Engineering Chemistry. Module 3, molecular spectroscopy and analytical techniques.

Spectroscopy, radiation and molecular energy

This module moves from fundamental light–matter interactions to spectroscopy and instrumental analysis:

1. Spectroscopy, radiation and molecular energy
2. Transmittance, absorbance and the Beer–Lambert law
3. Worked problems on absorbance and concentration
4. UV–visible spectroscopy and electronic transitions
5. Conjugation and predicting molecular transitions
6. UV–visible spectrophotometer: instrument and applications
7. Infrared absorption and types of vibration
8. Counting vibrations: carbon dioxide, water and HCN
9. Bond vibrations and force-constant calculations
10. Reading IR spectra and studying hydrogen bonding
11. Dielectric thermal analysis: principle, instrument and uses
12. Scanning electron microscopy: signals, instrument and uses
13. Revision sheet and practice problems

Interaction of radiation with matter

Spectroscopy

Spectroscopy is the study of how electromagnetic radiation interacts with atoms, ions, and molecules. Many spectroscopic methods provide rapid quantitative and qualitative analysis using minute sample quantities. Whether the sample can be recovered intact depends on the required sample preparation, incident radiation energy, and specific technique employed.

Electromagnetic radiation

Electromagnetic radiation consists of mutually perpendicular oscillating electric and magnetic fields propagating through space, characterised by wavelength ($\lambda$), frequency ($\nu$), or wavenumber ($\bar{\nu} = 1/\lambda$). The energy $E$ of a single photon is directly proportional to frequency and inversely proportional to wavelength:

where:

• $h$ is Planck's constant ($6.626 \times 10^{-34}\text{ J s}$)
• $c$ is the speed of light in vacuum ($3.00 \times 10^8\text{ m s}^{-1}$)
• $\nu$ is frequency in hertz ($\text{Hz}$ or $\text{s}^{-1}$)
• $\lambda$ is wavelength (commonly in $\text{m}$ or $\text{nm}$)
• $\bar{\nu}$ is wavenumber (commonly in $\text{cm}^{-1}$)

Across the electromagnetic spectrum—from radio waves through microwaves, infrared (IR), visible light, ultraviolet (UV), X-rays, to gamma rays—wavelength decreases progressively while frequency and photon energy increase. When calculating energies, ensure compatible length units: when using $c$ in $\text{m s}^{-1}$, convert $\lambda$ to metres ($\text{m}$) and $\bar{\nu}$ to $\text{m}^{-1}$ ($1\text{ cm}^{-1} = 100\text{ m}^{-1}$).

Fundamental radiation–matter processes

When electromagnetic radiation encounters matter, three primary interactions can occur:

1. Absorption: An atom or molecule absorbs a resonant photon and transitions from a lower energy state ($E_1$) to an allowed higher energy state ($E_2$), where $\Delta E = E_2 - E_1 = h\nu$. Typical absorption methods include UV–visible, infrared, microwave, and nuclear magnetic resonance (NMR) spectroscopy.
2. Emission: An excited species relaxes from a higher energy state ($E_2$) to a lower energy state ($E_1$) by releasing a photon of matching energy $\Delta E = h\nu$. Key examples include atomic emission and fluorescence spectroscopy.
3. Scattering: Incident radiation is redirected into new directions upon colliding with matter without necessarily undergoing direct resonant absorption. In Raman spectroscopy, inelastic light scattering occurs, causing scattered photons to gain or lose discrete amounts of vibrational or rotational energy.

Figure 1a: Qualitative schematic of photon absorption driving an upward transition from a lower to a higher energy state.

Figure 1b: Qualitative schematic of photon emission during relaxation from a higher to a lower energy state.

Watch out. Quantum mechanical transitions take place between any permitted lower and higher energy states that satisfy the specific selection rules—not exclusively between the absolute ground and highest excited levels. Furthermore, Raman spectroscopy is an inelastic scattering process, not an emission technique; and atomic force microscopy (AFM) is a mechanical scanning probe method, not optical spectroscopy.

Molecular energy levels and the Born–Oppenheimer approximation

A molecule distributes its total energy among translational, rotational, vibrational, and electronic degrees of freedom:

Translational energy

Translational energy ($E_{\text{trans}}$) arises from the unconstrained displacement of the molecule's centre of mass through three-dimensional space. Because translational quantum states in macroscopic containers are spaced by infinitesimal energy increments, they form an effective continuum and are separated from quantised internal states.

