Basic NMR Concepts - A Guide for the Modern Laboratory Chapter 1

Basic NMR Concepts: A Guide for the Modern Laboratory Description: This handout is designed to furnish you with a basic understanding of Nuclear Magnetic Resonance (NMR) Spectroscopy. The concepts implicit and fundamental to the operation of a modern NMR spectrometer, with generic illustrations where appropriate, will be described. It can be read without having to be in front of the spectrometer itself. Some basic understanding of NMR spectroscopy is assumed. I. Introduction II. Basics of FT-NMR: Six critical parameters. III. Applications of FT-NMR 1) Shimming, line widths, and line shapes 2) Signal-to-noise measurements 3) Integration 4) Homonuclear decoupling 5) 13 C-{1H} spectra 6) 13 C-{1H} DEPT spectra Introduction Nuclear Magnetic Resonance (NMR) is a powerful relatively non-selective analytical tool, which enables you to ascertain molecular structure including relative configuration, relative and absolute concentrations, and even intermolecular interactions. Once challenging and specialized NMR techniques have become routine. NMR is indeed an indispensable tool for the modern scientist. Chemists, with little knowledge of NMR, are now able to obtain 2- or even 3-dimensional spectra with a few clicks of a button. Care must be taken, however, when using such ‘black box’ approaches. While the standard parameters used in the set-up macros for experiments might be adequate for one sample, NMR system, or hardware configuration, they may be very wrong for another. A single incorrectly set parameter can mean the difference between getting an accurate, realistic spectrum and getting a meaningless result, or even worse, damaging equipment that often costs several hundreds of thousands of dollars. A basic understanding of a few key aspects of NMR spectroscopy can ensure that you obtain the best results possible. This guide is intended to highlight the most pertinent aspects of practical NMR spectroscopy. It is not meant to replace any formal training of the theory of NMR. "Modern pulse NMR is performed exclusively in the Fourier Transform mode. Of course it is useful to appreciate the advantages of the transform, and particularly the spectacular results that can be achieved by applying it in more than one dimension, but it is also essential to understand the limitations imposed by digital signal analysis. The sampling of signals, and their manipulation by computer, often limit the accuracy of various measurements of frequency and amplitude, and may even prevent the detection of signals altogether in certain cases. These are not difficult matters to understand, but they often seem rather abstract to newcomers to FT NMR. Even if you do not intend to operate a spectrometer, it is irresponsible not to acquire some familiarity with the interaction between parameters such as acquisition time and resolution, or repetition rate, relaxation times and signal intensity. Many errors in the use of modern NMR arise because of a lack of understanding of its limitations." Basics of FT NMR- Six Critical Parameters This section will give you enough information about FT-NMR experiments to avoid the most common errors. We will cover the most important parameters that affect any spectrum you may collect using an FT-NMR spectrometer. These are: 1. Spectrometer Frequency [sfrq] 2. Pulse Width [pw] 3. Acquisition Time [at] 4. Number of Points [np] 5. Sweep Width [sw] 6. Recycle Delay [d1] [The blue letters in square brackets following the parameter represent the mnemonic used (the command), on all Varian spectrometers in the VNMR software package. The parameters are discussed in more detail below.] The most basic and common pulse sequence you will encounter is the ‘1-PULSE’ FT-NMR experiment (e.g. seqfil = ‘s2pul’ in VNMR), which is the sequence used for routine 1H and 13C acquisitions. It can be represented as shown in Figure 1. In a typical NMR acquisition, this pulse sequence will be repeated many times in order to improve the signal-to-noise ratio (S/N), which increases with the square root of the number of transients that are averaged together (nt). The user can independently set each of the parameters shown in Figure 1. Knowledge of their purpose and function will help you obtain quality NMR spectra. On Varian spectrometers, you can view the current pulse sequence by typing ‘dps’. Pulse Width (pw) Recycle Delay (d1) Acquisition Time (at) Figure 1. Schematic representation of one pass of a simple ‘1-PULSE’ pulse sequence. 