28823 - Physical Chemistry 1

Learning outcomes

After following the course, the student owns the concepts of quantum chemistry and its elementry formalism.  He/she can solve simple quantum chemistry problems and is able to connect experimental chemical evidences to the theory, through numerical calculations and laboratory work.

Course contents

Origins of quantum mechanics

Black body radiation; photoelectric effect; hydrogen atom emission spectrum; wave properties of  matter (De Broglie); Bohr's H atom; Heisenberg indetermination principle.

Schrödinger wave equation and the particle in a box

1D box ; linear operators and eigenvalues problem; commutation of operators; meaning of Y ; applications; average values; 3D box; separation of variables; degeneration.

Quantum mechanics postulates and principles

1 ° postulate: Y describes the state of the system; properties of Y ; 2 ° postulate: quantum operators represent classical variables; angular momentum; properties of eigenvalues; 3 ° postulate: observables are eigenvalues of quantum operators; 4 ° postulate: expression for the average value; 5 ° postulate: dependence of Y on the time; wave functions ortho-normality.

The harmonic oscillator and the rigid rotor

Hooke's law; diatomic molecules, reduced mass, harmonic oscillator approximation; energy levels of the harmonic oscillator; harmonic oscillator model and vibrational spectra of diatomic molecules; Hermite's polinomials; the rigid rotor; molecular rotation of diatomic molecules.

Hydrogen and hydrogen-like atoms

Hamiltonian and wave functions of the H atom. Separability in three 1D wave functions; angular part and spherical harmonics, Y( q , f ) ; Legendre equations, Legendre polynomials and Legendre associated functions; Ylm( q , f ) as wave functions of L2; properties of the components of the angular momentum; commutation between L and its components; radial wave functions, R(r); Overall wave functions Y nlm (r, q , f ) ; meaning of Y nlm and orbitals; R(r), R(r)*R(r) e 4 p r 2 R(r) * R(r) ; p ± 1 e px py orbitals.

Variational principle and  perturbation theory

Definition of the variational principle. Simple examples. He atom. Linear combinations of know functions to set up a trial function. The secular determinant. 1º and 2º order perturbation theory. Application to the He atom.

Multi-electrons atoms

Electronic interaction term. Atomic units Hamiltonian. Slater functions. Hartree-Fock limit and correlation energy. Electronic spin. Spin-orbit coupling and fine structure. Spin wave functions. Overall wave functions and symmetry properties. 6° postulate. Representation of asymmetric wave functions  with Slater determinants. Atomic term symbols. Quantum numbers L, S, J. Electronic configurations Hund rules. Selection rules. Zeeman effect.

Diatomic Molecules.

H2+ and H2 Hamiltonians. Born-Hoppenheimer approximation. Molecular orbitals theory. Overlapping, Coulomb, and exchange integrals. Bonding and anti-bonding orbitals. LCAO-MO treatment of H2.  Energy classification of molecular orbitals. Simmetry of molecular orbitals of omonuclear diatomic molecules. Configurations of I and II groups omonuclear molecules. Eteronuclear diatomic molecules. SCF-LCAO-MO method. Molecular electronic states and molecular term symbols. Symmetry properties. Excited electronic states.

Polyatomic molecules.

Hybrid orbitals. Electronic configurations and structures of H2O and BeH2. Walsh correlation diagram. pelectrons. Hückel theory of molecular orbitals. Butadiene and delocalization energy. Electronic states of benzene and pyrazine.

Laboratory work.

Writing a Fortran computer program to calculate the level's energies for the hydrogen atom, and its applications. Reording and interpretation of an atomic spectrum.

Readings/Bibliography

D.A.McQuarrie & J.D.Simon, "Chimica Fisica" Zanichelli (Bologna) 2000.

 G.K.Vemulapalli, "Chimica Fisica" EdiSES (Napoli) 1998

Teaching methods

The lectures will explain the historical reasons which required the introduction of quantum chemistry, and its elementary chemical applications.

The course also includes:

- demonstrations of simple quantum chemistry problem solving and calculus.

- use of computational programs to calculate electronic energies.

- recording and interpretation of an atomic spectrum.

Assessment methods

The examination can be a written or an oral interview, or a combination of both, depending on the choise of the student. In addition, a report on the laboratory work is required.

Teaching tools

blackboard, beamer (PowerPoint projections), overhead projector, computers, training laboratory equipment

Links to further information

http://www.ciam.unibo.it/free-jets/

Office hours

See the website of Walther Caminati