In the Laboratory
W
An ABMX Spin System Study: From Experimental to Calculated Spectra Christine Cordier* ITODYS, Université Paris 7, Denis Diderot, 1 rue Guy de la Brosse, 75005 Paris, France;
[email protected] René Thouvenot,* Hani Amouri, and Michel Gruselle Laboratoire de Chimie Inorganique et Matériaux Moléculaires, Universite Paris 6, Pierre et Marie Curie, 4 place Jussieu, 75252 Paris cedex 05, France; *
[email protected] Generally, it is difficult for students to correlate experimental NMR results with the theoretical spin systems analysis (AM, AB, …) that is developed in a graduate-level course on NMR spectrometry. In this paper, the experimental 1H NMR spectrum of the cation [Co2(CO)5(µ-HC≡CCH2– PΦ2–CH2–PΦ2)]+, which includes both ABX and ABMX subspectra, is provided.1,W A set of additional 1H and 31P NMR spectra applying selective 31P decouplings and 31P broad-band decoupling jointly to proton selective decouplings is given to allow students to clearly analyze such subspectra. From these data, students are able to achieve the full assignment of the signals and to estimate the coupling constants. The theoretical analysis of ABX and ABMX spin models by a quantum mechanical treatment is described. The presence of two types of nuclei that resonate at very different frequencies within the same system greatly simplifies the calculations. When only two nuclei are strongly coupled (AB), the frequency of each line can be calculated easily. This example should encourage students to use this mathematical approach. Finally, the simulation is a good tool to check that students have correctly assigned the experimental spectrum and understood how the scalar coupling J, especially if it is strong, can modify the line frequency. We suggest the following pedagogical approach. 1. From the original FIDs implemented on a PC or a Bruker spectrometer, students proceed to the Fourier transformation to obtain the experimental spectra.
The compound studied, a cationic phosphonium complex (designated C+ throughout the paper), contains one phosphorus atom bonded to a cobalt metallic center of the cluster (P1) and the other one (P2 bearing the positive charge) is linked to a methylene group CH2. This complex C+ is chiral owing to the asymmetry of the basic tetrahedral [Co2C2] cluster structure: + Φ
Φ H3a
P1
C
(CO)2Co
+ C =
H3b P2
(CO)3Co
C C H1
C H2a
Φ Φ
H2b
The three NMR-observable nuclei with high natural abundance (1H, 99.985%; 31P, 100%; and 59Co, 100%) are like so many probes to study this ion. However, only 1H and 31P have to be considered. Actually, the 59Co nucleus because of its high quadrupole moment (Q = 0.40 × 1028 m2) (1) leads only to broad resonances for the nearby nucleus.
2. All the line frequencies from 4.3 to 6.1 ppm (1H NMR) are listed in both the standard and decoupled spectra. 3. The full assignment of the signals and an estimation of the 1H–1H coupling constants are done by the students. 4. The instructor guides the students for the quantum mechanical treatment, explaining the different terms of the Hamiltonian operators and introducing the wave functions and the energy of each stationary state. At this stage, the instructor mentions the basic wave functions that do or don’t mix. (This analysis leads to the expressions listed in Tables 3 [ABX] and 5 [ABMX]). 5. Starting from these background data, students can calculate the frequency of the allowed transitions found in Tables 4 and 6. Therefore, the correlation between the experimental and calculated transitions is possible. 6. The last part of the students’ work is to simulate the spectrum in the frequency range considered above.
The full set of the data required to perform the project is freely available.1 234
Figure 1. (1) 1H NMR spectrum; (2) 1H-decoupled 31P NMR spectrum.
