FUNDAMENTALS OF SPECTROSCOPY

The course is among the interdisciplinary activities of Master’s Degree Programme in Science and Technology of Bio and Nanomaterials, having the aim of providing graduates with a solid multidisciplinary education in physics, chemistry and biology, and the ability to hold positions of high responsibility in complex process management such as planning, synthesis and characterization of materials, of a biological nature too.
Within this framework, the course will provide a rigorous treatment of the spectroscopic phenomenon, covering the theoretical grounds as well as the corresponding formalism. The course will introduce also some relevant techniques employed for the spectroscopic characterization of biological molecules and macro-molecules, and for the studies on functionalized surfaces.

At the end of the course students should:
- have acquired a deep knowledge and understanding of both the theoretical concepts used in spectroscopy and the different formalisms employed;
- have acquired the knowledge of some relevant spectroscopic techniques for characterizing biological macromolecules and studying functionalized surfaces;
- be able to apply the different formalisms for rationalizing the outcomes coming from the different spectroscopic characterization techniques discussed during the course.

Basic knowledge in calculus (vectors, matrices, differential and integral calculus).

BASIC CONCEPTS OF QUANTUM MECHANICS
Hilbertian vector space, Hermitian operators and their properties. Schrödinger wave equation: time-dependent and time-independent equation. The generalized uncertainty principle; the quantum mechanical virial theorem.
Approximate solutions to the Schrödinger equation: perturbation theory for non-degenerate states and for degenerate states; the variation method. Examples and applications.
Processes of induced absorption, induced and spontaneous emission, and their corresponding Einstein transition-probability coefficients. Transition moment. Electric and magnetic interactions. Selection rules. Classification of spectroscopies. The harmonic oscillator, its eigenvalues and eigenfunctions. Spectroscopy of the harmonic oscillator. Extension to polyatomic system: normal modes of vibration.
The rigid rotator, its eigenvalues and eigenfunctions. The centrifugal distortion effect and its treatment within the framework of perturbation theory.
ROTATIONAL SPECTROSCOPY
The tensor of inertia. Principal axes of inertia and principal moments of inertia. Classification of molecules according to their principal moments of inertia: linear molecules, symmetric tops, asymmetric and spherical tops. Selection rules. Rotational spectrum within the rigid rotor approximation. The effects of centrifugal distortion on the rotational spectrum. The effects of isotopic substitution. Examples of microwave spectra.
INFRARED (IR) SPECTROSCOPY AND SOME EXPERIMENTAL TECHNIQUES
The vibrating diatomic molecule and the anharmonic corrections. The diatomic vibrating-rotator and its selection rules. Polyatomic molecules: selection rules and ro-vibrational spectra. Examples of infrared spectra. Discussion of some relevant modern experimental techniques: Attenuated Total Reflection (ATR) IR spectroscopy, Surface Enhanced InfraRed Absorption Spectroscopy (SEIRAS), Reflection-Absorption IR Spectroscopy (RAIRS), and Diffuse Reflectance Infrared Spectroscopy (DRIFT).
NUCLEAR MAGNETIC RESONANCE (NMR) SPECTROSCOPY
Review of spin angular momentum operators and their properties. Spin rotation and spin projection operators. Spin precession and Larmor frequency. The density matrix formalism and its application in NMR. Radio frequency pulse. Bloch equations and their solutions in laboratory (fixed) axes and rotating axes. Relaxation processes: longitudinal (spin-lattice) and transversal (spin-spin) processes. Description of the NMR instrument. The phase correction.
Descriptions of the main Hamiltonians employed for describing NMR spectroscopy. Direct product spaces. Product operator formalism. In-phase and anti-phase magnetization and their interconversion. Coherence quantum transfer. Description and analysis of some pulse sequences within the product operator formalism. The INEPT experiment (Insensitive Nuclei Enhanced by Polarization Transfer).
Bi-dimensional (2D-) NMR. Homo-nuclear and hetero-nuclear 2D-NMR spectroscopy. Description of some 2D-NMR experiments within the product operator formalism: homo-nuclear COrrelation SpectroscopY (COSY); Double Quantum-Filtered COSY (DQF-COSY); HETero-nuclear CORrelation spectroscopy (HETCOR). Basic concepts of solid-state NMR.
ELECTRON PARAMAGNETIC RESONANCE (EPR) SPECTROSCOPY
Review of the electron spin. Spin labels and spin probes. Description of the instrument. Descriptions of the main Hamiltonians employed for describing EPR spectroscopy. Anisotropy of the g-tensor and of the hyper-fine interaction in solid state samples. Examples and uses of EPR spectra.

For the quantum mechanics part the textbook mainly used in the course is
D. J. Griffiths, “Introduction to Quantum Mechanics”, Cambridge University Press, 2nd edition, 2016.
For the optical spectroscopies, the textbook mainly used in the course is
J. M. Hollas, “Modern Spectroscopy”, 4th edition, Wiley, 2003.
For the magnetic spectroscopies, the textbook mainly used in the course is
N. E. Jacobsen “NMR SPECTROSCOPY EXPLAINED: Simplified Theory, Applications and Examples for Organic Chemistry and Structural Biology”, John Wiley & Sons, 2007.

Some other suggestions on different topics.
A. Lund, M. Shiotani, S. Shimida, “Principles and Applications of ESR spectroscopy”, Springer, New York, 2011.

Oral examination (about 30’).
It consists in a series of questions about the different topics covered in the course; the students will be asked also to apply the different formalisms for describing a given spectroscopic experiment, and to discuss the corresponding outcomes.

Lectures coupled to examples on the use of some dedicated software packages.
The slides employed during each lecture (and the corresponding supplementary material) will be downloadable from the MOODLE web pages.

English

Accessibility, Disability and Inclusion

Accommodation and support services for students with disabilities and students with specific learning impairments:
Ca’ Foscari abides by Italian Law (Law 17/1999; Law 170/2010) regarding support services and accommodation available to students with disabilities. This includes students with mobility, visual, hearing and other disabilities (Law 17/1999), and specific learning impairments (Law 170/2010). In the case of disability or impairment that requires accommodations (i.e., alternate testing, readers, note takers or interpreters) please contact the Disability and Accessibility Offices in Student Services: disabilita@unive.it.

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