Infrared spectroscopy
Infrared spectroscopy, often abbreviated as IR spectroscopy, is a versatile analytical technique that identifies and characterizes chemical substances by measuring their absorption of infrared radiation, which excites specific vibrational modes within molecules.[1] This absorption occurs at wavelengths corresponding to the energy differences between vibrational ground and excited states, producing a spectrum that serves as a unique "fingerprint" for the sample's molecular composition and functional groups.[2] The core principle of infrared spectroscopy relies on the interaction of infrared light with molecular bonds, where absorption happens only when the radiation's frequency matches the natural vibrational frequency of a bond, such as stretching or bending motions.[3] These vibrations are quantized and governed by the reduced mass and force constant of the bond, analogous to Hooke's law for springs, with the energy given by E = h\nu, where \nu is the vibrational frequency. For a vibration to be observable (IR-active), it must induce a change in the molecule's dipole moment; symmetric vibrations, like the symmetric stretch in CO₂, do not produce such a change and are thus inactive.[4] The technique primarily operates in the mid-infrared region, spanning wavenumbers from approximately 4000 to 400 cm⁻¹ (corresponding to wavelengths of 2.5 to 25 μm), where most organic functional groups exhibit characteristic absorptions.[5] Modern infrared spectrometers predominantly employ Fourier transform infrared (FT-IR) methodology, which uses an interferometer to simultaneously measure all wavelengths, followed by mathematical transformation to generate the spectrum, offering advantages in speed, sensitivity, and resolution over traditional dispersive instruments. Samples can be analyzed in various states—gases, liquids, or solids—using techniques like transmission through thin films, attenuated total reflectance (ATR) for solids and liquids without preparation, or diffuse reflectance for powders.[6] Key spectral regions include the functional group area (above 1500 cm⁻¹) for identifying bonds like O-H (3200–3600 cm⁻¹) or C=O (1650–1750 cm⁻¹), and the fingerprint region (below 1500 cm⁻¹) for unique molecular patterns.[2] Infrared spectroscopy finds widespread applications across disciplines, including organic and inorganic chemistry for structural elucidation, pharmaceutical analysis for purity and polymorphism detection, environmental monitoring for pollutant identification, and materials science for polymer characterization.[6] In forensics, it aids in drug and trace evidence analysis; in agriculture and food science, it assesses quality and composition non-destructively; and in biomedical research, it examines microbial cells, biofilms, and tissue stress responses. Advanced variants, such as near-field nanoscale IR for high-resolution imaging beyond the diffraction limit, extend its utility to surface and biological imaging.[7]Basic Principles
Definition and Scope
Infrared spectroscopy is a vibrational spectroscopic technique that measures the absorption, emission, or reflection of infrared radiation by matter, primarily corresponding to transitions between molecular vibrational energy levels.[8] This interaction occurs when infrared photons excite molecular bonds, causing stretches, bends, or other deformations that reveal structural information about the sample.[8] The technique is widely applied in chemistry, materials science, and biology to identify and characterize compounds based on their unique spectral fingerprints.[9] The scope of infrared spectroscopy encompasses the infrared region of the electromagnetic spectrum, which lies between visible light and microwaves, with wavelengths ranging from approximately 0.78 μm to 1000 μm.[10] This region is subdivided into near-infrared (NIR, 14000–4000 cm⁻¹ or 0.78–2.5 μm), mid-infrared (MIR, 4000–400 cm⁻¹ or 2.5–25 μm), and far-infrared (FIR, 400–10 cm⁻¹ or 25–1000 μm), where spectra are typically reported in wavenumbers (cm⁻¹) for convenience in relating energy to frequency.[11] The MIR region is most commonly used for probing fundamental vibrational modes of molecular bonds, while NIR captures overtones and combination bands, and FIR addresses low-energy lattice vibrations in solids.[11] The energies involved (roughly 1–15 kcal/mol) align closely with those required for molecular bond vibrations, enabling selective excitation without electronic transitions.[8] Key advantages of infrared spectroscopy include its non-destructive nature, allowing samples to be analyzed without alteration or consumption, and its ability to provide rapid identification of functional groups such as carbonyls, hydroxyls, and amines through characteristic absorption bands.[12] This makes it particularly valuable for qualitative and quantitative assessments in diverse fields, from pharmaceutical quality control to forensic analysis.[9]Historical Development
