Vibrational, generally energy

The bending (or deformation) vibrations generally require less energy and take place at longer-wave-length than the corresponding stretching vibrations. 

However, the MEP may be a convenient measure of the progress of a molecule in a reaction, because in general a molecule will move, on average, along the MEP in a well-defined valley, and it is a good approximation of the motion of vibrationally cold systems (e.g., for photochemical reactions in which the excited state reactant has a small/controlled amount of vibrational excess energy). 

It will be noticed that two contributions to the vibrational potential energy, of the general form V(R ) and independent of the rotational and spin quantum numbers, have also been included in equation (7.124). These are corrections to Vn(R), the zeroth-order contribution to the electronic energy defined in equation (7.76). The first term, Vr d)(R), is the adiabatic contribution to the electronic energy, which we have discussed in section 2.7. It describes the first-order effect of the nuclear kinetic energy within the... 

If the excess energy is electronic, there is a chance that it may be emitted within a time of 10 to 10 sec as radiation if the transition is possible. Otherwise such electronic energy must be degraded by inelastic collisions to other forms of energy, usually vibrational. Generally it is found that the electronic states produced in chemical reactions are metastable, so that we may expect electronically excited states to follow the path of collisional dcexcitation. The rare cases of allowed transitions result in what are referred to as chemiluminescent reactions. ... 

J. H. Frederick and C. Woywood, General formulation of the vibrational kinetic energy operator in internal bond-angle coordinates. J. Chem. Phys. Ill, 7255-7271 (1999). 

A generalized energy level scheme for laser action is shown in Fig. 1. If the terminal laser level is the ground state and the initial and final laser states have equal degeneracies, then more than one-half of the ions must be excited to obtain an inverted population and 3-level laser action. If, instead, the terminal level 2 is above the ground state, then only an excited-state population in level 3 sufficient to overcome the Boltzmann population in level 2 is needed for population inversion. This drastically reduces the pumping requirements. Phonon-terminated or vibronic lasers are those in which level 2 is a vibrational-electronic state. 

The classical phase-space averages for bound modes in Eq. (11) are replaced by quantum mechanical sums over states. If one assumes separable rotation and uses an independent normal mode approximation, the potential becomes decoupled, and onedimensional energy levels for the bound modes may be conveniently computed. In this case, the quantized partition function is given by the product of partition functions for each mode. Within the harmonic approximation the independent-mode partition functions are given by an analytical expression, and the vibrational generalized transition state partition function reduces to... 

---