97678 - Molecular Modelling

Learning outcomes

At the end of the course the student knows the theoretical foundations and practical applications of the main models used in computational chemistry, can investigate the electronic structure, the geometric structure, and the dynamics of molecules, can understand simplified forms of calculation programs used in computational chemistry .

Course contents

The course is an introduction to molecular modeling. Models to describe the structure and properties of molecules and crystalline solids will be presented and critically discussed.

The course is organized into different themes:

- general introduction, to place molecular modeling in the current scientific and technological context,

- molecular mechanics and dynamics, presenting general theoretical and practical aspects, focusing on molecular systems in condensed phases,

- electronic structure of one-, two- and three-dimensional crystalline solids, as described via tight-binding approaches.

The course includes theoretical lectures and few computational labs for practical applications on realistic systems.

During the lectures, theoretical concepts will always be complemented by discussing practical applications, following state-of-the-art examples from the scientific literature.

At the end of the course, the students will acquire the basic concepts of molecular modelling, being able to critically approach the study of chemical-physical properties and structure-property relationships of complex systems in condensed phases. 

THEORETICAL PART.


T1. INTRODUCTION

historical background, evolution, developments

early molecular models (molecular geometries and electronic structures)

literature, bibliographic sources, tutorials and reference websites



T2. CLASSICAL MODELS: MOLECULAR MECHANICS

concept of force field

contributions to the force field (bonding and nonbonding interactions):

- bond stretching, angle bending and torsional - potential examples

- electrostatic interactions

- van der Waals interactions, dispersive interactions - examples of potentials

- hydrogen bonding

examples of force fields for molecular dynamics applications on gases, liquids and solids

brief remarks concerning the parameterization of the force fields


T3. CLASSICAL MODELS: MOLECULAR DYNAMICS

equations of motion and their integration

Verlet algorithm, brief introduction to other integration algorithms, analysis and choice of the time-step

introduction to ensembles and thermostats

steps for setting-up a molecular dynamics simulation

examples and essential analysis of the results


T5.INTRODUCTION AND REVIEW OF WAVES

mathematical description of a wave and definition of a plane wave

mathematical description of interference and diffraction phenomena

concepts of wave vector and reciprocal space

discussion about the importance of the wave formalism in modeling condensed phase systems


T6. ELECTRONIC STRUCTURE OF (CRYSTALLINE) SOLIDS

crystal lattices, real and reciprocal space

definition of Brillouin zone and examples

electronic energy dispersion relation:

- free electron

- quasi-free electron (periodic potential)

electronic structure of crystalline solids:

- Bloch's theorem,

- band theory

- density of states (DOS).

Kronig-Penney model

electronic properties of materials: insulators, semiconductors and conductors.

tight-binding approximation for one-, two- and three-dimensional periodic structures.

examples of carbon-based periodic molecular systems:

- 1D, linear chains (carbines)

- 2D, graphene and carbon nanotubes,

- 3D, graphite and diamond



COMPUTATIONAL LABS



EC1. CONSTRUCTION AND VISUALIZATION OF MOLECULAR STRUCTURES

molecular geometry (Cartesian coordinates, internal Z-matrix coordinates)

examples, construction and critical analysis of molecular structures

introduction to visualization programs (Molden, Avogadro, Chimera, VMD, etc.)


EC2. MOLECULAR STRUCTURE

examples of molecular mechanics

examples of potential surfaces and conformer search (introduction to stochastic algorithms and openBabel)


EC3. MOLECULAR DYNAMICS

simple examples of molecular dynamics:

- noble gas

- liquid system (e.g.: water)

- molecular solid

visualization and analysis of results


EC4. ELECTRONIC STRUCTURE OF PERIODIC SOLIDS

integration of the theoretical part with simple examples of band-structure calculations on simple periodic structures

brief introduction to solid-state softwares (e.g., QuantumEspresso, CRYSTAL, Cp2k, etc.)

Readings/Bibliography

Suggested books:

1) Molecular Modelling – Principles and Applications

Andrew R. Leach

(Longman)

2) Molecular Quantum Mechanics

Peter Atkins, Ronald Friedman

(Oxford University Press)

3) Introduction to Solid State Physics

Charles Kittel

(John Wiley & Sons, Inc., EIGHTH EDITION)

 

Scripts and scientific articles will be provided during the lectures.

Teaching methods

The course includes theoretical lectures and computational exercises for practical applications of theoretical methods on real molecular systems.

During the lectures, theoretical concepts will always be complemented by showing practical applications following state-of-the-art examples from the scientific literature

Assessment methods

Oral examination

Teaching tools

1) PC + beamer, openboard, lecture handouts
2) Computer exercises
3) Lecture materials presented in the lab will be made available to the student through the platform VIRTUALE.

Office hours

See the website of Daniele Fazzi