CHEM2304: Quantum Mechanics and Spectroscopy

Department of Chemistry,
University College London,
WC1H 0AJ

T: +44 (0)20 7679 1003

A A A

Course Organizer: Dr W A Brown

Lecturers: Dr K Holt, Prof M B Ewing and Prof N Kaltsoyannis

Normal prerequisite: CHEM1301

Units: 1/2

The aims of this course are to develop further quantum mechanics and thermodynamics and to extend the material of CHEM1301 to spectroscopy.

Assessment is based on Quantum Mechanics, Thermodynamics and one other section.

Students will be able to

apply the fundamental postulates of quantum mechanics to problems with exact and approximate solutions
use molecular orbital theory with diatomic molecules and Hückel theory with p electron systems
apply the second law of thermodynamics to homogeneous and heterogeneous systems
apply thermodynamics to phase equilibria and chemical equilibria
analyse chemical systems using atomic, rotational, vibrational and electronic spectroscopy
discuss the fates of electronically excited molecules

R Silbey, R A Alberty and M G Bawendi Physical Chemistry 4th Edition John Wiley. Earlier editions of Ailbey and Alberty are equally useful.

An acceptable alternative is:

P W Atkins and J de Paula Atkins' Physical Chemistry 8th edition, Oxford 2006; or earlier editions

Quantum Mechanics NK, 9 lectures

Fundamental postulates: the wavefunction, operators, expectation values, the Hamiltonian, the Schrödinger equation, eigenfunctions and eigenvalues.
Exact solutions: the particle in a box, simple harmonic oscillator, rigid rotor, hydrogen atom.
The helium atom: electron spin, ground and excited states of the helium atom.
Many-electron atoms.
Molecular orbitals: the Born-Oppenheimer approximation, potential energy surfaces, linear combination of atomic orbitals, the secular equations.
The two-orbital problem: bonding and antibonding orbitals, zero and non-zero overlap.
Homonuclear diatomics: molecular orbitals, parity, energy levels, bond-order.
Hückel Theory for p electrons: Secular equations, electron populations, bond-order, example of the allyl radical.

Thermodynamics MBE, 9 lectures

The second law of thermodynamics is introduced and its application to chemical systems is developed.
Equilibrium: thermal, hydrostatic, diffusive, and chemical.
Revision of the first law from CHEM1301: calorimetry; flow calorimetry of gases; isothermal and isenthalpic Joule Thomson coefficients and heat capacity.
Partial differentiation; importance of T and p , as variables.
Equalities of the second law of thermodynamics; thermodynamic surfaces; Gibbs and Helmholtz energies; entropy, Maxwell equations; variation of T and p ; Gibbs-Helmholtz equation; van't Hoff equation; integrated second-law equations; Gibbs-Duhem equation.
Homogeneous systems: use of integrals to determine the change in state of a phase. Gas expansions: isenthalpic and isentropic; liquefaction of gases;differences in heat capacities and compressibilities; the speed of sound.
Heterogeneous systems: densities and fields; applications of the Gibbs-Duhem equation; phase equilibrium; vapour pressure and the Clapeyron equation, Trouton's rule.
Tabulated thermodynamic data, calculation of equilibrium constants.

Spectroscopy KH, 9 lectures

Atomic Spectroscopy: The H atom, term symbols, selection rules, absorption and emission spectra for Na, the Helium atom, spectra of many electron atoms.
Molecular Spectroscopy: Born-Oppenheimer approximation, experimental techniques, rotational spectroscopy: selection rules, energy level expressions, intensities, centrifugal distortion, deriving bond lengths.
Vibrational Spectroscopy: harmonic and anharmonic oscillators, selection rules, force constants, vibration-rotation spectra, dissociation energies, hot bands.

UCL Chemistry