# NMR - Basic principles

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1 NMR - Basic principles Subatomic particles like electrons, protons and neutrons are associated with spin - a fundamental property like charge or mass. In the case of nuclei with even number of protons and neutrons, individual spins are paired and the overall spin becomes zero. owever, there are many cases such as 1 and 13 C, where the nuclei possess a net spin, which is important in Nuclear Magnetic Resonance (NMR) Spectroscopy. Spin of nuclei could be correlated with the number of protons and neutrons as: When there are even number of protons and even number of neutrons in the nucleus, the net spin is equal to zero. When there are odd number of neutrons and odd number of protons in the nucleus, it will have an integer spin (i.e. 1, 2, 3) If the sum of the number of neutrons and the number of protons is odd number, the nucleus will have a half-integer spin (i.e. 1/2, 3/2, 5/2). These observations can be summarized in terms of atomic mass and atomic number as shown below. I alfinteger alfinteger Integer Atomic Mass Odd Odd Even Atomic Number Odd Even Odd Examples 1 (1/2) 13 C (1/2) 2 (1) NMR active Zero Even Even 12 C (0) Not NMR active Nuclei are charged, and those with a net spin will have a magnetic moment (µ) which is give by µ = γ h / 2π...(1) (in fact µ = γ P where P is the angular momentum associated with the nuclei) 1

2 where I is the spin quantum number (with values ½, 1, 3/2 etc.) and γ = Gyromagnetic ratio, which is a characteristic constant for individual nuclei (h is Planck s constant) In Nuclear Magnetic Resonance Spectroscopy, we study the behavior of magnetic nuclei in presence of an external magnetic field. Quantum mechanics tells us that angular momentum vector of a nucleus with spin = I can have 2I+1 orientation with respect to an external magnetic field. Since the main aim of this chapter is to illustrate the use of NMR in the study of aromaticity, we will focus on the magnetic properties of 1 and see what special information 1 NMR spectroscopy provides when this nuclei ( 1 ) is part of an aromatic system. A nuclei such as 1 with spin = ½, can orient in two ways (2 x ½ + 1 = 2) with respect to the external field. Of these, the spin state represented as +1/2 (or α state) is of lower energy where as the one represented as -1/2 (or β state) is of higher energy. The former reinforces the applied field and the latter opposes it. The energy difference between the two spin states is proportional to the applied field and can be written as ΔE = hν = hγb 0 /2π...(2) where, h = Plank s constant, γ = Gyromagnetic ratio which is a characteristic constant for individual nuclei, B 0 = strength of the magnetic field at the nucleus From equation (2), it is clear that a radiation of frequency ν = γb 0 /2π possess the right amount of energy to effect a transition from lower energy α state to higher energy β state. Absorption of energy takes place only with a certain combinations of field strengths and radio frequencies during which the system is said to be in a state of resonance. For proton, γ = 2.675x10 8 T -1 s -1 If the NMR spectrometer is equipped with a magnet with a field of 7.046T, ν = γ B 0 /2π = x 10 8 T -1 S -1 x T 2 x = 300 x 10 6 z = 300 Mz 2

3 This can be pictorially represented as shown below: Energy Spin state I = -1/2 (β ) I = 1/2 Spin state I = +1/2 (α ) Field strength B 0 NMR experiments can be performed in one of the following ways, i) keep the external magnetic field strength constant and vary the frequency of radiation to see an absorption ii) keep the radio frequency constant and slowly vary the field strength until the splitting of spin states corresponds to the energy of radio wave. In new versions of instruments, instead of Continuous Wave (RF) sweeping, an intense radiofrequency pulse is used to excite all nuclei simultaneously and their individual absorptions determined using Fourier transform methods Shielding and Deshielding So far we were considering the magnetic moments generated by the spinning nucleus and its interaction with an external field. owever, in realty, nuclei are surrounded by electrons which also generate small local magnetic fields (B loc ) as they circulate. These local magnetic fields can either oppose or augment the external magnetic field. If the field created by the electron oppose the external field, nuclei experience an effective field which is smaller than the external field and it is said to be SIELDED. If the field created by the electron augments the external field, nuclei experience an effective field which is larger than the external field. It is said to be DE-SIELDED. i.e. B eff = B o - B loc 3

4 This can be represented as B eff = B o ( 1 - σ ) σ magnetic shielding or screening constant; depends on electron density. Equation (2) can now be written as ΔE = hν = hγ B o ( 1 - σ )/2π...(3) Equation (3) shows that magnetic field felt by individual nuclei varies depending upon their chemical environment; ΔE and hence the energy of the radiation required to excite them differ consequently. Diamagnetic and paramagnetic anisotropy Two effects that originate from electronic delocalization in aromatic systems are 1) External field induces a flow (current) of electrons in π system ring current effect 2) Ring current induces a local magnetic field with shielding (decreased chemical shift) and deshielding (increased chemical shifts) zones. This is the basis of diamagnetic anisotropy in aromatic systems which can be diagrammatically represented as shown below. In the case of compounds with unpaired electrons, paramagnetism associated with the net spin overrides the diamagnetic effects and lead to a different type of magnetic effect (vide infra) Chemical shift and δ scale As mentioned, effective magnetic field at individual nuclei vary depending upon their chemical environment. Radiofrequency required to excite them also will be different under different external field strengths. This means that if we take NMR spectra of a compound using instruments of different field strengths, peaks appear at different 4

