Ateneo - UPO

Introduction to Quantum Mechanics: wave function, operators, probabilistic interpretation. Schroedinger equations, expectation values, time evolution. Particle in a box, harmonic vibrations and anharmonic corrections, angular momentum operator. Hydrogen atom and overview of polyelectron molecules with an introduction to the Hartree-Fock method.
Molecular energies. Calculation and spectra of potential, translational, rotational, vibrational, and electronic energies.
Introduction to Spectroscopy: selection rules, techniques, and spectral interpretation.
Explicit calculation of the molecular partition function using the results obtained in the Quantum Mechanics section.

Notes from the teacher
P.W. Atkins e J. De Paula, "Chimica Fisica", Zanichelli
A.C. Philips “Introduction to Quantum Mechanics”, Wiley
I. Levine “Quantum Chemistry”, Prentice Hall

Provide the students with a quantitative description of molecular energy contributions and molecular spectroscopy. Present the concepts and the basic equations of statistical thermodynamics, showing the connections with classical thermodynamics. Illustrate some concepts of chemical kinetics. Provide a basic knowledge of Quantum Mechanical methods applied to chemistry. Communication skills: the students will be able to use a suitable chemical vocabulary in relation to the course arguments and methods. To develop his autonomous learning skills to deepen arguments of interest and his ability in making judgements and driving conclusions on the arguments treated during the course.

Calculus, Physics, Physical Chemistry I

Theoretical lessons.

Discussion in the classroom to check the learning process during the course. Solution of exercises in the classroom.

Oral exam, concerning the topics of Quantum Mechanics, Spectroscopy and Statistica Thermodynamics developed during the classes, to evaluate the candidate's knowledge and skills deeply and exhaustively.

The first part of the course introduces the quantum treatment of microscopic systems, with particular attention to concepts and techniques useful in the field of chemistry, and atomistic physics in general. The concepts of wave function and operator are defined, the probabilistic interpretation of the wave function is presented, and the basic techniques for quantum measurement and temporal propagation are described.
Model systems are described in detail: particle-in-a-box, energy barriers, and one-dimensional harmonic vibrations. Angular momentum operators are described and solved, and the hydrogen atom is described. Finally, methods for polyelectronic systems are outlined, with the Hartree-Fock equation.
The second part addresses the definition of molecular energy (potential and kinetic, divided into different contributions). For each contribution, the quantum mechanical equations necessary for defining the energy levels are presented (the solution to the equations is almost always qualitative). The fundamental concepts of molecular spectroscopy, Einstein coefficients, and line shape analysis are introduced. The theoretical rudiments of vibrational, electronic, and magnetic spectroscopy are presented. The basics of statistical mechanics, the concept of thermodynamic ensembles, the Boltzmann distribution, and the partition function are introduced. The partition functions associated with the various energy contributions defined in the first part of the course are calculated, and their relationship with macroscopic thermodynamic quantities is shown. Some basic concepts of chemical kinetics, reaction order, the Arrhenius equation, collision theory, and activated complex theory (Eyring) are introduced.

Knowledge and understanding: knowledge of the quantum mechanical treatment of angular mommentum, harmonic oscillator, hydrogen atom and Hartree-Fock method for polyelectronic systems; knowledge and understanding of the various contributions to molecular energy and methods to compute the corresponding spectra; basic knowledge of Spectroscopy; knowledge of the comcepts and applications of Statistical Thermodynamics, for the calculation of patition functions and thrmodynamic functions; achievement of a suitable scientific language.

Applying knowledge and understanding: capacity to interpret rotational, vibrational and electronic spectra using the basic principles of molecular energies and spectroscopy; ability to compute molecular energies and corresponding partition functions; capacity to apply Boltzmann distribution to chemical problems; capacity to apply quantum mechanical methods to solve simple chemical problems.

Making judgements: skill to critically analyze the elements related to Statistical Thermodynamics or Quantum Mechanics in complex and real-life problems ; capacity to analyse critically the spectroscopic applications to real problems.

Communication skills: ability to report on scientific topics, in particular related to physical chemistry, in a precise, concise and clear manner, both in written and oral form.

Learning skills: ability to use the teaching material for a critical and reasoned study, also for a subsequent autonomous acquisition of superior knowledge and for a continuous updating.