NMR Notes PDF

Murali Banavoth Associate Professor School of Chemistry University of Hyderabad Hyderabad, 500046 Teaching Syllabus  NMR The signal in nuclear magnetic resonance (NMR) spectroscopy arises from a difference in the energy levels occupied by the nuclei in the analyte. Quantum Mechanical Des...

Murali Banavoth Associate Professor School of Chemistry University of Hyderabad Hyderabad, 500046 Teaching Syllabus  NMR The signal in nuclear magnetic resonance (NMR) spectroscopy arises from a difference in the energy levels occupied by the nuclei in the analyte. Quantum Mechanical Description of NMR The first three of these quantum numbers tell us something about where the electron is relative to the nucleus and something about the electron’s energy. The last of these four quantum numbers, the spin quantum number, tells us something about the ability of an electron to interact with an applied magnetic field. The overall spin of a nucleus is a function of the number of protons and neutrons that make up the nucleus. NMR Active or Inactive Energy Levels in an Applied Magnetic Suppose we Field have a large population of 1H atoms. In the absence of an applied magnetic field the atoms are divided equally between their possible spin states: 50% of the atoms have a spin of +1/2 and 50% of the atoms have a spin of –1/2. Both spin states have the same energy Classical Description of NMR For simplicity, let's assume that in the population of nuclei available to us, there is an excess of just one nucleus with a spin state of +1/2. If we apply a source of radio frequency (RF) electromagnetic radiation along the x-axis such that its magnetic field component, B 1 is perpendicular to B0, then it will generate its own angular velocity in the xy-plane. When the angular velocity of the precessing nucleus matches the angular velocity of B1, absorption takes place and the spin flips. When the magnetic field B is removed = 1 Relaxation In the absence of relaxation, the system is saturated with equal populations of the two spin states and absorption approaches zero. This process of relaxation has two separate mechanisms: spin-lattice relaxation and spin-spin relaxation In spin-lattice relaxation the nucleus in its higher energy spin state, Figure b, returns to its lower energy state spin state, Figure a , by transferring energy to other species present in the sample (the lattice in spin-lattice). Spin-lattice relaxation is characterized by first-order exponential decay with a characteristic relaxation time of T1 that is a measure of the average time the nucleus remains in its higher energy spin state. Smaller values for T1 result in more efficient relaxation. If two nuclei of the same type, but in different spin states, are in close proximity to each other, they can trades places in which the nucleus in the higher energy spin state gives up its energy to the nucleus in the lower energy spin state. The result is a decrease in the average life-time of an excited state. This is called spin-spin relaxation and it is characterized by a relaxation time of T2 Continuous Wave NMR If we scan B1 while holding constant B0—or scan B0 while holding constant B1—then we can identify the Larmor frequencies where a particular nucleus absorbs. The result is an NMR spectrum that shows the intensity of absorption as a function of the frequency at which that absorption takes place. Because we record the spectrum by scanning through a continuum of frequencies, the method is known as continuous wave NMR. Fourier Transform NMR Before we apply the pulse, the population of nuclei are aligned parallel to the applied magnetic field. There is a slight excess of nuclei with spins of +1/2, which we can represent as a single vector that shows their combined magnetic moments along the z-axis as in Fig a. When we apply a pulse of RF electromagnetic radiation with a magnetic field strength of B1, the spin states of the nuclei tip away from the z-axis by an angle that depends on the nucleus's magnetogyric ratio, γ , the value of B1, and the length of the pulse. If, for example, a pulse of 5 μs tips the the magnetic vector by 45° (Figure b), then a pulse of 10 μs will tip the magnetic vector by 90° degrees (Figure c), so that it now lies completely within the xy-plane. Illustration showing the process of relaxation during an NMR experiment. The bottom row shows the net magnetic moment aligned with the z-axis, μz, as a function of time. The top row shows the net magnetic moment in the xy-plane with the figure on the top right showing the overall change in the net magnetic moment in three dimensions. Tracing the path of the magnetic vector with time, we would see that it follows a spiral-like motion as its contribution in the xy-plane decreases and its contribution along the z-axis increases. We measure this signal— called the free induction decay, or FID—during this period of relaxation. The FID for a system that consists of only one type of nucleus is the simple exponentially damped oscillating signal in Fig a. The Fourier transform of this simple FID gives the spectrum in Fig b that has a single peak. A sample with a more than one type of nucleus yields a more complex FID pattern, such as that in Fig c, and a more complex spectrum, such as the two peaks in fig d. Typical pulse sequence highlighting the total cycle time and its component parts: the pulse width, the acquisition time during which the FID is recorded, and a recycle delay before applying the next pulse and beginning the next cycle.  