Fundamentals of quantum chemistry

Fundamentals of Quantum Chemistry is intended to be an introductory course of the electronic theory of atoms and molecules, focusing on fundamental concepts rather than going deeply into formal details. Particular attention is given to building theoretical models for chemistry, including their origin, validity and limitations. The primary goal of the course is to enhance the understanding of chemistry through basic physics principles. The course also provides an introduction to vibrational, rotational and electronic spectroscopy of atoms and molecules.

Lectures:

Lectures:

1. Blackbody radiation. The photoelectron effect. Particles exhibit wave-like behavior. Atomic spectra and the Bohr model of the hydrogen atom. The Heisenberg uncertainty principle.

2. Postulates of quantum mechanics. The Schrodinger equation. The physical meaning associated with the wave function. Probability.

3. Using quantum mechanics on simple system: the free particle, the particle in a box, the harmonic oscillator, angular motion and the rigid rotator.

4. The hydrogen atom. Eigenvalues and eigenfunctions for the total energy. The hydrogen atom orbitals. The radial probability distribution function.

5. Variational method and perturbation theory.

6. Many electron atoms. Helium. Introducing electron spin. Indistinguishability of electrons. Slater determinants.

7. Quantum states for many-electron atoms and atomic spectroscopy. Good quantum numbers. Terms, levels, and atomic states.

8. The electronic Hamiltonian. H2+ molecule. The ground and excited states. LCAO MO function.

Classes:

1. Observables, operators, eigenfunctions and eigenvalues. Normalisation and orthogonality. Spherical and cartesian coordinates.

2. Operators and their formulation. Hermitian and linear operators. Commutation rules. Eigenvalues and experimental measurements.

3. Operators and quantum mechanics: the free particle, the particle in a box, the two-particle rigid rotator, the harmonic oscillator, and the electronic Hamiltonian.

4. The expectation value.

5. Using quantum mechanics on simple systems: the free particle, the particle in a box, the two-particle rigid rotator, the harmonic oscillator, and the electronic Hamiltonian.

6. The hydrogen atom. Solving the Schrodinger equation for the hydrogen-like ions..

7. Vibrational, rotational and electronic spectroscopy of diatomic molecules. Examples.

8. Independent particle model. Symmetric and antisymmetric wave function. Slater determinants.

9. Many-electron atoms. Good quantum numbers. Terms, levels and atomic states. Examples.

Laboratory:

1. Arithmetic in Maxima: introduction, arithmetic, addition, subtraction, scalar, multiplication, division, powers, exponentiation, , matrix multiplication, square root, float function, large numbers, precision, functions; sin, cos, tg, ctg, ln, linear and nonlinear equations, derivatives, integrals, Taylor series, plots of functions.

2. Maxima and Quantum Chemistry: normalization, operators, commutators, expectation values, plots of eigenfunctions and eigenvalues (energies); the particle in a box, the harmonic oscillator, the rigid rotator, the hydrogen atom and the hydrogen-like ions, radial and angular functions (Legandre polynomials, spherical harmonics, asscociated Legendre polynomials, Hermite polynomials, Laguerre polynomials).

Ideas of Quantum Chemistry, Lucjan Piela, Elsevier 2020, lecture notes.

Lecture: written exam.

Classes: written tests.

Required minimum score levels: satisfactory : 50%, satisfactory plus: 61%, good: 66%, good plus: 76%, very good: 81%.

Laboratory: individual projects

not applicable.