The discovery of infrared radiation is credited to British astronomer William Herschel, who in 1800 observed that the temperature of a thermometer increased when placed beyond the red end of the visible spectrum produced by sunlight passing through a prism, indicating the presence of invisible radiation with heating effects.[13] This finding laid the groundwork for infrared spectroscopy by establishing the existence of the infrared portion of the electromagnetic spectrum. Early efforts to measure infrared spectra were advanced by American physicist William Coblentz, who between 1905 and 1906 systematically recorded infrared absorption spectra of over 100 pure organic and inorganic substances using a bolometer detector and rock salt prism spectrometer.[14] His work, published in a seven-part series, provided the first comprehensive catalog of infrared spectra and demonstrated the technique's potential for identifying molecular structures, though limited by low resolution and sensitivity.[14] In the mid-20th century, technological improvements during and after World War II spurred the development of dispersive grating spectrometers, which replaced prisms with diffraction gratings for higher resolution in the 1940s and 1950s. Commercial instruments became available shortly after the war, with companies like Beckman Instruments and Perkin-Elmer introducing double-beam infrared spectrophotometers in the mid-1940s, enabling routine use in chemical analysis and accelerating adoption in industry and research.[15] The 1960s marked a revolutionary shift with the advent of Fourier transform infrared (FTIR) spectroscopy, leveraging Michelson interferometers to collect interferograms that are mathematically transformed into spectra via fast Fourier transform algorithms, offering superior speed, sensitivity, and resolution over dispersive methods.[16] French physicist Pierre Connes pioneered high-resolution FTIR applications, including planetary atmospheric spectra, while in the United States, Digilab released the first commercial FTIR spectrometer, the FTS-14, in 1970, equipped with minicomputers for data processing.[16] By the 1980s and 1990s, affordable microcomputers and detector arrays made FTIR the dominant technology, vastly expanding its accessibility.[15] In the 2010s, further integration of FTIR with microscopy and advanced computing enabled hyperspectral imaging for spatially resolved analysis at the micron scale, enhancing applications in materials science and biomedicine through automated data processing and multivariate analysis.[17]Theoretical Foundations
Molecular Vibrations and Modes
Molecules possess vibrational degrees of freedom arising from the relative motions of their atoms, which are probed by infrared spectroscopy through changes in dipole moments. For a molecule with N atoms, there are $3N total degrees of freedom, accounting for three-dimensional translations and rotations of the atoms. Three of these are translational degrees of freedom for the molecule as a whole, and two or three are rotational, leaving the remainder as vibrational degrees of freedom. Specifically, non-linear molecules have $3N - 6 vibrational modes, while linear molecules have $3N - 5.[18] Vibrational modes are classified into stretching and bending types. Stretching modes involve changes in bond lengths and can be symmetric, where bonds lengthen and shorten in phase, or asymmetric, where they move out of phase. Bending modes involve changes in bond angles and include scissoring (atoms approach and separate like scissors), rocking (a group of atoms moves in opposite directions in a plane), wagging (out-of-plane motion perpendicular to the molecular plane), and twisting (rotation about a bond axis). For example, water (H₂O), a non-linear triatomic molecule with N=3, exhibits three vibrational modes: a symmetric stretch, an asymmetric stretch, and a bending (scissoring) mode. Carbon dioxide (CO₂), a linear triatomic molecule with N=3, has four vibrational modes: a symmetric stretch, an asymmetric stretch, and two degenerate bending modes.