Molecular Spectroscopy

Abstract

Abstract These lecture notes provide a comprehensive introduction to molecular spectroscopy, beginning with the quantum mechanical description of one-electron atoms and extending to many-electron molecules and their spectroscopic properties. The course first develops the foundations of atomic structure through the Schrödinger equation, atomic spectra, and dipole selection rules, with particular emphasis on hydrogenic systems. The molecular framework is then introduced via the Born–Oppenheimer approximation and molecular orbital theory, starting from the H2+ ion and progressing to many-electron molecules. Key concepts such as linear combination of atomic orbitals (LCAO), Slater determinants, minimal basis approximations, hybridization, delocalized π-orbitals, Koopmans’ theorem, and the Hartree–Fock equations are systematically developed. The second part of the course focuses on molecular transitions and their interaction with electromagnetic radiation. Rotational, vibrational, vibration–rotation, and electronic spectroscopy are treated in detail, including rigid rotor and harmonic oscillator models, anharmonic corrections, normal mode analysis, Franck–Condon factors, Einstein coefficients, absorption, fluorescence, and Raman spectroscopy. Overall, the lectures establish a unified theoretical framework connecting quantum mechanics, molecular structure, and spectroscopic phenomena, providing students with both the conceptual foundations and analytical tools necessary to understand and interpret molecular spectra.