In the Laboratory
Study of an AB System within the 1H NMR Spectrum of a Maleamic Acid: Application of Chemical Exchange between Acid–Base Conjugates
W
Pierre Fellmann Institut de Biologie Physicochimique, UMR CNRS 7099, 13 rue Pierre et Marie Curie, 75005 Paris, France Alain Gevertz UFR de Chimie, Service d’Enseignement et d’Instrumentation, Université Paris 7 - Denis Diderot, 2 Place Jussieu, BP 75251, Paris cedex 05, France Christine Cordier* ITODYS, UMR CNRS 7086, Université Paris 7 - Denis Diderot, 1 Rue Guy de la Brosse, 75005 Paris, France; *
[email protected] When two nuclei, for example protons, are either magnetically equivalent or different but strongly coupled (∆ν兾J < 10),1 a first-order analysis cannot explain the NMR spectrum. In these cases, it is necessary to formulate the spin Hamiltonian and to solve the Schrödinger equation. Thus the study of an AB spectrum2 constitutes an interesting probe for methods of quantum chemistry when applied to spectroscopy. However, experimental verification requires compounds with appropriate values of ∆ν兾J; this is particularly difficult to realize for low values of this ratio, especially at high fields (200 MHz in this report). We propose a simple and inexpensive solution to this problem.
spectrum,
The AB Spectrum
or
The quantum treatment of an AB spectrum is described in many textbooks (1). We shall mention only some results. The quantities νk (k = 1–4), νM, νA, νB, 2C, ∆ν, ∆νi, ∆νe are defined on Figure 1. The coupling constant is given by the
(1)
J = ν1 − ν2 = ν3 − ν 4 and the resonance frequencies are calculated by ∆ν ∆ν and νB = νM − 2 2
νA = νM +
(2)
where
(
∆ν = 4C 2 − J 2
)
1
2
and 2C = ν1 − ν 3 = ν 2 − ν 4
∆ν = ( ∆νi ∆νe )
1
(3)
2
The two doublets, A and B, are dissymmetric, the outside lines (intensity Ie ) are smaller than the inside lines (Ii ). Their intensities can be expressed as Ie = Ii
( 2C (2C
− J) + J)
Ie ∆ν i = Ii ∆ν e
(4)
The quantity, νA or νB, deviates from the median frequency of the corresponding doublet where the shift is D =
( ν1
+ ν2 ) − νA = ν B − 2
D = C −
Figure 1. Schematic spectrum of an AB system with the variable defined graphically.
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Journal of Chemical Education
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( ν3
+ ν4 ) 2
( 5)
∆ν 2
Note, for high values of ∆ν兾J (weak coupling), we have an AX system for which Ie ∼ Ii and D ∼ 0. On the other hand, for ∆ν = 0 (A2 system), Ie = 0 and ∆νi = 0 and we observe a single line.
Vol. 83 No. 3 March 2006
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www.JCE.DivCHED.org
In the Laboratory
The Idea
Hazards
To verify the properties of an AB system experimentally, it is necessary to choose adequate values of the ∆ν兾J ratio (2). That requires a set of different compounds, which depends also on the frequency ν0 of the spectrometer: ∆ν = ν0(∆δ)10᎑6. We perform the experiment with a single compound, N-(2-nitrophenyl)maleamic acid, allowing the choice of any value of ∆ν兾J between 0 and 7, at 200 MHz (at ν0 MHz, the range would be 0 to 7ν 0兾200). N-(2-Nitrophenyl)maleamic acid is easy to synthesize (3) from 2-nitroaniline and maleic anhydride, both readily available and inexpensive:
Strong magnetic fields are present in the NMR laboratory. Standard precautions should be used. Dimethyl-d6 sulfoxide is toxic on inhalation, ingestion, and contact with skin. Maleamic acid and its derivatives should be handled with care. Results
NMR Sprectra The spectrum of maleamic acid (a) is shown in Figure 2. Chemical shifts for (a) and (b) are collected in Table 1. Attribution of signals resulted from couplings and considerations about intramolecular electronic effects (aromatic and olefinic protons) and comparative ability to exchange for acidic (broad line) and amide (narrow line) protons, which was confirmed by 2D NMR spectra (not shown). This work is interesting in itself, but we are only concerned with olefinic protons. Spectra of the olefinic protons that give an AB system are shown in Figure 3. We assume that δA and δB are the
The idea is to exploit the fast exchange between basic (b) and acidic (a) forms, mediated by migration of the labile proton.
RCOOH + RCOO −
RCOO− + RCOOH
Fast exchange is understood on the NMR scale, that is, τ
