Molecular physical chemistry [SCHIB303]

Learning outcomes

Master the basics of ab initio calculation (Hartree-Fock method) and be able to perform a numerical simulation to determine the electronic structure of a molecule using the Hartree-Fock method. Master the concepts of spin, molecular orbital and molecular wave function, atomic orbital basis (A.O.B.), density matrix and population analysis, ionisation energy, electro-affinity, electronegativity, hardness, polarizability. Master the notions of statistical thermodynamics leading to the determination of equilibrium constants and rate constants. Master the underlying concepts of partition function, translational, rotational, vibrational and electronic movements.

Objectives

The course consists of two parts: - It continues the teaching of Bac 2. It introduces the notion of electronic spin. It then focuses on the Hartree-Fock method and the determination of the electronic structure of complex molecules (derivation of the HF equation, its interpretation, its implementation) - It introduces the concepts of statistical thermodynamics and shows how to use the quantum structure of matter to determine the thermodynamic functions

Content

Partim 1 Table of contents I. Introduction and reminders I.A. Interpretation of hydrogen wave functions I.B. The independent model II. The spin II.A. The Stern and Gerlach experiment II.B. Pauli matrix formalism II.C. The indistinguishability of electrons and the Pauli exclusion principle II.D. Wave and spin functions of 2 and more electron systems III. The variational method III.A. The Variation Theorem III.B. Applications of the variational method to the helium and hydrogen atom III.C. The problem of linear variations IV. The Hartree-Fock method IV.A. Operators, integrals and matrix elements IV.B. Minimising the energy of a function described by a Slater determinant IV.C. Interpretation of the Hartree-Fock equation IV.D. Closed-layer systems IV.E. The L.C.A.O. approximation and the Roothaan-Hall equations IV.F. A first illustration of the Hartree-Fock method IV.G. The bases of atomic orbitals IV.H. Electron density, charges and population analysis IV.I. A second illustration of the Hartree-Fock method IV.J. A third illustration of the Hartree-Fock method IV.K. A fourth illustration of the Hartree-Fock Partim 2 method 0. Introduction I. Distributions I.A. Configurations and statistical weights I.B. Most likely distribution and partition function I.C. Status functions I.C.1. Internal energy I.C.2. Entropy I.C.3. Helmholtz free energy I.C.4. The pressure II. Perfect gases II.A. Reminder: The particle in a one-dimensional box of length L II.B. The particle in a parallelepipedic box of sides Lx, Ly and Lz II.C. Translational partition function and associated state functions II.D. Interpretation of dU III. Towards a description of real gases III.A. The Born-Oppenheimer approximation III.B. The nuclear Schrödinger equation and translational, rotational and vibrational motion III.C. Rotational movements III.D. The rotation partition function III.E. Vibration movements III.F. The vibration partition function III.G. The electronic score function III.H. The global partition function III.I. CP - CV and the ratio CP/CV = g III.J. Study of some gases III.K. Note on enthalpies of formation IV. Quantum statistics IV.A. Gibbs' paradox IV.B. Indistinguishability IV.C. Fermi-Dirac and Bose-Einstein statistics IV.D. Corrections to lnW and state variables V. Equilibrium constants V.A. Aspects of classical thermodynamics and definition of the equilibrium constant (case of a gas phase reaction) V.B. DGo from statistical thermodynamics V.C. Illustrations of equilibrium constant calculations VI. Speed constants VI.A. Potential energy surfaces VI.B. Determination of the rate constant and transition state theory