B016492 - COMPUTATIONAL CHEMISTRY

Italian

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.

1) Ira N. Levine, Quantum Chemistry, Quinta Edizione 2000, PRENTICE HALL, Upper Saddle River, New Jersey 07458
2) P. Atkins e J. De Paula, Chimica Fisica, Qunta Edizione Italiana 2012, Zanichelli Editore

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.

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

Lessons of theory will be held by using board and supported through the projection of slides. In the practice sessions numerical exercises will be solved in several manners: together with the teacher, in small groups of 2-4 students and individually. In addition to the official practice sessions (1 CFU), other sessions will be held, whose attendance is optional.

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

The exam consists of a written and oral test. The student will be admitted to the oral test only in the case the written test will be overcome.

===== WRITTEN TEST =====

The written tests consists of two tests of chemistry and/or physics and of one exercise of computational chemistry chosen among 2 that the student can find in the MOODLE environment. The students who have not overcome the physics and/or chemistry exams are called to go in for the physics and/or physics tests.

The written and oral tests will occur in different days. The written test will contribute by 20% to the final result. The physics and chemistry tests will have only the result "OVERCOME" and "NOT OVERCOME".

The oral test consists of one or more questions, in addition to the possible questions aimed to clarify the written test.

If overcome, the written test will hold till the end of February of the next year. Note that the exercise of computational chemistry will be evaluated only if the physics and/or chemistry tests will be overcome.

The time available to the student for completing the written test will depend on how many exercises he/she will have to do. Specifically, 30 min for each physics/chemistry test and 60 min for the computational chemistry exercise.

===== ORAL TEST =====

The oral test consists of a question about a topic presented in one of the lecture series (Chelli or Smulevich) and will be communicated by e-mail about 2 days before the oral test. An additional argument, chosen by the student, can also be required. Such an argument will concern the topics in the other lecture series. The list of possible questions can be found on the MOODLE environment. During the oral test, questions about the written test can also be done.

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.