Michael S. Bradley, PhD

Infrared (IR) and Raman bands are typically described in terms of peak location and peak height. The shape of the peak-its form, width, and asymmetry-is less well understood. Bandshapes largely depend upon interactions between vibrating molecules and their environment. An understanding of this relationship may enhance spectral interpretation and can explain unexpected behaviors, in both qualitative and quantitative analyses. This article presents basic concepts that influence line shapes and shows the complex lineshape changes in an apparently simple system of acetone and water.

	
	
	Standard physical chemistry humor holds that you start any model with a sphere, whether fitting cows or electron orbitals. Spectral interpretation starts with a similar first approximation: The vibrational spectra are built from harmonically oscillating independent molecules. However, spectra show unexpected bumps, peak shifts, and strange line shapes that change with temperature and concentration, so the truth is more complex. Cows sometimes have horns.
	
	This introductory article cannot fully encompass chemical dynamics and line shapes. Instead, we focus on general concepts, simply presented, without (much) mathematics or higher order complications. For instance, phenomena such as Fermi resonance and inversion doubling will not be addressed, although they affect even simple molecules like ammonia (1).
	
	


	
	The harmonic oscillator model results in a sequence of evenly spaced, well-defined vibrational energy levels, as seen in the left of Figure 1 (2). Transitions between these energy levels occur by absorption of energy, giving rise to extremely sharp peaks in the absorption spectrum. However, real molecules vibrate anharmonically, rotate, translate, and interact with their environment.

	At equilibrium, most molecules are in the ground vibrational state (as determined by the Boltzmann distribution). Some of these molecules transition to an excited state when the IR radiation or Raman excitation strikes the sample. Then, dynamics take over.

	Vibrationally excited molecules relax to the ground state within a few picoseconds (10

). Initially, all of the excited molecules are vibrating together (coherently), but motion and slight differences in vibrational frequencies randomize the oscillations-known as 

-also within a few picoseconds (the coherence lifetime, τ

). The spectrometer can only “see” the molecules while they are both excited and coherently vibrating. These phenomena combine to produce an effective lifetime, τ, that is dominated by whichever mechanism (relaxation or dephasing) results in the fastest decay (3).

	The first crucial rule for understanding the physics of lineshapes is that as the effective lifetime shortens, the linewidth broadens. Essentially this effect occurs because of the energy-time uncertainty principle, which can be stated as Δ

 is the spread of energies (essentially the line width) and Ä§ is Planck’s constant divided by 2π. Since 

 must increase as τ decreases to maintain the relationship. Derivation of this equation is beyond our scope; see the references for details (2,3).

	There are two interesting limiting cases (3). In the first limiting case, relaxation is much faster, meaning the coherence time is long by comparison (τ

). Alternately, molecular motions may be rapid, causing dephasing to be faster (τ

). In the first case (τc >> τa), the excited molecule relaxes before dephasing sets in. This is the case for solids, where the environment is relatively static. Within the solid, molecules can experience a statistical distribution of environments, and the line shape takes on the bell curve or Gaussian profile.

), dephasing is the dominant signal loss channel. Dephasing occurs in gases where molecules are in rapid continuous motion. The resulting line shape is Lorentzian, sharp in the center but with long wings.

	Liquids exist between these limits, where interactions prevent extremely rapid motion, but the molecules are not locked in place. As a result, τ

, which results in lineshapes with features of both Gaussian and Lorentzian character. The simplest model for this situation is a combined Gaussian-Lorentzian (G–L) profile, represented as 

 being the fraction of Lorentzian character (0 ≤ 

 ≤1). A more complex description for liquids is the Voigt profile, where the Gaussian and Lorentzian characters are convoluted (combined in the Fourier transform integral). The mathematical form for a Voigt profile allows the Gaussian and Lorentzian portions to have different line widths. Figures 2 and 3 show various shape changes when center frequency, peak height, and linewidths are held constant but the bandshape function changes (4).

