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The delicacy and beauty of two great rivers

3 September 2010 | Article
Published in Spectroscopy Europe/World Vol.  Issue  ()

Bill George,a Rob Lewisa and Neil Lewisb

aDepartment of Science and Sport, HESAS, University of Glamorgan, Pontypridd, CF37 1DL, UK
bMalvern Instruments Ltd, Enigma Business Park, Grovewood Road, Malvern, Worcs. WR14 1XZ, UK

This title combines parts of the two following texts separated in time by some 140 years but united in sentiment and celebration.

“ . . . that a glance at the prismatic spectrum of a flame may show it to contain substances which it would otherwise require a laborious chemical analysis to effect...1 Thus Sir John Herschel and Mr Fox Talbot laid the foundation of spectral analysis of unrivalled delicacy and beauty, since carried to perfection by Messrs. Bunsen, Kirchoff and other experimenters, presently to be mentioned” Mary Sommerville2

“There are two great rivers in physical chemistry. One is the river of thermodynamics, which deals with the relations between bulk properties of matter, particularly properties related to the transfer of energy. The other is the river of molecular structure, including spectroscopy, which deals with the structures and properties of individual atoms and molecules. These two great rivers flow together in the part of physical chemistry called statistical thermodynamics.”

Peter Atkins and Julio de Paula;3 Feedback “Without doubt the best introductory physical chemistry textbook that I am aware of . . . essential reading in our year 1 and 2 courses, Damien Murphy, Senior Lecturer, University of Cardiff

Spectroscopy is the measurement of the interaction of radiation with matter before or after spectral dispersion. This has been studied variously by physicists and chemists, has wide applications outside these traditional disciplines and cannot be owned by any particular community. The subject embraces both science (including mathematics) and technology (including computing) and contains many examples of differences, not always understood, between these cultures. It illustrates the unchanging and universal character of the relevant science, which is increasingly revealed by advances in the relevant technology. A very simple spectrum is that of atomic hydrogen which was described by Balmer4 in 1885 who showed that the wavelengths of four observed lines in the visible region possessed an integer relationship which enabled prediction of the wavelength of a fifth line near the ultraviolet region which was subsequently accurately measured and used to assign the Balmer series of lines in the hydrogen spectrum. Balmer had discovered a mathematical expression involving whole numbers, which later became identified as the quantum numbers for the hydrogen atom. This became the basis of all electronic energy levels following the early 20th century understanding of the quantum theory of atomic structure. The emission and absorption of electromagnetic radiation is understood in terms of apparent duality of this radiation in terms of waves (following Maxwell) or particles as quanta of energy (following Bohr, Planck and others).

Amongst the many branches of spectroscopy, the infrared (IR) region has a unique feature that sets it apart from others. One consequence is a deceptive simplicity in interpretation of spectral information compared with higher frequency (visible, ultraviolet, X-ray and gamma-ray methods) or lower frequency (microwave and radiowave methods including nuclear magnetic resonance and electron paramagnetic resonance). The special quality of IR spectroscopy is the apparent ability to understand spectra in terms of classical vibrations of molecules in which atoms are represented as small masses that are considered to vibrate at frequencies related to magnitudes of masses linked by bonds treated as springs with stiffness represented by force constants according to Hooke’s Law. A key difference from spectra at the immediately higher frequencies (visible region) or lower frequencies (microwave region) is that the former is associated with electronic and the latter with rotational changes. Unlike the case of vibrational spectra there is little or no classical explanation why spectral features in absorption or emission associated with these electronic or rotational processes are observed at discrete frequencies.

Coblentz5 in 1905 measured and published the earliest systematic collection of IR spectra and was able to correlate absorption bands with chemical structure. The interpretation of IR absorption in terms of molecular vibrations emerged decades later and in association with the work of Lecomte, Mecke and others. Early interpretations of IR spectra of complex molecules in terms of classical molecular vibrations were comprehensively reviewed in the 1950s by Bellamy6 to be followed by very many publications and similar books. There is a particular tension between classical and quantum treatment of vibrational spectra as measured in the IR compared with other spectral regions and methods. Bellamy6 in his Introduction states he was “... avoiding any theoretical discussion of the vibration–rotation spectra of small molecules...”. Early spectra from single beam spectrometers showed vibration–rotation spectra from atmospheric water vapour which caused difficulties in observing other spectra. In several public lectures Bellamy remarked “Some people call this fine structure. I call it filth”. The problem was to some extent resolved technologically by double beam or Fourier transform infrared (FT-IR) methods but leading to reduced sensitivity in some regions and best improved by removing water vapour and carbon dioxide as interfering gases from the beam of the spectrometer. A measure of an understanding of IR spectra following the work of Bellamy (B) compared with the publications by the Nobel Prize winner, Herzberg (H), was semi-quantitatively expressed as Susceptibility (S = B / H) by their contemporaries.

