Guia docente 2023_24 Facultade de Química

Physical Chemistry III: Quantum Chemistry

Contents

Topic	Sub-topic
1. Foundations of the quantum mechanics.	1.1. Origin of the quantum mechanics (experimental facts). Formalisms of the quantum mechanics. Non relativistic quantum mechanics. Atomic units. 1.2. Wavefunction. Constrains of the wavefunction. Wavefunctions for a single particle and a set of particles. Slater Determinants. Interpretation of the wavefunction. Normalization. Molecular and atomic wavefunctions. Separation of movements. 1.3. Operators. Hermiticity. Values for a magnitude. Eigenvalues. Orthogonality. Conmutation. Angular momentum operators. Ladder operators. Symmetry operators. Point groups. Symmetry classification of the wavefunctions (symmetry species). Character tables. 1.4. Half value. Most probable values. Uncertainty. Hypervirial and virial theorems. 1.5. Time-dependent Schrödinger equation. Stationary States (Non-time dependent Schrödinger equation).
2. Molecular translation	2.1. Free particle in 1-dimension and 3-dimension spaces. 2.2. Particle in a monodimentional box of infinite potential walls. 2.3. Particle in a 3-dimentional box. Level degeneration. 2.4. Infinite thick barriers. Reflection and transmission coefficients. 2.5. Finite thick barriers. Tunnelling.
3. Approximate treatments to resolve the equation of Schrödinger.	3.1. Variational Method. Eckart's Theorem. 3.2. Variational functions (linear combinations). Secular determinant. 3.3. Theory of time-independent perturbations in non degenerated levels. 3.4. Theory of independent perturbations of the time in degenerate levels. 3.5. Treatment semiclásico of the interaction radiation-matter: theory of dependent perturbations of the time. Consequences in the interaction inelástica radiation-matter. Integral moment dipolar of transition. Coefficients of absorption and broadcast stimulated. Coefficient of spontaneous broadcast. Half life of the states aroused. 3.6. Distribution of a sample of particles between his levels of energy (statistics of Maxwell-Boltzmann). Intensity of absorption and broadcast of radiation.
4. Molecular rotation.	4.1. Diatomic molecules: rigid Rotor. 4.2. Polyatomic molecules: spherical, symmetric and asymmetric tops. Rigid polyatomic rotors. 4.3. Centrifugal distortion in diatomic molecules.
5. Molecular vibration.	5.1. Harmonic oscillator (diatomic molecules). 5.2. Systems with connected harmonic oscillators (polyatomic molecules). 5.3. Effect of the molecular symmetry. 5.4. Limitations of the harmonic model. Anharmonic oscillator (diatomic molecules).
6. Electronic structure: one electron atoms.	6.1. Electrostatic model. Time-independent Schrödinger equation. 6.2. Results of the electrostatic model. Orbitals. 6.3. Electronic spin. Spin-orbit coupling. Fine structure. 6.4. Hyperfine structure. 6.5. Interpretation of electronic spectra of 1-electron atoms. Zeeman effect.
7. Electronic structure: many electron atoms.	7.1. Electrostatic model. Impossibility to solve Schrödinger equation exactly. 7.2. Description of the Hartree-Fock method. Limitations. 7.3. Angular momentum coupling. 7.4. Interpretation of electronic spectra of polyelectronic atoms.