Born–Oppenheimer approximation

The Born–Oppenheimer approximation states that because heavy atomic nuclei move much more slowly than light electrons, electronic motion can be treated independently of nuclear motions. Under this approximation, the total internal molecular energy ($E_{\text{int}}$) separates into distinct electronic, vibrational, and rotational contributions:

The energy separations between adjacent quantum states follow a strict hierarchical order:

Figure 2: Qualitative diagram of nested molecular energy levels. Each electronic state contains multiple vibrational levels ($v$), and each vibrational level contains closely spaced rotational levels ($J$). Spacing is schematic and not drawn to scale.

Atomic versus molecular spectra

The presence of chemical bonds fundamentally alters the nature of spectral transitions:

Atomic spectra

Atomic spectra arise from isolated gaseous atoms that possess only electronic degrees of freedom and lack chemical bonds, meaning they have no vibrational or rotational sublevels. Electronic transitions between discrete atomic orbitals therefore yield narrow, sharp line spectra (subject to Doppler and natural lifetime broadening).

Molecular spectra

Molecular spectra arise because molecules possess vibrational and rotational sublevels nested within each electronic state. An electronic transition in a molecule is accompanied by simultaneous vibrational and rotational co-transitions (vibronic and rovibronic coupling). In condensed phases or solution, rapid intermolecular collisions and solvent-solute interactions further broaden these closely packed transitions into broad band spectra.

Self-check questions

1. Question: Why does a gaseous atom produce sharp spectral lines whereas a molecule in solution produces broad UV–visible absorption bands?
   Answer: Gaseous atoms undergo electronic transitions purely between unperturbed, discrete atomic energy levels, yielding sharp lines. Molecules have vibrational and rotational energy sublevels nested within each electronic state. Simultaneous transitions across these closely spaced sublevels, combined with collisional dephasing and solvent interactions in solution, smear individual transitions into continuous, broad absorption bands.

2. Question: Arrange microwave, ultraviolet, and infrared radiation in order of increasing photon energy and state the primary molecular transition promoted by each.
   Answer: In order of increasing energy: $\text{Microwave } (\Delta E_{\text{rot}}) < \text{Infrared } (\Delta E_{\text{vib}}) < \text{Ultraviolet } (\Delta E_{\text{ele}})$

   • Microwave: Promotes rotational transitions.
   • Infrared: Promotes vibrational stretching and bending transitions.
   • Ultraviolet: Promotes electronic transitions between valence molecular orbitals.

Transmittance, absorbance and the Beer–Lambert law

When a beam of electromagnetic radiation passes through a sample solution, molecules absorb photons whose energies match allowed internal transitions. Consequently, the intensity of the emerging beam is lower than that of the entering beam. Quantitative absorption spectroscopy measures this attenuation to determine how much absorbing substance is present.

Transmittance and Absorbance

Consider a parallel beam of monochromatic radiation with incident intensity $I_0$ passing through a sample cell (cuvette) of path length $l$ containing an absorbing solution of molar concentration $c$. The radiation emerges with transmitted intensity $I$.

Figure 1: Attenuation of an incident light beam ($I_0$) passing through an absorbing solution of concentration $c$ and path length $x$ (or $l$).

Transmittance

Transmittance ($T$) is the fraction of incident radiation that successfully passes through the sample:

Because $T$ is a ratio of two intensities, it is dimensionless and ranges from $0$ (complete absorption) to $1$ (no absorption). Instrument readouts often express this value as percentage transmittance ($\%T$):

Transmittance decreases exponentially as concentration or path length increases.

Absorbance

Absorbance ($A$), historically termed optical density, is defined as the base-10 logarithm of the reciprocal of transmittance:

To convert directly from percentage transmittance to absorbance, substitute $T = \%T / 100$:

Like transmittance, absorbance is a dimensionless quantity.

Beer–Lambert Law and Derivation

Beer–Lambert Law

Beer–Lambert law states that when a parallel beam of monochromatic radiation passes through a homogeneous, non-scattering, dilute solution, the rate of decrease in radiation intensity ($-dI$) with respect to an infinitesimal thickness of the medium ($dl$) is directly proportional to both the local intensity $I$ and the molar concentration $c$ of the absorbing species. It unifies Lambert's observation (attenuation scales with path length) with Beer's observation (attenuation scales with concentration).

Watch out. Many introductory notes state that the Beer–Lambert law applies only to "coloured" solutions. In reality, the law applies to any absorbing species—including colourless solutions that absorb strongly in the ultraviolet (UV) or infrared (IR) regions.

Derivation Steps

1. Set up the differential rate equation: Express the rate of intensity loss across an infinitesimal layer of thickness $dl$:

   $$-\frac{dI}{dl} \propto I c \implies -\frac{dI}{dl} = k c I$$

where $k$ is a proportionality constant dependent on the wavelength and the absorbing species.

