- Docente: Francesco Zerbetto
- Credits: 11
- SSD: CHIM/02
- Language: Italian
- Moduli: Francesco Zerbetto (Modulo 1) Fabrizia Negri (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Photochemistry and molecular materials (cod. 8026)
Learning outcomes
The course will develop the knowledge necessary to bridge
molecular, surface and solid state properties and will investigate
also dynamical aspects of matter.
Course contents
Part 1 (F. Zerbetto): The concept of probability stochastic
and Bayesian probabilities. Examples and applications. Link with
the concept of multiplicity.
Further examples and applications of probability
conditioning. Introduction to probability distributions.
Probability distributions: binomial and multinomial distributions,
applications and examples of chemical interest, mean value and
variance, their meaning in chemistry and physics.
Calculation of the first and second moment for some observables.
The case of the expectation value of cos (theta) and cos ^ 2
(theta). Equipartition of energy. The Stirling's
approximation.
Random walk, the discrete model generates a Gaussian function.
Lagrange multipliers, introduction and simple applications.
Boltzmann equation, application to ideal gases: equation of state,
pressure balance between different containers.
The Boltzmann distribution with maximization of entropy, its
modification in the presence of physical constraints, examples and
applications.
Free energy and its meaning, Boltzmann distribution of the free
energy, partition functions, their applications, internal energy
and entropy in terms of partition functions.
Practical examples of partition functions, mean values and
thermodynamic functions. Brief introduction to the unit'of
measurement.
Use of units of measurement in simple examples and for simple
applications. Calculation of the translational partition function,
practical examples.
Partition function of rotational and vibrational degrees of
freedom, applications and examples. The chemical potential from
partition functions. The theory of the activated complex.
Introduction to the model of the disordered lattice. Vapor
pressure, cavitation energy, surface tension, interfacial
tension.
Entropy, energy, free energy and chemical potential of a
two-component system with the model of the disordered lattice, the
Bragg-Williams or mean field model.
Entropy, internal energy, free energy, chemical potential for
ternary systems; standard potential and significance of activity
with the model of the disordered lattice, the binodal curve and its
analytical expression. The spinodal curve, its expression and
simple applications; critical point as the third derivative of the
free energy. Introduction to equilibrium models in statistical
thermodynamics; isosbestic point; cooperative and non-cooperative
transitions. Model for non-cooperative equilibrium, totally
cooperative cases, and first neighbors or Zimm-Bragg cooperation
model. Cooperative model with degeneration. Nucleation and
crystallization. Ising model. Introduction to the Langmuir model
with the disordered lattice model. Michaelis-Menten and its
significance in materials science. Active transport and passive
transport by means of a carrier through an interface. Sabatier's
principle. Binding polynomials. Multiple binding by means of the
binding polynomials, Scatchard plot, Hill plot; micelles.
Formation of multilayer and the BET model. Pauling's cooperativity
model. Binding with relaxation; model of multiple binding with
excluded volume.
Introduction to the physical chemistry of polymers. Entropy and
internal energy according to Flory-Huggins, comparison with the
case of non-polymeric solutions.
Introduction to Dissipative Particle Dynamics, comparison with the
model of disordered lattice, computer simulations and practical
examples.
Flory-Huggins: free energy, chemical potential, miscibility of
polymers, the partition coefficient, dependence on the length of
the chain.
Flory-Huggins parameter at the critical point, <r>
<r^2>, Kuhn's model, random walk and probability of
cyclization.
Polymer radius; elasticity in one dimension; elasticity of many
chains for generic deformations. Entropy, internal energy and free
energy as a function of the density of the polymer: theta
conditions," poor "and" good " solvents.
Part 2 (F. Negri):
Program: The knowledge and understanding of intra-molecular properties and intermolecular interactions is fundamental for the design of new molecular materials. The modeling of these properties requires a critical choice and use of computational tools based on quantum-mechanics or classical mechanics The course therefore presents a panorama of the tools offered by computational chemistry for modeling charge and energy transport properties in conjugated molecular materials.
Content.
