Spin quantum number

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Spin_quantum_number

In physics, the spin quantum number is a quantum number (designated s) that describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle. It has the same value for all particles of the same type, such as s = 1/2 for all electrons. It is an integer for all bosons, such as photons, and a half-odd-integer for all fermions, such as electrons and protons. The component of the spin along a specified axis is given by the spin magnetic quantum number, conventionally written m_s. The value of m_s is the component of spin angular momentum, in units of the reduced Planck constant ħ, parallel to a given direction (conventionally labelled the z–axis). It can take values ranging from +s to −s in integer increments. For an electron, m_s can be either ++1/2 or −+1/2 .

The phrase spin quantum number was originally used to describe the fourth of a set of quantum numbers (the principal quantum number n, the azimuthal quantum number ℓ, the magnetic quantum number m, and the spin magnetic quantum number m_s), which completely describe the quantum state of an electron in an atom. Some introductory chemistry textbooks describe m_s as the spin quantum number, and s is not mentioned since its value 1/2 is a fixed property of the electron, sometimes using the variable s in place of m_s. Some authors discourage this usage as it causes confusion. At a more advanced level where quantum mechanical operators or coupled spins are introduced, s is referred to as the spin quantum number, and m_s is described as the spin magnetic quantum number or as the z-component of spin s_z.

Spin quantum numbers apply also to systems of coupled spins, such as atoms that may contain more than one electron. Capitalized symbols are used: S for the total electronic spin, and m_S or M_S for the z-axis component. A pair of electrons in a spin singlet state has S = 0, and a pair in the triplet state has S = 1, with m_S = −1, 0, or +1. Nuclear-spin quantum numbers are conventionally written I for spin, and m_I or M_I for the z-axis component.

The name "spin" comes from a geometrical spinning of the electron about an axis, as proposed by Uhlenbeck and Goudsmit. However, this simplistic picture was quickly realized to be physically unrealistic, because it would require the electrons to rotate faster than the speed of light. It was therefore replaced by a more abstract quantum-mechanical description.

Magnetic nature of atoms and molecules

The spin quantum number helps to explain the magnetic properties of atoms and molecules. A spinning electron behaves like a micromagnet with a definite magnetic moment. If an atomic or molecular orbital contains two electrons, then their magnetic moments oppose and cancel each other.

If all orbitals are doubly occupied by electrons, the net magnetic moment is zero and the substance behaves as diamagnetic; it is repelled by the external magnetic field. If some orbitals are half filled (singly occupied), the substance has a net magnetic moment and is paramagnetic; it is attracted by the external magnetic field.

History

Early attempts to explain the behavior of electrons in atoms focused on solving the Schrödinger wave equation for the hydrogen atom, the simplest possible case, with a single electron bound to the atomic nucleus. This was successful in explaining many features of atomic spectra.

The solutions required each possible state of the electron to be described by three "quantum numbers". These were identified as, respectively, the electron "shell" number n, the "orbital" number ℓ, and the "orbital angular momentum" number m. Angular momentum is a so-called "classical" concept measuring the momentum of a mass in circular motion about a point. The shell numbers start at 1 and increase indefinitely. Each shell of number n contains n² orbitals. Each orbital is characterized by its number ℓ, where ℓ takes integer values from 0 to n − 1, and its angular momentum number m, where m takes integer values from +ℓ to −ℓ. By means of a variety of approximations and extensions, physicists were able to extend their work on hydrogen to more complex atoms containing many electrons.

Atomic spectra measure radiation absorbed or emitted by electrons "jumping" from one "state" to another, where a state is represented by values of n, ℓ, and m. The so-called "transition rule" limits what "jumps" are possible. In general, a jump or "transition" is allowed only if all three numbers change in the process. This is because a transition will be able to cause the emission or absorption of electromagnetic radiation only if it involves a change in the electromagnetic dipole of the atom.

However, it was recognized in the early years of quantum mechanics that atomic spectra measured in an external magnetic field (see Zeeman effect) cannot be predicted with just n, ℓ, and m.

In January 1925, when Ralph Kronig was still a Columbia University Ph.D. student, he first proposed electron spin after hearing Wolfgang Pauli in Tübingen. Werner Heisenberg and Pauli immediately hated the idea: They had just ruled out all imaginable actions from quantum mechanics. Now Kronig was proposing to set the electron rotating in space. Pauli especially ridiculed the idea of spin, saying that "it is indeed very clever but of course has nothing to do with reality". Faced with such criticism, Kronig decided not to publish his theory and the idea of electron spin had to wait for others to take the credit. Ralph Kronig had come up with the idea of electron spin several months before George Uhlenbeck and Samuel Goudsmit, but most textbooks credit these two Dutch physicists with the discovery.

Pauli subsequently proposed (also in 1925) a new quantum degree of freedom (or quantum number) with two possible values, in order to resolve inconsistencies between observed molecular spectra and the developing theory of quantum mechanics.

Shortly thereafter Uhlenbeck and Goudsmit identified Pauli's new degree of freedom as electron spin.