2. Separate variables: Rearrange the equation to isolate intensity terms on the left and path length terms on the right:

   $$-\frac{dI}{I} = k c \, dl$$

3. Integrate across the cell boundaries: Integrate from the entrance boundary ($l = 0$, where intensity is $I_0$) to the exit boundary ($l = l$, where intensity is $I$):

   $$\int_{I_0}^{I} -\frac{dI}{I} = \int_{0}^{l} k c \, dl$$

4. Evaluate the definite integrals:

   $$-\left[\ln I\right]_{I_0}^{I} = k c [l]_0^l \implies \ln\left(\frac{I_0}{I}\right) = k c l$$

5. Convert to common logarithms: Convert from natural logarithms ($\ln$) to decadic logarithms ($\log_{10}$) using $\ln(x) = \ln(10) \log_{10}(x) \approx 2.303 \log_{10}(x)$:

   $$\log_{10}\left(\frac{I_0}{I}\right) = \left(\frac{k}{\ln 10}\right) c l = \left(\frac{k}{2.303}\right) c l$$

6. Define molar absorptivity: Define the molar absorption coefficient as $\varepsilon = k / \ln 10$. Substituting $A = \log_{10}(I_0 / I)$ yields the standard integrated law:

   $$A = \varepsilon c l$$

(Note: Some texts and diagrams denote the cuvette path length using $x$ rather than $l$, expressing the relationship as $A = \varepsilon c x$.)

Units of the Molar Absorption Coefficient ($\varepsilon$)

Molar Absorptivity

Molar absorption coefficient ($\varepsilon$) (or molar absorptivity) is a fundamental optical property measuring how strongly a chemical species attenuates light at a specified wavelength, solvent, and temperature. Because absorbance $A$ is dimensionless, the dimensions of $\varepsilon$ must cancel those of concentration $c$ and path length $l$ ($\varepsilon = A / (c l)$).

Watch out. Because $1\text{ L} = 1\text{ dm}^3$, expressing path length in decimetres ($\text{dm}$) simplifies the dimensional algebra ($\text{dm}^3 \text{mol}^{-1} \text{dm}^{-1} = \text{dm}^2 \text{mol}^{-1}$), which is why exam problems often use it. However, dividing by $0.1\text{ dm}$ instead of $1\text{ cm}$ makes the numerical value of $\varepsilon$ in $\text{dm}^2 \text{mol}^{-1}$ exactly $10$ times larger than the standard value in $\text{L mol}^{-1} \text{cm}^{-1}$. Always state your chosen path-length unit explicitly.

Calibration and Analysis

For a fixed cuvette path length $l$, plotting absorbance $A$ against molar concentration $c$ across a series of known standard solutions yields a linear relationship described by $A = (\varepsilon l)c$.

Figure 2: Ideal Beer–Lambert calibration plot of absorbance ($A$) versus concentration ($C$), with slope equal to $\varepsilon x$ (or $\varepsilon l$).

Ideally, the calibration line passes through the origin $(0,0)$ with a slope of $\varepsilon l$. Once established, the concentration of an unknown sample can be interpolated directly from the graph or calculated from a reference standard using the proportional ratio:

Spectroscopic Blank

Spectroscopic blank refers to an identical cuvette filled with pure solvent and all background reagents excluding the analyte. Because cuvette walls and solvent molecules reflect and absorb a small fraction of incident radiation, the spectrophotometer must be zeroed using a blank before sample measurement. This baseline correction minimizes solvent and cell contributions. If minor instrumental drift or reagent background persists, calibration data is fitted to a linear regression with an intercept ($A = \varepsilon l c + b$).

Assumptions and Deviations from Linearity

The linear relationship $A = \varepsilon c l$ holds strictly only when specific physical, chemical, and instrumental constraints are satisfied:

• Monochromatic radiation: The incident radiation must consist of a narrow wavelength band over which $\varepsilon$ is effectively constant. Broad polychromatic light or instrumental stray light causes severe negative deviations at high absorbance values.
• Dilute solutions: At high solute concentrations, inter-ionic and intermolecular electrostatic interactions perturb the electron charge distributions of the absorbing chromophore, altering $\varepsilon$. High concentrations also alter the solution's refractive index.
• Homogeneous, non-scattering medium: The solution must be clear and free from turbidity. Suspended colloidal particles scatter light away from the photodetector, generating artificially elevated apparent absorbance readings.
• Chemical stability: The absorbing species must not undergo concentration-dependent chemical equilibria (such as acid–base dissociation, association, tautomerism, or complexation) that alter the relative proportion of absorbing molecules upon dilution.

