Physical Chemistry II and Laboratory A - L

Module Physical Chemistry II and laboratory (Module 1)

The course is aimed to provide students with the basic physico-chemical knowledge necessary for the understanding of chemical bond, molecular spectroscopy and chemical kinetics. At the end of the course the student will be able to understand the basic principles of quantum-mechanical and spectroscopic methods and their applications to the determination of electronic and geometric structure of molecules. Also, he will  know the basics of chemical kinetics and the main methodologies for the theoretical and experimental study of chemical reactions.

The course aims to contribute to the acquisition of the following transversal skills:

- Knowledge and understanding: develop inductive and deductive reasoning skills and an understanding of chemical bonding, molecular spectroscopy and chemical kinetics.

- Ability to apply knowledge: ability to apply the acquired knowledge to rationally describe the electronic structure and geometry of molecules; ability to extract information from electronic, vibrational and rotational spectra of simple molecules; ability to study the kinetics of chemical reactions from a theoretical and experimental point of view.

- Judgment autonomy: develop critical reasoning skills and be able to correlate theoretical models to the behavior of molecules

- Communication skills: being able to demonstrate a full understanding of the subject with proper scientific language.

- Learning skills: demonstrate the development of of good learning  skills with ability of studying in-depth physico-chemical phenomena and processes

The couse consists of classes and class exercises.

I – The quantum description of atoms and molecules

•  Crisis of classical physics and birth of quantum theory.
•  Postulates of quantum mechanics. Wave functions and operators. Schrödinger equation.
•  Application to some simple systems. Particle in a one-dimensional box. Particle in a three-dimensional box. Tunnel Effect. Harmonic and anharmonic oscillator. Rigid rotor.
•  The hydrogen atom.
•  Polyelectronic atoms. Approximate methods for solving the Schrödinger equation: perturbative methods (outline); the variational method. Helium atom. Orbital approximation. Hartree-Fock self-consistent field method. Correlation energy. Independent electron theory for complex atoms. The Pauli principle. Aufbau.
• The chemical bond in diatomic molecules. Born-Oppenheimer approximation. The molecular orbital method and its application to the hydrogen ion molecule. Overlap, coulomb and exchange integrals and their contribution to the stability of the chemical bond. Bonding and antibonding molecular orbitals. Diatomic molecules with many electrons. Electronic structure in the MO scheme. σ and π orbitals. Aufbau for molecular orbitals. Electronic configuration and properties of homonuclear diatomic molecules.
• Polyatomic molecules. The Huckel method applied to ethylene, butadiene, cyclobutadiene, benzene. Delocalization energy. Charge distributions in a π system. π- and total bond order - Relationship between bond order and bond length. Extension of the Hückel method to heteroatom-containing molecules. Experimental evidence of the existence of molecular orbitals.
• Introductory outline of the electronic structure of solids.

II – Radiation-matter interaction and molecular spectroscopy

• Basic principles of molecular spectroscopy. Interaction of electromagnetic radiation with matter. Time-dependent Schrödinger equation. Time-dependent perturbation theory (outline). Selection rules for radiative transitions. Population of states and Boltzmann distribution. Conventional and non-conventional spectroscopies. Born-Oppenheimer approximation for spectroscopies. Diatomic molecules: separation of vibrational and rotational modes.
• Rotational Spectroscopy. Rotational energy levels and rotational spectra of diatomic molecules. Introduction to the classification of molecules from a rotational point of view (linear, spherical, symmetric, asymmetric) and related spectra.
• Vibrational spectroscopy. Vibrational spectra of diatomic molecules and selection rules according to the model of the harmonic oscillator. Application of the anharmonic oscillator model - Normal modes in polyatomic systems and vibrational spectra. Vibration-rotation spectra of di- and triatomic molecules.
• Electronic spectroscopy. Electronic transitions in diatomic and polyatomic molecules. Selection rules. The Franck-Condon principle and vibronic transitions. Photoelectron spectroscopy. The photoelectron spectrum of CO. Spectra of hydrides the VI group elements. Photoelectron spectra of substituted benzenes.
• The fate of excited electronic states. Photophysical processes. Einstein coefficients, spontaneous emission and stimulated emission. Fluorescence spectroscopy. Lasers and laser spectroscopy. Photochemical processes (outline).

III - Chemical kinetics

• The rate of chemical reactions. Simple kinetic laws and rate constants. Integration of simple kinetic equations. Temperature dependence of reaction rates. Reaction mechanisms. Elementary reactions. Consecutive and parallel reactions. Principle of the detailed balance. The steady state approximation. Complex reactions. Enzymatic kinetics.
• The dynamics of reactions. The collision theory: collision sphere, cross section, impact energy and steric factor. Transition state theory. Experimental study of molecular collisions. Angular distribution and velocities of reaction products. Rebound, stripping and complex formation mechanisms. Potential energy surfaces. The study of ultrafast reactions: femtochemistry (outline).
  

• D.A. McQuarrie, J.D. Simon - Physical Chemistry- A molecular approach - University Science Books
• G.K.Vemulapalli - Physical Chemistry - Prentice Hall
• P.W.Atkins, J. de Paula - Physical Chemistry – Oxford University Press
• P.W.Atkins, R.S.Friedman - Molecular quantum mechanics - Oxford University Press
• J.M. Hollas, Modern spectroscopy - Wiley
• Lecture notes and slides, and further didactic material directly supplied by the teacher.

The student is free to use, in alternative or in addition to the proposed textbooks, any other textbook (university level) of physical chemistry and molecular spectroscopy.

The exam is unified (integrated exam) for the present module (module 1) and laboratory module (module 2). It is aimed to (a) the acquisition of the basic concepts of the course and the ability to connect them with each other and with the experiments carried out in the laboratory; (b) the ability to clearly expose concepts using experimental data by applying scientific language, (the ability to use and quantitatively use the concepts and methodologies acquired during the course.

The exam includes a pre-selective written test and an oral test. The written test is aimed to evaluate the acquisition of the minimum skills concerning the three sections of the program, and the student's ability to apply them to the solution of simple problems similar to those proposed during the course. It will be followed, after a few days necessary for the evaluation of the written tests, by an oral exam that will focus both on the discussion of a laboratory experience and on topics of the theoretical course. It is not recommended to undertake the oral exam if a score lower than 15/30 is obtained in the pre-selective written test. The final mark will take into account both the result of the oral exam and of the laboratory reports, which must be delivered at least 15 days before the exam date.

The Born-Oppenheimer approximation

The UPS spectrum of CO

The steady state approximation