[19][1] These vibrational modes are described as normal modes, which represent independent, collective oscillations of the atoms where all parts of the molecule move in phase with the same frequency. In the harmonic oscillator approximation, valid for small-amplitude vibrations, each normal mode behaves like an independent harmonic oscillator. The vibrational frequency \nu for a mode is approximated by \nu \approx \frac{1}{2\pi} \sqrt{\frac{k}{\mu}}, where k is the force constant of the bond or angle, and \mu is the reduced mass of the oscillating units. This model assumes quadratic potential energy surfaces, simplifying the description of molecular vibrations.[20][21] Real molecules exhibit anharmonicity due to deviations from the ideal quadratic potential, particularly at larger amplitudes, leading to effects such as overtones (multiples of fundamental frequencies) and combination bands in infrared spectra. Anharmonicity arises from interactions between modes and finite bond lengths, causing the potential energy to include higher-order terms beyond the harmonic approximation.[21]Quantum Mechanical Basis
Infrared absorption arises from the quantization of molecular vibrational energy levels, which can be modeled using the quantum mechanical harmonic oscillator for diatomic or polyatomic bonds under the small-displacement approximation.[22] The potential energy of this model is parabolic, V(r) = \frac{1}{2} k (r - r_e)^2, where r is the internuclear distance, r_e is the equilibrium distance, and k is the force constant. Solving the Schrödinger equation yields discrete energy levels given by E_v = h \nu \left( v + \frac{1}{2} \right), where v = 0, 1, 2, \dots is the vibrational quantum number, h is Planck's constant, and \nu is the classical vibrational frequency, \nu = \frac{1}{2\pi} \sqrt{\frac{k}{\mu}}, with \mu as the reduced mass.[22] In this ideal case, transitions between levels occur only for changes \Delta v = \pm 1, corresponding to fundamental vibrational absorptions.[21] Real molecular bonds deviate from perfect harmonicity due to anharmonic effects, where the potential flattens at larger displacements and includes repulsive walls at short distances. The Morse potential provides a more accurate description: V(r) = D_e \left( 1 - e^{-a(r - r_e)} \right)^2, with D_e as the dissociation energy from the bottom of the well and a a parameter related to the curvature near equilibrium.[23] This model yields vibrational energy levels E_v = h \nu \left( v + \frac{1}{2} \right) - \frac{(h \nu)^2}{4 D_e} \left( v + \frac{1}{2} \right)^2 + \ higher-order\ terms, allowing for overtones at approximately $2\nu and combination bands involving multiple modes, though these are weaker than fundamentals.[24] Anharmonicity also leads to dissociation at finite energy, limiting the number of bound states to roughly v_{max} \approx \frac{D_e}{h \nu}.[25] The interaction between molecules and infrared radiation is governed by time-dependent perturbation theory, where the oscillating electric field of the photon acts as a perturbation on the molecular Hamiltonian. Absorption occurs when the photon energy h \nu_{photon} matches the energy difference \Delta E between vibrational states, promoting the molecule from a lower to a higher level. The transition rate is derived using first-order time-dependent perturbation theory, yielding the probability per unit time proportional to the square of the matrix element of the perturbation Hamiltonian.[26] This formalism connects to Einstein's coefficients: the absorption coefficient B_{if} (from initial state i to final state f) determines the rate as w_{if} = B_{if} \rho(\nu), where \rho(\nu) is the radiation energy density at frequency \nu, while the stimulated emission coefficient B_{fi} = B_{if} and spontaneous emission A_{fi} relate via A_{fi} = \frac{8\pi h \nu^3}{c^3} B_{if}. Both A and B depend on the dipole transition moment |\mu_{if}|^2.[27] Infrared vibrational transitions typically span energies of 0.01–1 eV, corresponding to wavenumbers of 100–4000 cm⁻¹ in the mid-infrared region, where $1\ \text{cm}^{-1} \approx 1.24 \times 10^{-4}\ \text{eV}. This range aligns with the thermal energy at room temperature (~0.025 eV), enabling population of low-lying vibrational states and observable absorptions.Selection Rules and Intensity