Self-Check Questions

1. Question: A solution transmits $25\%$ of incident monochromatic light at $450\text{ nm}$. What is its absorbance?
   Answer: Using the conversion formula $A = 2 - \log_{10}(\%T)$:

   $$A = 2 - \log_{10}(25) = 2 - 1.398 = 0.602$$

2. Question: Why does a spectrophotometric calibration curve often bend downwards (negative deviation) at high analyte concentrations?
   Answer: At elevated concentrations, solute–solute electrostatic interactions alter the molar absorptivity ($\varepsilon$), chemical equilibria may shift the active chromophore population, and instrumental stray light places an upper ceiling on accurately measurable absorbance.

Worked problems on absorbance and concentration

Strategy for Beer–Lambert Law Calculations

Quantitative spectrophotometry relies on the linear relationship between absorbance ($A$) and molar concentration ($c$) for dilute, homogeneous solutions measured with monochromatic light:

Here, $\varepsilon$ is the molar absorption coefficient and $x$ is the optical path length of the sample cell (cuvette). When solving numerical problems, keep three physical principles in mind:

1. Higher absorbance means higher concentration, but lower transmittance. A more concentrated solution absorbs more photons, so less transmitted light ($I$) reaches the detector relative to the incident beam ($I_0$). Therefore, as concentration increases, absorbance ($A$) increases while fractional transmittance ($T = I/I_0$) decreases.

2. Never confuse transmitted intensity with transmittance. Intensity ($I$) is radiative power per unit area, whereas fractional transmittance ($T = I/I_0$) is a dimensionless ratio between $0$ and $1$, often expressed as percentage transmittance ($\%T = 100 \times T$). Because absorbance is logarithmic:

3. Ratio methods eliminate constants under identical conditions. When a standard solution of known concentration ($c_1$) and an unknown sample ($c_2$) of the same chemical species are measured at the same wavelength, temperature, and solvent environment inside identical cuvettes (same $\varepsilon$ and $x$), the constants cancel out:

Watch out. Do not mix centimetres and decimetres when calculating $\varepsilon$. Because $1\text{ M} = 1\text{ mol L}^{-1} = 1\text{ mol dm}^{-3}$, keeping $x$ in $\text{cm}$ gives $\varepsilon$ in $\text{L mol}^{-1}\text{ cm}^{-1}$. Converting $x$ into $\text{dm}$ ($1\text{ cm} = 0.1\text{ dm}$) changes the numerical value of $\varepsilon$ by a factor of $10$ and gives units of $\text{dm}^2\text{ mol}^{-1}$ (since $\text{dm}^3\text{ mol}^{-1}\text{ dm}^{-1} = \text{dm}^2\text{ mol}^{-1}$, never $\text{dm}^3\text{ mol}^{-1}$).

Step-by-Step Worked Examples

Self-Check Questions

1. Question: Solution X has $\%T = 10\%$ and Solution Y of the same solute in the same cuvette has $\%T = 50\%$. Which solution is more concentrated, and by what factor?
   Answer: Solution X is more concentrated because it transmits less light ($A_X = \log_{10}(100/10) = 1.000$ vs $A_Y = \log_{10}(100/50) = 0.3010$). It is $\frac{1.000}{0.3010} = 3.32$ times as concentrated as Solution Y.

2. Question: Why is the molar absorption coefficient $\varepsilon = 34.95\text{ L mol}^{-1}\text{ cm}^{-1}$ numerically equal to $349.5\text{ dm}^2\text{ mol}^{-1}$?
   Answer: Because $1\text{ L} = 1\text{ dm}^3$ and $1\text{ cm} = 0.1\text{ dm}$, substituting these into the unit expression gives $1\text{ L mol}^{-1}\text{ cm}^{-1} = 1\text{ dm}^3\text{ mol}^{-1} (0.1\text{ dm})^{-1} = 10\text{ dm}^2\text{ mol}^{-1}$.

UV–visible spectroscopy and electronic transitions

UV–visible (UV–vis) spectroscopy

UV–visible (UV–vis) spectroscopy is an absorption spectroscopy technique that measures how molecules interact with electromagnetic radiation in the ultraviolet ($10\text{–}400\text{ nm}$) and visible ($400\text{–}800\text{ nm}$) regions. Because photons in these spectral bands carry sufficient energy to promote valence electrons from lower-energy ground-state molecular orbitals to higher-energy excited-state molecular orbitals, an absorption spectrum recorded in this region is known as an electronic spectrum. It is conventionally represented as a plot of absorbance ($A$) or molar absorptivity ($\varepsilon$) as a function of wavelength ($\lambda$, expressed in $\text{nm}$).

For practical chemical analysis, the ultraviolet–visible range is divided into three distinct operational domains:

• Far (vacuum) UV region ($< 200\text{ nm}$): High-energy radiation where atmospheric oxygen and common optical materials absorb strongly. Standard measurements require specialized vacuum chambers, nitrogen purge systems, and high-purity fluoride optics.
• Near-UV region ($200\text{–}400\text{ nm}$): Accessible using standard quartz (fused silica) cuvettes and standard benchtop optical paths in ambient air.
• Visible region ($400\text{–}800\text{ nm}$): Directly perceived by the human visual system. A substance appears coloured when it selectively absorbs specific visible wavelengths and transmits or reflects the complementary wavelengths.