1. Spectrometer Frequency [sfrq]: It is called a “1-PULSE” experiment because one radio frequency (Rf) pulse (pw) is applied per cycle. The Rf pulse excites the nuclei, which then emit Rf during the acquisition time, giving rise to an NMR signal in the form of an exponentially decaying sine wave, termed free-induction decay (FID). The Rf pulse has a characteristic frequency, called the spectrometer frequency (sfrq), which is dependent upon the nucleus you wish to observe and the magnetic field strength of the spectrometer. NMR spectrometers are generally named for the frequency at which hydrogen atoms resonate. Thus, a Varian INOVA 500 will cause hydrogen atoms to resonate at approximately 500 MHz. The precise spectrometer frequency defines the exact center of the NMR spectrum you measure. An Rf pulse that excites spins at only one exact frequency is not desirable because the NMR frequencies are spread out over a range of frequencies called the range of chemical shifts (corresponding to ~10 ppm of the applied magnetic field for 1H and ~250 ppm for 13C). Luckily, the short pulse lengths used in FT-NMR (e.g. ~10 µs) causes the Rf power to be distributed over a corresponding frequency spread (~1/pw, or 1/0.00001 seconds = ~100,000 Hz) due to the Heisenberg Uncertainty Principle. As you shorten the pulse length and increase power, uncertainty in the frequency results in a larger field of excitation (frequency range of power deposition). A longer, lower power pulse will have less frequency spread and can be used for frequency selective excitation or saturation. 2. Pulse width [pw]: Prior to applying an Rf pulse, the majority of nuclear spins are aligned parallel to the static magnetic field (B0). The axis of alignment is typically designated the Z-axis and the bulk magnetization is shown as a bold arrow (Figure 2, left side). Application of a short Rf pulse at the appropriate frequency will rotate the bulk magnetization by a specific angle. Pulses are generally described by this angle of rotation (also called flip angle). The angle of rotation is dependent on the intensity of the pulse (tpwr) and the width of the pulse (pw). The maximum measurable signal can be recorded following a 90º rotation or pulse. Thus, a 90º pulse width is defined as the amount of time the pulse of Rf energy is applied to the particular sample (90º is not 90º for all samples!) in order to flip the bulk magnetization from the Z-axis precisely into the X-Y plane, i.e., the condition shown in Figure 2A. For example, the 90º pulse width for 1H NMR experiments might be about 8 µs on the Varian Inova 500. It is often very useful to talk about the strength of the oscillating magnetic field associated with the Rf pulse in terms of the rotation frequency (rather than the time required to rotate the bulk magentization 90º). For example, if it takes 8 µs to rotate 90º, then using the same Rf intensity it will take 4*8µs = 32 µs to rotate 360º. The intensity of the Rf field can then be described as a magnetic field that causes the magnetization to rotate at a rate of 1/32 µs, or at 31,250 Hz (31.25 KHz). We call this magnetic field the B1 field, analogous to our description of the main static magnetic field (B0). (Note: a 300, 400, or 500 MHz static B0 field is roughly 10,000-20,000 times stronger than a typical oscillating B1 field that comes from the Rf pulse). The importance of learning this convention will become strongly apparent when you setup a homonuclear decoupling or nOe experiments, or perhaps a two-dimensional TOCSY experiment. The pulse width is entered in microseconds by typing pw=desired value in microseconds. The exact value is dependent upon the sample (nucleus, solvent, etc.) as well as the instrument (probe, etc.). Methods for measuring the pulse width will be discussed in another handout and are, for the most part, not required until you attempt advanced experiments. For routine one-dimensional survey experiments, most users use a 25 - 45º pulse for their data collection (Figure 2B). The reasons for this are discussed under recycle delay (d1). Z Z 900 A) Y PW= 10 µs (900) Y B0 X X Z Z 450 B) Y PW= 5 µs (450 ) Y B0 X X Figure 2. The bulk nuclear spin magnetization (bold arrow) for an NMR sample placed in a magnetic field aligned along the Z-axis before and after application of a pulse. 