Reduced masses

Force Constants and Spectroscopic Constants for Selected Diatomic Molecules 

Source Lide, D. R., CRCHandbookof Chemistry and Physics, 90th Edn., CRC Press, Boca Raton, FL, 2009, 9-108-9-112. 

FIGURE 12.12 Two different masses balanced on a see-saw center-of-mass pivot. 

This is an important simplification It says that in a system that rotates around a center-of-mass pivot point the individual masses can be represented by an equivalent single mass with a value of 

This implies that a real diatomic molecule can rotate around its center of mass while it vibrates 

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To detemiine k E) from equation (A3.12.9) it is assumed that transition states with positivefomi products. Notmg that / f = p dqf/dt, where p is the reduced mass of the separating fragments, all transition states that lie within and + dq with positive will cross the transition state toward products in the time interval dt = pj dqf p. Inserting this expression into equation (A3.12.9), one finds that the reactant-to-product rate (i.e. flux) through the transition state for momenPim p is... 

Since the reduced mass depends only on the masses of the atoms (1/p = + Mm for a diatomic), which... 

Consider an excited condensed-phase quantum oscillator Q, witli reduced mass p and nonnal coordinate q j. The batli exerts fluctuating forces on the oscillator. These fluctuating forces induce VER. The quantum mechanical Hamiltonian is [M, M]... 

Using Jacobi coordinates and reduced masses, the Hydrogen-Chlorine interaction is modeled quantum mechanically whereas the Ar-HCl interaction classically. The potentials used, initial data and additional computational parameters are listed in detail in [16]. 

For each pair of interacting atoms (/r is their reduced mass), three parameters are needed D, (depth of the potential energy minimum, k (force constant of the par-tictilar bond), and l(, (reference bond length). The Morse ftinction will correctly allow the bond to dissociate, but has the disadvantage that it is computationally very expensive. Moreover, force fields arc normally not parameterized to handle bond dissociation. To circumvent these disadvantages, the Morse function is replaced by a simple harmonic potential, which describes bond stretching by Hooke s law (Eq. (20)). 

If we think about two masses connected by a spring, each vibrating with respect to a stationary center of mass Xc of the system, we should expect the situation to be vei similar in form to one mass oscillating from a fixed point. Indeed it is, with only the substitution of the reduced mass p for the mass m... 

The hamionic oscillator of two masses is a model of a vibrating diatomic molecule. We ask the question, What would the vibrational frequency be for H2 if it were a hamionic oscillator The reduced mass of the hydrogen molecule is... 

Can the two-mass N—N system be regarded as a one-mass system having a reduced mass p If so, what is p ... 

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