The standard introductory benchtop working window spans $200\text{–}800\text{ nm}$, though modern research spectrophotometers often extend beyond these boundaries.

Molecular orbitals and electronic transitions

When a molecule absorbs an incident photon matching the transition energy $\Delta E$, an electron is promoted from an occupied molecular orbital to an unoccupied antibonding orbital according to the Planck–Einstein relation:

where:

• $h$ is Planck's constant ($6.626 \times 10^{-34}\text{ J s}$)
• $c$ is the speed of light in a vacuum ($3.00 \times 10^8\text{ m s}^{-1}$)
• $\lambda$ is the absorbed photon wavelength ($\text{m}$)

Ground-state valence electrons reside in three principal classes of molecular orbitals:

1. Sigma ($\sigma$) bonding orbitals: Low-energy, symmetrical orbitals housing strongly localized electrons that constitute single covalent bonds.
2. Pi ($\pi$) bonding orbitals: Higher-energy bonding orbitals formed by the lateral overlap of atomic $p$ orbitals, housing mobile electrons in double and triple bonds.
3. Non-bonding ($n$) orbitals: Orbitals containing localized, unshared valence lone pairs on heteroatoms such as oxygen ($\text{O}$), nitrogen ($\text{N}$), sulfur ($\text{S}$), and the halogens ($\text{X}$).

The higher-energy unoccupied levels are antibonding orbitals, designated as $\pi^*$ (pi-star) and $\sigma^*$ (sigma-star). In simple organic frameworks, orbital energy typically ascends in the order $\sigma < \pi < n < \pi^* < \sigma^*$. This hierarchy establishes four fundamental electronic promotions:

(Note: While this relative ordering provides a reliable heuristic, exact orbital energies depend on atomic electronegativity and molecular geometry.)

The four principal transition types

• $\sigma \to \sigma^*$ transitions: Promotion of an electron from a bonding $\sigma$ orbital into an antibonding $\sigma^*$ orbital. Due to the high thermodynamic stability and bond strength of single covalent bonds, this process requires high energy, producing absorption bands deep in the far-UV region ($\lambda < 150\text{ nm}$). Fully saturated hydrocarbons (such as methane, ethane, and cyclohexane) exhibit exclusively $\sigma \to \sigma^*$ transitions and are completely transparent across the routine $200\text{–}800\text{ nm}$ analytical window.
• $n \to \sigma^*$ transitions: Promotion of a non-bonding lone-pair electron ($n$) into an unoccupied $\sigma^*$ orbital. Saturated molecules bearing heteroatoms with lone pairs (e.g., alcohols, ethers, amines, alkyl halides) undergo these transitions. They require less energy than $\sigma \to \sigma^*$ transitions and generally occur between $150\text{ nm}$ and $250\text{ nm}$. Highly electronegative systems (methanol, methylamine) absorb in the far UV below $200\text{ nm}$, whereas heavier, polarizable systems (such as iodoalkanes) extend well into the accessible near-UV region above $200\text{ nm}$.
• $\pi \to \pi^*$ transitions: Promotion of an electron from a bonding $\pi$ orbital into an antibonding $\pi^*$ orbital in unsaturated compounds (alkenes, alkynes, aromatics, carbonyls). Isolated carbon–carbon double bonds absorb in the far UV (ethene exhibits $\lambda_{\max} \approx 169\text{ nm}$), whereas conjugated polyene systems shift into the routine $200\text{–}800\text{ nm}$ region. Most $\pi \to \pi^*$ transitions are symmetry- and spin-allowed, generating intense absorption bands ($\varepsilon_{\max} \approx 10^3\text{–}10^5\text{ L mol}^{-1}\text{ cm}^{-1}$). However, symmetry-forbidden $\pi \to \pi^*$ bands also exist, such as the weak benzenoid band centered at $255\text{ nm}$.
• $n \to \pi^*$ transitions: Promotion of a heteroatom lone-pair electron into an unoccupied antibonding $\pi^*$ orbital in unsaturated systems containing heteroatoms (aldehydes, ketones, carboxylic acids, esters, nitro groups). In simple carbonyl compounds, the $n$ and $\pi^*$ orbitals are mutually perpendicular, making the electric-dipole transition formally symmetry-forbidden. Molecular vibrations slightly disrupt molecular symmetry (vibronic coupling), permitting weak absorption ($\varepsilon_{\max} \approx 10\text{–}100\text{ L mol}^{-1}\text{ cm}^{-1}$) at longer wavelengths ($200\text{–}400\text{ nm}$) relative to $\pi \to \pi^*$ bands.

