The Nature of NMR Absorptions
• The two methyl groups of methyl acetate are nonequivalent
• The two sets of hydrogens absorb at different positions
• When the frequency of rf irradiation is held constant and the applied field strength is varied each nucleus in a molecule comes into resonance at a slightly different field strength, mapping the carbon-hydrogen framework of an organic molecule
Many good textbooks describe the theory of NMR spectroscopy in more detail, a selection of which are listed in Further reading at the end of this chapter.
Important NMR-active nuclei
Although all nuclei have at least one isotope that is, in principle, NMR active, most NMR spectra are based on just a few nuclear types. There are several reasons for this. One is that nuclei with I >½ have a property called a nuclear quadrupole moment that, in general, results in short lifetimes in the excited spin states and a rapid return to the low energy state, which gives very broad NMR lines. Secondly, many NMR-responsive nuclei exist at low natural abundances and so are difficult to detect without isotopic enrichment. Thirdly, the strength of the NMR response is related to the size of the nuclearmagnetic moment, for which many nuclei have rather small values and so have low detectability. Finally, some nuclei, once excited to the upper level, are slow to relax back to the ground state, which must occur before another scan can be added. This then incurs a time penalty for acquiring the summed scans necessary to improve detection limits. Sometimes these difficulties of low sensitivity, low natural abundance and long relaxation times come together.
The vector sum of the magnetic moments of one type of nuclei is a measure of the number of protons of that type in the molecule.
The determination of the magnetic moment for protons in each type of electronic environment forms the essence of the NMR experiment.
• NMR spectrometers are referred to as 300 MHz instruments, 500 MHz instruments, and so forth, depending on the frequency of the RF
radiation used for resonance.
• These spectrometers use very powerful magnets to create a small but measurable energy difference between two possible spin states.
Two decay routes (non-radiative):
1. Spin-Lattice Relaxation (T 1 ) -also called: longitudinal relaxation
-due to interactions between nuclear spin states and magnetic micro environments in the sample -magnetic micro environments must be at the Larmor Frequency of the absorbing nuclei in order to couple
Proton NuclearMagneticResonanceSpectroscopy Introduction:
The NMR Spectrum serves as a great resource in determining the structure of an organic compound by revealing the hydrogen and carbon skeleton. Historically, NMR was initially used to study the nuclei of Hydrogen atoms; however, any atom with an odd mass or atomic number has a nuclear spin that can be studied by NMR. Without the application of an applied magnetic field, protons are spinning in a randomly oriented manner and are generating a magnetic field (called the magnetic moment) 1 . However, once an external (applied) magnetic field is present the protons either align with (parallel) or against (anti parallel) it. The parallel orientation, called the alpha spin, has a lower energy than the anti parallel (beta) spin. The stronger the applied magnetic field the greater the energy difference (∆E) between the parallel and anti parallel states (Diagram 1) 2 . Therefore, the strength of the magnetic field determines the energy required to cause a nuclear spin flip. The energy difference (∆E) between the ground and excited states is approximately 0.02 cal/mol which correlates to radio wave photons. An NMR signal is created once the radio wave photons supplied match the (∆E) of the nucleus.
In this laboratory exercise we will learn how to use the Chemistry Department's NuclearMagneticResonance (NMR) spectrometer and how to interpret the spectra obtained using this spectrometer. NMR is one of the most powerful techniques available to the organic chemist for molecular structure determination. Therefore, knowing how to obtain and interpret NMR spectra is of critical importance.
and from 5 to 12%, respectively. Minor phospholipids were identified in forms of phosphatidic acid, lysophosphatidic acid, and phosphatidylglycerol 23 .
Discrimination between apple juices produced from different varieties has been achieved by applying principal components analysis (PCA) and linear discriminant analysis to 1H NMR spectra of the juices by Belton et al. Under optimum conditions a 100% success rate was achieved. Examination of the principal component loadings showed that the levels of malic acid and sucrose were two important chemical variables, but variations in the composition of the minor constituents were also found to make a significant contribution to the discrimination 24 .