Electron spin

Main article: Electron magnetic moment

A spin- 1 /2 particle is characterized by an angular momentum quantum number for spin s =  1 /2. In solutions of the Schrödinger-Pauli equation, angular momentum is quantized according to this number, so that magnitude of the spin angular momentum is

$${\displaystyle \Vert \mathbf{S}\Vert =\hslash \sqrt{s(s+1)}=\frac{\sqrt{3}}{2}\hslash .}$$

The hydrogen spectrum fine structure is observed as a doublet corresponding to two possibilities for the z-component of the angular momentum, where for any given direction z:

$${\displaystyle s_z=\pm \frac{1}{2}\hslash .}$$

whose solution has only two possible z-components for the electron. In the electron, the two different spin orientations are sometimes called "spin-up" or "spin-down".

The spin property of an electron would give rise to magnetic moment, which was a requisite for the fourth quantum number.

The magnetic moment vector of an electron spin is given by:

$${\displaystyle {\mathit{\mu }}_{\text{s}}=-\frac{e}{2m}{g}_{\text{s}}\mathbf{S}}$$

where ${\displaystyle -e}$ is the electron charge, ${\displaystyle m}$ is the electron mass, and ${\displaystyle g_{\text{s}}}$ is the electron spin g-factor, which is approximately 2.0023. Its z-axis projection is given by the spin magnetic quantum number ${\displaystyle m_{\text{s}}}$ according to:

$${\displaystyle {\mu }_z=-m_{\text{s}}{g}_{\text{s}}{\mu }_{\mathsf{B}}=\pm \frac{1}{2}{g}_{\text{s}}{\mu }_{\mathsf{B}}}$$

where ${\displaystyle {\mu }_{\mathsf{B}}}$ is the Bohr magneton.

When atoms have even numbers of electrons the spin of each electron in each orbital has opposing orientation to that of its immediate neighbor(s). However, many atoms have an odd number of electrons or an arrangement of electrons in which there is an unequal number of "spin-up" and "spin-down" orientations. These atoms or electrons are said to have unpaired spins that are detected in electron spin resonance.

Detection of spin

When lines of the hydrogen spectrum are examined at very high resolution, they are found to be closely spaced doublets. This splitting is called fine structure, and was one of the first experimental evidences for electron spin. The direct observation of the electron's intrinsic angular momentum was achieved in the Stern–Gerlach experiment.

Stern–Gerlach experiment

The theory of spatial quantization of the spin moment of the momentum of electrons of atoms situated in the magnetic field needed to be proved experimentally. In 1922 (two years before the theoretical description of the spin was created) Otto Stern and Walter Gerlach observed it in the experiment they conducted.

Silver atoms were evaporated using an electric furnace in a vacuum. Using thin slits, the atoms were guided into a flat beam and the beam sent through an in-homogeneous magnetic field before colliding with a metallic plate. The laws of classical physics predict that the collection of condensed silver atoms on the plate should form a thin solid line in the same shape as the original beam. However, the in-homogeneous magnetic field caused the beam to split in two separate directions, creating two lines on the metallic plate.

The phenomenon can be explained with the spatial quantization of the spin moment of momentum. In atoms the electrons are paired such that one spins upward and one downward, neutralizing the effect of their spin on the action of the atom as a whole. But in the valence shell of silver atoms, there is a single electron whose spin remains unbalanced.

The unbalanced spin creates spin magnetic moment, making the electron act like a very small magnet. As the atoms pass through the in-homogeneous magnetic field, the force moment in the magnetic field influences the electron's dipole until its position matches the direction of the stronger field. The atom would then be pulled toward or away from the stronger magnetic field a specific amount, depending on the value of the valence electron's spin. When the spin of the electron is ++ 1 /2 the atom moves away from the stronger field, and when the spin is −+ 1 /2 the atom moves toward it. Thus the beam of silver atoms is split while traveling through the in-homogeneous magnetic field, according to the spin of each atom's valence electron.

In 1927 Phipps and Taylor conducted a similar experiment, using atoms of hydrogen with similar results. Later scientists conducted experiments using other atoms that have only one electron in their valence shell: (copper, gold, sodium, potassium). Every time there were two lines formed on the metallic plate.

The atomic nucleus also may have spin, but protons and neutrons are much heavier than electrons (about 1836 times), and the magnetic dipole moment is inversely proportional to the mass. So the nuclear magnetic dipole momentum is much smaller than that of the whole atom. This small magnetic dipole was later measured by Stern, Frisch and Easterman.

Electron paramagnetic resonance

For atoms or molecules with an unpaired electron, transitions in a magnetic field can also be observed in which only the spin quantum number changes, without change in the electron orbital or the other quantum numbers. This is the method of electron paramagnetic resonance (EPR) or electron spin resonance (ESR), used to study free radicals. Since only the magnetic interaction of the spin changes, the energy change is much smaller than for transitions between orbitals, and the spectra are observed in the microwave region.

Derivation

For a solution of either the nonrelativistic Pauli equation or the relativistic Dirac equation, the quantized angular momentum (see angular momentum quantum number) can be written as:

$${\displaystyle \Vert \mathbf{s}\Vert =\sqrt{s(s+1)}\hslash }$$

where

• ${\displaystyle \mathbf{s}}$ is the quantized spin vector or spinor
• ${\displaystyle \Vert \mathbf{s}\Vert }$ is the norm of the spin vector
• s is the spin quantum number associated with the spin angular momentum
• ${\displaystyle \hslash }$ is the reduced Planck constant.

Given an arbitrary direction z (usually determined by an external magnetic field) the spin z-projection is given by

${\displaystyle s_z=m_s\hslash }$

where m_s is the secondary spin quantum number, ranging from −s to +s in steps of one. This generates 2 s + 1 different values of m_s.

