Out of total degrees of freedom 3N we consider 3 as rotational degrees of freedom. and 3 as transnational degrees of freedom and therefore 3N-6 for nonlinear and 3N-5 for linear molecule as vibrational degrees of freedom.
You question regards only linear molecules. Consider for example CO2. Fix a plane containing the molecule. There are two bending independent modes, one in the plane and one perpendicular to the plane. To describe this motion you can use two independent vibrational wave function. To describe properly the bending motion, you should consider also the phase between the two modes. Now let us think classically. The combination of two vibrational motion in perpendicular directions gives the so called Lissajous curves. If the amplitude of the oscillations are the same as well as the frequency, and the phase between the two oscillator is π/2, you have a circle, i.e. a rotational motion. Reporting this concept to the quantum representation, we can chose another base in place of the two harmonic oscillator for bending, and as alternative we can use a rotational base an one harmonic oscillator. Why this is preferred to a double harmonic oscillator, I cannot tell.
Consult "Advanced applied finite element methods" by Carl T F Ross, Elsevier, Oxford, UK.
Because for small deformations, sections of a beam for instance, tends to rotate with respect to the so-callad neutral axis. In fact, such efect is embodied in the inertia term when considering beam elements.
- Badges
- Science topic
- Similar topics
- Geoscience
- Atmospheric Sciences
- Atmosphere