# Experiment 6.03 Computational NMR

This collection of exercises uses computer simulations to explore the fundamental features of NMR that make it a uniquely powerful technique for probing the properties and behaviour of molecules.

To run an experiment, click on its name (in blue). Consult the printed notes for this experiment for instructions on how to interact with the applets.

1. Singlet spectrum

Free induction decay and spectrum of an NMR singlet

Here you will see the FID (left) and the corresponding spectrum (right) of an imaginary compound with a single magnetic nucleus, say a proton (1H). The FID is in the "time domain" (seconds) and the spectrum is in the "frequency domain" (Hertz). The general form of the FID is a damped oscillation; for its analytic form see the laboratory instructions.

2. Doublet spectrum

Free induction decay and spectrum of an NMR doublet

This exercise is similar to the previous one, but instead of a single line we see a "doublet", i.e. two lines of equal amplitude separated by a frequency J. This is the kind of spectrum one might see for a nucleus coupled to an adjacent proton (whose resonance is not shown). J would then be the spin-spin (or scalar) coupling constant.

3. Chemical shifts

Identification of compounds from chemical shifts and peak integrals

In simple cases, the structure of a molecule can easily be deduced from the integrals and chemical shifts [Ch2] of the lines in its 1H NMR spectrum, provided the molecular formula is known [p11].

4. Multiplet patterns

Multiplet patterns arising from spin-spin coupling

The interaction between nuclear spins (spin-spin coupling) in molecules in solution produces characteristic patterns in their NMR spectra called multiplets (doublets, triplets etc.) [Ch 3]. In this exercise you are given spectra of a nucleus A coupled to n equivalent X nuclei, whose spectra are not shown. You have to determine n and I, the spin angular momentum quantum number of the X nuclei [pp 24, 29].

5. Spin-spin coupling

Conformational analysis using spin-spin coupling constants

The "three bond" couplings between protons on adjacent carbon atoms, e.g. in the H-C-C-H fragment, depend on the dihedral angle between the two H-C-C planes. In particular, trans (Q = 180 ) and gauche (Q = 60 ) interactions have significantly different spin spin coupling constants (Jt and Jg respectively). The spectrum you are asked to interpret in this exercise is that of the a and two b protons in a conformationally mobile amino acid or peptide.

6. Chemical exchange

Rates of conformational equilibrium from linewidths

The NMR spectra of molecules participating in chemical or conformational equilibria show effects that depend on the rate of the forward and backward processes and the difference in resonance frequencies of the nuclei involved [Ch 4]. This exercise deals with a classic example of such "chemical exchange" effects: the internal rotation of the NO group in dimethylnitrosamine (Fig. 2).

7. Spin lattice relaxation

Spin-lattice relaxation times by inversion recovery

When the populations of the energy levels involved in NMR transitions are disturbed they return to equilibrium (the Boltzmann distribution) by a process called spin-lattice relaxation, in which energy is exchanged between the spins and their surroundings, the "lattice" [pp 56-7]. This process is often exponential, and has a time constant called the spin-lattice relaxation time, T1. The value of T1 for a nucleus is determined by the structure of the molecule (e.g. the proximity to the relaxing nucleus of other magnetic nuclei), and by the rate of rotation of the molecule in solution. The experiment most commonly used to measure T1 values is called the inversion recovery method [p 79]. In this exercise you "perform" a series of inversion recovery experiments on 1,3 dinitrobenzene to determine the relaxation times of its three 1H resonances.

8. Strong coupling

Spectra of strongly coupled spins

The NMR spectrum of a pair of coupled protons with different chemical shifts comprises two doublets - but the intensities of these four NMR lines are only equal, and the doublets are only centred at the two chemical shift positions, when the difference in resonance frequencies of the two spins is much larger than their spin spin coupling.

9. More multiplet patterns

Spectrum of a nucleus coupled to 3 spin-1/2 nuclei

We saw examples in exercise 4 of the multiplet patterns that can arise from the coupling to groups of equivalent nuclei. Here you can see the patterns for a nucleus coupled to up to 3 inequivalent spin - half nuclei (e.g. protons), whose NMR signals are not shown. The variables are the three coupling constants.

Starting with two of the couplings equal to zero, see how the spectrum changes when a second and then a third coupling is introduced. For different values of the three coupling constants you should be able to see a doublet, a triplet, a quartet, a doublet of doublets, a doublet of triplets, a triplet of doublets, a doublet of doublets of doublets and so on.

You can get some rather peculiar patters when some of the coupling constants have integral ratios, or when the sum of two of them equals the third.

Updated February 3, 2009.