5 positions and it would be difficult to compare them without applying corrections for differences in absorptions. To avoid this problem, a different system, based on chemical shift is often used. In this, we use a reference compound in our experiments. It is generally tetramethylsilane (TMS), which is unreactive with other organic compounds, is volatile, and gives an absorption which comes at upfield position in comparison with most of the protons important to organic chemists. In addition, its 12 protons are equivalent and give only a single signal with good intensity even at low concentration (~1% by volume). Solvent used in NMR experiments should not contain 1 due to interference; deuterated solvents such as CDCl 3, DMSO-D 6 etc. are generally used. Now let us see what are chemical shift and δ scale. As mentioned above, we use a solution of our compound in a deuterated solvent such as CDCl 3 containing a small amount of TMS as the internal standard. During the experiment, the instrument measures the resonance frequencies of the standard as well as that of the protons present in our sample. For convenience, let us assume that our sample has only one type of proton. Frequency of the protons in the standard is then subtracted from that of sample protons and then divided by the frequency of the standard. This gives a number called the chemical shift (δ) of that proton(s) with respect to TMS in parts per million. For instance, let us assume that the protons in the standard reaches the state of resonance (absorbs energy) at 300,000,000 z (300 megahertz), and protons in our sample reaches this state at 300,000,300 z in a given magnetic field (external field). The difference between the frequencies of our sample and that of the standard is 300 z. When we divide this by the resonance frequency of the sample, we get 300/300,000,000 = 1/1,000,000 which can be called as one part per million (or 1 ppm). Now let us study the same sample in a magnetic field of higher strength. Since ΔE = hν = hγb 0 /2π, protons of the internal standard will reach resonance at a higher frequency of 600,000,000 z (or 600 megahertz). For the same reason, the resonance frequency of our sample protons will also show a proportionate increase, and will reach resonance at 600,000,600 z. Although the difference here is 600 z, we have to divide it by the resonance frequency of the internal standard. That is, 600/600,000,000 = 1/1,000,000, = 1 ppm! So, chemical shift value remains the same irrespective of the instruments (field strengths). Although we did these calculations manually, all these are done automatically in the computer 5

6 associated with the NMR spectrometer. A correlation of radiofrequencies and δ values and their relative positions with respect to TMS (standard) is presented below. A representative 1 NMR spectrum is given below 6

7 Shielding and deshielding zones in Aromatic systems Due to the magnetic field generated by the circulating electrons, hydrogens which lie in the plane of the ring experiences a deshielding effect as shown below (A). At the same time those situated above and below the plane experience shielding, as the magnetic lines of force are opposite in direction with respect to the applied field. Similar effect, but to a lesser extent, can be seen in simple olefins (B), aldehydes etc. Applied magnetic field B 0 δ 7-8 ppm δ 5-7 ppm Illustrative examples: A B Chemical shift positions of hydrogen atoms which are placed in the shielding and deshielding zones of aromatic systems are given below. 7

8 Bridge head protons at -0.5 δ Outer protons at δ Inner protons 0.00 δ Outer ring protons at δ Outer protons 7.6 δ C 3 protons at δ 3 C C 3 [14]-annulene Outer protons at ~ 9 δ Inner protons at ~ -3 δ a b a at -0.3 δ b at 5.1 δ 1 & 7 at 6.4 δ 2-6 at 8.5 δ [18]-annulene Antiaromatic systems Antiaromatic systems are paratropic. That is, they are able to sustain a paramagnetic ring current (this doesn t mean that paramagnetic anisotropy arises due to electron delocalization as that in aromatic systems; for reference, see J. Phys. Org. Chem, 2003, 16: p ). This leads to shielding of outer ring protons and deshielding of inner protons (opposite to that of aromatic compounds which show diamagnetic effect). Examples presented below demonstrate the behavior of magnetic nuclei situated in an antiaromatic environment. 1) At -170 o C, inner protons of [12]-annulene comes at ~8 ppm and outer protons comes at ~6 ppm which is characteristic of antiaromaticity. Above -150 o C, all protons are magnetically equivalent showing conformational flexibility. Above -50 o C, it rearranges to a bicyclic system as shown below. above -50 o C [12]-annulene 8

9 2) At -130 o C [16]-annulene is paratropic with four central protons at δ, and twelve outer protons at 5.35 δ. Above -50 o C, all protons are magnetically equivalent showing conformational flexibility in solution [16]-annulene Nonaromatic 3) As discussed previously, the locked form of [14]-annulene show significant aromatic character, with outer protons resonating at δ and C 3 protons coming at δ. owever, the dianion of this compound is antiaromatic which is evident from the paramagnetic anisotropic effect seen in its NMR. Outer ring protons at δ Outer ring protons at -3 δ C 3 protons at δ C 3 protons at 21 δ 3 C C 3 reduction 3 C C 3 9

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