Watch out. Describing $\sigma \to \sigma^*$ and $n \to \sigma^*$ transitions as "UV–vis inactive" is inaccurate. They do absorb UV radiation; however, their absorption maxima fall below $200\text{ nm}$, placing them outside the detection window of routine benchtop instruments operating in air.

Chromophores, auxochromes, and spectral shifts

Chromophore

An isolated functional group or structural unit within a molecule responsible for absorbing electromagnetic radiation in a defined spectral region. Although historically defined as an impartor of visible color, in modern spectroscopy a chromophore refers to any light-absorbing group, even if absorption occurs strictly in the ultraviolet region (e.g., $\text{C=C}$, $\text{C=O}$, $-\text{NO}_2$, $-\text{N=N}-$, benzene rings, and even $\sigma$-bond frameworks in the vacuum UV).

Auxochrome

A saturated functional substituent bearing non-bonding electron pairs (such as $-\text{OH}$, $-\text{OR}$, $-\text{NH}_2$, $-\text{NR}_2$, or halogens) that does not absorb significantly above $200\text{ nm}$ on its own, but systematically alters both the wavelength and molar absorptivity when directly attached to a chromophore. Auxochromes delocalize their lone pairs into the adjacent $\pi$ system via resonance ($n\text{–}\pi$ conjugation) or inductive effects, generally shifting absorption toward longer wavelengths and increasing band intensity.

Wavelength of maximum absorbance ($\lambda_{\max}$)

The specific wavelength corresponding to the absorption peak of an electronic transition band. It serves as a diagnostic physical parameter governed by molecular conjugation, auxochromic substitution, and solvent interactions.

Spectral shifts and intensity modifications

Structural substitution or solvent changes produce four distinct spectral modifications:

• Bathochromic shift (Red shift): Displacement of an absorption band to a longer wavelength (lower excitation energy, smaller $\Delta E$).
• Hypsochromic shift (Blue shift): Displacement of an absorption band to a shorter wavelength (higher excitation energy, larger $\Delta E$).
• Hyperchromic effect: An increase in the molar absorptivity ($\varepsilon_{\max}$), reflecting enhanced transition probability.
• Hypochromic effect: A decrease in the molar absorptivity ($\varepsilon_{\max}$), reflecting suppressed transition probability.

Self-check questions

1. Which electronic transitions occur in propanone (acetone, $\text{CH}_3\text{COCH}_3$), and which transition occurs at the longest wavelength?
   Answer: Propanone contains single $\text{C–H}$ and $\text{C–C}$ $\sigma$ bonds, a $\text{C=O}$ double bond ($\sigma + \pi$), and non-bonding lone pairs ($n$) on the carbonyl oxygen atom. Consequently, it exhibits four possible promotions: $\sigma \to \sigma^*$, $n \to \sigma^*$, $\pi \to \pi^*$, and $n \to \pi^*$. Because the $n \to \pi^*$ transition possesses the smallest energy difference ($\Delta E$), it absorbs photons of the lowest energy and therefore appears at the longest wavelength ($\lambda_{\max} \approx 280\text{ nm}$).

2. Why is the $n \to \pi^*$ absorption band of an aldehyde significantly weaker than its $\pi \to \pi^*$ absorption band?
   Answer: The non-bonding orbital ($n$) of the carbonyl oxygen lies in the molecular plane, whereas the $\pi^*$ orbital is oriented perpendicular to the molecular plane. Because spatial orbital overlap between $n$ and $\pi^*$ is nearly zero, the electric-dipole transition integral is formally forbidden by symmetry selection rules. Weak absorption occurs only via vibronic coupling (molecular vibrations temporarily breaking local symmetry), yielding a low transition probability and a correspondingly low molar absorptivity ($\varepsilon_{\max} \approx 10\text{–}100\text{ L mol}^{-1}\text{ cm}^{-1}$), compared to the fully symmetry-allowed $\pi \to \pi^*$ transition ($\varepsilon_{\max} > 10^4\text{ L mol}^{-1}\text{ cm}^{-1}$).

Conjugation and predicting molecular transitions

Effect of conjugation on absorption wavelength

Conjugation

Conjugation occurs when two or more multiple bonds alternate with single bonds (such as $-\text{CH}=\text{CH}-\text{CH}=\text{CH}-$), enabling their $\pi$ orbitals to overlap across the intervening single bonds. This delocalization spreads the $\pi$ electrons over an extended molecular framework, generating a manifold of closely spaced $\pi$ bonding and $\pi^*$ antibonding molecular orbitals.