In infrared spectroscopy, a vibrational transition is allowed only if it results in a change in the molecular dipole moment during the vibration. This condition, known as the gross selection rule for electric dipole transitions, requires that the derivative of the dipole moment μ with respect to the normal coordinate Q of the vibration be non-zero, i.e., \partial \mu / \partial Q \neq 0.[1] Without this change, the interaction between the molecular vibration and the oscillating electric field of the infrared radiation is negligible, rendering the mode infrared-inactive. Within the harmonic oscillator approximation, the specific selection rule for vibrational quantum number v dictates that only fundamental transitions with \Delta v = \pm 1 are permitted, corresponding to excitations from the ground state (v=0) to the first excited state (v=1) or vice versa.[28] Anharmonicity relaxes this rule, allowing overtone transitions with \Delta v > 1 (e.g., \Delta v = 2 for the first overtone) and combination bands, though these are typically weaker due to smaller transition moments.[29] Symmetry considerations, analyzed through point group theory, further determine activity: a mode is IR-active if its symmetry species transforms like one of the dipole moment components (x, y, or z). For example, in linear CO₂ (D_{\infty h} symmetry), the symmetric stretch (\sigma_g^+) is inactive because it preserves the dipole moment, while the asymmetric stretch (\sigma_u^+) is active as it induces a temporary dipole.[30] These rules build on the quantum energy levels of molecular vibrations, ensuring only compatible transitions contribute to the spectrum. The intensity of an IR absorption band reflects the strength of the transition and is quantified by the integrated absorbance A, which is proportional to the square of the transition dipole moment matrix element |\langle \psi_f | \hat{\mu} | \psi_i \rangle|^2 multiplied by the population of the initial state, governed by the Boltzmann distribution.[8] Experimentally, this relates to concentration via the Beer-Lambert law: A = \epsilon c l, where \epsilon is the molar absorptivity (dependent on the transition moment), c is the analyte concentration, and l is the path length. Stronger dipole changes yield higher \epsilon values, leading to more intense peaks, while thermal population effects favor lower-energy fundamentals over hot bands from excited initial states. IR spectral peaks exhibit characteristic shapes due to broadening mechanisms: homogeneous broadening from finite vibrational lifetimes produces Lorentzian profiles, while inhomogeneous effects like Doppler or environmental variations yield Gaussian profiles; real spectra often show Voigt profiles as convolutions of both. Lorentzian tails arise from lifetime uncertainty (\Delta E \Delta t \approx \hbar), with full width at half maximum (FWHM) inversely proportional to lifetime, whereas Gaussian broadening reflects statistical distributions in velocity or solvation.[31] In the fingerprint region (typically below 1500 cm^{-1}), numerous allowed vibrational modes overlap, producing complex, unique patterns that serve as molecular "fingerprints" for identification, as the interplay of active modes encodes structural details without isolated group assignments.[2] This utility stems from the density of IR-active fundamentals, bends, and interactions in polyatomic molecules, enabling comparison to reference spectra for compound verification.[32]Instrumentation
Dispersive Spectrometers
Dispersive spectrometers represent the traditional approach to infrared (IR) spectroscopy, employing optical elements to physically separate wavelengths of IR radiation before detection. These instruments scan across the spectrum sequentially, measuring intensity at individual wavelengths to construct the full spectrum point by point. Unlike interferometric methods, they rely on dispersion via prisms or diffraction gratings within a monochromator to achieve wavelength selection.[33] The primary components of a dispersive IR spectrometer include a broadband IR radiation source, a monochromator for dispersion, a detector for signal measurement, and a mechanical chopper for signal modulation. Common sources are the Globar, a silicon carbide rod heated electrically to 1300–1500 K, which emits continuous radiation peaking around 2 μm and covering approximately 0.5–50 μm,[34] and the Nernst glower, a cylindrical filament of rare earth oxides (such as zirconium, yttrium, and erbium oxides) heated to approximately 2000 K, providing emission from 0.5–25 μm with higher intensity in the mid-IR region.[35] The monochromator typically uses either prisms made of alkali halides like NaCl (effective for 2.5–15 μm but limited to resolutions of about 10 cm⁻¹ due to material dispersion) or reflection gratings (blazed for IR wavelengths, capable of resolutions down to ~1 cm⁻¹ across broader ranges). Detectors are thermal devices such as thermocouples, which generate a voltage from the temperature difference between an IR-absorbing hot junction and a reference cold junction, or bolometers, which measure resistance changes in a temperature-sensitive element (e.g., metal film or semiconductor) upon IR absorption. A rotating chopper wheel, operating at 5–30 Hz, modulates the IR beam to convert the signal to an alternating current, enabling lock-in amplification to distinguish it from ambient thermal noise.