The allowed values for s are non-negative integers or half-integers. Fermions have half-integer values, including the electron, proton and neutron which all have s = ++ 1 /2 . Bosons such as the photon and all mesons) have integer spin values.

Algebra

The algebraic theory of spin is a carbon copy of the angular momentum in quantum mechanics theory. First of all, spin satisfies the fundamental commutation relation:

$${\displaystyle [S_i,S_j]=i\hslash {ϵ}_{ijk}{S}_k,}$$

$${\displaystyle \left[S_i,S^2\right]=0}$$

where ${\displaystyle {ϵ}_{ijk}}$ is the (antisymmetric) Levi-Civita symbol. This means that it is impossible to know two coordinates of the spin at the same time because of the restriction of the uncertainty principle.

Next, the eigenvectors of ${\displaystyle S^2}$ and ${\displaystyle S_z}$ satisfy:

$${\displaystyle S^2|s,m_s⟩={\hslash }^{2}s(s+1)|s,m_s⟩}$$

$${\displaystyle S_z|s,m_s⟩=\hslash m_s|s,m_s⟩}$$

$${\displaystyle S_{\pm }|s,m_s⟩=\hslash \sqrt{s(s+1)-m_s(m_s\pm 1)}|s,m_s\pm 1⟩}$$

where ${\displaystyle S_{\pm }=S_x\pm i{S}_y}$ are the ladder (or "raising" and "lowering") operators.

Energy levels from the Dirac equation

In 1928, Paul Dirac developed a relativistic wave equation, now termed the Dirac equation, which predicted the spin magnetic moment correctly, and at the same time treated the electron as a point-like particle. Solving the Dirac equation for the energy levels of an electron in the hydrogen atom, all four quantum numbers including s occurred naturally and agreed well with experiment.

Total spin of an atom or molecule

For some atoms the spins of several unpaired electrons (s₁, s₂, ...) are coupled to form a total spin quantum number S. This occurs especially in light atoms (or in molecules formed only of light atoms) when spin–orbit coupling is weak compared to the coupling between spins or the coupling between orbital angular momenta, a situation known as L S coupling because L and S are constants of motion. Here L is the total orbital angular momentum quantum number.

For atoms with a well-defined S, the multiplicity of a state is defined as 2S + 1. This is equal to the number of different possible values of the total (orbital plus spin) angular momentum J for a given (L, S) combination, provided that S ≤ L (the typical case). For example, if S = 1, there are three states which form a triplet. The eigenvalues of S_z for these three states are +1ħ, 0, and −1ħ. The term symbol of an atomic state indicates its values of L, S, and J.

As examples, the ground states of both the oxygen atom and the dioxygen molecule have two unpaired electrons and are therefore triplet states. The atomic state is described by the term symbol ³P, and the molecular state by the term symbol ³Σ⁻
_g.

Nuclear spin

Atomic nuclei also have spins. The nuclear spin I is a fixed property of each nucleus and may be either an integer or a half-integer. The component m_I of nuclear spin parallel to the z–axis can have (2I + 1) values I, I–1, ..., –I. For example, a ¹⁴N nucleus has I = 1, so that there are 3 possible orientations relative to the z–axis, corresponding to states m_I = +1, 0 and −1.

The spins I of different nuclei are interpreted using the nuclear shell model. Even-even nuclei with even numbers of both protons and neutrons, such as ¹²C and ¹⁶O, have spin zero. Odd mass number nuclei have half-integer spins, such as 3/ 2  for ⁷Li,  1 /2 for ¹³C and 5/ 2  for ¹⁷O, usually corresponding to the angular momentum of the last nucleon added. Odd-odd nuclei with odd numbers of both protons and neutrons have integer spins, such as 3 for ¹⁰B, and 1 for ¹⁴N. Values of nuclear spin for a given isotope are found in the lists of isotopes for each element. (See isotopes of oxygen, isotopes of aluminium, etc. etc.)

Functional magnetic resonance spectroscopy of the brain

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Functional_magnetic_resonance_spectroscopy_of_the_brain

Functional magnetic resonance spectroscopy of the brain (fMRS) uses magnetic resonance imaging (MRI) to study brain metabolism during brain activation. The data generated by fMRS usually shows spectra of resonances, instead of a brain image, as with MRI. The area under peaks in the spectrum represents relative concentrations of metabolites.

fMRS is based on the same principles as in vivo magnetic resonance spectroscopy (MRS). However, while conventional MRS records a single spectrum of metabolites from a region of interest, a key interest of fMRS is to detect multiple spectra and study metabolite concentration dynamics during brain function. Therefore, it is sometimes referred to as dynamic MRS, event-related MRS or time-resolved MRS. A novel variant of fMRS is functional diffusion-weighted spectroscopy (fDWS) which measures diffusion properties of brain metabolites upon brain activation.

Unlike in vivo MRS which is intensively used in clinical settings, fMRS is used primarily as a research tool, both in a clinical context, for example, to study metabolite dynamics in patients with epilepsy, migraine and dyslexia, and to study healthy brains. fMRS can be used to study metabolism dynamics also in other parts of the body, for example, in muscles and heart; however, brain studies have been far more popular.

The main goals of fMRS studies are to contribute to the understanding of energy metabolism in the brain, and to test and improve data acquisition and quantification techniques to ensure and enhance validity and reliability of fMRS studies.

