Atomic and Molecular Spectra Fundamentals

The electromagnetic spectrum is continuous, extending from low-frequency radio waves to high-energy gamma radiation. Named regions describe useful ranges rather than fixed physical endpoints. Spectroscopy selects a region and interaction suited to the property being investigated.

In vacuum, c = λν relates wavelength and frequency, and E = hν gives photon energy. Spectroscopic wavenumber is 1/λ; when wavelength is in centimetres, its unit is cm⁻¹. Frequency remains fixed when light enters a medium, while wavelength changes with propagation speed, so state which wavelength convention is being used.

Different spectral regions probe different interactions. UV-visible radiation commonly drives electronic transitions; mid-IR, approximately 4000–400 cm⁻¹, probes molecular vibrations; microwaves can probe molecular rotation; and radiofrequency radiation probes nuclear-spin transitions in an applied magnetic field. XRF uses characteristic X-ray emission after excitation, whereas XRD measures diffraction from ordered structure.

The reason each region drives a different technique is straightforward: the photon energy must match the spacing of the transition you want to excite. Electronic transitions in organic molecules sit at a few electron-volts and that is the UV-Vis region. Vibrational transitions sit at tenths of an electron-volt and that is the IR region. Rotational transitions sit at thousandths of an electron-volt and that is the microwave region.

Nuclear-spin transitions in a magnetic field are commonly probed by radiofrequency excitation. Energy scales depend on the nucleus and magnetic field. A technique can also probe a vibrational energy difference through Raman scattering using visible or near-IR incident light, so the incident spectral region is not always the same as the measured transition gap.

Atoms and atomic ions have quantised electronic states. The simple hydrogenic model gives approximate energies proportional to −Z²/n², including about −13.6/n² eV for hydrogen. Real precision spectroscopy includes additional effects, and multi-electron atoms require a more complete treatment than inserting a shielding correction into the hydrogen formula.

Absorption can excite an allowed transition when the radiation overlaps its spectral profile. An excited species may emit a photon on relaxation or transfer energy through non-radiative processes. Cascades through intermediate levels mean that emitted photons need not always have the energy of the original absorbed photon.

Sodium has familiar visible D-lines near 589 nm. Neutral mercury has a prominent line near 253.7 nm. Accurate wavelengths, level assignments and transition probabilities should be obtained from an evaluated source such as the NIST Atomic Spectra Database rather than inferred from a colour alone.

Other useful analytical lines include calcium near 422.7 nm, potassium near 766.5 nm, lead near 283.3 nm and arsenic near 193.7 nm. A line assignment needs adequate spectral discrimination, background assessment and reference information. One unresolved peak can include more than one contribution.

This is the entire physical basis of atomic spectroscopy in a forensic lab. AAS reads the absorbance of a hollow-cathode lamp's element-specific line by atomic vapour from the sample (lead in a paint chip dissolved in nitric acid; mercury in fish tissue cold-vapour generated).

AES and ICP-OES detect optical emission from excited species. ICP-MS instead uses a plasma to generate ions and separates them by mass-to-charge ratio. XRF measures characteristic X-ray fluorescence after excitation.

Real lines have finite profiles shaped by natural, Doppler, pressure and other broadening effects, together with instrumental resolution. Spectral overlap and structured background can affect atomic measurements. Suitable line choice, background correction and calibration depend on the element, matrix and actual method; no generic national standard substitutes for that assessment.

A molecule has all the electronic levels an atom has, but it also vibrates and rotates. Each electronic state therefore carries a stack of vibrational sub-levels, and each vibrational sub-level carries a stack of rotational sub-levels.

Molecular transitions can involve electronic, vibrational and rotational structure. Closely spaced transitions can merge into bands at the available resolution, particularly in condensed phases. Gas-phase spectra can resolve much finer structure; broad bands are not an unavoidable feature of every molecular measurement.

The vibrational modes of a non-linear molecule with N atoms are 3N - 6 in number (3N - 5 for linear molecules). They split into two families. Stretching modes change bond lengths, either symmetrically (both bonds extending and contracting in phase) or asymmetrically (one extending while the other contracts). Bending modes change bond angles, with four named varieties: scissoring (in-plane symmetric bend), rocking (in-plane asymmetric bend), wagging (out-of-plane symmetric bend) and twisting (out-of-plane asymmetric bend).

A normal mode has a frequency influenced by masses, force constants and coupling, but it appears in an IR spectrum only if the relevant dipole-moment condition is met. Approximate group-frequency regions can help assign features: many carbonyl stretches occur around 1,700 cm⁻¹, while hydrogen bonding can broaden and shift O–H bands. The exact position depends on the chemical environment.

