Fundamentals of quantum chemistry 0600-S1-EN-FQCh

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).

Total student workload

Contact hours with teacher: • participation in lectures 20 hrs • classes 20 hrs - laboratory 10 hrs - consultation 15 hrs Self-study hours: • preparation for lectures – 5 hrs • preparation for classes – 20 hrs - preparation for lab work and data analysis – 5 hrs - preparation for the examination - 20 hrs Altogether: 115hrs (4 ECTS) Altogether: 115hrs (4 ECTS

Learning outcomes - knowledge

W1: The student knows and understands the basics of quantum chemistry;, the postulates of quantum mechanics and their application to the description of atoms and molecules, and the theoretical basis of various atomic and molecular spectroscopies. K_W14

Learning outcomes - skills

U1: The student understands the importance of quantization in physics and chemistry. U2: The student can build and solve simple quantum-chemical models. U3: The student is able to independently use the Maxima mathematical package to solve quantum-chemical problems and models. K_U03, K_U04

Learning outcomes - social competencies

K1: The student independently and effectively works with a large amount of information, understands the relationships between phenomena, and draws correct conclusions using the principles of logic. K2: The student thinks creatively to improve existing solutions or create new ones, focuses on the continuous acquisition of knowledge, skills and recognizes the need for ongoing personal and professional development. K3: The student is aware of the limitations of their own knowledge and understands the need for further education. They work systematically and maintain a positive attitude when facing the difficulties in achieving their goals, and they meet deadlines; K4: The student understands the need to work systematically on any projects and recognizes the importance of computer science and computational quantum chemistry in chemical sciences and practice. K5:he student independently implements the agreed goals, makes independent and sometimes difficult decisions, and can search for information in the professional literature without assistance. K_K01, K_K02, K_K03, K_K05, K_K06, K_K07

Teaching methods

Expository teaching methods: Lecture: A conventional lecture using multimedia Classes and Laboratory: The meetings will be divided into two parts. The first part, a traditional approach will focus on understanding basic quantum chemical definitions and models. In the the second part, students will learn the basics of the Maxima package and use the program to solve the problems discussed during the lectures and classes.

Online teaching methods

- cooperation-based methods

Prerequisites

Prerequisites: Elementary mathematics.

Course coordinators

Maria Barysz
Piotr Jankowski

Assessment criteria

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

Practical placement

not applicable.

Additional information

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 0600-S1-EN-FQCh in USOSweb