In a comparable series of conjugated polyenes, extended delocalization systematically narrows the separation between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). As a result, the transition energy $\Delta E$ for the lowest-energy $\pi \rightarrow \pi^*$ excitation decreases. Because photon energy and wavelength are inversely proportional:

where $h$ is Planck's constant ($\text{J}\cdot\text{s}$), $c$ is the speed of light ($\text{m}\cdot\text{s}^{-1}$), and $\lambda$ is wavelength in metres, a diminished HOMO–LUMO energy gap shifts the absorption maximum ($\lambda_{\max}$) toward longer wavelengths (a bathochromic or red shift).

Consider the progression across linear conjugated alkenes:

• Ethene ($\text{CH}_2=\text{CH}_2$, 1 double bond, 2 $\pi$ molecular orbitals): $\lambda_{\max} \approx 169\text{ nm}$ (vacuum UV region).
• 1,3-Butadiene ($\text{CH}_2=\text{CH}-\text{CH}=\text{CH}_2$, 2 conjugated double bonds, 4 $\pi$ molecular orbitals): $\lambda_{\max} \approx 217\text{ nm}$ (near-UV region).
• 1,3,5-Hexatriene ($\text{CH}_2=\text{CH}-\text{CH}=\text{CH}-\text{CH}=\text{CH}_2$, 3 conjugated double bonds, 6 $\pi$ molecular orbitals): $\lambda_{\max} \approx 250\text{ nm}$ (typically $247\text{--}258\text{ nm}$ depending on stereochemistry and solvent).

When conjugation extends over many double bonds, $\Delta E$ decreases into the visible spectrum ($400\text{--}800\text{ nm}$), imparting visible colour to the substance. For instance, lycopene—the red carotenoid chromophore in ripe tomatoes—possesses 11 conjugated carbon–carbon double bonds. Its strong visible absorption band ($\lambda_{\max} \approx 470\text{--}505\text{ nm}$) captures blue-green wavelengths, transmitting brilliant red light to the observer.

Watch out. Do not place benzene ($\text{C}_6\text{H}_6$) at the end of the linear polyene sequence simply by citing its $255\text{ nm}$ band. Cyclic aromatic delocalization gives benzene degenerate frontier orbitals and three distinct absorption bands: an intense allowed band at $184\text{ nm}$, a medium band at $204\text{ nm}$, and a weak symmetry-forbidden band near $255\text{ nm}$. Comparing a forbidden aromatic transition directly with the strongly allowed $\pi \rightarrow \pi^*$ band of an open-chain polyene or cyclic diene is misleading.

Predicting electronic transitions from molecular structure

To determine the allowable electronic transitions for a given molecular species, inspect its constituent chemical bonds and non-bonding valence electrons:

1. Identify $\sigma$ bonds: All organic molecules possess $\sigma$ frameworks (including the $\sigma$ component of multiple bonds). They possess occupied $\sigma$ and unoccupied $\sigma^*$ orbitals, permitting $\sigma \rightarrow \sigma^*$ transitions that absorb in the high-energy vacuum-UV region ($<150\text{ nm}$), outside conventional UV–Vis spectrophotometer ranges ($200\text{--}800\text{ nm}$).
2. Identify $\pi$ bonds: Molecules containing double or triple bonds ($\text{C}=\text{C}$, $\text{C}\equiv\text{C}$, $\text{C}=\text{O}$, or aromatic rings) possess occupied $\pi$ and unoccupied $\pi^*$ orbitals, enabling $\pi \rightarrow \pi^*$ transitions whose spectral intensity depends on symmetry and transition selection rules.
3. Identify non-bonding ($n$) lone pairs: Heteroatoms (such as $\text{O}$, $\text{N}$, $\text{S}$, or halogens) contain non-bonding valence lone pairs occupying $n$ orbitals:
   • Saturated heteroatoms: When bonded strictly via single bonds (alcohols, ethers, amines), they exhibit $n \rightarrow \sigma^*$ transitions (typically below $200\text{ nm}$) in addition to $\sigma \rightarrow \sigma^*$ transitions.
   • Unsaturated heteroatoms: When incorporated into multiple bonds (such as carbonyl groups in aldehydes, ketones, or esters), both $\pi^*$ and $\sigma^*$ acceptor orbitals exist. These compounds exhibit low-energy, symmetry-forbidden (weak) $n \rightarrow \pi^*$ bands alongside intense $\pi \rightarrow \pi^*$, $n \rightarrow \sigma^*$, and $\sigma \rightarrow \sigma^*$ excitations.