[36][37][38] In operation, IR radiation from the source passes through sample and reference compartments in a double-beam configuration to compensate for source fluctuations and solvent absorption. The beams then enter the monochromator, where the prism or grating disperses the radiation into its spectral components; a scanning mechanism rotates the dispersive element or adjusts entrance/exit slits to select successive narrow wavelength bands (typically 1–10 cm⁻¹ wide). The modulated beam at each selected wavelength reaches the detector, producing an electrical signal proportional to transmittance, which is recorded as the monochromator scans from ~4000 cm⁻¹ to 400 cm⁻¹. This sequential acquisition requires sensitive detectors due to the low photon flux in IR.[37][33] Dispersive spectrometers offer high spectral resolution in targeted narrow wavelength ranges, making them suitable for detailed studies of specific bands, with grating-based systems achieving ~1 cm⁻¹ resolution. However, their point-by-point scanning leads to slow acquisition times (often several minutes per spectrum) and lower signal-to-noise ratios compared to Fourier transform IR (FTIR) spectrometers, which benefit from multiplex detection. Historically, dispersive instruments dominated IR spectroscopy from their development in the mid-1940s through the 1970s, enabling widespread adoption in organic structural analysis, but they were largely supplanted by commercial FTIR systems in the late 1970s due to the latter's speed and sensitivity advantages. They remain in use today for specialized high-resolution applications, such as monitoring single IR wavelengths in kinetic studies or near-IR regions.[36][39][37]Fourier Transform Infrared (FTIR) Spectrometers
Fourier transform infrared (FTIR) spectrometers represent a significant advancement in infrared instrumentation, employing interferometry to measure spectra in the time domain before computationally converting data to the frequency domain. At the core of an FTIR spectrometer is the Michelson interferometer, which splits incoming infrared radiation from a broadband source using a beam splitter, directing one beam to a fixed mirror and the other to a moving mirror. The recombined beams interfere, producing an interferogram as a function of the optical path difference δ created by the moving mirror's translation. This interferogram I(δ) is mathematically described by the integral I(\delta) = \int_{-\infty}^{\infty} B(\nu) \cos(2\pi \nu \delta) \, d\nu, where B(ν) is the spectral intensity as a function of wavenumber ν.[40] To obtain the infrared spectrum, the interferogram undergoes a Fourier transform, yielding the intensity spectrum B(ν) via B(\nu) = 2 \int_{0}^{\infty} I(\delta) \cos(2\pi \nu \delta) \, d\delta. In practice, this is implemented using a discrete fast Fourier transform (FFT) algorithm on digitized interferogram data sampled at precise intervals, enabling efficient computation even for high-resolution spectra. Unlike dispersive spectrometers that sequentially scan wavelengths, FTIR captures the entire spectral range simultaneously in each interferogram measurement.[40][41] FTIR offers key advantages over dispersive methods, including the Fellgett or multiplex advantage, where all wavelengths contribute to the signal throughout the measurement, improving the signal-to-noise ratio (S/N) by a factor approximately proportional to the square root of the number of resolution elements for detector-noise-limited cases. Additionally, the Jacquinot or throughput advantage arises from the interferometer's slitless design, allowing a larger aperture and higher light collection efficiency—often 10 to 100 times greater than in dispersive systems—enhancing sensitivity for low-light samples. Rapid scanning of the moving mirror further enables high-speed data acquisition, with spectra collected in seconds.[41][42][43] The primary components of an FTIR spectrometer mirror those of dispersive instruments—such as the infrared source, sample compartment, and detector—but incorporate interferometer-specific elements like the beam splitter and mirrors, typically coated for infrared transmission. A helium-neon (HeNe) laser provides a monochromatic reference beam for precise zero-path-difference tracking, ensuring accurate sampling during mirror motion via interferogram modulation at the laser's frequency. Detectors commonly include deuterated triglycine sulfate (DTGS) pyroelectric sensors for room-temperature operation or mercury cadmium telluride (MCT) semiconductor detectors cooled with liquid nitrogen for faster response and higher sensitivity in the mid-infrared range.