Learning objectives
Quantum mechanical description of molecular structure and properties<br />
Prerequisites
Introduction to quantum mechanics (Introduzione alla Meccanica Quantistica). <br />
Course unit content
<br /> <br />A few exact solution of the Schroedinger equations and applicationto molecular problems:<br />the particle in the box -- electronicabsorption spectra of linear conjugated dyes;<br />the harmonicoscillator- vibrations of a biatomic molecule;<br />coupled harmonicoscillators-- vibrations of a polyatomic molecule;<br />rigid rotor andangular momenta -- rotational spectra of biatomocmolecules<br />Interlude: spin<br />The hydrogen atom<br /><br />Symmetry: symmetry operation, groups, representation,irreducible representations, direct product.<br />SymmetryandHamiltonians:symmetry of eigenstates, symmetry anddegeneracy,block-diagonalizationofHamiltonian matrices, non-anishingintegrals<br />Indistinguishableparticles: fermions and bosons<br />Anintroductionto secondquantization: ilharmonic oscillatorsandphonons,generalization tobosons; fermions and Slaterdeterminants,one- andtwo-electronoperators in th eformalism of secondquantization.<br /><br />Approximatesolutions of time-independent problems:<br />perturbationtheory,<br />variazional approach<br /><br />Molecules:<br />adiabaticapproximation,<br />Hydrogen molecule: a short introduction to thevalence bond and molecular orbital pictures of chemicalbond;<br />basicdescriptionof: biatomic molecules,polyatomic moleculesand hybridhorbitals,conjugated molecules, transition metalcomplexes;<br />Model Hamiltonians: ab initio vs semiempiricalmodels<br />Semiempirical Hamiltonians: Huckel and extended Huckelmodels, PPP and ZDO approximations, ...<br />Interacting electrons: SCFsolution and molecular orbitals, an introduction to valencebond and density functional.<br /><br />Molecularspectroscopy:<br />Electromagneticradiation,photons, the dipoleapproximation formatter-radiationinteraction;time-dependentperturbation theory,transition probability,the Fermigoldenrule.<br />One-photon processes: absorption; stimulated and spontaneousemission<br />Opticalspectroscopy:elettronic spectroscopy (selectionrules,Frank-Condon principle,Stokes shift); vibrationalspettroscopy(infrared absorption andRaman scattering,selection rules)<br />Magneticspectroscopy: NMR and ESRbasicexperiments; NMR (chemical shft,dipolarcoupling, J-coupling),FT-NMR,a primer; ESR (an introduction tothe spin Hamilton.)
Bibliography
M.A.Ratner, G.C.Schatz, Introduction to Quantum Mechanics in Chemistry,Prentice Hall (2000) , integrated with chapters from other books,available at local libraries
Teaching methods
Theoretical course, integrated with the experimental work in theLaboratorio di Chimica Fisica (Laboratory of Physical Chemistry)<br />
