FCK3313 Quantum Chemistry 9.0 credits

The course consists of two parts. The essential quantum mechanics that is required later is covered in the first part. The basic quantum mechanical principles and their applications to model systems once mentioned in the basic course are discussed in detail. Approximative methods are introduced. The interaction between electromagnetic radiation and molecules is discussed, which then leads to the basic principles of various optical (such as infrared and Raman) spectroscopies.

Methods of quantum chemical calculations and their applications in chemistry and biochemistry are treated in the second part of the course. The Hartree-Fock method, its theoretical background and implementation but also post-Hartree-Fock methods and the density functional theory are described and discussed. Their application for calculating molecular properties such as energies, molecular geometries, vibrational spectra and features of chemical reactions is introduced and illustrated. This part of the course includes quantum-chemical calculation assignments, where a modern quantum chemical software package is used for computing molecular properties and chemical reactions.

• the theoretical basis and framework of quantum mechanics
• quantum mechanical behavior of simple systems such as harmonic oscillator and rigid rotor
• the basic properties of the spin and the framework that can be applied in spin quantum mechanics
• explanation of the indistinguishability of quantum mechanical objects and the consequences of this with emphasis on the Pauli principle
• the theoretical basis for time-dependent perturbation theory and how it can be used to consider the interaction between electromagnetic radiation, atoms and molecules
• Born-Oppenheimer approximation and emergence of spectroscopic selection rules
• the theoretical basis behind the variational method and linear variation functions and application of these methods to simple atomic and molecular systems, such as the hydrogen atom, the hydrogen molecule and molecule ions
• construction of many-electron wavefunctions as Slater-determinants based on single-electron wavefunctions within the orbital-approximation, and how the properties of these approximate wavefunctions compare to more exact wavefunctions
• the theoretical basis and approximations behind the Hartree-Fock method, and how these approximations affect the accuracy and the applicability of the Hartree-Fock methods for calculations on atomic and molecular systems
• how the Hartree-Fock method is implemented using Roothans equations in modern quantum chemical programs
• the theoretical basis behind post-Hartree-Fock and density functional theory methods and their implementation and use in quantum chemistry
• calculation of molecular properties and analyzing chemical reactions using modern quantum chemical software

After completion of the course the student should have the knowledge and ability to:

• Describe in detail the formalism of quantum mechanics, relate to, reflect over, and summarize the concepts of quantum mechanics in order to define, calculate and explain the behavior of quantum mechanical model systems.
• Describe, reflect upon, explain and apply basic quantum chemical theory for atomic and molecular many-electron systems to the computation of molecular properties, chemical reactivity and molecular spectroscopy.

Eligible for studies at the third-cycle level.

D. J. Griffiths: Introduction to Quantum Mechanics, 2nd ed
A. Szabo and N. S. Ostlund, Modern Quantum Chemistry, Dover, 1995

If the course is discontinued, students may request to be examined during the following two academic years.

• LAB1 - Laboratory work, 3.0 credits, grading scale: P, F
• TEN1 - Written exam, 6.0 credits, grading scale: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Tore Brinck

Istvan Furo

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

The course replaces course F3B5201 - Molecular Spectroscopy and Quantum Chemistry. Given jointly by the master course KD2360.