[44][45] To mitigate artifacts in the transformed spectrum, apodization applies a window function to the interferogram before Fourier transformation, tapering the data edges to suppress sidelobes from finite truncation while broadening the main lobe. Common functions include the Happ-Genzel (similar to a cosine bell) for balanced resolution and noise reduction or the Blackman-Harris for strong sidelobe suppression in quantitative analysis. This processing step is essential for producing clean, interpretable spectra without introducing excessive distortion.[46][47]Experimental Methods
Sample Preparation Techniques
Sample preparation in infrared (IR) spectroscopy is essential to ensure that the sample interacts effectively with the IR beam while minimizing artifacts and interferences, allowing for accurate transmission or reflection measurements across gas, liquid, and solid phases.[48] Traditional methods focus on creating thin, uniform sample layers or controlled environments to achieve optimal path lengths and avoid saturation of strong absorption bands. For gas samples, long-path gas cells with path lengths of 10 to 100 cm are commonly employed to enhance sensitivity for low-concentration analytes, typically fitted with NaCl windows that transmit mid-IR radiation effectively.[49] These cells allow the gas to flow through or be statically held, enabling the recording of absorption spectra as the IR beam passes multiple times via mirrors.[50] Pressure broadening effects must be considered, as increased gas pressure leads to collisional line broadening, which can alter spectral resolution and linewidths proportionally to pressure, often requiring operation at reduced pressures (e.g., 10-100 Torr) for sharp rotational-vibrational features.[51] Liquid samples are prepared as thin films sandwiched between two IR-transparent plates, such as KBr or NaCl, to achieve a path length of about 0.01-0.05 mm and prevent total absorption in strong bands like C-H stretches.[48] For non-volatile liquids, this method provides a simple transmission setup, though volatile solvents may require sealed cells to avoid evaporation.[52] Nujol mulls, involving dispersion in mineral oil between plates, are occasionally adapted for viscous liquids but are more standard for solids; they introduce C-H bands that must be subtracted. Attenuated total reflectance (ATR) techniques bypass extensive preparation for non-volatile liquids by directly placing the sample on a crystal surface, where the evanescent wave probes a shallow depth (typically 0.5-5 μm).[53] Solid samples often require dispersion in an IR-transparent matrix to form uniform mixtures for transmission analysis. The KBr pellet method involves grinding 1-2% by weight of the finely powdered sample (particle size <2 μm) with anhydrous KBr, then pressing at 10-15 tons to form a 1 mm thick, 13 mm diameter disk that is nearly transparent to IR.[54] This technique suits crystalline solids but demands dry conditions to avoid moisture artifacts. For powders and irregular solids, diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) collects scattered IR from the sample surface diluted in KBr (up to 5-10%), providing spectra without pressing and suitable for quantitative analysis of surface properties.[55] Polymers, which may not disperse well, can be analyzed via pyrolysis, where a small sample (1-10 mg) is heated to 500-800°C in a controlled furnace, volatilizing fragments for gas-phase IR detection with minimal initial preparation.[56] Common challenges in sample preparation include water interference, where atmospheric moisture or residual H₂O in samples produces broad OH stretching bands around 3700-3500 cm⁻¹ and bending at 1640 cm⁻¹, overlapping key functional group regions and necessitating dry nitrogen purging or desiccated environments.[57] Solvent subtraction is critical when using solutions, involving recording a background spectrum of the pure solvent and digitally removing its contributions to isolate analyte bands, though incomplete subtraction can introduce baseline distortions.[58] Since the early 2000s, diamond ATR crystals have become a dominant modern alternative, offering durable, high-pressure-resistant surfaces for minimal-preparation analysis of all sample types; a small amount of liquid, solid, or powder is simply pressed against the crystal, enabling rapid, non-destructive measurements with penetration depths of 1-3 μm and effective range down to 400 cm⁻¹.[59] This approach has largely supplanted traditional methods in routine labs due to its ease and reproducibility.[60]Spectral Acquisition and Analysis