Basic principles

Studied nuclei

Like in vivo MRS, fMRS can probe different nuclei, such as hydrogen (¹H) and carbon (¹³C). The ¹H nucleus is the most sensitive and is most commonly used to measure metabolite concentrations and concentration dynamics, whereas ¹³C is best suited for characterizing fluxes and pathways of brain metabolism. The natural abundance of ¹³C in the brain is only about 1%; therefore, ¹³C fMRS studies usually involve the isotope enrichment via infusion or ingestion.

In the literature ¹³C fMRS is commonly referred to as functional ¹³C MRS or just ¹³C MRS.

Spectral and temporal resolution

Typically in MRS a single spectrum is acquired by averaging enough spectra over a long acquisition time. Averaging is necessary because of the complex spectral structures and relatively low concentrations of many brain metabolites, which result in a low signal-to-noise ratio (SNR) in MRS of a living brain.

fMRS differs from MRS by acquiring not one but multiple spectra at different time points while the participant is inside the MRI scanner. Thus, temporal resolution is very important and acquisition times need to be kept adequately short to provide a dynamic rate of metabolite concentration change.

To balance the need for temporal resolution and sufficient SNR, fMRS requires a high magnetic field strength (1.5 T and above). High field strengths have the advantage of increased SNR as well as improved spectral resolution allowing to detect more metabolites and more detailed metabolite dynamics.

fMRS is continuously advancing as stronger magnets become more available and better data acquisition techniques are developed providing increased spectral and temporal resolution. With 7-tesla magnet scanners it is possible to detect around 18 different metabolites of ¹H spectrum which is a significant improvement over less powerful magnets. Temporal resolution has increased from 7 minutes in the first fMRS studies to 5 seconds in more recent ones.

Spectroscopic technique

In fMRS, depending on the focus of the study, either single-voxel or multi-voxel spectroscopic technique can be used.

In single-voxel fMRS the selection of the volume of interest (VOI) is often done by running a functional magnetic resonance imaging (fMRI) study prior to fMRS to localize the brain region activated by the task. Single-voxel spectroscopy requires shorter acquisition times; therefore it is more suitable for fMRS studies where high temporal resolution is needed and where the volume of interest is known.

Multi-voxel spectroscopy provides information about group of voxels and data can be presented in 2D or 3D images, but it requires longer acquisition times and therefore temporal resolution is decreased. Multi-voxel spectroscopy usually is performed when the specific volume of interest is not known or it is important to study metabolite dynamics in a larger brain region.

Advantages and limitations

fMRS has several advantages over other functional neuroimaging and brain biochemistry detection techniques. Unlike push-pull cannula, microdialysis and in vivo voltammetry, fMRS is a non-invasive method for studying dynamics of biochemistry in an activated brain. It is done without exposing subjects to ionizing radiation like it is done in positron emission tomography (PET) or single-photon emission computed tomography (SPECT) studies. fMRS gives a more direct measurement of cellular events occurring during brain activation than BOLD fMRI or PET which rely on hemodynamic responses and show only global neuronal energy uptake during brain activation while fMRS gives also information about underlying metabolic processes that support the working brain.

However, fMRS requires very sophisticated data acquisition, quantification methods and interpretation of results. This is one of the main reasons why in the past it received less attention than other MR techniques, but the availability of stronger magnets and improvements in data acquisition and quantification methods are making fMRS more popular.

Main limitations of fMRS are related to signal sensitivity and the fact that many metabolites of potential interest can not be detected with current fMRS techniques.

Because of limited spatial and temporal resolution fMRS can not provide information about metabolites in different cell types, for example, whether lactate is used by neurons or by astrocytes during brain activation. The smallest volume that can currently be characterized with fMRS is 1 cm³, which is too big to measure metabolites in different cell types. To overcome this limitation, mathematical and kinetic modeling is used.

Many brain areas are not suitable for fMRS studies because they are too small (like small nuclei in brainstem) or too close to bone tissue, CSF or extracranial lipids, which could cause inhomogeneity in the voxel and contaminate the spectra. To avoid these difficulties, in most fMRS studies the volume of interest is chosen from the visual cortex – because it is easily stimulated, has high energy metabolisms, and yields good MRS signals.

Applications

Unlike in vivo MRS which is intensively used in clinical settings, fMRS is used primarily as a research tool, both in a clinical context, for example, to study metabolite dynamics in patients with epilepsy, migraine and dyslexia, and to study healthy brains.

fMRS can be used to study metabolism dynamics also in other parts of the body, for example, in muscles and heart; however, brain studies have been far more popular.

The main goals of fMRS studies are to contribute to the understanding of energy metabolism in the brain, and to test and improve data acquisition and quantification techniques to ensure and enhance validity and reliability of fMRS studies.

Brain energy metabolism studies

fMRS was developed as an extension of MRS in the early 1990s. Its potential as a research technology became obvious when it was applied to an important research problem where PET studies had been inconclusive, namely the mismatch between oxygen and glucose consumption during sustained visual stimulation. The ¹H fMRS studies highlighted the important role of lactate in this process and significantly contributed to the research in brain energy metabolism during brain activation. It confirmed the hypothesis that lactate increases during sustained visual stimulation and allowed the generalization of findings based on visual stimulation to other types of stimulation, e.g., auditory stimulation, motor task and cognitive tasks.