a b s t r a c t
Cement is the ubiquitous material upon which modern civilisation is built, providing long-term strength, impermeability and durability for housing and infrastructure. The fundamental chemical interactions which control the structure and performance of cements have been the subject of intense research for decades, but the complex, crystallographically disordered nature of the key phases which form in hardened cements has raised difﬁculty in obtaining detailed information about local structure, reaction mechanisms and kinetics. Solid-state nuclearmagneticresonance (SS NMR) spectroscopy can resolve key atomic structural details within these materials and has emerged as a crucial tool in characterising cement structure and properties. This review provides a comprehensive overview of the application of multinuclear SS NMR spectroscopy to understand compositionestructureeproperty relationships in cements. This includes anhydrous and hydrated phases in Portland cement, calcium aluminate cements, calcium sulfoaluminate cements, magnesia-based cements, alkali-activated and geopolymer cements and synthetic model systems. Advanced and multidimensional experiments probe 1 H, 13 C, 17 O, 19 F, 23 Na, 25 Mg, 27 Al, 29 Si, 31 P, 33 S, 35 Cl, 39 K and 43 Ca nuclei, to study atomic structure, phase evolution, nanostructural development, reaction mechanisms and kinetics. Thus, the mechanisms controlling the physical properties of cements can now be resolved and understood at an unprecedented and essential level of detail.
Protein structure can be investigated with increasing ease and precision using the modern techniques of structural biology. Not surprisingly, research focus has shifted to the study of the structure and function of large proteins, protein complexes or even membrane embedded proteins; yet, even the basic determinants of protein structure and folding are still poorly understood. In addition to intramolecular interactions, protein structure appears to be governed by contributions from solvation effects. The importance of the latter is illustrated by the effects of the interaction with various solutes, leading to the protein folding or denaturation. Observing interactions between solvent species and a protein remains challenging using the currently available experimental techniques for various reasons. For example, X-ray crystallography requires the artificial environment of a crystal, and furthermore cannot observe disordered conformations, while in nuclearmagneticresonance (NMR) spectroscopy, dynamic effects reduce the ability to observe intermolecular solvent/protein interactions.
Distribution of Particles between magnetic quantum states
In absence of magnetic field, E of 2 states are identical so # of nuclei in 2 states are equal
In magnetic field the nuclei want to be oriented with the magnetic field so they are in their lowest E state. When we were in UV we used the Boltzmann distribution to calculate the # of atoms in ground and excited states, and found that the number in the excited state was incredibly small. Even in the IR we found that the number in the excited state was usually < 1% of the molecules. What about the NMR, where we are using very low frequencies and Energies
The _E is the energy difference between the _ and _ spin states. This depends on the applied magnetic field. As shown by the graph above, the greater the strength of the applied magnetic field, the larger the energy difference between the two spin states. When radiation, that has the same energy as the _E, is placed upon the sample, the spin flips from _ to _ spin states. Then, the nuclei undergoes relaxation. Relaxation is when the nuclei return to their original state. In this process, they emit electromagnetic signals whose frequencies depend on _E as well. The H- NMR spectrometer reads these signals and plots them on a graph of signal frequency versus intensity. Resonance is when the nuclei flip back and forth between _ and _ spin states due to the radiation that is placed on them. To summarize, an NMR signal is observed when the radiation supplied matches the _E. And, the energy required to cause spin flip is dependent on the magnetic environment experienced by the nucleus.
The sensitivity of NMR spectroscopy to the local atomic-scale environment offers great potential for the characterisation of a diverse range of solid materials. Despite offering more information than its solution-state counterpart, solid-state NMR has not yet achieved a similar level of recognition, owing to the anisotropic interactions that broaden the spectral lines and hinder the extraction of structural information. Here, we describe the methods available to improve the resolution of solid-state NMR spectra, and the continuing research in this area. We also highlight areas of exciting new and future development, including recent interest in combining experiment with theoretical calculations, the rise of a range of polarisation transfer techniques that provide significant sensitivity enhancements and the progress of in situ measurements. We demonstrate the detailed information available when studying dynamic and disordered solids, and discuss the future applications of solid-state NMR spectroscopy across the chemical sciences.
creates a complex, time varying field about each nucleus (Lattice field) some of the magnetic components of this field will be varying at the
Larmor frequency and will interact with the nucleus of interest to cause it to relax from upper to lower state. The nucleus gives up its spin energy to the thermal motion of the lattice (⇒ tiny increase in sample
Proton NuclearMagneticResonance ( 1 H-NMR) Spectroscopy Theory behind NMR:
In the late 1940’s, physical chemists originally developed NMR spectroscopy to study different properties of atomic nuclei, but later found it to be useful in determining the molecular structure of organic compounds. The theory behind NMR comes from the spin, I 1 of a nucleus. Just as electrons have a +1/2, -1/2 spin, certain nuclei also experience charged spins that create a magnetic field (called the magnetic moment), which allows chemists to study them using NMR. Nuclei with even numbers of both neutrons and protons experience NO spin and nuclei with odd numbers of both neutrons and protons have integer spins. Nuclei that have the sum of protons and neutrons equal to an odd number (like 1 H and 13 C) have half-integer spins. When there is no external or applied magnetic field (B 0 ), the nuclear spins orient randomly; however, when there is an applied magnetic field, the nuclei orient themselves with or against the larger applied field. The -spin state is parallel to the applied force and has lower energy than the _- spin state that is antiparallel to the applied force. The energy difference (_ E) between the - and _-spin states depends on the strength of the applied magnetic field. The greater the strength of the applied magnetic field, the greater is the _ E between the - and _-spin states 2 . The _ E between the - and _-spin state is ~0.02 cal mol -1 , which lies in the radio frequency region. The emitted energy in this region produces an NMR signal.
