Course Identification

Theory and Practice of NMR Spin Relaxation in Liquids

Lecturers and Teaching Assistants

Arthur Palmer

Course Schedule and Location

First Semester
09:00 - 16:00

Field of Study, Course Type and Credit Points

Chemical Sciences: Workshop; Elective; 2.00 points
Physical Sciences: Credit points must be approved by the Board of Studies
Life Sciences: Credit points must be approved by the Board of Studies


9:00-10:30 lecture
11:00-12:30 lecture
3:00-4 mix of problem sessions/tutorials
30 hour lectures plus 10 hour tutorials + exam

On October 11th-12th the course will take place at Wolfson Auditorium.

On the rest of the days the course will take place at FGS room C.





Language of Instruction


Attendance and participation

Expected and Recommended

Grade Type

Numerical (out of 100)

Grade Breakdown (in %)


Evaluation Type

Take-home exam

Scheduled date 1


Estimated Weekly Independent Workload (in hours)



The course will develop the theoretical basis for nuclear magnetic spin relaxation in liquids. The course begins with the Bloch and Solomon equations and extends to the Bloch-Wagsness-Redfield theory for fast-limit stochastic processes, such as rotational diffusion and intramolecular motions. The course continues with the Bloch-McConnell and stochastic Liouville equations for relaxation driven by stochastic processes outside the fast-limit regime, such as chemical exchange. The course concludes with key applications of spin relaxation in modern NMR spectroscopy, including the TROSY effect and characterization of dynamic properties of biological macromolecules. The lectures are augmented by problem and tutorial sessions in which students will work collaboratively, along with the instructor, to reinforce lecture material, to develop expertise in simulating NMR relaxation phenomena, and to gain experience in analyzing experimental spin relaxation data sets.

Lecture 1: Introduction: Review of the Bloch equations density matrix quantum mechanics.

Problem session 1: Example calculations using the Bloch and density matrix formalisms.

Lecture 2:  Introduction to transverse relaxation: Random phase model for adiabatic transverse relaxation and computer simulation of transverse relaxation.

Tutorial session 1: Computer simulations of magnetization phase evolution.

Lecture 3:  Introduction to longitudinal relaxation: Solomon equations and the nuclear Overhauser effect.

Problem session 2: Extensions of the Solomon equations and calculations of spin diffusion.

Lecture 4: Fast-limit relaxation: Bloch-Wangsness-Redfield (BWR) theory and the Redfield equations.

Problem session 3: Deriving rate expressions using the BWR theory.

Lecture 5: Applications of BWR theory and the secular approximation.

Problem session 4: Model calculations using the BWR theory.

Lecture 6: Stochastic physics: Stochastic correlation functions, models for rotational diffusion and internal dynamics, and computer simulations of molecular dynamics.

Tutorial session 2: Computer simulations of stochastic processes.

Lecture 7: Outside the fast-limit: Slow processes and chemical exchange, the Bloch-McConnell equations, and the stochastic Liouville equation.

Tutorial session 3: Computer simulations of chemical exchange processes.

Lecture 8: Cross-correlated relaxation and the TROSY effect.

Problem session 5: Pulse sequence analysis for TROSY experiments.

Lecture 9: Methods and applications of nuclear spin relaxation to characterize fast-limit rotational diffusion and intramolecular dynamics of biological macromolecules.

Tutorial session 3: Analysis of sample nitrogen-15 and deuterium relaxation data sets.

Lecture 10: Methods and applications of nuclear spin relaxation dispersion to characterize chemical exchange dynamic and kinetic processes in biological macromolecules.

Tutorial session 4: Analysis of sample relaxation dispersion and CEST data sets.      


Learning Outcomes

Students will gain both qualitative and quantitative understanding of the main theoretical and experimental aspects of spin relaxation in NMR spectroscopy.

Students will become proficient in performing calculations and computer simulations at an to illustrate theoretical and experimental aspects of spin relaxation.

Students will gain expertise in practical aspects of the use of spin relaxation to study dynamic processes in biological macromolecules by analyzing model data sets.

Reading List