May 25, 2020   11:13 a.m. Urban
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Course syllabus 428T0_4D - Theory of Intermolecular Interactions (FCFT - 2019/2020 - post-graduate studies)

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Slovak University of Technology in Bratislava
Course unit code:
Course unit title:
Theory of Intermolecular Interactions
Mode of completion and Number of ECTS credits:
Exam-PhD (6 credits)
Course contents:
1.Introduction to the thermodynamic of real gases. (allowance 2/0)
The equation of state - The virial coefficients. An ultra-simplified theory of the equation of state of dilute gases. An ultra-simplified theory of the equation of state of dense gases
and liquids. Introduction to the statistical mechanical theory of the equation of state.
The Kinetic Theory of gases - The transport coefficients.An ultra-simplified kinetic theory of dilute gases. Introduction to the rigorous kinetic theory of gases.The equations of change and their applications.
c.Intermodular Forces - Intermolecular Potential Energy Functions. Sources of information about intermolecular forces. Contributions to the intermolecular forces. Empirical intermolecular potential functions.

Introduction to the thermodynamic of real gases (continued). (allowance 2/0)
Classical mechanics. Equations of motion in classical mechanics. The Liouville equation. The virial theorem.
b.Molecular collisions in classical mechanics.Summational invariants of an encounter. The trajectories of the individual particles during a collision. The angle of deflection in a collision.
Quantum mechanics. Experimental manifestations of non-classical behavior. Wave-mechanical description of systems. Operators in wave mechanics. Indistinguishability of identical particles. Approximation methods for solving the Schrodinger equation. The quantum mechanical virial theorem.
Molecular collisions in quantum mechanics. Interaction of two-particles: the phase shifts. Probability of an angle of deflection.

3.Electromagnetic basis of intermolecular forces. (allowance 2/0)
Electrostatics. Coulombic interaction between charges and charge distribution.The electrostatic potential and the electric field intensity. Multipole moments. The "one-center" expansion. The "two-center" expansion. Behavior of electric dipoles.
Polarization of matter and the electric susceptibility.Polarizability and polarization. Electric susceptibility in terms of the dielectric constant.The electric susceptibility in terms of the molecular properties.
Maxwell's equations of electromagnetism. Maxwell's equations of Electromagnetism. Maxwell's equations in a vacuum. The scalar and vector potentials; magnetic multipoles. The magnetization of matter. Maxwell's equations for a material medium.
Magnetization of matter and the magnetic susceptibility. The magnetic susceptibility in terms of the magnetic permeability.

4.The theory of intermolecular forces. (allowance 2/0)
Intermolecular Potential Energy Functions. The concept of an intermolecular potential energy function. Separation of electronic and nuclear motions (Born-Oppenheimer separation). Information about intermolecular potentials from the virial theorem.Equivalence of classical and quantum mechanical intermolecular forces.Quantum mechanical calculation of the intermolecular potential energy.
The polarizability of molecules.Variational method for the calculation of polarizabilities.The polarizability of molecular hydrogen. The additivity of bond polarizabilities.Polarizability and other properties of atoms from screening constants.
The London dispersion forces between symmetrical molecules. A simplified theory of dispersion forces based upon the Drude model. Second-order perturbation treatment of dispersion forces. Higher terms in the expression for the dispersion energy. The influence of "retardation" on the dispersion forces at large distances.
Dispersion Forces between Asymmetric Molecules. Dispersion forces between asymmetric molecules at large separations.Dispersion forces between asymmetric molecules at intermediate separations.Energy of dispersion between long conjugated double-bond molecules.

5.The theory of intermolecular forces (continued). (allowance 2/0)
a.Forces between molecules having permanent electric moments. The energy of induction. The potential energy of interaction averaged over orientations. The relative magnitude of the contributions to the intermolecular potential.
b.Hydrogen bonds as electrostatic forces.
c.Quantum treatment of resonance and electrostatic forces. The nature of resonance forces. Quantum interaction of two ideal dipoles in linear molecules.Quantum interaction between two ideal dipoles in symmetrical tops.

