Ok, I think there are some English issues here, so let's take this one line at a time
Rajini said:
hi,
atoms in a molecule normally vibrate.
No, atoms do not vibrate, molecules vibrate through motion of the atoms about a common center of mass. This motion is determined by the connectivity of the atoms through chemical bonds, which can be thought of like "springs", each with an associated spring constant. Thus, it is usually a good approximation to treat the vibrational motion of molecules as harmonic, at least at low energies.
One molecule cannot vibrate in all modes perfectly (but it can vibrate in ground state in all modes, something random).
I have no idea what that sentence was intended to convey. The vibrational motion of a molecule in the harmonic limit can be expressed in a complete basis set of orthogonal normal modes. Each normal mode can be represented as an independent harmonic oscillator, and so in this limit, it is completely reasonable for all of the modes of the molecule to be excited to any arbitrary vibrational state (i.e. quantum number). For example, in the harmonic limit, for the OP's 3-mode molecule example, you could easily have 1 quantum in each mode, or two quanta in each mode, or 3 quanta in one mode and zero in the others. *In the harmonic limit*, those states would be stable for an indefinite period of time (i.e. they are eigenstates). Of course, in any real molecule, the modes are not completely harmonic, which leads to anharmonic coupling terms that allow energy to flow between the modes over time, this is the well-known phenomenon of intramolecular vibrational redistribution, or IVR.
Each mode also has a finite zero-point energy (ZPE), so even in the vibrational ground state of the molecule (i.e. zero quanta in each mode), there is some vibrational energy in the molecule. However, the ZPE is an intrinsic property of the quantum system and cannot be "accessed" by chemical or physical processes.
Each mode of vibration has its own energy, i.e. in order to make the atom to vibrate in a particular mode one have to excite the by molecule supplying photon of specific energy.
That is not completely true, the normal modes *can* be excited by electromagnetic radiation (i.e. photons), however they can also be excited (or de-excited) by collisions with other molecules. This is called T-V energy transfer, (translation to vibration).
Normally one varies this photon energy from 0 to 1000 cm-1 (0 to 123 meV).
No, the vibrational spectrum of molecules ranges from about 50-100 cm-1 (the terahertz regime), for large amplitude motions of heavy molecules, up to about 4000 cm-1, for stretching vibrations of light, strongly bonded molecules like H2 and HF.
Why you do like this? vibrational properties are fundamental and are important for predicting many properties of the molecule, eg., symmetry properties, bonding, force constant, etc.
Ok, I agree with that completely
Moreover, vibration is not dependent on temperature and even at 0 K they will vibrate.
No, this is not true. Vibration is *completely* dependent on temperature. You can define a Boltzman population for each normal mode that describes the probability that a given quantum state will be populated at a given temperature. These factors increase with temperature, and thus so does the average internal energy for an ensemble of molecules at a given temperature. In fact, all molecules have a thermal dissociation threshold, which is the temperature where the average internal energy of the molecules is large enough to break the weakest chemical bond in the molecule.
Finally, it can be misleading to say that molecules "vibrate" even at zero K. I prefer to say that they have vibrational ZPE, which is completely correct, and does not give the impression that they are somehow moving. They certainly are not "moving" in the classical sense.
