B016492 - COMPUTATIONAL CHEMISTRY

Italian

The aim of the course is to provide theoretical background of the chemistry relative to the atomic and molecular nature of the matter and to the key concepts of electronic properties, chemical bond and quantization of physical observables. On the basis of the acquired knowledges, the student should be able to solve problems of computational quantum chemistry in a critical and independent way.

Historical background of quantum mechanics. The Schrödinger equation. Operators. Postulates and fundamental theorems of quantum mechanics. The particle in a box. The harmonic oscillator. Angular momentum. The rigid rotor. The hydrogen atom. The variation method. Electronic spin and the Pauli principle. Many-electron atoms. The chemical bond. Electronic configurations of molecules. The Hückel method.

The knowledge acquired in the courses of chemistry, physics and mathematics is very useful for a fruitful participation to the course.

Lessons of theory (6 CFU) and optional practice (1 CFU) consisting of the solution of numerical excercices.

Written and oral exam.

Historical background of quantum mechanics. Useful mathematical concepts (vectors, complex numbers, differential equations, determinants). Wave functions and probability. The time-dependent and time-independent Schrödinger equation. Operators in quantum mechanics (linear operators, Hermitian operators, eigenfunctions and eigenvalues of a quantum mechanical operator, commutation rules). Postulates and fundamental theorems of quantum mechanics. Physical observables. Orthonormalization of wave functions. The Heisenberg uncertainty principle. The free particle in one-dimension. The particle in a one- and three-dimensional box. Degeneracy of an energy level. The harmonic oscillator: classical and quantum treatments. Eigenfunctions and eigenvalues of the angular momentum of a one-particle system. Wave functions and energy of a two-particle rigid rotor. The hydrogen atom. The variation method. Linear variation functions. Electronic spin and the Pauli principle. Slater determinants. Many-electron atoms. Examples of the helium and litium atoms. Coulombic and exchange energies. The Born-Oppenheimer approximation. The chemical bond. The linear combination of atomic orbitals: LCAO method. Example of the hydrogen molecule ion. Bonding and antibonding orbitals. Electronic configurations of molecules. Hybrid orbitals.The Hückel method. Excercices.

1) Ira N. Levine, Quantum Chemistry (fourth or fifth edition).
2) D.A. McQuarrie e J.D. Simon, Chimica Fisica, Zanichelli editor.

Optional practice will be done for the solution of numerical exercices.