Zero-point energies of vibrations

The energetics given in Table 2 must be corrected for zero-point energy of vibration to convert the energies to enthalpies ... 

Triple- and quadruple-excited configurations included Zero point energy of vibrations included... 

As an example the discussion here is based on the discrimination between reactivity at a C—H and a C—D bond. There is no discrimination between the electronic, rotational or translational properties of H and D atoms. The vibrational frequencies observed by infrared spectroscopy are near the values of 2900 cm for C—H and 2100 cm for C—D. The zero point energy of vibration e is given by... 

We may fix our attention on the minimum of the potential-energy curve in Fig. 7 and ask how much higher the lowest vibrational level will lie. This energy gap between the potential minimum and the lowest vibrational level is equal to the vibrational energy of the molecule at the absolute zero of temperature and is known as the zero-point energy of... 

Kaplan and Thornton (1967) used three different sets of vibrational frequencies to estimate the zero-point energies of the reactants and products of the equilibrium, which provided three different isotope exchange equilibrium constants 1-163, 1-311 and 1-050. The value 1-311 is considered to be most reasonable, whereas the others are rejected as unrealistic for the case in hand. Calculations using the complete theory led to values that varied from 1-086 to 1-774 for different sets of valence-force constants for the compounds involved. 

A clear-cut dependence of the activation energy on the heat (enthalpy) of the reaction, which is equal, in turn, to the difference between the dissociation energies of the ruptured (Z> ) and the formed (D j bonds, was established for a great variety of radical abstraction reactions [1,2,16]. In parabolic model, the values of Dei and Def, incorporating the zero-point energy of the bond vibrations, are examined. The enthalpy of reaction AHe, therefore, also includes the difference between these energies (see Equation [6.7]). 

On a cautionary note, if there is strong electronic coupling between the reactant and product states that serves to reduce the electronic barrier in the proton-transfer coordinate below the zero-point energy of the transferring vibration, then... 

Hase s trajectory value for the association rate constant, /cp of 1.04 cm- s maybe used in conjunction with the above Langevin value of the collisional stabilization rate constant to yield a unimolecular dissociation rate constant of 3.75 x 10 ° s and a lifetime of 27 ps. In each case, these values are in excellent agreement with the order of magnitude of lifetimes predicted by Hase s calculations for cr/CHjCl collisions at relative translational energies of 1 kcal mor , rotational temperatures of 300 K, and vibrational energies equal to the zero-point energy of the system. 

---