Basic Principle of Spectroscopy

Spectroscopy Definition

Spectroscopy deals with the study of interaction of electromagnetic radiation with matter. Electromagnetic radiation is a simple harmonic wave of electric and magnetic fields fluctuating orthogonal to each other.

Spectroscopy

Spectroscopy: An electromagnetic wave showing orthogonal electric and magnetic components (A); a sine wave (B); and uniform circular motion representation of the sine function (C).

A simple harmonic function can be represented by a sine wave

Sine wave is a periodic function and can be described in terms of the circular motion. The value of at any point is simply the projection of vector on the y-axis, which is nothing but A sin θ . Equation (1) can therefore be written in terms of angular velocity, ω.

where, = displacement in time and is the velocity of the electromagnetic wave. If the wave completes ν cycles/s and the wave is travelling with a velocity metres/ sec, then the wavelength of the wave must be  metres.

Energy of electromagnetic radiation

Energy of an electromagnetic radiation is given by 

Where h is Planck’s constant and has a value of 6.626 × 10-34 m2·kg·s-1. Based on the energy, electromagnetic radiation has been divided into different regions.

The region of electromagnetic spectrum human beings can see, for example, is called visible region or visible spectrum. The visible region constitutes a very small portion of the electromagnetic spectrum and corresponds to the wavelengths of ~400 – 780 nm.

The energy of the visible spectrum therefore ranges from ~2.5 × 10-19 to ~5 × 10-19 Joules. It is not convenient to write such small values of energy; the energies are therefore written in terms of electronvolts (eV). 

One electronvolts equals 1.602 × 10-19 Joules. Therefore, the energy range of the visible spectrum is ~1.6 – 3.1 eV. Spectroscopists, however, prefer to use wavelength or frequency or wavenumber instead of energy.

Spectroscopy

Electromagnetic spectrum

Quantization of energy

As put forward by Max Planck while studying the problem of Blackbody radiation in early 1900s, atoms and molecules can absorb or emit the energy in discrete packets, called quanta (singular: quantum). A molecule can possess energies in different forms such as vibrational energy, rotational energy, electronic energy, etc. Introduction to the structure of an atom in a General Chemistry course mentions about the electrons residing in different orbits/orbitals surrounding the nucleus, typically the first exposure to the discrete electronic energy levels of atoms. In much the same way, rotational and vibrational energy levels of molecules are also discrete. A molecule can jump from one energy level to another by absorbing or emitting a photon of energy that separate the two energy levels

Spectroscopy

Transitions of a molecule between energy levels, E1 and E2 by absorbing/emitting the electromagnetic radiation

Electromagnetic spectrum and the atomic/molecular processes

Molecules undergo processes like rotation, vibration, electronic transitions, and nuclear transitions. The energies underlying these processes correspond to different regions in the electromagnetic spectrum.

Radiofrequency waves: Radiofrequency region has very low energies that correspond to the energy differences in the nuclear and electron spin states. These frequencies, therefore, find applications in nuclear magnetic resonance and electron paramagnetic resonance spectroscopy.

Microwaves: Microwaves have energies between those of radiofrequency waves and infrared waves and find applications in rotational spectroscopy and electron paramagnetic resonance spectroscopy.

Infrared radiation: The energies associated with molecular vibrations fall in the infrared region of electromagnetic spectrum. Infrared spectroscopy is therefore also known as vibrational spectroscopy and is a very useful technique for functional group identification in organic compounds .

UV/Visible region: UV and visible regions are involved in the electronic transitions in the molecules. The spectroscopic methods using UV or visible light therefore come under ‘Electronic spectroscopy’.

X-ray radiation: X-rays are high energy electromagnetic radiation and causes transitions in the internal electrons of the molecules.

Spectroscopy

The range of atomic/molecular processes the electromagnetic radiation is involved in.

Mechanisms of interaction of electromagnetic radiation with matter

In order to interact with the electromagnetic radiation, the molecules must have some electric or magnetic effect that could be influenced by the electric or magnetic components of the radiation.

In NMR spectroscopy, for example, the nuclear spins have magnetic dipoles aligned with or against a huge magnetic field. Interaction with radio frequency of appropriate energy results in the change in these dipoles.

Rotations of a molecule having a net electric dipole moment, such as water will cause changes in the directions of the dipole and therefore in the electrical properties.

Vibrations of molecules can result in changes in electric dipoles that could interact with the electrical component of the electromagnetic radiation.

Electronic transitions take place from one orbital to another. Owing to the differences in the geometry, size, and the spatial organization of the different orbitals, an electronic transition causes change in the dipole moment of the molecule.

Panel A shows the rotation of a water molecule around its centre of mass. The change in the dipole moment as a result of rotation in plotted in panel B. Panel C shows the change in dipole moment of water due to asymmetric stretching vibrations of O—H bond. Panel D shows an electronic transition from π to π* orbital and the geometry of the two orbitals.

The above examples suggest that a change in either electric or magnetic dipole moment in a molecule is required for the absorption or emission of the electromagnetic radiation.

Absorption peaks and line widths

Absorption of radiation is the first step in any spectroscopic experiment. Absorption spectra are routinely recorded for the electronic, rotational, and vibrational spectroscopy. It is therefore important to see how an absorption spectrum looks like. As we have already seen, a transition between states takes place if the energy provided by the electromagnetic radiation equals the energy gap between the two states i.e. 

This implies that the molecule precisely absorbs the radiation of wavelength, λ and ideally a sharp absorption line should appear at this wavelength

An idealized spectrum for a single wavelength transition (A) and an experimentally obtained spectrum (B)

In practice, however, the absorption lines are not sharp but appear as fairly broad peaks for the following reasons.

Instrumental factors: The slits that allow the incident light to impinge on the sample and the emerging light to the detector have finite widths. Consider that the transition occurs at wavelength, λt. When the wavelength is changed to λt∆λ or λt– ∆λ , the finite slit width allows the radiation of wavelength, λt to pass through the slits and a finite absorbance is observed at these wavelengths. The absorption peaks are therefore symmetrical to the line at λ λt.

Sample factors: Molecules in a liquid or gaseous sample are in motion and keep colliding with each other. Collisions influence the vibrational and rotational motions of the molecules thereby causing broadening. Two atoms/molecules coming in close proximity will perturb the electronic energies, at least those of the outermost electrons resulting in broadening of electronic spectra. Motion of molecules undergoing transition also causes shift in absorption frequencies, known as Doppler broadening.

Intrinsic broadening: Intrinsic or natural broadening arises from the Heisenberg’s uncertainty principle which states that the shorter the lifetime of a state, the more uncertain is its energy. Molecular transitions have finite lifetimes, therefore their energy is not exact. If ∆is the lifetime of a molecule in an excited state, the uncertainty in the energy of the states is given by:

The small fluctuations in the baseline are referred to as noise. Noise is the manifestation of the random weak signals generated by the instrument electronics. To identify the sample peaks clear of the noise, the intensity of the sample peaks has to be at least 3-4 times higher than the noise. 

A better signal-to-noise ratio is obtained by recorded more than one spectra and averaging; the noise being random gets cancelled out. 

The light sources used in the instruments emit radiations of different intensities at different wavelengths and usually the detector sensitivity is also wavelength-dependent. 

A reasonable horizontal baseline for the samples can easily be obtained by subtracting the spectrum obtained from the solvent the sample is dissolved in.

Other features of the spectroscopy and the spectra obtained will be discussed as and when they arise in the following lectures.

Further Readings

Reference