Vibration–rotation fine structure is determined by molecular size, geometry and symmetry. A highly cited vibration–rotation spectrum in text books is for HCl gas, which is a basis of the determination of many of its physical properties and is shown in Figure 1. The calculated properties include observation and approximate proportions of the 37Cl and 35Cl isotopes. The energy expression for the non-rigid rotor function has terms in J (rotational quantum number) and J2 the coefficients of which permit calculation of rotational constant (Bv) in each of the two lowest vibrational quantum states (B1 and B0) which extrapolate to the equilibrium state, Be. Bond lengths calculated from these rotational constants are r1, r0 and re. The observed vibrational transitions from the vibrational quantum number, V = 0 to the V = 1 (fundamental) and V = 2 (first overtone) levels permit calculation of the anharmonicity constant, which measures departure from the harmonic function determined by Hooke’s law. The harmonic and anharmonic potential energy functions are shown in Figures 2 and 3. It is apparent from Figure 3 that the bond length of HCl (as the mid-point of the lines shown) increases progressively from the equilibrium minimum energy level to higher V levels.

In the case of large molecules it cannot always be obvious whether all of the 3N – 6 or 3N – 5 (if linear) vibrations are IR and/or Raman active. The answer is provided by the methods of Group Theory in which elements of symmetry and corresponding symmetry operations are the equivalents of numbers and arithmetical operations. The intensity of an IR or Raman band depends on the transition moment of the molecular transition. The transition moment is zero for a forbidden mode but finite for a permitted mode. The transition moment may be calculated analytically for small molecules but whether or not a transition moment is finite or zero in vibrational spectroscopy is readily determined by Group Theory.

The rotational spectum of HCl also permits calculation of bond length in the V = 0 level together with the centrifugal distortion constant. The latter is described by a classical model in terms of progressive increase of bond length and of moment of inertia at higher rotational frequencies with consequent progressive reduction in peak separations (approximately 2B) between observed rotational bands at higher frequencies as shown in Figure 4. Here rotational transitions are permitted between adjacent rotational levels as shown. Because there is an inverse relationship between values of rotational frequency and rotational constant (B) and B is small for HCl, the rotational frequency for HCl is observed in the far-IR region; rotational spectra of molecules with larger values of rotational constant are observed at lower frequencies usually in the microwave region. Rotational spectra require a change in dipole moment during rotation for activity in order for a spectral peak to observed. This is understood by classical theory in terms of molecular interaction with the electric field of the electromagnetic incident radiation.

Three gases for which spectra are widely observed are water vapour, carbon dioxide and methane. Their symmetry elements differ in the following way and each set of symmetry elements defines the Point Group to which each structure belongs: non-linear, H2O, includes two mutually perpendicular planes and a two-fold axis.

Linear CO2, includes a centre of inversion and a degenerate pair of two mutually perpendicular two-fold rotational axes. Tetrahedral CH4 includes a number of two-fold and three-fold axes and planes of symmetry. It is a simple matter to determine the symmetry properties of any molecule and those of all vibrations of that molecule leading to determination of the activity of each vibration in the infrared and/or Raman spectrum using Group Theory.

Spectra of H2O, CO2 and CH4 have been observed in the atmosphere of extra-solar planets. All three compounds are associated with forms of life, hence the presence of such molecules beyond the solar system may indicate extra-terrestrial life has existed, does exist or will exist elsewhere in our own galaxy, the “Milky Way”, or in distant other galaxies. This is one of the few areas of knowledge with a demonstrable universal dimension based on astronomical spectroscopic measurements.