¹H fMRS measurements were instrumental in achieving the current consensus among most researchers that lactate levels increase during the first minutes of intense brain activation. However, there are no consistent results about the magnitude of increase, and questions about the exact role of lactate in brain energy metabolism still remain unanswered and are the subject of continuing research.

¹³C MRS is a special type of fMRS particularly suited for measuring important neurophysiological fluxes in vivo and in real time to assess metabolic activity both in healthy and diseased brains (e.g., in human tumor tissue). These fluxes include TCA cycle, glutamate–glutamine cycle, glucose and oxygen consumption. ¹³C MRS can provide detailed quantitative information about glucose dynamics that can not be obtained with ¹H fMRS, because of the low concentration of glucose in the brain and the spread of its resonances in several multiplets in the ¹H MRS spectrum.

¹³C MRSs have been crucial in recognizing that the awake nonstimulated (resting) human brain is highly active using 70%–80% of its energy for glucose oxidation to support signaling within cortical networks which is suggested to be necessary for consciousness. This finding has an important implication for the interpretation of BOLD fMRI data where this high baseline activity is generally ignored and response to the task is shown as independent of the baseline activity. ¹³C MRS studies indicate that this approach can misjudge and even completely miss the brain activity induced by the task.

¹³C MRS findings together with other results from PET and fMRI studies have been combined in a model to explain the function of resting state activity called default mode network.

Another important benefit of ¹³C MRS is that it provides unique means for determining the time course of metabolite pools and measuring turnover rates of TCA and glutamate–glutamine cycles. As such, it has been proved to be important in aging research by revealing that mitochondrial metabolism is reduced with aging which may explain the decline in cognitive and sensory processes.

Water resonance studies

Usually, in ¹H fMRS the water signal is suppressed to detect metabolites with much lower concentration than water. Though, an unsuppressed water signal can be used to estimate functional changes in the relaxation time T2* during cortical activation.

This approach has been proposed as an alternative to the BOLD fMRI technique and used to detect visual response to photic stimulation, motor activation by finger tapping and activations in language areas during speech processing. Recently functional real-time single-voxel proton spectroscopy (fSVPS) has been proposed as a technique for real-time neurofeedback studies in magnetic fields of 7 tesla (7 T) and above. This approach could have potential advantages over BOLD fMRI and is the subject of current research.

Migraine and pain studies

fMRS has been used in migraine and pain research. It has supported the important hypothesis of mitochondria dysfunction in migraine with aura (MwA) patients. Here the ability of fMRS to measure chemical processes in the brain over time proved crucial for confirming that repetitive photic stimulation causes higher increase of the lactate level and higher decrease of the N-acetylaspartate (NAA) level in the visual cortex of MwA patients compared to migraine without aura (MwoA) patients and healthy individuals.

In pain research fMRS complements fMRI and PET techniques. Although fMRI and PET are continuously used to localize pain processing areas in the brain, they can not provide direct information about changes in metabolites during pain processing that could help to understand physiological processes behind pain perception and potentially lead to novel treatments for pain. fMRS overcomes this limitation and has been used to study pain-induced (cold-pressure, heat, dental pain) neurotransmitter level changes in the anterior cingulate cortex, anterior insular cortex and left insular cortex. These fMRS studies are valuable because they show that some or all Glx compounds (glutamate, GABA and glutamine) increase during painful stimuli in the studied brain regions.

Cognitive studies

Cognitive studies frequently rely on the detection of neuronal activity during cognition. The use of fMRS for this purpose is at present mainly at an experimental level but is rapidly increasing. Cognitive tasks where fMRS has been used and the major findings of the research are summarized below.

Cognitive task	Brain region	Major findings
Silent word generation task	Left inferior frontal gyrus	Increased lactate level during the task in young alert participants, but not in young participants with prolonged wakefulness and aged participants implying that aging and prolonged wakefulness may result in a dysfunction of the brain energy metabolism and cause impairment of the frontal cortex.
Motor sequence learning task	Contralateral primary sensorimotor cortex	Decreased GABA level during the task suggesting that GABA modulation occurs with encoding of the task.
Prolonged match-to-sample working memory task	Left dorsolateral prefrontal cortex	Increased GABA level during the first working memory run and continuously decreased during subsequent three runs. Decrease of GABA over time correlated with decreases in reaction time and higher task accuracy.
Presentation of abstract and real world objects	Lateral occipital cortex	Higher increase in glutamate level with the presentation of abstract versus real world objects. In this study fMRS was used simultaneously with EEG and positive correlation between gamma-band activity and glutamate level changes was observed.
Stroop task	Anterior cingulate cortex (ACC)	Demonstration of phosphocreatine dynamics with 12s temporal resolution. Stroop task for this study was chosen because it has been previously shown that left ACC is significantly activated during the performance of stroop task. The main implication of this study was that reliable fMRS measures are possible in the ACC during cognitive tasks.

Nuclear magnetic resonance spectroscopy of carbohydrates

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance_spectroscopy_of_carbohydrates

Carbohydrate NMR spectroscopy is the application of nuclear magnetic resonance (NMR) spectroscopy to structural and conformational analysis of carbohydrates. This method allows the scientists to elucidate structure of monosaccharides, oligosaccharides, polysaccharides, glycoconjugates and other carbohydrate derivatives from synthetic and natural sources. Among structural properties that could be determined by NMR are primary structure (including stereochemistry), saccharide conformation, stoichiometry of substituents, and ratio of individual saccharides in a mixture. Modern high field NMR instruments used for carbohydrate samples, typically 500 MHz or higher, are able to run a suite of 1D, 2D, and 3D experiments to determine a structure of carbohydrate compounds.

