Nuclear Magnetic Resonance Spectroscopy Introduction ORGANIC I LABORATORY W. J. Kelly

WHAT IS NMR SPECTROSCOPY? Nuclear magnetic resonance, or NMR as it is abbreviated by scientists, is a phenomenon which occurs when the nuclei of certain atoms are immersed in a static magnetic field and exposed to an oscillating electromagnetic field. Some nuclei experience this phenomenon, and others do not, dependent upon whether they possess a property called spin. Nuclear magnetic resonance spectroscopy is the use of the NMR phenomenon to study physical, chemical, and biological properties of matter. As a consequence, NMR spectroscopy finds applications in several areas of science. NMR spectroscopy is routinely used by chemists to study chemical structure using simple one-dimensional techniques. Two-dimensional techniques are used to determine the structure of more complicated molecules. The versatility of NMR makes it pervasive in the sciences.

WHAT IS SPECTROSCOPY? Spectroscopy is the study of the interaction of electromagnetic radiation with matter. The Light of Knowledge is an often used phrase. Most of what we know about the structure of atoms and molecules comes from studying their interaction with light (electromagnetic radiation). Different regions of the electromagnetic spectrum provide different kinds of information as a result of such interactions.

WHAT IS ELECTROMAGNETIC RADIATION? Realizing that light may be considered to have both wave-like and particle-like characteristics, it is useful to consider that a given frequency or wavelength of light is associated with a "light quanta" of energy we now call a photon. As noted in the following equations, frequency and energy change proportionally, but wavelength has an inverse relationship to these quantities. The frequency of electromagnetic radiation may be reported in cycles per second or radians per second. Frequency in cycles per second (Hz) have units of inverse seconds (s-1) and is given the symbol 

SPIN PROPERTIES OF ATOMIC NUCLEI What is spin? The Simple explanation Spin is a fundamental property of nature like electrical charge or mass. Spin is a measure of angular momentum (rotation about an axis) hence the term Spin comes in multiples of 1/2 (0, 1/2, 1, 3/2, 2, 5/2…) and can be + or -. Protons, electrons, and neutrons possess spin. Individual unpaired electrons, protons, and neutrons each possesses a spin of 1/2 Atomic nuclei composed of neutrons and protons may also possess spin. The spin of an atomic nucleus is determined by the number of protons and neutrons in the nucleus. Atoms with and odd number of protons will have spin Atoms with an odd number of neutrons will have spin Atoms with an odd number of both protons and neutrons will have spin Atoms with an even number of both protons and neutrons will not have spin The value of nuclear spin is represented by the symbol I, the nuclear spin quantum number. (I = 0, 1/2, 1, 3/2, 2, 5/2….) A nucleus with spin of I can exist in (2I+1) spin states.

SPIN PROPERTIES OF ATOMIC NUCLEI What is spin? The fundamental explanation. The shell model for the nucleus tells us that nucleons (protons and neutrons), just like electrons, fill orbitals. When the number of protons or neutrons equals 2, 8, 20, 28, 50, 82, and 126, orbitals are filled. Because nucleons have spin, just like electrons do, their spin can pair up when the orbitals are being filled and cancel out. Odd numbers mean unfilled orbitals, that do not cancel out. COMMON NUCLEI WITH SPIN Nuclei Unpaired Protons Unpaired Neutrons Net Spin 1H 1 0 1/2 2H 1 1 1 31P 1 0 1/2 23Na 1 2 3/2 14N 1 1 1 13C 0 1 1/2 19F 1 0 1/2 Almost every element has an isotope with spin

MAGNETIC PROPERTIES OF ATOMIC NUCLEI What is the physical result of spin? A spinning charge generates a magnetic field. An atomic nucleus has an inherent charge due to the protons within it. Thus an atomic nucleus with spin (I>0) will have a magnetic field associated with it. The nucleus generates a magnetic dipole along the spin axis, and the intrinsic magnitude of this dipole is a fundamental nuclear property called the nuclear magnetic moment,. The nuclear angular momentum quantum number I determines the nuclear magnetic moment according to the following equation: Where both N and mN are constants for a given nucleus N A spinning nuclei behaves as if it were a tiny bar magnet = N mN [I(I + 1)]1/2

MAGNETIC PROPERTIES OF ATOMIC NUCLEI For our purposes, consider the behavior of a 1H atom. The magnetic moment  is a vector quantity, that is it has both magnitude and direction. In the absence of an external magnetic field, the magnetic moments of a collection of a large number of hydrogen atoms orient themselves in a random fashion. That is, no particular orientation is preferred. RANDOM ORIENTATION

THE EXTERNAL MAGNETIC FIELD If two magnets are brought near each other they will exert a force on each other and will try to align themselves. For simple bar magnets, the favored alignment is parallel (north pole of one magnet faces the south pole of the second). Similarly, when a magnetic nucleus (I>0) is placed between the poles of an external magnet, it too will try to align itself with respect to this externally applied magnetic field (Bo).

