Pauli's Exclusion Principle states that no two electrons in the same atom can have identical values for all four of their quantum numbers. In other words, (1) no more than two electrons can occupy the same orbital and (2) two electrons in the same orbital must have opposite spins (Figure 46(i) and (ii)).

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Figure 46. Electron spin and magnetic moment. (i) electron pairs with opposite spins cancel out magnetic moments, (ii) electron pair in an orbital cannot have parallel spins (Pauli's exclusion principle), (iii, iv and v): randomly oriented electrons do not result in net magnetism, (vii, viii and ix): electrons parallel to an applied field cause net magnetic moment.

In general, opposing spins (proton +1/2 and neutron −1/2) of the proton and the neutron cancel the magnetic field. In certain cases, such as hydrogen atom or certain isotopes, nuclear magnetic moment may be significant. Although electron spin generates magnetic momentum, the opposite spins of the two electrons in the same orbital cancel out their magnetic momentum with no residual magnetic momentum. Atoms with unpaired electrons spinning in the same direction contain net magnetic moments and are weakly attracted to magnets. The overall magnetic activity depends upon the alignment of their unpaired electrons. If they exhibit random movement (Figure 46(iii–v)), there will be no net magnetic moment. However, if the unpaired electrons are parallel to the same direction, the particles exhibit magnetic moment.

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Resin Restorative Materials

B.W. Darvell DSc CChem CSci FRSC FIM FSS FADM, in Materials Science for Dentistry (Tenth Edition), 2018

•5.3 Singlet states

Now, electrons are usually paired in their molecular orbitals and, according to the Pauli exclusion principle, their spins must be anti-parallel, that is, in opposite directions. This is known as a singlet state (S). When radiation is absorbed to promote an electron, the spin of the excited electron is conserved – the same as it was in the ground state (because the simultaneous change of both electronic energy and spin is forbidden according to the quantum number rules). The result is called an excited singlet state (S2 in Fig. 5.2). This conserved spin permits the ready return of the electron to its previous state (S1) through a fluorescent emission since it can, of course, re-enter the original orbital without breaking the Pauli exclusion principle.

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Magnetic Resonance Imaging Diagnostics of Human Brain Disorders

Madan Kaila, Rakhi Kaila, in Quantum Magnetic Resonance Imaging Diagnostics of Human Brain Disorders, 2010 Symmetry of Spins under Exchange (The Parity Principle) <10> (Figure 3.6(f))

When there are two particles of different species in an ensemble, both space and spin labels may be exchanged. This is called Pauli's exclusion principle. Using the spherical coordinate frame of reference (r, θ, φ), which describes space and spin of the two particles, one can break the state function in space. One may say either r=−r, or r=r, but θ=πθ and φ=π+φ. Therefore, under exchange, the radial part remains unchanged; in contrast, the angular-momentum (spin) part becomes antisymmetric under exchange.

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Biopolymers-graphene oxide nanoplatelets composites with enhanced conductivity and biocompatibility suitable for tissue engineering applications

Biswadeep Chaudhuri, in Fullerens, Graphenes and Nanotubes, 2018

12.4 Characteristics of Graphene

Graphene possesses properties different from any other carbon molecule, such as benzene and other allotropies. With such properties, graphene has provided advantages in TE and in other fields such as cancer therapy and drug delivery. Its noble properties, such as electrical conductivity, elasticity, dielectric constant, surface charge, and adsorption of protein and low molecular weight substances, favors stem cells differentiation, and neural or myoblast cells proliferation (Feng and Liu, 2011; Ryu and Kim, 2013; Wheeler, 2013; Utesch et al., 2011).

12.4.1 Electroconductivity of Graphene

Electrical conductivity of graphene is due to sp2-hybridized carbon atoms. Three of the outer carbon atoms form sigma bonds with neighboring three electrons. The remaining one electron forms a π bond. In accordance with the Pauli exclusion principle, the outermost shells of the C-atoms are filled. σ-bond forms solid and stable bonds. In the π bond, only half of each C-atom p-orbital is filled. The electrical conductivity of graphene arises due to such bond formation.

12.4.2 Adsorption of Proteins and Low Molecular Weight Substances

Graphene has the unique property that can be utilized for tissue engineering; its ability to adsorb protein and low molecular weight chemicals. In order to either grow or communicate with neighboring cells (Feng and Liu, 2011; Ryu and Kim, 2013; Wheeler, 2013; Utesch et al., 2011), cells secrete various substances. Such substances are adsorbed onto the graphene surfaces and affect cell proliferation and differentiation.

