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Vår 2016
KJE-3103 Quantum Chemical Methods - 10 stp
The course is administrated by
Institutt for kjemi
Type of course
Theoretical subject. The course is available as a singular or elective course independent of study program, also to exchange students. The course is offered on condition that a minimum number of students register for the course.
Course overlap
KJE-8103 Quantum chemical methods 10 stp
Course contents
The elucidation of the electronic structure of molecules is a formidable task. The goal is to obtain an accurate description of the wavefunction describing the electrons in a molecule. For that purpose one has to solve the time-independent Schrödinger equation for the electrons. The equation itself is a reasonably simple multivariate differential equation. There are however two main challenges: on the one hand molecules have a large number of electrons (medium-sized molecules have the order of 100 electrons) and the dimensionality of the problem soon becomes so large that standard methods applied to the resolution of differential equations become inapplicable. The second challenge is the accuracy demand. The electronic energy of a medium-sized molecule is of the order of 1000 Hartree (1Hartree ~ 627Kcal/mol) and for chemical processes a difference of 1Kcal/mol (0.002 Hartree) can have large implications determining e.g. which reaction is faster, the equilibrium between two species and the enantiomeric excess. Therefore, the problem not only requires the solution of a differential equation with a large number of dimensions, but to yield meaningful results for chemistry applications, one has do so with very high accuracy (six digits or more).
To deal with this problem, theoretical chemistry has devised a wide range of methods starting from the simplest Hartree-Fock (HF) method to the ¿golden standard¿ of Full Configuration Interaction (FCI). In between HF and FCI are many methods and each of them has its strengths and weaknesses. The course will first introduce the second quantization (SQ) formalism, which provides effective tools to deal with a many-particle system. The features of electronic wavefunctions are thereafter presented, emphasizing those aspects that the different approximate methods will be able to reproduce in their quest for a good approximation to the true wave function. Finally, several wave function methods are presented (Hartree-Fock, Möller-Plesset, Configuration interaction, Multiconfiguration Self Consistent Field, Coupled Cluster) showing their strengths and weaknesses. Particular attention will be dedicated to HF which is the basis for all the more advanced methods. The other methods will be presented at a more cursory level although more attention can be dedicated to a specific method depending on the students¿ interest.
To deal with this problem, theoretical chemistry has devised a wide range of methods starting from the simplest Hartree-Fock (HF) method to the ¿golden standard¿ of Full Configuration Interaction (FCI). In between HF and FCI are many methods and each of them has its strengths and weaknesses. The course will first introduce the second quantization (SQ) formalism, which provides effective tools to deal with a many-particle system. The features of electronic wavefunctions are thereafter presented, emphasizing those aspects that the different approximate methods will be able to reproduce in their quest for a good approximation to the true wave function. Finally, several wave function methods are presented (Hartree-Fock, Möller-Plesset, Configuration interaction, Multiconfiguration Self Consistent Field, Coupled Cluster) showing their strengths and weaknesses. Particular attention will be dedicated to HF which is the basis for all the more advanced methods. The other methods will be presented at a more cursory level although more attention can be dedicated to a specific method depending on the students¿ interest.
Application deadline
Applicants from Nordic countries: 1 June for the autumn semester and 1 December for the spring semester. Exchange students and Fulbright students: 1 October for the spring semester and 15 April for the autumn semester.
Admission requirements
Admission requires a Bachelor`s degree (180 ECTS) in Chemistry or equivalent.
The course also requires calculus and linear algebra knowledge. Other knowledge which is useful in connection with the course is Hilbert spaces, Complex analysis, as well as Electromagnetism.
Local admission, application code 9371 - singular courses at Master's level.
Objective of the course
Knowledge:
The candidate will...
- explain the formal structure of Second Quantization (SQ)
- make use of SQ to obtain one- and two-electron operators
- show the connection between first and second quantization
- employ SQ for states and operators with explicit spin description
- show how to express orbital rotations (states and operators) in SQ
- identify the properties of exact electronic wave functions
- show which properties of a wave function are fulfilled for each of the main classes of wave function method
- explain the main features of the following wave function methods: Hartree-Fock, Mölle-Plesset Perturbation Theory, Configuration Interaction, Multiconfiguration Self Consistent Field Method, Coupled Cluster Theory, Full Configuration Interaction
- derive the Hartree-Fock equations for a closed-shell system from first principles
- show the validity of the Brillouin and Koopmans theorems for Hartree-Fock
- explain the main optimization methods: DIIS, quadratic method, trust-radius method.
Skills:
The candidate will...
- derive the properties of creation and annihilation operators from their commutation relations
- connect number states of SQ to Slater determinants
- show the connection between 1- and 2- electron densities in first quantization (FQ) with their SQ counterparts
- explain the structure of spin free operators, spin operators and mixerd operators
- express orbital rotations in terms of exponential operators
- show the connection between creation operators in the new basis with the ones in the old basis
- use the Backer-Campbell-Hausdorff (BCH) expansion to derive the Taylor expansion of the energy expectation value
- explain the features of the FCI method for H2 in minimal basis
- show strengths and weaknesses of the different wave function methods covered in the course
General competence:
The candidate will...
- explain the use of Second Quantization in quantum chemistry
- show the mathematical basis of the optimization methods used in wave function theory
- show the connection between exact wavefunctions and the approximations used in QC
- show how to find the optimal wave function method given the problem at hand
- use Hartree-Fock theory as a basis for a deep understanding of the main wave function methods
Language of instruction
The language of instruction is English and all of the syllabus material is in English. The reports will be written in English. The questions at the oral exam will be given in English or Norwegian if the candidate so wishes. Answers to questions may be given in English or Norwegian/Scandinavian language.
Teaching methods
Lectures: 30 h, Seminars: 30 h
Assessment
A final oral exam at the end of the course (duration approximately 1h, grade in the A-F scale)
Candidates that receive the grade F can repeat the oral exam the following semester. The reports and their evaluation will be kept unless the student wishes to repeat them.
Students are expected to attend lectures and take part in the seminar sessions.
Candidates that receive the grade F can repeat the oral exam the following semester. The reports and their evaluation will be kept unless the student wishes to repeat them.
Students are expected to attend lectures and take part in the seminar sessions.
Recommended reading/syllabus
Helgaker, Jørgensen, Olsen, Molecular Electronic Structure Theory, Ed. Wiley.
The textbook is also available through the library, and two-three copies can also be borrowed internally from members of the theoretical chemistry group.
Details of the course are given through Fronter, the learning portal of the university. Only registered students for the course will have access to Fronter.
The textbook is also available through the library, and two-three copies can also be borrowed internally from members of the theoretical chemistry group.
Details of the course are given through Fronter, the learning portal of the university. Only registered students for the course will have access to Fronter.