Journal of Chemical Education • Vol. 79 No. 2 February 2002 • JChemEd.chem.wisc.edu
In the Laboratory
Analysis of the Experimental Spectra 1H
and proton-decoupled 31P NMR spectra of C+ are presented in Figure 1 (spectra 1 and 2, respectively). On the phosphorus spectrum, the two signals are easily assigned from their line width. The high-frequency broad resonance (43.0 ppm) is assigned to P1, for which the relaxation time t2 is short because of the quadrupole moment of the cobalt neighbor. The low-frequency signal (26.7 ppm) is attributed to P2. The 1 H NMR spectrum (Fig. 1-1) shows a set of multiplets between 7.2 and 8.1 ppm for the aromatic protons (this NMR range will not be described in the paper). We focus on the four signals (A to D) ranging from 4.3 to 6.1 ppm corresponding to five nonequivalent protons: H1 and the two pairs of diastereotopic protons H2a, H2b and H3a, H3b. The most deshielded line (singlet) is easily assigned to H1.
Under high-resolution conditions, this line appears as a multiplet and it sharpens significantly under 31P broad-band decoupling. This indicates a long-range coupling with P1 and P2. C multiplet results from overlap of two multiplets as shown by the 31P-decoupled spectrum (Fig. 2-8) and the selective proton irradiations (Fig. 2-4–7). Selective 31P-decoupling experiments (Figs. 2-2 and 2-3) allow assignment of the B multiplet and the right part of C to the H2 system and the D multiplet and the left part of C to the H3 system (Table 1). Estimated coupling constants from the experimental spectra are also listed. Neglecting the cobalt nucleus, the rigorous analysis of the 1H spectrum from 4.3 to 6.1 ppm requires consideration of a complex system of seven spins (H1, H2a, H2b, H3a, H3b, P1 and P2). This can be approximated to H1 and to two subsets {H2a, H2b, P2} as ABX system and {H3a, H3b, P1, P2} as ABMX, where the M and X nuclei are P1 and P2, respectively. We will consider only the AB part of both systems. According to the literature, the 2JP–P coupling through a PIII– C–PIII linkage is very weak (≤1.5 Hz) (2), which allows a first-order approximation to be used for this P–P coupling. Quantum Mechanical Treatment of the ABX and ABMX Systems Before the simulation exercise, it is convenient to review the theoretical analysis of the ABX and ABMX spectra assuming spin 1⁄2 and γ positive for all nuclei (3–5). For both systems, the basic wave function, ϕk, and the total spin quantum number, F, (F = Σm i) associated with each stai tionary state, k, are given in Table 2. A transition between the two states Ψ′′ (fundamental state) and Ψ′ (excited state) is allowed when the following general relationship is satisfied: Ψ′*||Ψ′′ ≠ 0, where , the spin Hamiltonian operator, is = z + J with z = Σh νizi i
where
νi =
γi 2π
B 0 1 – σi
and
J =
Σ hJ ijij , i, j i
i j = zi zj +
i+j + ij+ 2
+ and being “raising” and “lowering” operators. Resolving such a scalar product leads to the simple selection rule on the quantum number F : ∆F = 1 for the Table 1. Chemical Shifts and Coupling Constants for Protons in the Range of 4.3 to 6.1 ppm Figure 2. (1) 1H NMR spectrum (no decoupling). (2) Selective decoupling of 31P at 43.0 ppm. (3) Selective decoupling of 31P at 26.7 ppm. (4) BB 31P decoupling plus selective decoupling of the D proton. (5) BB 31P decoupling plus selective decoupling of the B proton. (6) BB 31P decoupling plus selective decoupling of the A proton. (7) BB 31P decoupling plus selective decoupling of the C protons. (8) BB 31P decoupling. NOTE: The ABX system, {H2a, H2b, P2}, simplifies to an AB system when P2 is irradiated (spectrum 3). Also, experiments of selective P1 decoupling (spectrum 2) and BB 31 P decoupling (spectrum 8) modify the ABMX {H3a, H3b, P1, P2} to ABX and AB, respectively.
Nucleus
δ/ ppm
J/Hz H1
H2a
H2b H3a
H1
5.99
—
H2a
5.21