Main article: Nuclear magnetic resonance

Carbohydrate NMR observables

Chemical shift

Main article: chemical shift

Common chemical shift ranges for nuclei within carbohydrate residues are:

• Typical ¹H NMR chemical shifts of carbohydrate ring protons are 3–6 ppm (4.5–5.5 ppm for anomeric protons).
• Typical ¹³C NMR chemical shifts of carbohydrate ring carbons are 60–110 ppm

In the case of simple mono- and oligosaccharide molecules, all proton signals are typically separated from one another (usually at 500 MHz or better NMR instruments) and can be assigned using 1D NMR spectrum only. However, bigger molecules exhibit significant proton signal overlap, especially in the non-anomeric region (3-4 ppm). Carbon-13 NMR overcomes this disadvantage by larger range of chemical shifts and special techniques allowing to block carbon-proton spin coupling, thus making all carbon signals high and narrow singlets distinguishable from each other.

The typical ranges of specific carbohydrate carbon chemical shifts in the unsubstituted monosaccharides are:

• Anomeric carbons: 90-100 ppm
• Sugar ring carbons bearing a hydroxy function: 68-77
• Open-form sugar carbons bearing a hydroxy function: 71-75
• Sugar ring carbons bearing an amino function: 50-56
• Exocyclic hydroxymethyl groups: 60-64
• Exocyclic carboxy groups: 172-176
• Desoxygenated sugar ring carbons: 31-40
• A carbon at pyranose ring closure: 71-73 (α-anomers), 74-76 (β-anomers)
• A carbon at furanose ring closure: 80-83 (α-anomers), 83-86 (β-anomers)

Coupling constants

Main article: coupling constant

Direct carbon-proton coupling constants are used to study the anomeric configuration of a sugar. Vicinal proton-proton coupling constants are used to study stereo orientation of protons relatively to the other protons within a sugar ring, thus identifying a monosaccharide. Vicinal heteronuclear H-C-O-C coupling constants are used to study torsional angles along glycosidic bond between sugars or along exocyclic fragments, thus revealing a molecular conformation.

Sugar rings are relatively rigid molecular fragments, thus vicinal proton-proton couplings are characteristic:

• Equatorial to axial: 1–4 Hz
• Equatorial to equatorial: 0–2 Hz
• Axial to axial non-anomeric: 9–11 Hz
• Axial to axial anomeric: 7–9 Hz
• Axial to exocyclic hydroxymethyl: 5 Hz, 2 Hz
• Geminal between hydroxymethyl protons: 12 Hz

Nuclear Overhauser effects (NOEs)

Main article: Nuclear Overhauser effect

NOEs are sensitive to interatomic distances, allowing their usage as a conformational probe, or proof of a glycoside bond formation. It's a common practice to compare calculated to experimental proton-proton NOEs in oligosaccharides to confirm a theoretical conformational map. Calculation of NOEs implies an optimization of molecular geometry.

Other NMR observables

Relaxivities, nuclear relaxation rates, line shape and other parameters were reported useful in structural studies of carbohydrates.

Elucidation of carbohydrate structure by NMR spectroscopy

Structural parameters of carbohydrates

The following is a list of structural features that can be elucidated by NMR:

• Chemical structure of each carbohydrate residue in a molecule, including
  • carbon skeleton size and sugar type (aldose/ketose)
  • cycle size (pyranose/furanose/linear)
  • stereo configuration of all carbons (monosaccharide identification)
  • stereo configuration of anomeric carbon (α/β)
  • absolute configuration (D/L)
  • location of amino-, carboxy-, deoxy- and other functions
• Chemical structure of non-carbohydrate residues in molecule (amino acids, fatty acids, alcohols, organic aglycons etc.)
• Substitution positions in residues
• Sequence of residues
• Stoichiometry of terminal residues and side chains
• Location of phosphate and sulfate diester bonds
• Polymerization degree and frame positioning (for polysaccharides)

NMR spectroscopy vs. other methods

Widely known methods of structural investigation, such as mass-spectrometry and X-ray analysis are only limitedly applicable to carbohydrates. Such structural studies, such as sequence determination or identification of new monosaccharides, benefit the most from the NMR spectroscopy. Absolute configuration and polymerization degree are not always determinable using NMR only, so the process of structural elucidation may require additional methods. Although monomeric composition can be solved by NMR, chromatographic and mass-spectroscopic methods provide this information sometimes easier. The other structural features listed above can be determined solely by the NMR spectroscopic methods. The limitation of the NMR structural studies of carbohydrates is that structure elucidation can hardly be automatized and require a human expert to derive a structure from NMR spectra.

Application of various NMR techniques to carbohydrates

Complex glycans possess a multitude of overlapping signals, especially in a proton spectrum. Therefore, it is advantageous to utilize 2D experiments for the assignment of signals. The table and figures below list most widespread NMR techniques used in carbohydrate studies.

Heteronuclear NMR techniques in carbohydrate studies, and typical intra-residue (red) and inter-residue (blue) atoms that they link each to other.

Homonuclear NMR techniques in carbohydrate studies, and typical intra-residue (red) and inter-residue (blue) atoms that they link each to other.

