Nuclear Magnetic Resonance Spectroscopy
Nuclei have an intrinsic spin angular momentum just like electrons. The
solutions for nuclei are structured in a similar manner:
nuclear angular momentum vector
spin quantum number (property of nucleus)
, ( 1) , ( 2), ... ,
spin eigenfunction ( , , ,...)
m I I I I
Exercise: Write out specific equations for the cases of I=1/2 and I=1. Use the
vector model to interpret them. Discuss the relationship between I and the
numbers of protons and neutrons present in an atom.
In a magnetic field, the states are no longer degenerate in energy. There are
different energy levels possible (two for nuclei that have spin ½) and transitions
between them can be detected just like in other forms of spectroscopy. The
transition energy depends on several things:
Strength of the applied field (Bo) Magnetogyric ratio of nucleus (contained in the “g” factor) Electronic environment of the nucleus
The transition energy can be expressed (N is the nuclear magneton):
N (1 )
275.051 x 10 / N
[ ] 7.623 (1 )
I o N
I o N
h g B
MHz g B
Examine the data for selected nuclei and compute more specific formulae
OLD NMR: Field (B) was varied and frequency of radiation was held constant
NEW FT-NMR: Field (B) is held constant and frequency is varied in the
neighborhood of 300 MHz (hence the name of the spectrometer).
To ensure that spectra are the same on all instruments, we use a relative scale
called the chemical shift:
6( ) 10H TMS
Exercise: What is the field strength of our instrument? What is the frequency
range corresponding to a 10 ppm window on our instrument?
Exercise: How do you compute chemical shifts in Gaussian? What are the
units? How can you compare to experiment? What is Absolute Shielding?
Conventions and Terminology for C-13 Chemical Shifts
Rationalize the chart above in terms of electronic structure and the induced
magnetic field which can either oppose or align with the applied magnetic field.
Where do Solvents Appear? Additivity Rules for functional Groups
J-resolved spectra: example ethylbenzene