	Normally, vibrational bands involve transitions from the ground state to the first excited state (v = 0 to v = 1). However, thermal energy can cause vibrational hot bands to arise. Hot bands result when the first vibrational energy level is significantly populated. The excitation can then cause a transition from the first excited state to the second (v = 1 to v = 2). In a harmonic oscillator, this would occur at the exact same frequency as the v = 0 to v = 1 transition (the left of Figure 1). However, anharmonicity lowers the v = 2 energy slightly, making the 1→2 transition slightly lower in energy than the 0→1 transition (the right of Figure 1). Thus, hot bands appear as an asymmetry or shoulder on the low frequency side of a peak. Hot bands are more pronounced at low frequencies (easier to populate the v = 1 level) and in elevated temperature situations.

	Isotope shifts occur because of the dependence of vibrational frequency on mass. Simply stated, as the mass of an oscillator increases, the frequency goes down (5). For example, the Raman spectrum of the carbon tetrachloride symmetric stretch shows five bands at high resolution, because of 

 shifting in that order to lower frequencies (mass increases), and with peak heights proportional to the relative isotopic concentrations of each. These peaks are closely spaced, because the change in reduced mass is small; at low resolution, this effect makes the peak look distorted; at high resolution, individual peaks appear. The similar isotope shift seen in HCl vapor is a standard physical chemistry experiment, where isotopes of both hydrogen and chlorine cause peak shifts.

	Intermolecular interactions strongly affect lineshapes in liquids. Dipolar forces and hydrogen bonding are two crucial players in this. We examine the acetone–water binary mixture system as an illustration. In pure acetone, the carbonyl groups on adjacent molecules align weakly because of their dipoles. The high vapor pressure (easy evaporation) of acetone results as the molecules don’t hold together tightly. As water is added, hydrogen bonding between water and the carbonyl oxygen takes over as a stronger force, and the environment of the acetone molecules changes rapidly. Hydrogen bonding also acts like a discharge path for the vibrational energy, causing the carbonyl vibration to relax rapidly (6).

	The spectra shown here were collected using a Thermo Scientific Nicolet iS50 Fourier transform infrared (FT-IR) spectrometer and its built-in attenuated total reflectance (ATR) capability with diamond crystal. The Peak Resolve algorithm of the Thermo Scientific OMNIC software was used for the curve fitting.

 and the lower frequency C-H bands show a variety of differing responses to the increasing water concentration. Figure 4 (carbonyl) and Figure 5 (CH) show this clearly.

	The carbonyl peak shifts to lower frequency (red shifts) as hydrogen bonding lowers the vibrational energy. The band also broadens because of the rapid energy relaxation caused by the hydrogen bonds (shorter lifetime = broader peak). The peak height changes both because of the dilution factor and the changing bandwidth that spreads the signal over a wider range. At the same time, the peak assumes an increasingly Gaussian shape. The results of fitting the spectra with a Gaussian–Lorentzian combination band are shown in Table I. The band is still just the carbonyl mode, but any spectral interpretation must recognize these complex changes.

 modes are affected differently. The methyl groups don’t like being pushed closer together so the tighter association caused by hydrogen bonding shifts their vibration to higher frequency (blue shift). The band still broadens because of collisionally induced relaxation (shorter lifetime again). However, there is even more going on here.

	Close examination of both C-H bands reveals the appearance of a new peak. Initially, a single peak is required to fit the pure acetone band. We fixed the location of this peak (±1.5 cm

) and then added a second peak to the fitting routine. This second peak was also found to be stable in location (also ±1.5 cm

) even when left free to change. The resulting fits are shown in Figure 6. This combination of two bands easily fits the profile. The apparent peak shift is caused by the changing relative importance of two acetone environments. The band at 1219–1222 cm

 is due to self-associated acetone, while the 1230–1233 cm

 band is likely because of an acetone–water complex. There is no water band in this region and the highly dilute acetone shows that the initial band is largely gone. These observations support the idea that two different domains exist within the liquid. The first, corresponding to the acetone–acetone interactions of the pure liquid, drops quickly while the second-associated with a water–acetone complex-becomes increasingly pronounced (though decreasing in intensity because of dilution).

