Why reduced mass

Thus among the huge mass of accumulated commodities the simplest wants would go unsatisfied. New Word List Word List. Save This Word!

We could talk until we're blue in the face about this quiz on words for the color "blue," but we think you should take the quiz and find out if you're a whiz at these colorful terms. Origin of reduced mass First recorded in — Cancel Report. Create a new account. Log In. Powered by CITE. Are we missing a good definition for reduced mass?

Don't keep it to yourself Submit Definition. The ASL fingerspelling provided here is most commonly used for proper names of people and places; it is also used in some languages for concepts for which no sign is available at that moment.

There are obviously specific signs for many words available in sign language that are more appropriate for daily usage. Browse Definitions. Get instant definitions for any word that hits you anywhere on the web! Two clicks install ». Quiz Are you a words master? But this is just a trivial difference due to a different scaling of the coordinates, and the authors are wrong to imply that their treatment is more appropriate than the standard one.

In fact, the authors obtain different numerical results than the standard treatment for the imaginary frequency and the tunneling correction because they are inconsistent. The inconsistency is most easily explained by a one-dimensional example.

We have just explained that the value to use for the mass m depends on the scaling of the coordinate y. When one is consistent, the effect of scaling y is exactly canceled by the change in m in eq 9.

The masses corresponding to rectilinear coordinates are constants. Chemists often prefer to use coordinates such as bond distances and bond angles, which are nonlinear functions of atomic Cartesians. Such coordinates are called curvilinear. Rectilinear coordinates correspond to straight lines in an atomic Cartesian coordinate system, whereas curvilinear coordinates correspond to curved lines in such a system.

For curvilinear coordinates, the masses depend on geometry, i. Furthermore, unlike eqs 1, 3, and 5, there are cross terms in the kinetic energy. Thus the mass array m i with one index must be replaced by a tensor or matrix with two indices.

Harmonic vibrational analysis is suitable for small displacements 2a from a stationary point, which may be an equilibrium geometry or a saddle point. The standard treatment of harmonic vibrations in curvilinear coordinates 2c was developed for equilibrium geometries, but it is equally valid at saddle points. In the standard treatment, the geometry dependence of the masses is ignored, and harmonic frequenices are evaluated at the stationary-point geometry.

It was appreciated by the original workers that this is sufficient because of the restriction of harmonic analysis to small vibrations, 2c and in fact the curvilinear and rectilinear treatments always give the same frequencies at geometries where the gradient of V vanishes. As explained above, the source of error is that this mass is used with an inconsistent force constant.

If the force constant were evaluated by eq 10 with the same coordinate as used to calculate the mass, then all differences from the standard treatments 2,4,5 would disappear.

All conclusions about tunneling in ref 1 are affected by this fundamental error and are meaningless. No dynamical approximation is implied. An effective mass is a mass used for some coordinate in order to take account of other degrees of freedom that are not treated explicitly or that are treated approximately as, for example, in some treatments of tunneling 8. All masses in ref 1, except the original atomic masses, are reduced masses. Reference 1 concluded that one-dimensional tunneling models in the literature have used an inappropriate mass, and the essence of our comment so far is that this conclusion is based on an inconsistent evaluation of the reduced mass.

But we want to make it clear that this is not a defense of one-dimensional tunneling models, which are seldom justified in cases where tunneling is significant. Asked 6 years, 10 months ago. Active 6 years, 10 months ago. Viewed 7k times. Improve this question. RobChem RobChem 1 1 gold badge 4 4 silver badges 11 11 bronze badges.

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John Alexiou John Alexiou David Hammen David Hammen For example in the hydrogen atom. Do we treat proton as it doesn't exist and an electron-like particle moves in a uniform potential with different mass or it exists? Is it just mathematical trick?