91910 - Molecular Materials: Properties and Modelling

Learning outcomes

With this course the student acquires knowledge of the main computational techniques useful for the study of molecules and aggregates in their ground and excited states and for the study of static and dynamic properties of molecular materials.

Course contents

Knowledge and understanding of intramolecular properties and intermolecular interactions is fundamental for the design of new molecular materials. Modeling these properties involves choosing and using computational tools based on quantum chemistry or classical mechanics. The course therefore presents, in the first part, an overview of the computational tools available to chemical modeling and, in the second parte, applications to selected case studies concerning the modeling of charge and energy transport properties in conjugated molecular materials.

1. The tools of quantum chemistry.

a) Multi-electronic wave functions: Hartree product and Slater determinant.

b) Expression of the total energy of the polyelectronic molecule: example on H2.

c) Integrals defining energy contributions: core, Coulomb and exchange. Monoelectronic and bielectronic integrals.

d) Derivation of the HF equations.

e) HF equations in matrix form on an atomic basis: Roothan Hall formulation.

f) Orbital basis sets based on Gaussian functions. Polarization functions and diffuse functions. Pople notation.

2. Quantum-chemical methods: beyond the Hartree Fock method.

a) Koopmans' theorem, ionization potential, electron affinity.

b) Unrestricted HF method.

c) Electronic correlation. Coulomb and Fermi holes. Static and dynamic correlation.

d) Density functional theory (DFT).

e) Kohn-Sham equations. Jacob's ladder of functionals.

f) the TDDFT approach.

g) Other methods that introduce electronic correlation with the variational approach: configuration interaction (CI), Full CI, truncated CI, CIS, CID, CISD. Brillouin theorem.

h) MCSCF method, definition of CASSCF, choice of the active space. Outline of MR-CI and CASPT2.

i) Methods that introduce electronic correlation with the perturbative approach: MP2.

l) The concept of size consistency in quantum-chemical methods.

3. Investigation of potential energy surfaces.

a) Topology of potential energy hypersurfaces. Minimum, maximum points, saddle points, transition states.

b) Introduction to methods for optimizing geometries.

c) First order methods, steepest descent. Second-order methods, Newton-Raphson.

d) Cartesian coordinates and internal coordinates.

4. Empirical force fields of molecular mechanics.

a) Main intra- and inter-molecular potential energy terms and their most widely used functional form.

b) Multi-pole expansion and Coulomb expression for electrostatic interactions.

c) The atom type concept.

5. Molecular dynamics  simulations.

 a) Concept of ensemble and phase space in statistical thermodynamics.

b) Discretization of time and integration of the equations of motion in Molecular Dynamics. Example: Verlet algorithm.

c) Molecular Dynamics in ensembles other than NVE through the use of thermal baths. 

d) Initial conditions. Periodic boundary conditions and calculation of intermolecular interactions with the minimum image convention approach and with the use of the cutoff radius.

6. Molecular aggregates.

Case study 1: Charge transport in organic semiconductors:

a)Marcus rate constant and reorganization energy

b)Calculation of internal reorganization energy from the adiabatic potential method 

c) Singlet open-shell conjugated molecules

Case study 2: Excited states of molecular aggregates

a) Kasha’s exciton model

b) J and H aggregates

c) The role of charge transfer states

 

 

 

Readings/Bibliography

A. Leach, “Molecular Modelling Principles and Applications”, Prentice Hall, 2001.

C.J. Cramer, "Essentials of Computational Chemistry", John Wiley & Sons, 2004.

Jan H. Jensen, "Molecular Modeling Basics", CRC Press, 2010.

 

Lecture notes

Teaching methods

The course consists of lectures accompanied by practical sessions in the computer lab. The practical sessions focus on the application of the concepts presented in the lectures to specific case studies. The objective is to train the student to the practical use of the tools of chemical modeling applied to the study of electronic structure properties and intermolecular interactions in molecular materials.

Assessment methods

The assessment of learning takes place through the final exam, which verifies the acquisition of the knowledge and skills expected through the performance of a written test without the help of notes or books, followed by a short oral examination

The written tests consist of a series of questions on the concepts presented in the theoretical lessons and questions that refer to the practical sessions in computer lab.

The overall score of the questions in the written test exceeds 30/30 and the test is considered passed if a minimum score of 18/30 is obtained. If the student does not obtain the score of 18/30 he/she must repeat the test.

Teaching tools

The didactic tools include PC, projector, practical sessions in laboratory.

Office hours

See the website of Fabrizia Negri