 to 3600 cm-1 range C-H bond-stretching occurs near 3000 cm"1. 

As a bond stretches and breaks, there is established a continuous connection between the translational coordinate along which fragment separation occurs and the vibrational motions of the molecule. Since the bond stretching motion is not, in general, a normal mode of vibration, it is necessary to understand how the vibrational modes can combine to give the decomposition mode. 

Consider a linear triatomic AAA molecule where the atoms have mass m. Assume that the potential energy for the linear internal bond-stretching motion is given by... 

IR absorptions due to double bond stretching motions (1663 cm and 1655 cm ) change on dimerization. In the dimer, absorption for an isolated double bond appears, and that for a conjugated double bond moves to longer wavelengths. 

The application of this result to the determination of bond stretching force constants in molecules encounters two difficulties. First, real molecules are not exactly harmonic oscillators. Secondly, although the only mode of vibration possible in diatomic molecules is a bond stretching motion, the vibrations of polyatomic molecules are much more complicated, and cannot be expressed as consisting only of a combination of bond stretching motions. We discuss these two problems in turn in the next two sections. 

The bond stretching motions and bond bending motions discussed in Section 2.1.4 only had certain energies. Bond rotations are just another example of an internal degree of freedom within molecules. Therefore, why are we not explicitly discussing quantized energy states for bond rotations ... 

Other possible basis vectors include true spatial vectors such as a dipole-moment component (e.g. or a displacement of an atom along a direction defined by a bond (i.e. a bond stretching motion). More elaborate basis vectors are also useful one very important one consists of the set of three Cartesian-axis displacements of each of the N atoms in a molecule, and has a dimensionality of 3N. We will see this basis vector in action in Section 8.5.3, where we use symmetry to characterize a set of molecular fundamental vibrational modes. We can also use the wavefunction of a molecular orbital as a basis vector, and so classify that orbital according to the effects of the various symmetry operations acting on that wave-function (Section 9.3). Even a tensor such as the molecular polarizability can be used as a basis vector. Throughout this book we use a number of subscript labels for the different basis vectors we discuss. The convention we use is as follows. 

To reliably describe PT reactions in the gas and condensed phases, the usual parameterization of a force field in terms of harmonic bonded interactions is not sufficient. H-bonded systems are quite anharmonic around the bottom of the well for bond-stretching motions, and angular bending vibrations are equally affected. Furthermore, the hydrogen motion between the donor and acceptor atoms is strongly coupled to the donor-acceptor motion. These aspects need to be taken into account for a reliable model of hydrogen or proton motion between a donor-acceptor pair. 

---