Environmental Effects on NMR Spectra Relationship between the Larmor frequency for a nucleus, , its magnetogyric ratio, , and the primary applied magnetic field strength, If this is the only thing that determines the frequency where absorption takes place, then all compounds that contain hydrogens will yield a 1H NMR spectrum with a single peak at the same frequency. If all spectra are identical, then NMR provides little in the way of useful information. Cluster of peaks between 250 Hz and 300 Hz, which have a greater total intensity, are for the six hydrogens in the two methyl groups (– CH3 ) and that the cluster of peaks around 400 Hz are due to the methylene group (–CH2 –) why the location of a nucleus within a molecule—what we call its environment—might affect the frequency at which it absorbs and why a particular absorption line might appear as a cluster of individual peaks instead of as a The NMR Spectrum's Scale (Relative) One complication is that instruments with identical nominal values for B0 likely will have slightly different actual values, which leads to small variations in the frequency at which a particular hydrogen absorbs on different instruments. We can overcome this problem by referencing a hydrogen's measured frequency to a reference compound that is set to a frequency of 0. For example, the most intense peak in the NMR spectrum for propane, Figure , has a frequency of 269.57 Hz when measured on an NMR with a nominal field strength of 300 MHz, which means that its frequency is 269.57 Hz greater than the reference, which is identified as TMS. The reference compound is tetramethylsilane, TMS, which has the chemical formula of (CH3)4Si in which four methyl groups are in a tetrahedral arrangement about the central silicon. TMS has the advantage of having all of its hydrogens in the same environment, which yields a single peak. Its hydrogen atoms also absorbs at a low frequency that is well removed from the frequency at which most other hydrogen atoms absorb, which makes it How Can We Create a Universal Scale? The frequency at which a particular Absorption occurring at a higher/lower frequ hydrogen absorbs is different when using a 60 MHz NMR than it is when using a 300 MHz NMR. To create a single scale that is independent of B0 we divide the peak's frequency, relative to TMS, by B0, expressing both in Hz, and then report the result on a part- Example, the most intense per-million scale by multiplying by 106 peak in the NMR spectrum for propane, has a frequency of 269.57 Hz; the NMR on which the spectrum was Record the spectrum of propane on a 60 MHz instrument, then we expect that this peak to recorded had a field strength appear at 0.899 ppm, or a frequency of: of 300 MHz. The peaks for the two types of hydrogen in propane are shifted downfield relative to the reference and the methylene hydrogens are shifted further downfield than the methyl hydrogens. Both groups appear as clusters of peaks instead of as single peaks. Chemical shifts are useful for determining structural information for molecules Chemical shifts are the result of shielding from the magnetic field associated with a molecule's circulating electrons. The splitting of a peak into a multiplet of peaks is the result of the shielding of one nucleus by the nuclei on adjacent atoms, and is called spin-spin coupling. The six hydrogens in the two methyl groups are sufficiently close to the two hydrogens in the methylene group that the spins of the methylene hydrogens can affect the frequency at which the methyl hydrogens absorb. Pascal's triangle defines the splitting patterns in 1H NMR. The annotation shows how the values in any row of Pascal's triangle give are derived from the previous row. This shows us that for six equivalent nuclei we expect to find seven peaks with relative peak areas (or other measure of the signal) of 1:6:15:20:15:6:1. The pattern also is know as the N+1 rule as the N equivalent hydrogens will split the peak for an adjacent hydrogen into peaks Comparing the experimental NMR for propane with its simulated spectrum based on spin-spin splitting and the 2:6 ratio of methylene hydrogens relative to methyl hydrogens. The overall agreement between the two spectra is pretty good. The splitting of the individual peaks is designated by the coupling constant, J, which is shown in Figure for both the experimental and the calculated spectra. Note that the coupling constant is the same whether we are considering the effect of the methyl hydrogens on the methylene hydrogens, or the effect of the methylene hydrogens on the methyl hydrogens. Values of the coupling constant become smaller the greater the distance between the nuclei. The treatment of spin-spin coupling above works well if the difference in the chemical shifts for the two nuclei is significantly greater than the magnitude of their coupling constant. When this is not true, the splitting patterns can become much more complex and often are difficult to interpret. The original spectrum (top) shows two doublets, suggesting that we have two individual nuclei that are coupled to each other. If we irradiate the nucleus on the right at its frequency, we can saturate its ground and excited states such that it ceases to absorb. As a result, the nucleus on the left no longer shows evidence of spin-spin coupling to the nucleus on the right (middle) and appears as a singlet. When we turn off the decoupler (bottom) the spin-spin coupling between the two nuclei returns more quickly than relaxation returns the NMR Spectrometers Most instruments, however, use pulses of RF radiation to excite all nuclei at the same time and then use a Fourier transform to recover the signals from the individual nuclei. Components of Fourier Transform Spectrometers Thus, a 400 MHz NMR has a magnet with a field strength of Early instruments used a permanent magnet and were limited to field strengths of 0.7, 1.4, and 2.1 T, or 30, 60, and 90 MHz. As higher frequencies provide for greater sensitivity