	While the description here has focused on visible changes to the spectra, such changes in mixtures can easily impact a calibration. Temperature also changes lineshapes because of changes in associative or repulsive interactions. The peak height does not change linearly, but shows impacts of peak shifting, broadening, and splitting. Building a calibration based on peak height alone could lead to errors. The peak area is responding linearly, as the total area under the curve relates to the concentration-there is no water band growing in the same region-so area calibrations would be more stable.

	Lineshapes of materials respond to intermolecular interactions. These effects cause bands to shift, narrow or broaden and even change their fundamental shape. Strange humps and shoulders or unexpected doublets can appear because of isotopes or changing associations. At a qualitative level, this can influence peak assignments and peak tables. Furthermore, these changes can affect quantitative calibrations if improperly used. Understanding lineshapes, even in a cursory manner, will assist in the assignment and analysis of IR and Raman bands.

Molecular Spectra and Molecular Structure Vol. II: Infrared and Raman Spectra of Polyatomic Molecules

 (Von Nostrand, New Jersey, 1945). 
	(2) M. Diem, 

Introduction to Modern Vibrational Spectroscopy

 (New York, John Wiley and Sons, 1993), Chapter 2.
	(3) W.G. Rothschild, 

 (New York, John Wiley and Sons, 1984), Chapter 4.
	(4) P. Pelikán, M. Ceppan, and M. Liška, 

Applications of Numerical Methods in Molecular Spectroscopy

 (Boca Raton, CRC Press, 1993), Chapter 2.
	(5) C.W. Garland, J.W. Nibler, and D.P. Shoemaker, 

7th Edition (New York, McGraw-Hill, 2003), Chapter XIV.
	(6) M. Bradley and J. Krech, 

 is the marketing manager for FT-IR and FT-IR microscopes at Thermo Fisher Scientific in Madison, Wisconsin. Direct correspondence to: 

Articles

Infrared and Raman bands are typically described in terms of peak location and peak height. The shape of the peak-its form, width, and asymmetry-is less well understood. Bandshapes largely depend upon interactions between vibrating molecules and their environment. An understanding of this relationship may enhance spectral interpretation and can explain unexpected behaviors, in both qualitative and quantitative analyses. This paper presents basic concepts that influence line shapes and shows the complex lineshape changes in an apparently simple system of acetone and water.

Lineshapes in IR and Raman Spectroscopy: A Primer

Thermal decomposition provides valuable information about the chemical composition of a material. Although thermal gravimetric analysis (TGA) measures small weight losses during a heating ramp, it cannot identify the chemicals corresponding to the weight loss. The sensitivity and speed of FT-IR makes it an ideal detector for the TGA evolved gas, but the interpretation of the large data files resulting from this hyphenated technique can be formidable. In this article, we describe an integrated approach that makes analyzing these large data sets much simpler.

Operators working with materials like rubbers, plastics, resins, pharmaceuticals, adhesives, and packaging need to understand differences between competitive products, causes of failures, or the origin of potentially toxic off-gassing. Standard analytical procedures are often incapable of distinguishing subtle differences like the presence of low-concentration additives or contaminants. Further, the same components may be present in two different materials, but the process used to make the products — such as the processing temperature — may vary, causing the interactions between components in the material to differ. This can lead to poor performance, such as early material fatigue or material failure. A complete analysis requires these materials to be deformulated — essentially torn apart to expose their underlying nature. Thermal TGA is a common tool for doing this. A temperature ramp is applied to the sample and the breakdown tracked through weight loss as components vaporize. Attaching a heated transfer line from the TGA outlet to a heated gas cell in the FT-IR spectrometer enables spectra to be acquired in real time as the gases evolve. The resulting data set contains several hundred spectra creating a complex data analysis challenge. Commonly, thermal degradation results in numerous chemicals being evolved simultaneously — not one at a time — resulting in a series of mixture spectra. The Thermo Scientific™ OMNIC™ Mercury TGA algorithm deconvolutes these spectra and provides both identification and time evolution information, completing the deformulation analysis.  

