Università degli Studi di Perugia

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Chemical sciences
Study-unit Code
Theoretical chemistry and computational modelling
Francesco Tarantelli
  • Francesco Tarantelli - Didattica Ufficiale
  • 63 ore - Didattica Ufficiale - Francesco Tarantelli
Course Regulation
Coorte 2019
Learning activities
Discipline chimiche inorganiche e chimico-fisiche
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
Advanced quantum mechanics. Perturbation theory. Angular momentum algebra. Spin and spin eigenfunctions. The Hartree-Fock method (RHF, UHF). Second quantization. Creation and annihilation operators. Post-Hartree-Fock methdos. RPA. Configuration Interaction. CAS-SCF. Coupled-cluster. Green's functions. Density-functional theory. Time-dependent perturbation theory.
Reference texts
Lecture notes written by the teacher.
Educational objectives
The student will get to know the main tools and methods of theoretical chemistry. The student will understand the theoretical and computational aspects of post-Hartree-Fock methods and will be able to assess their practicability, advantages and limits in the context of modern computational chemistry.
It helps proficiency if the student already has some familiarity with the basic concepts of quantum mechanics and the orbital model in chemistry.
Teaching methods
Frontal lectures aided by slides written on-the-fly and projected. The slides are collected in a pdf file at the end of each lecture and made available to the students.
Other information
The teacher may be contacted at any time via email for appointments, questions and further assistance.
Learning verification modality
Oral examination. The student will be asked two/three questions in order to assess his/her degree of understanding and critical evaluation of the main subjects. He should be able to assist his/her presentation by writing the main schemes or equations involved. The exam duration does not normally exceed 20 minutes.
Extended program
The postulates of quantum mechanics. Wave-packet and its motion. Physical observables and operators. Eigenvalues and eigenfunctions. Hilbert space and variational principle. Heisenberg relations. Schrödinger equation and evolution operator. Stationary states and resonances. Heisenberg representation. Density matrices.
Rayleigh-Schrödinger perturbation theory and Brillouin-Wigner perturbation theory. RSPT calculations. Matrix perturbation theory. Effective hamiltonian.
Antisymmetry and spin. Angular-momentum algebra. Spin eigenfunctions. Spin and Hartree-Fock theory. RHF. Direct-SCF. Moller-Plesset perturbation theory. Basis-set superposition error.
Creation and annihilation operators. The hamiltonian in second quantization. Field operators and density operator. Thouless theorem and HF stability. The RPA method. Coupled-cluster and Configuration Interaction. Size consistency. CASSCF method.
Green's functions. One-particle GF and its spectral representation. Ionization spectrum. Dyson equation and approximation methods.
Density Functional Theory. Hohenberg and Kohn theorems. Thomas-Fermi model. Kohn-Sham equation. Exchange-correlation functionals.
Time-dependent hamiltonian. Sudden approximation. Intermediate representation. Perturbation series for the time-evolution operator. Linear-response theory. State transitions.
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