THE EXTERNAL MAGNETIC FIELD In the macroscopic world, two magnets can be aligned in an infinite number of orientations . At the atomic level, these alignments are quantized. There are only a finite number of alignments a nucleus can take against an external magnetic field. This number depends on the value of its spin number I. Each possible alignment is assigned a value called Iz which ranges from -I to +I in steps of 1. These orientations are referred to as spin states. The diagram illustrates the possible spin states for a spin 1/2 nucleus. In quantum mechanical terms, the nuclear magnetic moment of a nucleus can align with an externally applied magnetic field of strength Bo in only 2I + 1 ways, either parallel or opposing Bo. The energetically preferred orientation has the magnetic moment aligned parallel with the applied field (spin +1/2) and is often given the notation a, whereas the higher energy anti-parallel orientation (spin -1/2) is referred to as b.

QUANTIZED SPIN STATES AND NET MAGNETIZATION When a “magnetic” nuclei of I=1/2 such as a hydrogen atoms are placed in an external magnetic field only two spin states are possible. The two states labeled  (+1/2) and  (-1/2) have different energies. Since nature always prefers the lower energy situation, more hydrogens will “choose” the  state over the  state, although the population difference will be small.

GYROSCOPIC PRECESSION Magnets, when brought together, will align exactly parallel to each other and will maintain this alignment in a static fashion. Magnetic nuclei, due to restrictions described by quantum mechanics, do not align exactly parallel to or against the external magnetic field but rather, they align at an angle. This has an important consequence that can be illustrated by considering a gyroscope. A spinning gyroscope, when placed in a specific orientation, will tend to hold that orientation despite the effects of external forces like gravity. In a vertical gravity field (gravity pulling straight down) a gyroscope placed vertically will maintain this orientation motionlessly. If a force is applied to the gyroscope perpendicular to the gravity field, it will rotate about an axis parallel to the gravity field demonstrating something call precession. The frequency of this precession depends on two factors, the force exerted by the gravity field, and the force exerted by the gyroscope

NUCLEAR PRECESSION  = Bo/2 Just as a gyroscope will precess in a gravitational field, the magnetic moment μ associated with a spinning spherical charge will precess in an external magnetic field. In the following illustration, the spinning nucleus has been placed at the origin of a cartesian coordinate system, and the external field is oriented along the z-axis. The angular frequency at which this precession occurs is given by  = Bo/2 and is called the Larmor frequency. The value, , is the magnetogyric ratio and is characteristic for each type of nucleus. It relates to the strength of the nucleus' magnetic field. H is the strength of the externally applied magnetic field. For example, a 1H atom in a magnetic field H=1.41 Tesla has a Larmor frequency of 60 megahertz (MHz).

SPIN STATE ENERGY AND Bo The orientations a magnetic nucleus can take against an external magnetic are not of equal energy. Spin states which are oriented parallel to the external field are lower in energy than in the absence of an external field. In contrast, spin states whose orientations more nearly oppose the external field are higher in energy than in the absence of an external field The difference in energy between the two spin states is dependent on the external magnetic field strength, and is always very small. The following diagram illustrates that the two spin states have the same energy when the external field is zero, but diverge as the field increases.

SPIN STATE TRANSITIONS Where an energy separation exists there is a possibility to induce a transition between the various spin states. By irradiating the nucleus with electromagnetic radiation of the correct energy (as determined by its frequency), a nucleus with a low energy orientation can be induced to "jump" to a higher energy orientation. The absorption of energy during this transition forms the basis of the NMR method. If rf energy having a frequency matching the Larmor frequency is introduced at a right angle to the external field (e.g. along the x-axis), the precessing nucleus will absorb energy and the magnetic moment will flip to its I = _1/2 state. This excitation is shown in the following diagram

SPIN STATE POPULATION INVERSION Magnetic Nuclei such as hydrogen atoms when placed in a static external magnetic field will always have a slight excess of population of atoms in the lower energy  state. By irradiating the nucleus with electromagnetic radiation of the correct energy (as determined by its frequency), a nucleus with a low energy  orientation can be induced to "jump" to a higher energy  orientation. The absorption of energy during this transition forms the basis of the NMR method.