Figure 1 shows a Thermo Scientific Nicolet™ iS™50 FT-IR spectrometer and the TGA-IR accessory. The flexible transfer line, heatable to 300 °C, couples the outlet of the TGA to the IR gas cell. 

Figure 1: TGA-IR accessory mounted in the sample compartment of the Nicolet iS50 FT-IR spectrometer.			

The TGA-IR data set is three dimensional — frequency versus intensity (the spectrum) versus time. Typical TGA experiments ramp and hold for 30–60 min. The FT-IR normally collects multiple scans resulting in one spectrum about every 5 s. For a 1 h run, this yields 720 spectra — a daunting analytical challenge. 

Figure 2 shows the TGA-IR results for the thermal decomposition of a wood sample. The top of the figure contains the temperature ramp and first derivative weight loss from the TGA and a Gram-Schmidt (GS) profile. The GS profile essentially shows the total change in the IR signal (similar to a chromatogram). The bottom pane contains the spectrum collected at one time point. The analytical challenge involves the extraction of useful information from this data set. 

Figure 2: TGA-IR results for wood sample. The top section includes the temperature ramp and the first derivative of the weight loss (from the TGA), along with the Gram-Schmidt profile for the FT-IR data. The bottom is a spectrum at a single time point.			

The key function of deformulation analysis involves identifying the various components and measuring a unique time/temperature response curve (profile) for each component. The profiles reveal when a gas starts evolving (time = temperature) and the duration of the gas evolution. Manual processing can take upwards of an hour. The Mercury TGA algorithm automates the analysis, by first performing a multivariate curve resolution (MCR) analysis on the series of spectra to extract the causes of the spectral differences observed in the data set. The MCR approach creates vectors that correspond to the linearly independent spectral features; these vectors are commonly called Pure Component spectra. Further processing ends with library searching and profile preparation and presentation. 

The wood sample TGA-IR data file in Figure 2 consisted of 450 spectra. The database chosen for the final step was the 460 spectra from the High Resolution Nicolet™ TGA Vapor Phase library. The complete process resulted in the presentation of Figure 3 in less than 20 s. The upper left corner of the display is the GS Profile, as seen in Figure 2. Below that are the calculated time profiles for each evolved gas component. Note how the gases evolve at different times during the deformulation, with a complex pattern of overlapping profiles. To the right of the profiles are the spectra of the identified gases from the library. The table at the bottom provides text information about the search results. The last profile and spectrum, labeled "Unknown," show what is essentially a residual of the analysis — the spectral components of the overall run for which the algorithm has not yet accounted. In this case, the unknown profile is mostly noise, indicating that the majority of the spectral features are assigned. 

Figure 3: The Mercury TGA result for the wood sample shown in Figure 2.			

The upper right window is critical to the user experience. This shows the composite spectrum (in red) synthesized from the library spectra of the identified species compared to the actual spectrum (in blue) at a particular time point. Note this does not include the "Unknown" component, so it represents the analytical results only. Scrolling the time bar in the GS pane (upper left) allows the user to compare each spectrum to a calculated composite at that time — essentially playing back the synthetic and actual series files simultaneously. This display allows the user to assess if the algorithm has identified all of the critical components in the file. The algorithm allows the user to add more components and re-calculate, until complete identification of all off-gassing components has been accomplished. 

Deformulation remains a core requirement for many materials laboratories. While weight loss and identification are important, the additional information gleaned from the time (temperature) dependence of the gas evolutions provides insights into the process used to create the material. The unique combination of quantitative data from the weight loss, qualitative analysis of the components, and process insights from the profiles shows the strong motivation behind the hyphenated TGA-IR technique. 

Thermal decomposition provides valuable information about the chemical composition of a material. Although thermal gravimetric analysis (TGA) measures small weight losses during a heating ramp, it cannot identify the chemicals corresponding to the weight loss.

Michael S. Bradley, PhD

Articles

Lineshapes in IR and Raman Spectroscopy: A Primer

Using Multivariate Curve Resolution to Identify the Evolved Gases Created During a TGA-IR Experiment