Spectral acquisition in infrared (IR) spectroscopy begins with the collection of a background spectrum, also known as an empty cell or reference scan, which captures instrumental and environmental contributions such as solvent or atmospheric interferences.[61] This background is subtracted from the sample spectrum to isolate the analyte's signal, ensuring accurate representation of molecular vibrations.[61] Typical resolution settings range from 4 cm⁻¹ to 8 cm⁻¹, with 4 cm⁻¹ being common for routine analyses to balance detail and acquisition time without excessive broadening of peaks.[62] To enhance the signal-to-noise ratio (S/N), multiple scans—often 16 to 64—are averaged, as the S/N improves proportionally to the square root of the number of scans, reducing random noise while preserving spectral features.[63][64] Following acquisition, data processing refines the raw spectra for reliable interpretation. Baseline correction eliminates drifting offsets or sloping backgrounds caused by scattering or instrumental drift, using methods such as polynomial fitting or piecewise linear subtraction to flatten the spectrum without distorting peak shapes.[61] Smoothing reduces high-frequency noise via the Savitzky-Golay filter, which performs local least-squares polynomial fitting over a moving window (typically 11–21 points) to preserve peak widths and heights better than simple averaging.[65] Normalization scales the spectrum to a standard intensity, often to unit area or maximum absorbance, facilitating comparisons across samples.[66] Spectra are commonly converted from transmittance (T = I/I₀) to absorbance (A = -log₁₀ T) units, as absorbance follows a linear relationship with concentration per Beer's law, aiding quantitative work.[67] Qualitative analysis involves peak picking to identify absorption maxima corresponding to vibrational modes, followed by matching the overall "fingerprint" region (typically 1500–400 cm⁻¹) against reference libraries.[68] Automated algorithms detect peaks above a noise threshold, assigning wavenumbers and relative intensities for functional group inference.[68] Databases like the NIST Chemistry WebBook provide evaluated IR spectra for thousands of compounds, enabling hit-quality indexing via similarity metrics such as correlation coefficients to confirm molecular identities.[69] For quantitative analysis, Beer's law (A = ε b c, where ε is the molar absorptivity, b the path length, and c the concentration) underpins concentration determination from peak heights or areas at characteristic wavenumbers.[70] In multicomponent mixtures, least-squares deconvolution fits the observed spectrum as a linear combination of reference spectra, solving for individual concentrations while accounting for overlapping bands.[71] This method assumes additivity of absorbances and is effective for systems obeying the law, with matrix inversion or iterative algorithms minimizing residuals.[70][72] Common artifacts must be addressed to avoid misinterpretation. Atmospheric CO₂ and H₂O bands (e.g., CO₂ at ~2350 cm⁻¹ and H₂O at ~3400–3600 cm⁻¹ and 1600 cm⁻¹) are removed by subtracting a pre-recorded atmospheric spectrum or through instrument purging with dry nitrogen, ensuring they do not overlap sample features.[73] Stray light, which causes baseline elevation and reduced dynamic range, is corrected by measuring instrument response with a blocked beam and subtracting this scatter contribution, particularly important in dispersive systems.[74]Spectral Features
Absorption Regions and Bands
The infrared spectrum is conventionally divided into three primary regions based on wavelength or wavenumber: the near-infrared (NIR, approximately 14,000–4,000 cm⁻¹), mid-infrared (MIR, 4,000–400 cm⁻¹), and far-infrared (FIR, 400–10 cm⁻¹). The MIR region is the most widely utilized for molecular vibrational analysis, as it corresponds closely to the energies of fundamental vibrational transitions. Within the MIR, the higher-wavenumber portion from 4,000 to 1,500 cm⁻¹ is known as the group frequency region, where stretching vibrations involving light atoms, such as X-H bonds (X = C, N, O), dominate and provide initial clues to functional group presence. The lower MIR portion, from 1,500 to 600 cm⁻¹, constitutes the fingerprint region, characterized by complex skeletal bending, stretching, and deformation modes unique to the overall molecular structure, enabling compound identification through pattern matching. Below 600 cm⁻¹ in the FIR, absorption bands arise from