and resolution, modern instruments use a tightly wrapped coil of wire— typically a niobium/tin alloy or a niobium/titanium wire—that becomes superconducting when cooled to the temperature of liquid He (4.2K). The result is a magnetic field strength of as much as 21 T or 900 MHz for 1H NMR. The magnetic coil is held within a reservoir Locking the Magnetic Field of liquid He, which, itself, is held within a reservoir of liquid N Samples for NMR are prepared using a solvent in which the protons are replaced with deuterium. For example, instead of using chloroform, CHCl3 , as a solvent, we use deuterated chloroform, CDCl3, where D is equivalent to 2H. This has the benefit of providing a solvent that will not contribute to the signals in the NMR spectrum. It also has the benefit that 2H has a spin of I =1, and a corresponding Larmor frequency. By monitoring the frequency at which 2H absorbs, the instrument can use a feed-back loop to maintain its value by adjusting the magnet's field strength. Shimming A magnetic field that is not homogeneous is like a table with four legs, one of which is just a bit shorter than the others. To balance the table, we place a small wedge, or shim, under the shorter leg. When a magnetic field is not homogeneous, small, localized adjustments are made to the magnetic field using a set of shimming coils arranged around the sample. Shimming can be accomplished by the operator by monitoring the quality of the signal for a particular nucleus, however, most instruments use an algorithm that allows the instrument to shim itself. The sample is placed in a cylindrical tube (Figure), that is made from thin-walled borosilicate glass and is 180 mm long and 5 mm in diameter. The tube is then inserted into a teflon sleeve—called a Spinner. Designed to both situate the sample at the proper depth within the sample probe, and to spin the sample about its long axis. This spinning is used to ensure that the sample averages out any inhomogeneities in the magnetic field not resolved by shimming.  Sample Probe In the design on the left, which uses a permanent magnet, the applied magnetic field, B0 , is oriented horizontally across the sample's diameter and the radio frequency electromagnetic radiation and its field B1, is oriented vertically using a spiral coil. In the design on the right, which is used with a superconducting magnet, the applied magnetic field, B0, is oriented vertically and the pulse of radio frequency electromagnetic radiation and its field, B1, is Data Processing Following a pulse that is applied for 1–10 μs, the free-induction decay, FID, is recorded for a period of time that may range from as little as 0.1 seconds to as long as 10 seconds, depending on the nucleus being probed. The FID is an analog signal in the form of a voltage, typically in the μV range. This analog signal must be converted into a digital signal for data processing, which is called an analog-to-digital conversion, ADC. Two important considerations are needed here: how to ensure that the signal—more specifically, the location of the peaks in the NMR spectrum—is not distorted, and how to accomplish the ADC when the frequencies are on the order of hundreds of MHz.  Managing MHz Signals The instrument in Figure is a 400 MHz NMR. This is a range of frequencies that is too large for an analog-to-digital convertor to handle with accuracy. The frequency window of interest to us, however, is typically 10 ppm for H NMR. For a 400 MHz NMR this corresponds to just 4000 Hz, with the useful range running from 400.000 MHz to 400.004 MHz. Subtracting the instrument's frequency of 400 MHz from the signal's frequency limits the latter SignaltoIntegrators the range of 0–4000 Hz, a range that is easy for an ADC to handle. Integrating to determine the area under the peaks provides a way to gain some quantitative information about the sample. Figure shows the integration of the NMR of propane first seen earlier. Integration of the peak for the two methyl groups gives a result of 1766 and integration of the peak for the methylene group gives a result of 710. The ratio of the two is 2.5, which is somewhat smaller than the expected 3:1 ratio. Applications of Proton NMR Proton (1H) NMR finds use for both qualitative analyses and quantitative analyses. Proton NMR is an essential tool for the qualitative analysis of organic, inorganic, and biochemical compounds Identification of Compounds The spectra in this figure are for a set of four simple organic molecules, each of which has a chain of three carbons and an oxygen: 1-propanol, 2-propanol, propanal, and propanoic acid. The first two of these molecules are alcohols, the third is an aldehyde, and the last is an acid. The main spectrum runs from 0–14 ppm, with insets showing the spectra over a narrower range of 0–5 ppm. Each of these molecules has a terminal –CH group that is the most upfield peak in its spectrum, appearing between 0.94 – 1.20 ppm. Each of these molecules has a hydrogen that either is bonded to an oxygen or a hydrogen bonded to the same carbon as the oxygen. The hydrogens in the –OH groups of the two alcohols have similar shifts of 2.16 ppm and 2.26 ppm, but the aldehyde hydrogen in the –CHO group and the acid hydrogen in –COOH are shifted further downfield appearing at 9.793 ppm and 11.73 Quantitative Analysis A quantitative analysis requires a method of standardization, which for NMR usually makes use of an internal standard. A good internal standard should have high purity and should have a relatively simple NMR spectrum with peaks that do not overlap with the analyte or other species present in the sample. If we are interested in only the relative concentrations of the analyte and the internal standard, then we can use the following formula