IntroductionTheory of NMR spectroscopyKineticsExperimentalData analysisWritten laboratory reportReferencesReferencesExperiment 7: Dynamic NMR spectroscopy(Dated: April 19, 2010)I. INTRODUCTIONIn general spectroscopic experiments are divided into two categories: optical spectroscopy and magnetic spec-troscopy. In previous experiments optical spectroscopy based techniques (e.g., UV/VIS absorption and fluorescence)were applied to obtain information about molecules. In this experiment Nuclear Magnetic Resonance (NMR) methodwill be used to study molecular dynamics. NMR is the most widely applied magnetic spectroscopy method. It is animportant tool for studying molecular structures and molecular dynamics of both organic and inorganic compounds.For example, for synthetic chemists it offers a great tool for identifying molecules. Another well-known magnetic res-onance technique is Electron Spin Resonance (ESR; sometimes also called Electron Paramagnetic Resonance; EPR),which can be used for studying radical species.Both NMR and ESR methods are based on the Zeeman effect, where the degenerate spin energy levels are splitby an external magnetic field. In addition to the Zeeman splitting, the possible spin – spin interactions will modifythe energetics and result in additional structure in the magnetic resonance spectra. The energy level structure of thespins is interrogated by electromagnetic radiation, which in the case of NMR is usually in the radio frequency range(MHz range) and for ESR in the microwave region (GHz range). Both optical and magnetic resonance techniques arebased on interaction of the molecules with electromagnetic radiation. Both NMR and ESR are absorption experimentsand thus in both experiments absorption of photons by a given sample is studied. While in the optical spectroscopyexperiments the oscillating electric field component of the electromagnetic radiation induces transitions, the magneticresonance experiment utilizes the magnetic field component of the radiation. This identifies the principal differencebetween the two fields of spectroscopy. A NMR spectrum displays either frequency or magnetic field (“energy”) onthe x-axis and a quantity related to the absorption of photons on the y-axis. However, in most cases the unit for thex-axis is usually chosen as ppm, which represents a relative shift from a standard sample (tetramethylsilane; TMS).Note that in ESR a first derivative of the absorption is usually shown. A typical NMR spectrum is shown in Fig. 1.For more information on NMR and ESR spectroscopy, see Refs. [1–3].FIG. 1: A typical proton NMR spectrum (vanillin).The main objective of this experiment is to introduce the technique of dynamic NMR (DNMR) and demonstratehow it can be used to obtain information about time- dependent molecular level phenomena. Our secondary aim isto observe the increase in the rate constant that occurs for the methyl exchange in dimethylformamide (DMF; seeFig. 1) as temperature is increased. The rate constants can be related to the activation energy of rotation for theC-N bond in DMF.Typeset by REVTEXFIG. 2: A 2-D structure of DMF.II. THEORY OF NMR SPECTROSCOPYThe spin angular momentum of a proton gives rise to a magnetic moment vector ~µ:~µ = γH~I with~I =³ˆIx,ˆIy,ˆIz´(1)where~I is the nuclear spin angular momentum vector-operator with the Cartesian operator components given aboveand γHis the magnetogyric ratio for protons (≈ 2.67522 × 108s−1T−1). If an external field is placed along a givenz-axis, we need to know the magnetic moment of the nuclear spin along that axis:ˆµz= γHˆIz(2)When this magnetic moment interacts with the external magnetic field, the Hamiltonian (i.e., the operator that yieldsthe total energy when it operates on spin-eigenstate wavefunctions) is given by:ˆH = ~µ ·~B ≈ ˆµzBz= γHˆIzBz(3)The spin eigenstates for a single proton are just | + 1/2 > (or |α >) and | − 1/2 > (or |β >) and operating on themwith the Hamiltonian of Eq. (3) gives the energies of the spin levels in presence of the external magnetic field:ˆH | +12i =12γHBz| +12i andˆH | −12i = −12γHBz| −12i (4)Note that without the external field both spin states have the same energy (i.e., they are degenerate). In order toseparate them, NMR experiment requires the external magnetic field. The energy difference between the spin levelsis:∆E = γHBz(5)A classical analog of a proton (with nuclear spin 1/2) in a magnetic field is shown in Fig. 3. A classical bar magnetcan have any orientation with respect to the external field but a spin can only have two orientations. The resonancecondition (Eq. (5)) also relates the magnetic field strength units to the frequency units.The selection rule (i.e., between which levels transitions can be observed) in NMR spectroscopy requires that thereis a unit change in nuclear spin. In the above one-spin system, this corresponds to changing the nuclear spin fromstate | − 1/2 > to | + 1/2 >. In ESR the requirement is that the electron spin must change by one in a transition.The selection rules become important when there are multiple spins present in the molecule and they dictate whichtransitions are observed experimentally.The above one-proton example yields just one absorption line in the NMR spectrum, which is located at somefixed value of ∆E. However, when a proton is chemically bound to a molecule, the electronic structure may increase(paramagnetic contribution to shielding) or reduce (diamagnetic contribution to shielding) the local magnetic fieldseen by the proton. This induces a chemical shift from the free proton value. The chemical shift (δ) is expressed inppm units (see Fig. 1) according to the following formula:δ =νsubstance− νT MSν0(6)2FIG. 3: Analogy between a proton and a bar magnet in presence of external magnetic field.where νvsubstanceis the resonance frequency for the sample (Hz), νTMSis the resonance frequency for the TMS standard(Hz) and ν0is the operating frequency of the spectrometer (Hz; for example, 60 MHz). The main advantage of usingthis scale is that it does not depend on the field strength of the NMR magnet used. Thus we conclude that eachproton in a given molecule will give at least one peak in an NMR spectrum. The lines will overlap if they haveidentical chemical shifts or are separated from each other if they have different chemical shifts. It has been observedthat based on the chemical shift, it is possible to identify where the