Spectroscopy

Spectroscopy is defined as the study of the interaction of electromagnetic waves with materials. Spectroscopy is used to gain knowledge about the structure of the material.

A molecule in space can have energies in various forms; rotational energy, vibrational energy or electronic energy. These energies of molecules are quantized and a particular molecule can exist in different rotational and vibrational energy levels. The molecules can move from one level to another level only by a sudden jump involving a finite amount of energy.

Generation of absorption spectrum

Consider two possible vibrational energy state of a molecule, E₁ and E₂. Transition can take place between the levels E₁ and E₂ provided the appropriate amount of energy can be either absorbed or emitted by the system. If a molecule in state 1 is subjected to electromagnetic radiation of a single frequency (monochromatic radiation, where h is Plank constant),then energy will be absorbed from the incident radiation and the molecule will jump to state E₂. A detector placed to collect the radiation after its interaction with the molecule will show a decrease in the intensity of frequency v₁ decreased. If a radiation beam of wide range of frequencies is used, the detector will show that energy has been absorbed only from the v₁ frequency and intensity of all others frequencies are unaffected. This results is an absorption spectrum.

Molecular Vibrations

Vibration motion is described as stretching or bending depending on the nature of the change in molecular shape. Further, vibration motion can be symmetric / antisymmetric. Wave mechanics implies that any molecule can never have zero vibrational energy, that is atoms can never be completely at rest relative to each other. The harmonically oscillating molecules can undergo vibrational changes determined by simple selection rules obtained from Schrödinger equation.

The vibrations of nuclei in a molecule can be characterized with properties of the normal mode vibration. Nuclei vibrate at the same frequency and in the same phase. Nuclear motion does not cause rigid body movement (translation) or rotation of molecules. A molecule vibrates at its equilibrium position without shifting its center of gravity. Each type of molecule has a defined number of vibration modes and each mode has its own frequency. Vibration frequency varies with vibration type. The number of normal vibration modes in a molecule is related to the degrees of freedom in molecular motion. For N atomic nuclei in a molecule, there are 3N degrees of freedom as each nucleus can move in x, y or z directions. Among these, three are related to translation of a molecule along x, y or z direction as a rigid body and three related to rotation of a molecule around the x, y or z axes as a rigid body. Hence total vibration modes of an N- atomic molecule is 3N 6 .For a linear molecule the rotation around the bond axis is meaningless, considering the nuclei as points in space. Thus, there are only two rotational degrees of freedom for the molecule and the total vibration modes are 3N – 5.

Types of vibrations in a molecule:

• Stretching vibration
• In-planar bending vibration
• Out-of-planar bending vibration

For polyatomic molecules, the vibrations are complicated. For example, water which is a non-linear tri-atomic molecule has three allowed vibration as shown in Fig 1 [3N-6 = 3 ; N is the no of atoms in molecule]. For carbondioxide, a linear tri-atomic molecule, the number of allowed vibration is 3N-5 = 4. In Fig. 1 these vibrations are shown. For CO₂, there are two bending vibrations; one as shown in the figure in which the atoms moves in plane of the paper and the other in which oxygen atoms moves simultaneously into and out of the plane is not shown here. These two vibrations are identical except in directions.

Fig. 1 : Fundamental vibrations of (a) water molecule (b) carbon-dioxide molecule