3. Acquisition time (at): Thus far, we have sent an Rf pulse through the sample and flipped the bulk magnetization by a specific angle. The nuclear spins are no longer at equilibrium and will eventually return to equilibrium along the Z-axis. One of the most extraordinary aspects of NMR is that the relaxation back to equilibrium takes from 106-1012 times longer than many other spectroscopies that you routinely utilize! In Figure 1, the decaying sine wave represents this process of Free Induction Decay (FID), which is a plot of emitted radio intensity as a function of time. The time it takes to acquire the FID is called the acquisition time and is set by the parameter ‘at’. For most nuclei of interest to chemists, relaxation times are within the range of 10-1 to 10 seconds. One of the most important concepts that chemists should learn is that routine matching of the acquisition time to the full decay time of the FID is a primary goal in recording quality NMR data. A natural inclination might be to just increase the acquisition time to maximize the amount of signal that is acquired (up to some “safe” limit). However, increasing the acquisition time is only advantageous up to a point. Moreover, it will be detrimental if extended too far. Care and forethought should be taken when adjusting ‘at’: too long and you will acquire noise unnecessarily; too short and extraneous wiggles will show up at the base of the peaks. 4. Number of points (np): The tiny analog signal emitted from the sample (in microvolts) is amplified, mixed, filtered, and attenuated prior to digitization, which is required for further computer processing. The ADC (analog-to-digital converter) converts the analog FID into a series of discrete points along the FID signal envelope. This is the number of points (np). In general, the more points used to define the FID, the higher resolution. The number of points (np), FT sfrq = 500.075 MHz Figure 3. Fourier transform of the FID for estrone acquired at 500 MHz. Note: the spectrometer frequency you use, in general, will not be exactly 500 MHz. spectral width (sw), and acquisition time (at) are interrelated. Changing one of these parameters will affect the other two (see below). 5. Spectral Width (sw): While the FID contains all the requisite information we desire, it is in a form that we cannot readily interpret. Fourier transforming the time-domain (seconds) FID (commonly referred to as FT or FFT for Fast Fourier Transform) will produce a frequency domain (seconds-1) spectrum with the familiar peak shapes and intensities, as shown in Figure 3. The frequency domain spectrum has two important parameters associated with it; the spectrometer frequency (sfrq), discussed earlier, and the spectral width (often times erroneously called the sweep width)(referred to as sw - see Figure 4). It is important to remember that the spectral width in ppm is independent of the spectrometer operating frequency; however, since the number of Hz per ppm is dependent on the spectrometer operating frequency, the spectral width in Hz will change depending upon the spectrometer used. For example, at a spectrometer frequency of 300 MHz, a spectral width of 3000 Hz is needed to measure a 10 ppm frequency range, since each ppm contains 300 Hz (10 ppm x 300 Hz/ppm = 3000 Hz). At a spectrometer frequency of 500 MHz, a spectral width of 5000 Hz is needed to measure 10 ppm (10 ppm x 500 Hz/ppm). 500 MHz 300 MHz 10 ppm 0 ppm 10 ppm 0 ppm 3000 Hz 0 Hz 5000 Hz 0 Hz Figure 4. The spectral width in ppm and Hertz at different spectrometer frequencies. Note the difference in the spectral width in Hertz for the two spectrometers. The sweep width (sw), number of points (np), and the acquisition time (at) are related by the following equations: np 2sw (1) 1 2sw = np at (2) at = and € res = where ‘res’ refers to the digital resolution of the spectrum. The digital resolution is in units of Hz/point, and the rule-of-thumb is that the digital resolution (in Hertz) should be € less than one half the natural peak width at half-height. This ensures that each peak is described by at least 3 points. For example, if your peak width at half-height is 0.5 Hz, the digital resolution should be less than 0.25 Hz. Therefore, if your spectrometer frequency is 500 MHz, your total spectral width is 5000 Hz (10 ppm) and your required digital resolution (res) is 0.25 Hz/point, rearranging equation 2 gives you the minimum number of points required for adequate digital resolution: np = 2sw = 40,000 points res (3) Since the computer works most efficiently if the number of points is a power of 2, the closest larger power of 2 would automatically be used, which, in this case, is 65,536 € points. The spectral width, number of points, and acquisition time can be specified when operating the spectrometer, usually by typing the appropriate mnemonic followed by an equals sign and the numeric value (e.g. np=64000). The spectrometer will set the units automatically. Generally, Varian’s automatically change the number of points according to equation 2 if the acquisition time or sweep width are changed. 