NMR experiment	Description	Information obtained
1H 1D	1D proton spectrum	measurement of couplings, general information, residue identification, basis for carbon spectrum assignment
13C BB	Proton-decoupled 1D carbon-13 spectrum	detailed information, residue identification, substitution positions
31P BB, 15N BB	Proton-decoupled 1D heteronuclei spectra	additional information
APT, 13C DEPT	attached proton test, driven enhanced polarization transfer (edited 1D carbon-13 spectrum)	assignment of CH2 groups
13C Gated, 31P Gated	Proton-coupled 1D carbon-13 and heteronuclei spectra	measurement of heteronuclear couplings, elucidation of anomeric configuration, conformational studies
1H,1H J-resolved	2D NMR plot showing J-couplings in second dimension	accurate J-couplings and chemical shift values for crowded spectral regions
1H DOSY	2D NMR plot with proton spectra as a function of molecular diffusion coefficient	measurement of diffusion coefficient, estimate of molecular size/weight, spectral separation of different molecules in a mixture
1H,1H COSY	Proton spin correlation	proton spectrum assignment using vicinal couplings
COSY RCT, COSY RCT2	Proton spin correlation with one- or two-step relayed coherence transfer	proton spectrum assignment where signals of neighboring vicinal protons overlap
DQF COSY	Double-quantum filtered proton spin correlation	J-coupling magnitudes & number of protons participating in the J-coupling
1H HD dif	Selective differential homodecoupling	line shape analysis of the overlapped proton signals
TOCSY (HOHAHA)	Total correlation of all protons within a spin system	distinguishing of spin systems of residues
1D TOCSY	TOCSY of a single signal	extraction of a spin system of a certain residue
NOESY, ROESY	Homonuclear Nuclear Overhauser effect correlation (through space)	revealing of spatially proximal proton pairs, determination of a sequence of residues, determination of averaged conformation
1H NOE dif	Selective differential NOE measurement	studies of proton spatial contacts
1H,13C HSQC	Heteronuclear single-quantum coherence, direct proton-carbon spin correlation	carbon spectrum assignment
1H,31P HSQC	Heteronuclear single-quantum coherence, proton-phosphorus spin correlation	localization of phosphoric acid residues in phosphoglycans
1H,13C HMBC	Heteronuclear multiple-bond correlation, vicinal proton-carbon spin correlation	determination of residue sequence, acetylation/amidation pattern, confirmation of substitution positions
1H,X 1D HMBC	HMBC for a single signal	assignment of proton around a certain carbon or heteroatom
1H,13C HSQC Relay	Implicit carbon-carbon correlation via vicinal couplings of the attached protons	assignment of neighboring carbon atoms
1H,13C HSQC-TOCSY	Correlation of protons with all carbons within a spin system, and vice versa	assignment of C5 using H6 and solving similar problems, separation of carbon spectrum into subspectra of residues
1H,X 1D NOE	Heteronuclear NOE measurement	heteronuclear spatial contacts, conformations

Research scheme

NMR spectroscopic research includes the following steps:

• Extraction of carbohydrate material (for natural glycans)
• Chemical removal of moieties masking regularity (for polymers)
• Separation and purification of carbohydrate material (for 2D NMR experiments, 10 mg or more is recommended)
• Sample preparation (usually in D₂O)
• Acquisition of 1D spectra
• Planning, acquisition and processing of other NMR experiments (usually requires from 5 to 20 hours)
• Assignment and interpretation of spectra (see exemplary figure)
• If a structural problem could not be solved: chemical modification/degradation and NMR analysis of products
• Acquisition of spectra of the native (unmasked) compound and their interpretation based on modified structure
• Presentation of results

Approximate scheme of NMR (blue) and other (green) techniques applied to carbohydrate structure elucidation, and information obtained (in boxes)

Carbohydrate NMR databases and tools

Multiple chemical shift databases and related services have been created to aid structural elucidation of and expert analysis of their NMR spectra. Of them, several informatics tools are dedicated solely to carbohydrates:

• GlycoSCIENCES.de
  • over 2000 NMR spectra of mammalian glycans
  • search of structure by NMR signals and vice versa
• CSDB (carbohydrate structure database) contains:
  • over 4000 NMR spectra of bacterial, plant and fungal glycans,
  • search of structure by NMR signals and vice versa
  • empirical spectra simulation routine optimized for carbohydrates,
  • statistical chemical shift estimation based on HOSE algorithm optimized for carbohydrates,
  • structure generation and NMR-based ranking tool.
• CASPER (computer assisted spectrum evaluation of regular polysaccharides). contains:
  • chemical shift database,
  • empirical spectra simulation routine optimized for carbohydrates,
  • online interface.
  • structure matching tool. Both proton and carbon C and H chemical shifts can be used to access structural information.

Simulation of the NMR observables

Comparative prediction of the 13C NMR spectrum of sucrose using various methods. Experimental spectrum is in the middle. Upper spectrum (black) was obtained by empirical routine. Lower spectra (red and green) were obtained by quantum-chemical calculations in PRIRODA and GAUSSIAN respectively. Included information: used theory level/basis set/solvent model, accuracy of prediction (linear correlation factor and root mean square deviation), calculation time on personal computer (blue).

