1. Intermolecular Complexes A Study in Equilibria Using NMR and Optical Spectroscopy

2. Background Material Neutral molecules that are electron deficient ( acceptor – A ) such as s-trinitrobenzene and electron rich ( donor – D ) such as anthracene, can interact to form complexes, DA. The evidence for such a complex is the appearance of color when the (usually) colorless D and A are mixed. The D and A usually form 1:1 complexes according to: A + D DA where the donor and acceptor are in equilibrium according to:

4. The ground state of the complex is mainly neutral and is represented by the wavefunction: where a >> b indicating there is some transfer of charge from the donor molecule to the acceptor. Thus, these are called charge-transfer (CT) complexes or electron-donor- acceptor (EDA) complexes. Similarly, for the excited state of the complex: Where a * >> b * indicates an ionic state.

5. The objective of the experiment is to obtain the equilibrium constant for a CT complex and the molar absorptivity of its CT transition. OPTICAL SPECTROSCOPY OF CT COMPLEXES The total amount of donor and acceptor molecules, regardless of association, are [D] o and [A] o, respectively. Then the equilibrium constant becomes:

6. At the CT transition frequency, the Lambert-Beer Law gives the concentration of the complex: Inserting the spectroscopic values for [DA] into the equilibrium constant expression gives: This may be simplified by taking [D] o >> [A] o but keeping both of these concentrations relatively small, nonetheless.

7. These assumptions produce the Benesi-Hildebrand equation: Which is linear with a slope of 1/Kε and an intercept of 1/ε. Thus measurement of the absorbance of a variety of solution of differing concentrations of donor and acceptor will provide both the equilibrium constant for the complex as well as the molar absorptivity of the CT transition.

8. Determination of Equilibrium Constant by NMR Any equilibrium is dynamic so the D and A molecules are constantly exchanging partners. Rapid chemical exchange will affect the NMR spectrum of the molecules since a complexed molecule is in a different environment than a free molecule. The chemical shift ( δ ) of the protons of the free D and A will differ from those in the complex. The difference in chemical shifts can be analyzed in a similar fashion to that leading to the Benesi-Hildebrand equation. The resulting chemical shift equation is:

9. δ o D – chemical shift of protons in uncomplexed donor δ obs D – observed chemical shift of donor protons in the solution of donor and acceptor δ DA D – chemical shift of donor protons in the pure complex determined by a plot of δ D with concentration of D on the molal concentration scale. This quantity is equivalent to the molar absorptivity m D – molality of the donor solution. The equation may be rewritten in the form of the Benesi- Hildebrand equation:

10. where Δ D obs = δ D obs – δ o D and Δ D DA = δ D DA – δ o D. Note that the last term is not directly measurable thus behaving like the molar absorptivity of the CT complex. It is Obtained from the NMR equation analogous to use of the Benesi-Hildebrand equation to obtain the molar absorptivity. It is desirable to have as simple a NMR spectrum as possible. The complex of hexamethylbenzene (HMB) with tetracyanoethylene (TCNE) provides such a system since all of the protons on the HMB are equivalent and there are no protons on the TCNE.

11. Objective The equilibrium constant for the complex formation will be determined using optical and NMR spectroscopy. The molar absorptivity of the CT band and the chemical shift of the donor protons in the complex will also be determined. These quantities will be calculated by using the Benesi-Hildebrand equation for the optical quantities and a modified form of the equation for the chemical shifts. The value of the equilibrium constant obtained by the two different methods will be compared.

12. Procedure Schedule the 300MHz (or better) NMR for your experiment. Prepare a stock solution of 8 x 10 -6 M TCNE in deuterochloroform. –Dissolve HMB in 2mL of the TCNE solution to make five solutions of differing concentration of HMB (see writeup) Prepare a separate solution of HMB by dissolving 0.08 mole of HMB in 3mL of deuterochloroform.

13. Transfer 0.5mL of the six solutions to clean, separate NMR tubes Measure the chemical shifts of the HMB protons in each sample. The same solutions may be used to measure your optical absorption spectra. Some may have to be adjusted to allow for optimum absorbances. Weigh 1 mL (delivered) of each solution.

14. Analysis of Data Plot [A] o /A {1/Δ obs D } vs. 1/[D] o { 1/m D } and determine best straight line. Determine the molar absorptivity (complex chemical shift) from the intercept. Use the value of the slope and the molar absorptivity (complex chemical shift) to calculate the K from the optical (NMR) data. Compare the values for the K. Explain your results.