6. Recycle delay (d1): On Varian’s this delay time is named d1 and appears at the beginning of the pulse sequence (see Figure 1). In practice, this delay should be thought of as coming after the acquisition time. It is an important parameter and plays a vital role in obtaining accurate integration. After the Rf pulse, the nuclear spins do not instantly return approach equilibrium; rather, they each relax according to a time constant called T1 (longitudinal relaxation time, which parameterizes any approximation of the time necessary for the magnetization to approach the Z-axis). Individual T1 time constants are dependent on many factors including nuclear environment, temperature, and solvent. T1’s for carbon atoms are typically much longer than T1’s for hydrogen atoms. Since each nucleus in a molecule is immersed in a different magnetic environment, their T1’s will not be the same. Not allowing enough time for relaxation between pulses will cause varied attenuation of the signals and inaccurate integration (see Integration Section for more details). When a 90° pulse is used to excite the spins (Figure 2A), a total time (TT) between pulses of 5xT1 is necessary in order to have nearly complete relaxation. (Zmagnetization = (1 – e-(elapsed time/T1)), where 1 – e-5 = ~ .99326). If a pulse width less than 90° is used, the total time can be proportionally less, and intensity distortions due to differential relaxation effects can be minimized. This is one reason why the standard pulse width for 1D 1H NMR experiments are in the range of 25 - 45º. The total time between measured transients is given by the following equation, where TT is the total time and d1 is the recycle delay: TT = pw + at + d1. Since the pulse width is in microseconds while the acquisition time and recycle delay are in seconds, the pulse width can usually be ignored, leaving us with the equation: TT = at + d1 (4) The optimum recycle delay can be computed by rearranging the equation to give € d1 = TT − at As an example of the above, if your longest T1 is 600 msec, then the total time (where € (5) TT=5x T1) must be at least 3 seconds, to completely avoid relaxation based distortions of signal intensity. Take Home Lesson These six parameters provide the foundation on which all NMR experiments are built. Appreciation of them will go far in the correct acquisition and interpretation of your NMR spectra, thus, saving precious time and effort. This not only applies to simple 1-PULSE experiments, but also is equally important in 2-D and 3-D NMR spectroscopy. Applications of FT-NMR 1. CHCl3 Peak Width at Half Height (LW1/2). The purpose of this section is to acquaint you with proper peak shape and the problems that are caused by improper shimming. NMR peaks have a shape that is called Lorentzian. A Lorentzian line can be expressed mathematically and has three parameters: amplitude [A], width at half height in Hz [LW1/2] and position, in Hz [X0]. An example of a Lorentzian line with LW1/2 = 0.25 Hz is shown below, in Figure 5. Xo Y= A(LW1/ 2 ) 2 (LW1/ 2 ) 2 + 4(X 0 − X) 2 A LW1/2 A = Amplitude LW1/2 = Peak width at half height, in Hz X 0 = Peak position, in Hz -5 -3 -1 1 Hertz 3 5 € Figure 5. Lorentzian line with LW1/2=0.25 Hz. The minimum obtainable peak width at half-height is directly related to the resolution of an instrument; i.e., how close two peaks can be and still be distinguishable. Resolution is usually measured using o-dichlorobenzene, which has very narrow lines in its 1H NMR spectrum. The manufacturers' resolution specification is usually 0.20 Hz, although peak widths of less than 0.10 Hz are obtainable by an expert shimmer. Manufacturers of NMR instruments, however, have traditionally separated the resolution specification from the lineshape specification. Line shapes for 1H NMR spectra are usually specified using CHCl3 and the specifications are stated in terms of the peak width at half-height, 0.55%, and 0.11 % height of the CHCl3 peak. The latter two percentages are chosen because they are the height of the l3C satellites of the CHCl3 line and one-fifth this height. These values are meaningful only when compared with the half-height width. From the mathematical equation for a Lorentzian line (see Figure 5), the line width at 0.55% height is calculated to be 13.5 times LW1/2, while the line width at 0.11 % height is calculated to be 30 times the LW1/2. So, if the peak width at half-height is 0.30 Hz, the calculated values are 4.0 Hz at 0.55% and 9.0 Hz at 0.11 %. For comparison, the manufacturer's specifications are 10-15 Hz and 20-30 Hz at 0.55% height and 0.11 % height, respectively. These values are larger than the theoretical values because the line widths at 0.55% and 0.11 % height are very sensitive to shimming. Other factors that influence line shape