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Second semester
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Learning outcomes of the course unit

Knowledge and understanding: The student will acquire basic and advanced tool to describe the quantum mechanical treatment of time-dependent problems as needed to rationally use spectroscopic techniques of interest in chemistry. A few commonly adopted spectroscopic techniques will be described in detail.

Applying knowledge and understanding: The students will acquire the tools to formally describe and rationalize the knowledge about spectroscopic techniques acquired in previous courses (electronic and vibrational spectroscopy, NMR, etc). Moreover the students will be able to plans spectroscopic experiments to acquire molecular information from measurements run on macrosocpic samples.

Learning skills: Students will acquire basic and advanced the technical-scientific language typical of quantum-mechanics applied to time-dependent systems and to the interaction between the radiating field and matter. The student will therefore be able to read and understand advanced technical-scientific literature in the field.

Communication skills: The student will master the specialistic language needed to interact with specialists in the field of chemistry, physics and material science. The student will be able to reliably transmit complex information into a language accessible to the non-specialistic audience while maintain the correctness of relevant information.

Making judgments: The student will re-structure in a formal and on more advanced basis the basic concepts acquired in previous courses about quantum mechanics and/or spectroscopic techniques.


To fruitfully access the course the student must master the basic concepts of quantum mechanics and its application to chemistry.

Course contents summary

Basic concepts: Electromagnetic spectrum, absorbance,Fourier transforms

Electromagnetic radiation

Time dependent perturbation theory (linear order)

Linear response theory

The density matrix

Optical spectrosocpy (electronic and vibrational)

NMR in solution

Course contents

A few very basic concepts:
* the electromagnetic spectrum
* measuring an absorption spectrum: absorbance
* Fourier transforms

Elettromagnetic radiation:
* classic and quantistic description
* radiation-matter interaction

Time-dependent perturbation theory
* general discussion
* absorbance and emission of monochromatic radiation
* electric dipole approximation
* absorbance, spontaneous and stimulated emission

Linear response theory
* responce and susceptibility functions: Steady-state and time-resolved experiments
* density matrix: pure and mixed states, populations and coherences, thermodynamic equilibrium.
* density matrix: temporal evolution
* Steady-state experiments: active and passive processes, Kramers-Krönig relations
* complex dielectric constant: refractive index and extinction coefficient (advanced topic)
* microscopic formulation of the response and susceptibility functions (advanced topic)
* reduced density matrices: relaxation and bandshapes

Optical spectroscopy
* the adiabatic approximation
* selection rules
* vibrational spectroscopy: normal coordinates, internal coordinates, group frequencies, FT-IR and Raman spectroscopies (hints)
* electronic spectroscopy: absorption, Frank-Condon principle and band-shapes, fluorescence, Kasha rule, fluorescence excitation, phosphorescence. Organic chromophores, solvatochromy.
* Optical spectroscopy with polarized light: polarizability tensor. ORD and CD spectra (advanced topic)

Magnetic spectroscopy
* the basic NMR and ESR experiments
* solution NMR: chemical shift and J-coupling
* FT-NMR: basic experiment and some more refined measurements
* systems of many non-interacting spins, density matrices and product operators
* systems of many interacting spins, density matrices and product operators (advanced topic)
* an introduction to 2D- NMR (advanced topic)

Recommended readings

G.C.Schatz, M.A.Ratner, Quantum Mechanics in Chemistry, Dover (2002)
J. McHale Molecular Spectroscopy
S. Fischer, P. Scherer, Theoretical Molecular Biophysics, Springer (2010)
M.H. Levitt, Spin Dynamics, Wiley
lecture notes available to the students on specific topics

Teaching methods

The course develops in 40 hours of frontal teaching during which the students are guided to the understanding of basic and applicative concepts of optical and magnetic spectroscopy. A CFU (15 hours) is devoted to laboratory work, where the student acquire practical skills in fluorescence spectrosocpy.

Assessment methods and criteria

The final oral exam verifies (a) the acquisition of basic and advanced concepts of the quantum mechanics of time-dependent systems, (b) the formal and applied understanding of spectroscopic techniques of interest in chemistry; (c)the ability to express complex concepts in a clear and precise way, properly using the technical-scientific language; (d) the ability to plan spectroscopic experiment to extract specific information; (e) the ability to use the acquired knowledge to solve new problems as required to fruitfully enter the professional life or to face postdoctoral studies.

A successfull approach to (a) and (b) set the minimum requirement to pass the exam. Five points are assigned to (c), four to (d) and three to (e). Laude requires the knowledge of advanced topics as marked in the extended program.

The unsuccessful student is allowed another trial after 2 weeks, but in no case more than twice per session. After 4 unsuccessful exams, the student can access the exam only once per session.

Other informations

Lecture notes are available to the students.

The teacher is available upon request for discussions and clarifications about specific topics.