1. Molecular materials: organic semiconductors.
a) P and n doping of organic and inorganic semiconductors: effect of doping on orbital levels of organic chromophores.
b) Comparison between HOMO-LUMO levels and work function of metal electrodes. Charge injection and transport inside the semiconductor.
c) Band and hopping regimes for charge transport in organic semiconductors. Polaronic charge carriers .
d) Excitonic interaction. Frenkel states and charge transfer states.
e) Rate charge transfer described by Marcus equation: electronic coupling and electron-phonon coupling.
f) Intramolecular reorganization energy: adiabatic potential method and determination of Huang-Rhys factors to estimate intramolecular reorganization energies.
g) Direct and indirect methods for the calculation of electronic and excitonic couplings.
h) Anisotropy of charge transport and effects induced by thermal disorder.
2. Methods for the characterization of potential energy surfaces.
a) Topology of potential energy hypersurfaces. Minima, maxima, saddle points, transition states.
b) Introduction to algorithms for geometry optimization.
c) First order methods, steepest descent. Second order methods, Newton-Raphson.
d) Cartesian coordinates and internal coordinates.
3. Computational methods for the evaluation of intra- and inter- molecular properties with quantum-chemistry tools.
a) Poly-electronic wave-functions: Hartree product and Slater determinant.
b) Derivation of the total energy expression for H2 a simple polyelectronic molecule.
c) Core integrals, Coulomb and Exchange integrals. Mono-eletronic and bi-electronic integrals determining the energy expression.
d) Derivation of HF equations.
e) HF equations in matrix form on atomic basis: Roothan Hall formulation.
f) Orbital basis sets based on Gaussian wavefunctions. Polarization and diffuse functions. Pople notation.
4. Quantum-chemical methods: beyond the Hartree Fock.
a) Koopmans's theorem, ionization potential, electronic affinity.
b) Unrestricted HF.
c) Electronic correlation. Coulomb and Fermi hole.
d) Methods based on density functional theory (DFT).
e) Kohn-Sham equations. Local density, gradient corrected, and hybrid functionals. Introduction to long range corrected functionals and to the TDDFT method.
f) Other methods introducing electron correlation with the variation approach: configuration interaction (CI), full CI, truncated CI, CIS, CID, CISD. Brillouin's theorem. Introduction to MCSCF, definition of CASSCF, choice of active space. Introduction to MR-CI and CASPT2.
g) Methods introducing electronic correlation with the perturbation approach: MP2. The concept of size consistency in quantum-chemical methods.
5. Molecular dynamics and empirical force fields.
a) Statistical thermodynamics: ensemble definition and phases' space.
b) Time step discretization and equation of motion integration in molecular dynamics. Example: derivation of the Verlet algorithm.
c) Molecular dynamics in ensembles different from the NVE using thermal baths.
d) Comparison between molecular dynamics and Monte Carlo simulations as regard their application to flexible chemical systems.
e) Initial conditions. Periodic boundary conditions and calculation of intermolecular interactions with the approach of the minimum image convention and using a cutoff radius.
f) Equilibration. Trajectory analysis and temporal average calculation. Radial distribution function for gases, liquids and solids. Root mean square displacement and relation to the diffusion coefficient.
g) Transport phenomena. Derivation of the diffusion equation or Fick's second law. Brownian motion and Gaussian probability. Derivation of the Einstein equation for the diffusion.
h) Molecular mechanics empirical force fields. Fundamental terms and their general functional form. Multipolar expansion and Coulomb equation for electrostatic interactions. Atom type concept.
Auto-correlation functions. Brief introduction to kinetic Monte Carlo simulations for the investigation of transport properties.Readings/Bibliography
K.A. Dill, S. Bromberg, Molecular Driving Forces, Garland
Science
A. Leach, “Molecular Modelling Principles and Applications”, Prentice Hall, 2001.
Lectures notesTeaching methods
This course is formed by frontal lectures accompanied by problem solution and sessions in the computational laboratories. During laboratory sessions the student applies the notions acquired by following the frontal lectures and learns how to choose and use the tools of chemical modeling applied to the study of chemical properties and inter-molecular interactions.
Assessment methods
Written examination with a number of questions and problems. The time allocated for the written examination is 2 hours for each module. The total score exceeds 30/30. Module 1 also requires a viva.
The final mark of the course “ Proprietà di materiali molecolari” is calculated as the weighted average on the basis of the credit numbers of the two modules: Module 1, Prof. Zerbetto, and Module 2, Prof. Negri.Teaching tools
PC, projector, Power Point presentations, blackboard
Office hours
See the website of Francesco Zerbetto
See the website of Fabrizia Negri