include the quality of the NMR tube, sample spinning, sample concentration, dissolved oxygen, and paramagnetic impurities. The latter three will lead to an overall broadening of the lines. Shimming: The term ‘shimming a magnet’ is a piece of NMR jargon that harks back to the early days of NMR spectroscopy. Originally, permanent magnets were used to provide the external magnetic field. To obtain the most homogenous field across the sample, the pole faces of the magnet had to be perfectly aligned, and to accomplish this, small pieces of wood, or ‘shims’, were hammered into the magnet support, so as to physically move the poles relative to each other. Luckily, nowadays you will not be required to bring hammer and wooden shims to the spectrometer. Shimming is accomplished by changing the applied current for a set of coils surrounding the probe. This applied current will create small magnetic fields in the region of your sample that will either enhance or oppose the static magnetic field. Your goal will be to adjust these coil fields by a series of mouse clicks to obtain the most homogeneous magnetic field across your sample, which is usually observed as an increase in the lock signal. It is important for you to have a basic understanding of line shape so you can judge when: (1) your shimming is off, and (2) you need to spend more time shimming your sample. The best way to avoid problems is to establish a procedure, such as the one detailed below. I. Always load a shim file that matches the current probe (e.g. probe = ‘as’ ) when you sit down at the instrument. You should never assume the previous user left the instrument with a standard shim file loaded. Without reloading standard shims, you will have to start where the last person stopped - and that might include someone who shimmed for a short sample, a bad tube, a viscous sample, etc. II. Be aware of lock parameters, especially if you only shim on the lock display (as most novice users will). Establish lock transmitter power and gain levels that work for most of your samples. If you encounter a sample that seems to require an unusually high power or gain setting, there is a problem with your sample and/or the instrument, and shimming on the lock level may be difficult or impossible. III. Shimming problems are confirmed only if the problem is visible on every peak in your spectrum. If, for example, only one peak is doubled, the problem is sample related, and can't be shimmed away. Remember, anomalies close to the base of intense single lines may not be visible on less intense peaks unless the vertical scale is increased. IV. Establish a shimming method. Shimming is an ‘art form’ that requires patience and practice. You should always approach shimming with some method that works for you to give acceptable results. Example: load a shim file; adjust the lock level to a maximum with Z1, then Z2, then Z1, then Z3, and then Z1. V. Spinning side bands should always be below 2%. If spinning side bands are above 2%, turn off the spinner air, optimize the X and Y shims, then turn the spinner air back on and re-optimize Z1, Z2, and Z3. If this does not solve the problem, consider transferring your sample to another tube. Knowledge of correct line shape can help you correct problems such as those shown in Figure 6. Although the peak in Figure 6b may have a line width at half-height that is less than 0.50 Hz, it is obviously poorly shimmed. You should never accept a poorly shimmed line shape such as is shown in Figure 6b, where a single line is expected. On the pages that follow are some line shape defects and the shims that should be adjusted to correct the problem. You will also notice that the FID will show the problem as well, but may not be as easy to diagnose. In general, odd-order longitudinal shims (Zl, Z3, Z5) affect the line shape symmetrically while even-order longitudinal shims (Z2, Z4) cause a non-symmetrical line shape. The higher the order (Z4 is higher order than Z2), the lower (closer to the base of the peaks) the problem is observed. Figure 6. From G. Chmurny and D. Hoult, “The ancient and honorable art of shimming.” Concepts in Magnetic Resonance, 1990, 2, 131-149. Shimming Take Home Lesson The ‘art’ of shimming resides in the fact that there is no single set of rules that work for every sample, spectrometer, person, or even time of year. Personal experience is the best and, frankly, the only way to master shimming. That being said, knowledge of correct and incorrect line shapes will allow you to decide quickly whether your sample is correctly shimmed. You will have to decide whether the return (a better line shape) is worth the time spent achieving that line shape.