For a centrosymmetric molecule in the usual vibrational electric-dipole and polarizability framework, the mutual-exclusion rule prevents a mode from being both IR- and Raman-active. Some modes can be inactive in both. This rule does not require every vibration in every molecule to appear in exactly one of the two spectra.

IR activity requires a change in dipole moment; Raman activity requires a change in polarizability. For a centrosymmetric molecule, a mode cannot be both IR- and Raman-active. That mutual-exclusion statement is not a universal rule for all molecules.

Rotational structure is often most readily resolved in appropriate gas-phase experiments; pressure, temperature and resolution affect visibility. NMR probes nuclear-spin behaviour, while EPR/ESR probes suitable unpaired-electron spin systems and commonly uses microwave excitation. These methods require a magnetic field and cannot be explained by molecular vibration alone.

When a photon meets a molecule, three things can happen. The photon can be absorbed, promoting the molecule to an excited state and disappearing from the beam. The molecule can return to the ground state and emit a photon, often at a different wavelength because some of the excitation energy has dissipated as heat.

Or the photon can scatter off the molecule, either elastically (no energy change) or inelastically (a small energy exchange with a vibrational mode). Each outcome is the basis of a family of techniques.

Absorption methods include UV-Vis electronic spectroscopy, IR vibrational spectroscopy and atomic absorption. Beer–Lambert behaviour can support quantitative optical measurements under suitable conditions. NMR detects nuclear magnetisation through a different experimental and quantitative framework; A = εbc is not a universal equation for every spectroscopy technique.

Emission techniques include atomic emission (AES, ICP-OES) where excited atoms in a flame or plasma radiate their characteristic lines, and molecular fluorescence and phosphorescence where electronically excited molecules drop back to the ground state.

For a typical closed-shell organic molecule, fluorescence commonly involves emission between states of the same spin multiplicity, often S₁ to S₀. Phosphorescence involves a change of multiplicity, often T₁ to S₀. Fluorescence is often faster, but actual lifetimes depend on the system, coupling and competing pathways rather than fixed universal time intervals.

Rayleigh scattering is elastic: the photon changes direction without the Raman energy exchange. Raman scattering is inelastic, with the scattered photon losing or gaining energy corresponding to a molecular excitation or relaxation. The measured shift supplies vibrational or rotational information; fluorescence and background can complicate an actual spectrum.

Spectral regions guide method selection, but interpretation also requires the actual interaction. UV-Vis often examines electronic transitions and mid-IR examines vibrations. A carbonyl band or a visible absorption maximum supports a chemical hypothesis; position alone does not uniquely identify a molecule in an unknown mixture.

NMR resonance frequencies depend on the nucleus and magnetic field. Chemical shifts describe relative nuclear environments and also depend on solvent, temperature and reference conventions. Higher field can improve chemical-shift dispersion in hertz, but it does not automatically resolve every isomer or establish a seized material’s structure.

XRF and X-ray absorption involve electronic processes including core-level interactions. XRF measures characteristic fluorescence after excitation, while absorption measurements can probe edge and local-environment information. XRD is different: it measures diffraction associated with ordered structure rather than assigning a core-electron transition to each reflection.

SEM-EDS uses an electron beam to generate characteristic X-rays and can examine elemental associations at selected locations. XRF uses X-ray excitation. XRD probes ordered structure through diffraction. Morphology, elemental composition and crystalline phase answer different questions, and none alone establishes a unique forensic origin.

The forensic relevance of the line-vs-band distinction is direct. Line spectra fingerprint elements; that is why AAS and ICP-OES are the techniques of choice for "is there arsenic in this viscera, and how much".

Molecular spectra can support comparison or structural interpretation when diagnostic features and reference evidence are adequate. Isotope measurements answer another question: for example, strontium ratios in suitable material can be compared with environmental and biological information. They may constrain possible origins but do not uniquely locate a person by themselves.

Evaluated reference databases, method documentation and suitable standards support spectral interpretation. Their scope matters: an atomic wavelength database supplies different information from a forensic identification scheme or an instrument operating procedure. Use each for the question it actually addresses.

A practical interpretation sequence is to identify the physical quantity on each axis, confirm units and acquisition conditions, assess reference and blank data, and then examine whether the signal supports the proposed assignment. A Raman shift, an IR wavenumber and an elemental mass-to-charge ratio are not interchangeable merely because all appear as peaks.

Related reading: UV-Vis Spectrophotometry and the Beer-Lambert Law.

Related reading: Fluorescence and Phosphorescence Spectroscopy.

Related reading: Raman Spectroscopy and Comparison with IR.

Related reading: Nuclear Magnetic Resonance (NMR) Spectroscopy.