Minimum translational/rotational energy

The molecular mechanics or quantum mechanics energy at an energy minimum corresponds to a hypothetical, motionless state at OK. Experimental measurements are made on molecules at a finite temperature when the molecules undergo translational, rotational and vibration motion. To compare the theoretical and experimental results it is... 

Activation Parameters. Thermal processes are commonly used to break labile initiator bonds in order to form radicals. The amount of thermal energy necessary varies with the environment, but absolute temperature, T, is usually the dominant factor. The energy barrier, the minimum amount of energy that must be suppHed, is called the activation energy, E. A third important factor, known as the frequency factor, is a measure of bond motion freedom (translational, rotational, and vibrational) in the activated complex or transition state. The relationships of yi, E and T to the initiator decomposition rate (kJ) are expressed by the Arrhenius first-order rate equation (eq. 16) where R is the gas constant, and and E are known as the activation parameters. 

AU,) - the differences between the depths of different minima so going down from a shallower to a deeper minimum of the molecular PES means decreasing the Gibbs free energy and such a process generally has an equilibrium constant larger than unity. However, for precise calculations, the terms coming from translations, rotations and vibrations also must be taken into account. 

A similar minimum value for the combined translational and rotational energy can be developed by noting that E — E + Ei A- E + B (J — ). This yields... 

Under laboratory conditions, molecules contain vibrational, translational and rotational energies which are not fairly partitionable among chemical bonds. For convenience, our analysis considers the molecules at their potential minimum, i.e., with reference to their hypothetical vibrationless state at O K the role of vibrational energies is treated as a separate problem. The measure for what holds the atoms together in a molecule is thus offered by the difference... 

Relative molecular enthalpies then result simply as the sum of the minimum potential energy V°, Z/yj, and the rotational and translational enthalpy contributions (= 3 RT). By experience, the // -contributions of different conformational minima of a molecule rarely differ by more than 1 kcal mole"-1 (see also Section 6.2.4.). Vibrational entropy contributions may be evaluated in a similar way as//vibr. 

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