IRRADIATION FREQUENCY VS FIELD STRENGTH Strong magnetic fields are necessary for nmr spectroscopy. The international unit for magnetic flux is the tesla (T). The earth's magnetic field is approximately 10-4 T at ground level. For nmr purposes, this small energy difference (ΔE) is usually given as a frequency in units of MHz (106 Hz), ranging from 20 to 900 Mz, depending on the magnetic field strength. Irradiation of a sample with radio frequency (rf) energy corresponding exactly to the spin state separation of a specific set of nuclei will cause excitation of those nuclei in the +1/2 state to the higher -1/2 spin state. ENERGY OF A PHOTON E = h SPIN STATE ENRGY DIFFERENCE E = hBo/2 WHEN E = E, SPIN FLIP OCCURS h hBo/2 THE NECESSARY FREQUENCY IS:  Bo/2

NMR EXPERIMENT When magnetically active nuclei are placed into an external magnetic field, the magnetic fields align themselves with the external field into two orientations. During the experiment, electromagnetic radiation of a specific frequency is applied. By sweeping the magnetic field, an energy difference between spin states will occur that has the same energy as that f the applied radio frequency and plot of frequency versus energy absorption can be generated. This is the NMR spectrum

THE CHEMICAL SHIFT Since protons all have the same magnetic moment, we might expect all hydrogen atoms to give resonance signals at the same field / frequency values. Fortunately for chemistry applications, this is not true. Below are a number of representative proton signals displayed over the same magnetic field range. It is not possible, of course, to examine isolated protons in the spectrometer; but from independent measurement and calculation it has been determined that a naked proton would resonate at a lower field strength than the nuclei of covalently bonded hydrogens. The range of field / frequency values for all hydrogen atoms in a “Chemical” environment is called the CHEMICAL SHIFT. The range of resonance frequencies, or bandwith, for most hydrogens in organic molecules in an external magnetic field (Bo=1.41T) is 600-1000 Hz, a very small range.

DIAMAGNETIC SHIELDING Why should the proton nuclei in different compounds behave differently in the nmr experiment? 
The answer to this question lies with the electron(s) surrounding the proton in covalent compounds and ions. Since electrons are charged particles, they move in response to the external magnetic field (Bo) so as to generate a secondary field that opposes the much stronger applied field. This secondary field shields the nucleus from the applied field, so Bo must be increased in order to achieve resonance (absorption of rf energy). Thus Bo must be increased to compensate for the induced shielding field. When an atom is placed in a magnetic field, its electrons circulate about the direction of the applied magnetic field. This circulation causes a small magnetic field at the nucleus which opposes the externally applied field. The magnetic field at the nucleus (the effective field) is therefore generally less than the applied field by a fraction  . B = Bo (1-)

SHIELDING AND DESHIELDING In a molecule, the nucleus is always surrounded by an electron cloud. Since the electron's magnetic field opposes the external magnetic field, the nucleus is "shielded" from the full force of the external magnetic field. Heff (Beff)is normally less than Ho (Bo). Within a molecule there are factors which can increase or decrease the electron density surrounding a nucleus. Factors which reduce the electron density are said to deshield the nucleus since Heff at the nucleus increases. Similarly, factors which increase the electron density are said to "shield" the nucleus since Heff will decrease

CHEMICAL SHIFT - ELECTRONEGATIVITY A nucleus is shielded or deshielded whenever it is influenced by the magnetic fields of nearby electrons. The closest electrons to a nucleus are those that bond the nucleus to its neighbouring atoms. Any factor that effects the distribution of these bonding electrons will also effect the degree of shielding the nucleus experiences. Electronegative atoms have an affinity for electrons. The more electronegative the atom is, the stronger this affinity. Consider the following two cases; an 1H atom bonded to a carbon; an 1H atom bonded to an oxygen. Carbon is less electronegative than oxygen. In an oxygen-hydrogen bond, the bonding electrons will be drawn towards the oxygen. The electron density around the hydrogen atom will be reduced in comparison to the same hydrogen bonded to a carbon atom. In the case of an O-H bond, hydrogen has a lower electron density surrounding it and is, therefore, less shielded. Electronegative atoms or electron withdrawing functional groups are considered to be deshielding. Electropositive atoms or electron donating functional groups are considered to be shielding.

BANDWIDTH - PPM SCALE The resonance frequency / magnetic field range for hydrogens in organic compounds show below is very small. On a spectrometer where the proton transition frequencies are nominally 60 MHz, the chemical shift frequency changes may be only hundreds of hertz; about a million times smaller than the resonance frequency. . Because of this relationship, chemical shifts are typically reported as a fraction of the nominal resonance frequency. Due to their small size, parts-per-million (ppm) are used. On a 60 MHz spectrometer, a 60 Hz chemical shift is reported as a (60 / 60,000,000) = 1 ppm shift

CHEMICAL SHIFT -  SCALE The chemical shift of a nucleus is the difference between the resonance frequency of the nucleus and a standard, relative to the standard. This quantity is reported in ppm and given the symbol delta, . .  = shift in Hz from TMS/spectrometer frequency In NMR spectroscopy, this standard is often tetramethylsilane, Si(CH3)4, abbreviated TMS. The chemical shift is a very precise metric of the chemical environment around a nucleus