Watch out. Distinguish between all possible electronic transitions and symmetry-allowed transitions, and check chemical names carefully. Handwritten notes often mislabel $\text{CH}_3\text{COCH}_3$ as "propanol"; $\text{CH}_3\text{COCH}_3$ is propanone (acetone), a ketone with $n \rightarrow \pi^*$ and $\pi \rightarrow \pi^*$ transitions, whereas propanol ($\text{CH}_3\text{CH}_2\text{CH}_2\text{OH}$) is a saturated alcohol lacking $\pi^*$ orbitals. Furthermore, in aniline ($\text{C}_6\text{H}_5\text{NH}_2$) and phenol ($\text{C}_6\text{H}_5\text{OH}$), the heteroatom lone pair is on a substituent attached to the benzene ring and can delocalize into the aromatic $\pi$ system (giving coupled $\pi \rightarrow \pi^*$ bands with partial charge-transfer character) rather than acting as an isolated carbonyl-type $n \rightarrow \pi^*$ chromophore.

Orbitals and transitions in common organic compounds

Worked concept examples

Self-check questions

1. Question: Why is ethanol suitable as a spectroscopic solvent for recording the UV spectrum of 1,3-butadiene above $210\text{ nm}$?
   Answer: High-purity ethanol contains only $\sigma$ single bonds and non-bonding lone pairs on oxygen, producing transitions ($n \rightarrow \sigma^*$ and $\sigma \rightarrow \sigma^*$) that absorb below its standard solvent cut-off wavelength ($\approx 205\text{--}210\text{ nm}$). Because it remains transparent across the near-UV and visible regions, it does not obscure the primary $\pi \rightarrow \pi^*$ absorption band of 1,3-butadiene ($\lambda_{\max} \approx 217\text{ nm}$).

2. Question: Which transitions occur in benzaldehyde ($\text{C}_6\text{H}_5\text{CHO}$) above $200\text{ nm}$, and how do their intensities compare?
   Answer: Benzaldehyde displays both an intense, symmetry-allowed $\pi \rightarrow \pi^*$ band (due to conjugated aryl–carbonyl $\pi$ delocalization, molar absorptivity $\varepsilon > 10^4\text{ L}\cdot\text{mol}^{-1}\cdot\text{cm}^{-1}$) and a weak, symmetry-forbidden $n \rightarrow \pi^*$ band (arising from oxygen lone-pair excitation into the $\pi^*$ orbital, $\varepsilon \approx 10\text{--}100\text{ L}\cdot\text{mol}^{-1}\cdot\text{cm}^{-1}$) shifted toward longer wavelengths in the near-UV region.

UV–visible spectrophotometer: instrument and applications

UV–visible spectrophotometer

A UV–visible spectrophotometer is an analytical instrument designed to measure the attenuation of ultraviolet and visible radiation as it passes through a chemical sample. Modern analytical laboratories predominantly utilize double-beam spectrophotometers, which split incident radiation into two separate paths to continuously compare the sample against a reference blank. This configuration automatically compensates for source intensity fluctuations, solvent absorbance, and detector drift.

Optical path and working principle

In a standard double-beam dispersive spectrophotometer, light propagates through a coordinated sequence of optical and electronic stages:

1. Radiation generation: A continuous dual-lamp source emits polychromatic radiation spanning the ultraviolet ($200\text{--}400\text{ nm}$) and visible ($400\text{--}800\text{ nm}$) spectra.
2. Wavelength selection: The polychromatic beam enters a monochromator, where dispersing elements isolate an exceptionally narrow band of wavelengths ($\lambda$) transmitted via an exit slit.
3. Beam splitting: A beam splitter or rotating mirrored sector (chopper) divides the monochromatic beam alternately or simultaneously into two optical paths: a reference beam and a sample beam.
4. Sample and reference transmission:
   • The reference beam traverses a reference cell containing pure solvent and reagents, yielding an emergent intensity $I_0$.
   • The sample beam traverses the sample cuvette containing the dissolved analyte, yielding an emergent intensity $I$.
5. Detection: The emergent beams strike a photosensitive detector (either alternately using a single detector or simultaneously using matched paired detectors), converting radiant optical energy into a proportional electric current.
6. Ratio electronics and amplification: An amplifier and ratio circuit compute the ratio between $I$ and $I_0$, correcting for optical baseline drift and system asymmetries.
7. Readout and recording: The microprocessor evaluates the absorbance value and displays the resulting spectrum as an absorbance versus wavelength plot:

Where:

• $A$ is the dimensionless absorbance (optical density).
• $I_0$ is the radiant intensity transmitted through the reference blank ($\text{W m}^{-2}$).
• $I$ is the radiant intensity transmitted through the absorbing sample ($\text{W m}^{-2}$).

Figure: A representative UV–visible absorption spectrum plotting absorbance against wavelength, with peak absorption occurring at $\lambda_{\max}$.

Instrument components