The Raman effect led to a Nobel prize following discovery in 19287 and is comprehensively described by Long.8 It arises from very weak non-elastic scattering of incident radiation (stronger at scattering to lower frequencies) and is observed in a sample irradiated by a strong monochromatic source such as a mercury arc or nowadays a laser beam followed by a monochromator and a detector, initially a photographic camera plate but later a photoelectric or other modern detector. Early Raman spectrographs would have been recognised by Newton as closely related to his ground breaking observation of the visible solar spectrum in 1644.

Raman spectroscopy is complementary to microwave and IR spectroscopy in providing rotation, vibration and vibration–rotation spectra of gases but with different activity criteria (dipole moment is replaced by polarisation as the necessary feature of change during the molecular process). For example the vibration–rotation spectrum of HCl has a missing central feature in the IR (Figure 1) but a strong central feature in the Raman but with sub-bands at twice the separation observed in the IR. Other differences occur between IR and Raman spectra of water, carbon dioxide and methane in the gas state. If a molecule has a centre of inversion the rule of mutual exclusion applies stating that no vibration can be both IR and Raman active. This relates to a more general observation for the gas or condensed state that bands which appear strong by the one method are often weak in the other. Similarly solvents which have strong features in one may be weak in the other. For example, water is a good solvent for Raman spectroscopy but less suitable as a solvent for IR spectroscopy for which cell materials may be also water soluble.

It follows that a complete assignment of a vibration spectrum requires both infrared and Raman spectra. Assignments permit the calculation of the thermodynamic properties including entropy and enthalpy by statistical methods, within assumptions, and illustrate the earlier assertion

“These two great rivers flow together in the part of physical chemistry called statistical thermodynamics”.3

Spectroscopic instrumentation was initially purpose built by university and other research workers but the rapid growth of analytical and industrial applications led to the parallel growth of instrument manufacturers from the mid-20th century. These instrument platforms have continued to evolve rapidly, taking advantage of advances in both miniaturisation and computing technology to produce a wide variety of spectrometers that have transcended the boundaries of the laboratory and evolved into either handheld or robust industrial process control systems. Other advances, particularly in detector technology, have seen the emergence of Raman and IR imaging systems and microscopes. Today IR imaging spectrometers are easily capable of generating 100,000 or more FT-IR spectra in less than a minute! These instruments can produce “pictures” of biological tissue and other structurally complex materials non-destructively and non-invasively, based upon the IR molecular fingerprints of the intrinsic chemical components from which they are comprised. The state of art of recent science and technology methods are exemplified by work pioneered by E.N. Lewis et al.9 following his earlier work at the University of Glamorgan in association with BP, Sunbury, UK, and subsequently at NIH Bethesda, USA.

Clearly Sommerville2 was a remarkable mid 19th century prophet of spectroscopic things to come based on early observations of analytical applications and described by her as of “delicacy and beauty”. The wider ambience of the subject in terms of the meeting of “two great rivers” within the topography of physical science is well expressed by Atkins and de Paula.3 There have been many applications to analysis, structure determination and statistical thermodynamics, with spectacular advances made possible by modern detector technology and imaging systems.


  1. J.F.W. Herschel, Treatise on Light (1827); W.F. Fox Talbot, “Facts relating to optical science. No. I”, Phil. Mag. Series 3 4(20), 112–114 (1834); link.
  2. Mary Sommerville, On Molecular and Microscopic Science, Vol. 1. John Murray, London, p. 134 (1869).
  3. P. Atkins and J. de Paula, Elements of Physical Chemistry. Oxford University Press, p. 524 (2009).
  4. J.J. Balmer, Annalen der Physik und Chemie N. F. 261(5), 80–87 (1885). doi: 10.1002/andp.18852610506
  5. W.W. Coblentz, Investigation of Infrared Spectra. Carnegie Institution Publications (Bull. No. 35), Washington, DC (1905).
  6. L.J. Bellamy, The Infrared Spectra of Complex Molecules. Methuen and Co., London (1959).
  7. C.V. Raman and K.S. Krishnan, Nature 122, 12 (1928). doi: 10.1038/122012b0
  8. D.A. Long, The Raman Effect: A Unified Treatment of the Theory of Raman Scattering by Molecules. Wiley (2001).
  9. E.N. Lewis, P.J. Treado, R.C. Reeder, G.M. Story, A.E. Dowrey, C. Marcott and I.W. Levin, “FTIR spectroscopic imaging using an infrared focal-plane array detector”, Anal. Chem. 67, 3377 (1995). doi: 10.1021/ac00115a003
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