In this publication, we have thoroughly reviewed the abiding applications of average Hamiltonian theory, Flo- quet theory, and Floquet-Magnus expansion from very different perpectives in spin quantum physics of nuclearmagneticresonance. We also have presented some potential theories in NMR such as Fer expansion, Chebychev approximation, and possibly Cayley method. The combinations of two or more of the theories therein described will provide a framework for treating time-dependent Hamiltonian in quantum physics and NMR in a way that can be easily extended to both synchronized and several non-synchronized modulations. We hope this publica- tion will encourage the use of Floquet-Magnus and Fer expansions as numerical integrators as well as the use of Floquet-Magnus expansion as alternative approach in designing sophisticated pulse sequences and analyzing and understanding of different experiments. We also hope that this review will contribute to motivate spin dy- namics experts in NMR to consider other perspectives and approaches beyond the scope of the current popular or used theories in the field of nuclearmagneticresonance. They are also many remarkable applications of the theory of NMR that we do not discuss in this review such as quantum information processing and computing.
Nuclearmagneticresonancespectroscopy (NMR) is the great tool for elucidating the molecular structure of organic compounds and inorganic complexes. This technique gives the information regarding the number of magnetically distinct nuclei under investigation and gives the vital facts about the nature of the surrounding nuclei. The hydrogen and carbon nuclei are the major constituents of inorganic and organic complexes. Proton and carbon-13 NMR are the important tool used to investigate the structures in organic and inorganic complexes (organometallics). The chemical environment around each proton under investigation is different and it is possible to differentiate them. This characteristic feature is due to different chemical environments around each nuclei. The external magnetic field influences the valence electrons and is highly affected and these tend to generate a magnetic field, that too in opposite direction to the applied magnetic field. This characteristic is used for the application of lanthanide complexes as Shift Reagents (SR).
SSNMR spectroscopy has been extensively used for the characterization of MOFs. 2,3 1 H and 13 C SSNMR experiments have become a routine technique to study organic linkers. 12-19 2 H NMR experiment is employed to examine the flexibility of the framework and the dynamics of the guest species inside of micropores. 20-23 The local environments around several metal centers are also probed by SSNMR experiments, such as 27 Al, 24-26 45 Sc, 27 71 Ga, 28 25 Mg 11,29 and 67 Zn 10 . Despite its importance, direct determination of the number of non-equivalent sites by SSNMR experiments, in particular H, is rare due to the poor 1 H spectral resolution in solids, which is severely limited by the narrow 1 H chemical shift range and the strong 1 H– 1 H homonuclear dipolar coupling. 30 Several approaches were used in the literature to mitigate this problem including ultrafast magic-angle spinning (MAS) 30,31 and “isotopic ( 2 H) dilution”. 32-35 Moreover, performing 1 H SSNMR experiments at high magnetic fields provides an additional benefit in spectral resolution since chemical shifts (in Hz) scale linearly with the magnetic field strength, while 1 H– 1 H dipolar coupling remains constant. However, the systematic examination of the feasibility of these strategies in MOFs, which usually consist of three-dimensional networks of dipolar coupling, is absent to date.
reaction using a cell extract incubated with an initial concentration of 8.5 mM F6P and no G6P, collected at a 60 ◦ pulse angle over 47 min (0.8 s acquisition, 0.5 s relaxation). Additional NMR parameters are described in Section 3.3 . In this reaction, F6P was converted in reverse to G6P as the reaction approached equilibrium. The time course is not shown to full equilibration; final concentrations were 5 and 2.8 mM for G6P and F6P respectively. TEP is an internal standard; (b) Reversible Michaelis–Menten equation (see Table 1 ) fitted to PGI progress curves derived from NMR data: equilibrium values are represented by the red contour line (—), arrows indicate both the metabolite concentrations and the direction of reaction as each time course progresses towards equilibrium ( →→→ ). The rate was normalised to total protein concentration. Substrate and product concentration axes are in logarithmic scale. R 2 = 0.99.