Physical properties, chemical properties, formulas Shedding real light on molecular structure: Wavelength Frequency ν Wavelength λ Frequency ν Velocity c = 2.998 10 8 m s -1 The Electromagnetic Spectrum λ ν = c Energy of a photon: E = hν = hc/λ h = Planck s constant = 6.626 10-34 J s 1
Emission and Absorption Spectroscopy Nuclear Magnetic Resonance Spectroscopy Let s go for a spin! Electron Spin: A Fourth Quantum Number The Stern-Gerlach Experiment 2
Nucleus: nucleons: protons, neutrons -these also have spin properties: up, down #n #p A Z Total Spin I 0 Examples 4 He, 12 C, 16 O, 32 S - spins add together in a complicated way to give total nuclear spin I, characteristic of a given type of nucleus - some general guidelines. 1, 2, 3, ½, 3/2, 5/2, 2 H, 14 N (I = 1) 10 B (I = 2) 1 H, 13 C, 19 F, 31 P (I = ½) 35 Cl, 37 Cl (I = 3/2) 127 I (I = 5/2) The net nuclear spin gives rise to a number of spin states #spin states = 2I +1 Spin states characterized by m I or I z values: For a given I value, m I = I z = +I, I-1, I-2,..,-I+1, -I. e.g. for I = 0, m I = 0 (only!) for I = ½, m l = +½, -½ for I = 1, m l = +1, 0, -1 Normally all nuclear spin states are degenerate same energy -degeneracy can be removed by application of an external magnetic field 3
Amount of splitting of the nuclear spin states, E, is directly proportional to the applied magnetic field strength B 0 is directly proportional to magnetogyric ratio γ of the particular nucleus type h E = γ ( ) B = γ h B0 2π ( γ ν = ) B 2π 0 0 = hν ν is the frequency of the EM radiation required for the transition from the lower to the upper spin states Nucleus 1 H 2 H 13 C 19 F γ (10 6 rad/tesla sec) 267.53 41.1 67.28 251.7 Field strength B 0 (Tesla) 1.00 4.70 7.05 1.00 1.00 4.70 7.05 1.00 Frequency ν (MHz) 42.6 200. 300. 6.5 10.7 50.0 75.0 40.0 Increasing B 0 increases E Increasing B 0 results in a higher frequency ν of EM radiation required to produce the transition For a given B 0, different types of nuclei have different E, thus different ν values Precession Interaction of the nuclear magnetic moment and the applied field causes the rotational axis to precess about the field axis (z-axis) (like a toy top) Precessional frequency or Larmor frequency ω EM radiation with ν values in MHz range are radio waves So far: allows us to identify which types of atoms our molecule has by monitoring which EM frequencies are absorbed at a given applied magnetic field strength (but limited to those nuclei with I 0!) For a given field strength B 0, nuclei of different types precess at different Larmor frequencies according to their magnetogyric ratio γ values: H ω B 0 ω = γb 0 4
Mechanism of Absorption When a photon of, say, ν = 60 MHz encounters this spinning charged system the two can couple and change the spin state of the proton. This state is called nuclear magnetic resonance, and the nucleus is said to be in resonance with the incoming radio wave ν = ω/2π = γβ 0 /2π Ε H ω B 0 Mechanism of Absorption To observe a spectroscopic transition, need a population difference between the two states involved. The energy difference corresponding to 60 MHz ( E = hν) is 2.39 x 10-5 kj mol -1. Thermal energy at room temperature (298 K) is sufficient to appreciably populate both energy levels. H ω The energy difference is small, so rapid exchange is occurring between the two populations, but there is always a net excess of protons in the lower energy state. Mechanism of Absorption From the Boltzman distribution equation we can calculate the population of each energy state: N upper /N lower = e - E/k T = e -hν/kt @ 298 K the ratio is 1,000,000 / 1,000,009! There is an excess population of 9 nuclei in the lower energy state! Transitions As the applied B 0 increases, exchange becomes more difficult and the excess increases: Frequency (MHz) 60 80 100 200 300 Excess nuclei 600 96 In each case, it is these few nuclei that allow us to observe NMR 9 12 16 32 48 5
When radio radiation is applied to a sample both transitions upward and downward are stimulated. If too much radiation is applied both states completely equilibrate called saturation no NMR signal can be observed. Two mechanisms for relaxation: 1. spin-spin or transverse relaxation, exchange with other nuclear spins, characterized by time constant T 2 2. spin-lattice or longitudinal relaxation, transfer of energy to surroundings (heat), characterized by time constant T 1 Shielding If all protons ( 1 H nuclei!) absorbed the same amount of energy in a given magnetic field, not much information could be obtained. But protons ( 1 H nuclei!) are surrounded by electrons that shield them from the external field. Circulating electrons create an induced magnetic field that opposes the external magnetic field. Electronic Motion A permanent magnet will induce a current carrying loop to spin: Shielding In the same way, electrons in orbitals will start to circulate when the molecule is placed in an external magnetic field. This circulation of electrons creates another magnetic field that opposes the external field. B 0 6
