Energy, Stretching

An ultrashort mid-IR pulse excited a C-H stretching vibration (-3000 cm ) of neat acetonitrile at 300 K. The loss of C-H stretching energy occurred in 3 ps. Only 1% of that energy was transferred to the C N stretch (2250 cm ), where it remained for -80 ps. Most of the energy was lost from the C-H stretch by the process,... 

The derivatives are evaluated at R = Rq and the (0) term is normally set to zero this is just the zero point for the energy scale. The second term is zero as the expansion is around the equilibrium value. In its simplest form the stretch energy can thus be written... 

Usually the constants involved in these cross terms are not taken to depend on all the atom types involved in the sequence. For example the stretch/bend constant in principle depends on all three atoms. A, B and C. However, it is usually taken to depend only on the central atom, i.e. = k , or chosen as a universal constant independent of atom type. It should be noted that cross tenns of the above type are inherently unstable if the geometry is far from equilibrium. Stretching a bond to infinity, for example, will make str/bend go towards — oo if 0 is less than If the bond stretch energy itself is harmonic (or quartic) this is not a problem as it approaches +oo faster, however, if a Morse type potential is used, special precautions will have to be made to avoid long bonds in geometry optimizations and simulations. 

The essential idea of the Alexander model, a global balance of interaction and stretching energies, can be applied to other situations involving tethered chains besides the good solvent case. In theta or poor solvents, the interaction term must be modified to account for poorer solvent quality. A simple limit is precisely at the theta point [29, 30] where binary interactions effectively vanish (% = 1/2 or v = 0). The leading term in Fim now accounts for three-body interactions ... 

The Alexander model allows a simple approach to this problem. Within this model, each tethered chain is, in effect, confined within a cylindrical capillary of diameter d. Combining Eq. 5 and 7, we can express the stretching energy as ... 

Compression (stretching) energy, Wi, for which we choose Crowley s form, Eq. (51). For small undulations this becomes... 

The C=C harmonic vibrational frequency is calculated at 1671 cm-1 in free ethylene and is infrared (IR) forbidden. Its IR intensity is therefore expected to remain low in the vinyl series of compounds. The C=C stretch energy is calculated to be 1687 cm-1 in propene and then decline to 1629 4 cm-1 for X = Si - Pb. As in the equilibrium bond distance, there is also a very small counter-trend change in the vibrational frequency going from X = Sn to X = Pb that indicates a slight strengthening of the C=C bond. 

The stretching energy is given by a sum of quadratic (harmonic) and cubic teims ... 

Example 1. Dissociation of H O by symmetric stretch Reference calculations are first performed at equilibrium geometry, using a simple basis of contracted gaussian functions [8]. The molecule is then dissociated by symmetric stretch, energies being calculated at bond length intervals of AR = Q.2Re up to i = 6.0J e (where dissociation is effectively complete). 

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