heavy-atom motions, including metal-ligand vibrations in coordination compounds and lattice vibrations in solids./Spectroscopy/Vibrational_Spectroscopy/Infrared_Spectroscopy/Infrared_Spectroscopy)[1][75] In the NIR region, absorptions primarily result from overtones and combination bands of fundamental MIR vibrations, such as the first overtone of O-H stretching appearing around 6,800 cm⁻¹ (approximately twice the fundamental frequency near 3,400 cm⁻¹). These bands are inherently weaker—often 10 to 100 times less intense than fundamentals—due to the anharmonic nature of molecular potentials, which reduces transition probabilities for higher-order processes. Modern extensions into the low-wavenumber FIR and terahertz (THz) regime (down to 10 cm⁻¹ or ~0.3 THz) have expanded applications to phonon modes in crystalline materials, revealing low-energy collective vibrations not accessible in standard MIR measurements.[76][77][78] IR absorption bands exhibit characteristic shapes and widths influenced by molecular environment and relaxation processes. In condensed phases like liquids or solutions, typical band widths at half-height range from 10 to 20 cm⁻¹, arising from vibrational relaxation (on picosecond timescales) and rotational dephasing, which shorten the excited-state lifetime and broaden lines via the energy-time uncertainty principle. Asymmetry in band profiles often stems from Fermi resonance, where a fundamental vibration couples with a nearby overtone or combination band of similar energy and symmetry, leading to splitting and intensity redistribution. Solvent effects further modulate band characteristics; for instance, hydrogen bonding in protic solvents causes O-H stretching bands to shift to lower wavenumbers (e.g., from ~3,600 cm⁻¹ in dilute non-polar media to ~3,300 cm⁻¹ in water) and broaden significantly due to inhomogeneous broadening from varying hydrogen-bond strengths and rapid exchange dynamics.[79]/Spectroscopy/Vibrational_Spectroscopy/Vibrational_Modes/Combination_Bands_Overtones_and_Fermi_Resonances)[8]Characteristic Group Frequencies
Characteristic group frequencies in infrared spectroscopy correspond to the distinctive wavenumber ranges associated with the vibrational modes of specific functional groups, enabling the identification of molecular structures through spectral pattern matching. These absorptions are primarily due to stretching and bending vibrations of bonds, with stretching modes generally appearing at higher wavenumbers than deformations. The consistency of these frequencies across similar compounds makes them invaluable for qualitative analysis, often serving as the first step in interpreting an IR spectrum.[80] The diagnostic power lies in correlating observed peaks to known group frequencies, though exact positions can vary slightly based on molecular environment. For example, the C-H stretching vibrations distinguish between aliphatic and unsaturated hydrocarbons: alkanes absorb at 3000-2850 cm⁻¹, while aromatic C-H stretches occur at 3100-3000 cm⁻¹. Similarly, the carbonyl C=O stretch is a hallmark of ketones, aldehydes, and carboxylic derivatives, typically in the 1750-1650 cm⁻¹ range, with subtypes like esters at higher frequencies (~1735 cm⁻¹) and conjugated amides at lower (~1650 cm⁻¹). Hydroxyl O-H stretches provide another clear indicator, with free O-H in dilute solutions showing sharp peaks at 3650-3580 cm⁻¹ and hydrogen-bonded O-H in alcohols or phenols appearing as broad bands from 3550-3200 cm⁻¹.[81][1] The following table summarizes representative characteristic frequencies for common organic functional groups, focusing on stretching modes for diagnostic purposes:| Functional Group | Vibration Type | Wavenumber Range (cm⁻¹) | Typical Intensity | Notes/Example |
|---|---|---|---|---|
| Alkane C-H | Stretch | 3000–2850 | Strong (s) | Symmetric and asymmetric stretches in CH₃ and CH₂ groups. |
| Aromatic C-H | Stretch | 3100–3000 | Medium (m) | Often accompanied by =C-H bend at 900–700 cm⁻¹. |
| O-H (alcohols, phenols; H-bonded) | Stretch | 3550–3200 | Strong, broad (s, br) | Broadening due to hydrogen bonding; free O-H sharper at ~3600 cm⁻¹. |
| C=O (ketones) | Stretch | 1720–1700 | Strong (s) | Saturated acyclic; shifts lower with conjugation. |
| C=O (esters) | Stretch | 1750–1730 | Strong (s) | Higher frequency due to electronegative oxygen. |
| C=O (amides) | Stretch | 1680–1630 | Strong (s) | Lower due to resonance with N lone pair. |
| C≡C (alkynes) | Stretch | 2260–2190 | Variable (m-w) | Weak if symmetric; stronger in terminal alkynes. |
| C=C (alkenes) | Stretch | 1680–1620 | Variable (m-w) | Intensifies with conjugation. |