Shielding Shielded Nuclei Magnetic field felt at the nucleus: B N (= B eff = B local ) = B 0 - σb 0 = B 0 (1-σ) where σ is the shielding constant Magnetic field strength must be increased for a shielded proton to flip at the same frequency. Thus the local field is modulated by the local electronic or chemical environment of the nucleus. Known as the chemical shift. 7.0459 T A small, but NOTICABLE, effect! Protons in a Molecule Depending on their chemical environment, protons in a molecule are shielded by different amounts. most deshielded least deshielded The Chemical Shift low field high field 7
NMR Signals The number of signals shows how many different kinds of protons (H atoms!) are present. The location of the signals shows how shielded or deshielded the proton is. The intensity of the signal shows the number of protons (H atoms!) of that type. The NMR Spectrometer There are two types of NMR spectrometer, continuous wave (CW) sweep and Fourier Transform (FT). CW instruments have been almost entirely phased out. RF (MHz) oscillator RF Detector Magnet Magnetic Field Strength Field Strength Magnet Type Frequency 1.41T permanent 60 MHz 2.35T electromagnet 100 MHz 4.70T superconducting 200 MHz 7.05T 300 MHz...... 21.2T 900 Mhz Modern NMR Recall the concept of precession of the spinning nuclear magnet in the applied magnetic field: H ω B 0 µ = magnetic moment Frequency is that required to observe 1 H signals 8
Behaviour of a collection of spinning nuclei: Spin population difference Net moment or magnetization Phase coherence of spins Transfer of magnetization from z-axis to x,y-plane The x,y component of the magnetization is detected electronically as the resonance signal Application of a second magnetic field B 1 (magnetic field of EM radiation) matching Larmor frequency Rather than show the magnetization vectors precessing about the z-axis, we will now make the x- and y-axes rotate about the z-axis with the Larmor frequency. -Initial alignment of net magnetization M along z-axis -Apply a pulse of B 1 along x-axis -Causes phase coherence of spins and rotation of M by angle θ, value depends on pulse duration Transfer from the stationary laboratory coordinate system to a rotating coordinate system. Magnetization along the y-axis after 90 pulse Free Induction Decay FID 9
- the magnetization along the y-axis decays by spin-spin relaxation, time constant T 2 -So far, only one type of nucleus, one frequency -Real sample, different H s, different frequencies due to shielding effects -Coordinate system rotating at one fixed frequency -Some H magnetizations rotate in the x,y-plane - the magnetization along the z-axis subsequently reappears by spin-lattice relaxation, time constant T 1 -The magnetization along the y-axis (detector) oscillates between + and values with a cosine dependence on time FID C H 3 O C CH 3 O -Overall decay still that of spin-spin relaxation, T 2 C H 3 C OCH 3 -Horizontal difference between two peaks is inverse of frequency difference between B 1 and the Larmor frequency C H 3 CH CH 2 C O OH OH 10
0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 t1 sec Chem 325 NMR Intro Fourier Transform The FID is magnetization as a function of time. Need to transform the time-domain data into frequencydomain data. The Fourier Transform Mathematically simulate the FID with a number of sine waves, distance between the peaks is related to the frequency of the signal FT time frequency The NMR Graph Peak positions (x-axis scale): 1. Field strength: 1.500000000 versus 1.500002085 T cumbersome and depends on resonance frequency! 2. Resonance frequency at constant field strength: 60000000 versus 60000089 Hz cumbersome and depends on magnetic field strength! The NMR Graph Use a reference and quote all field strengths or frequencies relative to the field or frequency of the reference peak. The δ Scale: Bref - Bsample 0.000002085-6 δ = = = 1.39 10 B 1.500000000 ref i.e. The sample signal is shifted by 1.39 ppm relative to the reference. The chemical shift is 1.39 ppm. Sample signal is at δ = 1.39 relative to the reference (δ = 0). OR ν ref -ν sample 88.8 Hz δ = = = 1.39 10 6 ν 63.87 10 Hz ref δ values INDEPENDENT of applied field or frequency -6 11
H 3 C CH 3 Si CH 3 CH 3 Tetramethylsilane TMS TMS is added to the sample (internal standard). Soluble in most organic solvents. Since silicon is less electronegative than carbon, TMS protons are highly shielded. Signal defined as zero. Organic protons absorb downfield (to the left) of the TMS signal. All 12 H s identical, strong signal. Also used for 13 C spectra. Chemical Shift Measured in parts per million. Ratio of shift downfield from TMS (Hz) to total spectrometer frequency (Hz). Same value for 60, 100, or 300 MHz machine. Called the delta (δ) scale. Delta Scale 12