Several approaches to simulate NMR observables of carbohydrates has been reviewed. They include:

• Universal statistical database approaches (ACDLabs, Modgraph, etc.)
• Usage of neural networks to refine the predictions
• Regression based methods
• CHARGE
• Carbohydrate-optimized empirical schemes (CSDB/BIOPSEL, CASPER).
• Combined molecular mechanics/dynamics geometry calculation and quantum-mechanical simulation/iteration of NMR observables (PERCH NMR Software)
• ONIOM approaches (optimization of different parts of molecule with different accuracy)
• Ab initio calculations.

Growing computational power allows usage of thorough quantum-mechanical calculations at high theory levels and large basis sets for refining the molecular geometry of carbohydrates and subsequent prediction of NMR observables using GIAO and other methods with or without solvent effect account. Among combinations of theory level and a basis set reported as sufficient for NMR predictions were B3LYP/6-311G++(2d,2p) and PBE/PBE (see review). It was shown for saccharides that carbohydrate-optimized empirical schemes provide significantly better accuracy (0.0-0.5 ppm per ¹³C resonance) than quantum chemical methods (above 2.0 ppm per resonance) reported as best for NMR simulations, and work thousands times faster. However, these methods can predict only chemical shifts and perform poor for non-carbohydrate parts of molecules. As a representative example, see figure on the right.

Radio frequency

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Radio_frequency

Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around 20 kHz to around 300 GHz. This is roughly between the upper limit of audio frequencies and the lower limit of infrared frequencies. These are the frequencies at which energy from an oscillating current can radiate off a conductor into space as radio waves, so they are used in radio technology, among other uses. Different sources specify different upper and lower bounds for the frequency range.

Electric current

Electric currents that oscillate at radio frequencies (RF currents) have special properties not shared by direct current or lower audio frequency alternating current, such as the 50 or 60 Hz current used in electrical power distribution.

• Energy from RF currents in conductors can radiate into space as electromagnetic waves (radio waves). This is the basis of radio technology.
• RF current does not penetrate deeply into electrical conductors but tends to flow along their surfaces; this is known as the skin effect.
• RF currents applied to the body often do not cause the painful sensation and muscular contraction of electric shock that lower frequency currents produce. This is because the current changes direction too quickly to trigger depolarization of nerve membranes. However, this does not mean RF currents are harmless; they can cause internal injury as well as serious superficial burns called RF burns.
• RF current can easily ionize air, creating a conductive path through it. This property is exploited by "high frequency" units used in electric arc welding, which use currents at higher frequencies than power distribution uses.
• Another property is the ability to appear to flow through paths that contain insulating material, like the dielectric insulator of a capacitor. This is because capacitive reactance in a circuit decreases with increasing frequency.
• In contrast, RF current can be blocked by a coil of wire, or even a single turn or bend in a wire. This is because the inductive reactance of a circuit increases with increasing frequency.
• When conducted by an ordinary electric cable, RF current has a tendency to reflect from discontinuities in the cable, such as connectors, and travel back down the cable toward the source, causing a condition called standing waves. RF current may be carried efficiently over transmission lines such as coaxial cables.

Frequency bands

Main article: Radio spectrum

The radio spectrum of frequencies is divided into bands with conventional names designated by the International Telecommunication Union (ITU):

Frequency range	Wavelength range	ITU designation		IEEE bands
		Full name	Abbreviation
Below 3 Hz	>105 km			—
3–30 Hz	105–104 km	Extremely low frequency	ELF	—
30–300 Hz	104–103 km	Super low frequency	SLF	—
300–3000 Hz	103–100 km	Ultra low frequency	ULF	—
3–30 kHz	100–10 km	Very low frequency	VLF	—
30–300 kHz	10–1 km	Low frequency	LF	—
300 kHz – 3 MHz	1 km – 100 m	Medium frequency	MF	—
3–30 MHz	100–10 m	High frequency	HF	HF
30–300 MHz	10–1 m	Very high frequency	VHF	VHF
300 MHz – 3 GHz	1 m – 100 mm	Ultra high frequency	UHF	UHF, L, S
3–30 GHz	100–10 mm	Super high frequency	SHF	S, C, X, Ku, K, Ka
30–300 GHz	10–1 mm	Extremely high frequency	EHF	Ka, V, W, mm
300 GHz – 3 THz	1 mm – 0.1 mm	Tremendously high frequency	THF	—

Frequencies of 1 GHz and above are conventionally called microwave, while frequencies of 30 GHz and above are designated millimeter wave. More detailed band designations are given by the standard IEEE letter- band frequency designations and the EU/NATO frequency designations.

Applications

Communications

Radio frequencies are used in communication devices such as transmitters, receivers, computers, televisions, and mobile phones, to name a few. Radio frequencies are also applied in carrier current systems including telephony and control circuits. The MOS integrated circuit is the technology behind the current proliferation of radio frequency wireless telecommunications devices such as cellphones.

Medicine

Main article: Medical applications of radio frequency

Medical applications of radio frequency (RF) energy, in the form of electromagnetic waves (radio waves) or electrical currents, have existed for over 125 years, and now include diathermy, hyperthermy treatment of cancer, electrosurgery scalpels used to cut and cauterize in operations, and radiofrequency ablation. Magnetic resonance imaging (MRI) uses radio frequency fields to generate images of the human body.

Measurement

Test apparatus for radio frequencies can include standard instruments at the lower end of the range, but at higher frequencies, the test equipment becomes more specialized.

Mechanical oscillations

While RF usually refers to electrical oscillations, mechanical RF systems are not uncommon: see mechanical filter and RF MEMS.