.... but anyway I would not try to prove what prove what has been know for at least 100 years and widely used by thousands of organic chemists nearly that long. Go here:
http://www.chemguide.co.uk/analysis/ir/interpret.html#top And then to their introduction link at top, etc.
The below molecule shown at the link is used as it has five different molecular bonds (The C-C bond and 3 C-H bonds are not explicitely shown, but the C of the methal group (CH3) is with a C-C bond to the other C and then three Hs bond to it.
The absorption graph shows what wavelengths excite which bonds, but not always just one as I will discuss. Here is some text from the link I will comment on, but first Note wavenumbers are directly proportional to the photon energy.
"... The carbon-oxygen single bond also has an absorbtion in the fingerprint region, varying between 1000 and 1300 cm-1 depending on the molecule it is in. You have to be very wary about picking out a particular trough as being due to a C-O bond. ...
The C-H bond (where the hydrogen is attached to a carbon which is singly-bonded to everything else) absorbs somewhere in the range from 2853 - 2962 cm-1. ..."
Note that the light hydrogen proton vibration against the rest of the molecule is energetic but not able to shake (and thus excit many other bonds as the momentum in its motion is not large as if it were heavier. The range of photons that can excite it is relative narrow in energy - about as pure excitation of only part of the molecule as happens.
When the photon is absorbed it initially just shakes one bond but that soon spreads to others, like a set of many springs joining many different masses.
In None of these IR absorption case is and electron removed or even transfered from one atom of the molecule to another.....