The theory of intermolecular forces (continued). (allowance 2/0)
Long-range interactions between a proton and a hydrogen or helium atom. Quadrupole-quadrupole forces between atoms not in 5-states.
b.Intermolecular forces from microwave spectra.
The broadening of lines in microwave spectra. Information about long-range forces from pressure broadening.

The theory of intermolecular forces (continued). (allowance 2/0)
a.Determination of the quadrupole moment of the water molecule. Theoretical determination. Empirical determination.
The potential energy of the crystal lattice. The zero-point energy of the crystal lattice. Determination of the forces between noble gas atoms.

The kinetic theory of dilute gases. (allowance 2/0)
The kinetic theory distribution functions.Physical description of non-equilibrium systems. Physical derivation of the Boltzmann equation. The Boltzmann equation from the Liouville theorem. The distribution in velocities.
Enskog's solution of the Boltzmann Equation. The Enskog series. The first-order perturbation solution. The integral equations. Several important integral theorems.Establishment of a variational principle.
Application of the variational principle (the Sonine polynomial
The formulation of the transport coefficients. Coefficients of diffusion and thermal diffusion. Coefficient of viscosity. Coefficient of thermal conductivity. Explicit formulae for the transport coefficients.

9.Transport phenomena of dilute gases (continued). (allowance 2/0)
The flux vectors and the transport coefficients. Mass transfer and the diffusion coefficients. Momentum transfer and the viscosity coefficients. Energy transfer and the thermal conductivity coefficient.
b.Summary of kinetic theory formulae for pure gases and mixtures. The coefficient of viscosity. The coefficient of thermal conductivity. The coefficient of diffusion. The coefficient of thermal diffusion.
Transport coefficients for simple potentials. Rigid elastic spheres. Point centers of repulsion. The Sutherland model. The square-well potential.

10.Transport phenomena of dilute gases (continued). (allowance 2/0)
a.Transport coefficients for the Lennard-Jones (6-12) potential. The dynamics of a collision; calculation of cross-sections. The coefficient of viscosity of pure gases. The coefficient of viscosity of mixtures. The coefficient of thermal conductivity. The coefficient of diffusion. The thermal diffusion ratio.
Comparison of several spherical non-polar potential functions.
Transport coefficients for polar gases and gas mixtures. Viscosity of pure gases. Viscosity and diffusion for mixtures containing one polar component.

Quantumchemical methods and approaches. (allowance 2/0)
Hartree-Fock method. Molecular orbital, eigenvectors and eigenvalues​​. Correlation energy. Möller-Plesset perturbation theory. Method coupled clusters.
Supermolecular approach. Basis set supperposition error. Counter-poisse correction.
Intermolecular perturbation theories. Symmetrically adapted perturbation theory. Perturbation theories formulated using orthogonalized and biortogonalized molecular orbitals.

Quantum chemical calculations of intermolecular forces. (allowance 2/0)
The interaction between two hydrogen atoms.
The energy of interaction between noble gas stom. Interaction of two helium atoms. Interaction of two neon atoms. Interaction of two argon atoms.
Interaction of a hydrogen atom with a hydrogen molecule. Eyring semi-empirical method. Direct first-order perturbation and dispersion energy calculation.
Interaction between two hydrogen molecules. The chemical or valence energy. The long-range energy of interaction.
Interaction of He with an excited He atom or a proton. The interaction of a normal and a metastable helium atom. The interaction of a normal helium atom with a proton.

Solvent effects on the physical properties of molecules. (allowance 2/0)
Calculations solvation energies. Continuum models - COSMO, IEF PCM. DFT approaches.
Conformation of the molecules in solution.
Calculations of the Nernst and Henry constants.

Last modification made by Ing. Tomáš Molnár on 04/26/2019.

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