12.4.3 Graphene Promotes Mesenchymal Stem Cells Interaction

Kalbacova and coworkers (2010) showed that graphene-based substrates successfully promote human mesenchymal stem cells (hMSCs). Their study, based on MSCs adhesion and proliferation, demonstrated that MSCs proliferated much better when cultured on graphene films, compared to other substrates (Kalbacova et al., 2010). Although graphene is usually hydrophobic in nature, other parameters in combination such as surface chemistry, nanoroughness and texture, create a favorable platform for the MSCs to grow better. Cellular attachment involves physicochemical linkages between the cells (MSCs) and the graphene surface through ionic forces or adsorption of any conditioning molecules such as proteins. Furthermore, differentiation of mouse skeletal myoblasts cells (Levy-Mishali et al., 2009) was carried out on graphene-based substrates and these cells grew better on GO because of their nanostructural features and important physicochemical properties.

E.H. Ivanova, in Encyclopedia of Analytical Science (Second Edition), 2005

Atomic Structure and Spectra

For a strong absorption of electromagnetic radiation the lower energy state of the analyte atom must be highly populated and all selection rules must be observed. In order to examine these criteria, both energy states involved in the transition of the atom should be known. The upper energy state is not known for all elements, but even in such cases important conclusions may be drawn from the spectral term of the lower energy state, which is usually the ground state of the atoms. Therefore, the derivation of the electronic configuration of the atoms will be discussed.

The distribution of electrons in an atom is governed by two atom-building principles:


The orbitals (energy levels) are occupied in order of increasing orbital energy.


All electrons in an atom must be present in a different microstate, i.e., the electrons must be distinguishable at least in one of their quantum numbers (Pauli's exclusion principle).

The principal quantum number n defines the shell in which the electron is located; the maximum number of electrons taken up in a shell is 2n2. Within the shell the electrons reside in orbitals of different symmetry, described by the angular momentum quantum number l, which can take values of 0, 1, 2,…, n. An orbital can accommodate up to two electrons having opposite spins. Each of the electrons is characterized by the inner quantum number j that can take values of l±1/2.

The general atom-building principles (a) and (b) are supplemented by rules that depend on the magnetic and chemical behavior of the elements:


The special stability of the electronic configuration of the noble (inert) gases allows the classification of electrons into two main groups: core electrons, present in a noble gas shell, and valence electrons, present in subshells. Core electrons are not involved in chemical reactions and do not contribute to the generation of spectroscopic terms, which means that the elucidation of electronic configurations is greatly simplified, e.g.,


The special stability of the half-filled and completely filled d and f subshells has the consequence that the configurations predicted by the rules (a) and (b) only are less stable than the configuration predicted by the supplementary rule (d):
ZSymbolElectron configurationNmsE1 (eV)D0 (eV)

Elements with resonance lines between 193.70 nm (As) and 852.11 mm (Cs) and characteristic concentrations c1%−1 were selected. Z is the number of electrons, Nms the number of microstates, E1 the first ionization energy, and D0 the bond dissociation energy of the corresponding monoxide MO.


The resonance line, i.e., the line due to the transition between the ground state and the lowest excited state, must be situated within the spectral range of standard atomic absorption spectrometers (190–860 nm).


The characteristic concentration, i.e., the concentration yielding 1% absorption (or 0.0044 absorbance), must be lower than 100 mg l−1.

The excitation energies of the noble gases, the halogens, and sulfur are so high that the corresponding resonance lines are situated in the vacuum ultraviolet (UV) region, where oxygen intensively absorbs. In some cases this nonspecific absorption can be reduced by the use of a shielding gas (e.g., Ar or N2).

The elements can be classified into four spectrochemical groups on the basis of E1 and D0: (a) E1≥7.0 and D0≤4.2; (b) E1≤7.0 and D0≤4.2; (c) E1≤7.0 and D0≥4.2, and (d) E1≥7.0 and D0≥4.2.

The number of microstates Nms resulting from the corresponding electron configuration varies between one for electron configurations with closed valence shells and 34320 for Gd. Nms can serve as a measure of the complexity of the atomic absorption (and emission) spectra. An element with a large number of microstates also has a large number of spectroscopic terms and atomic lines, because of the many different term combinations possible.

According to the selection rules, transitions are allowed for which the angular momentum quantum number l increases by one unit, while the principal quantum number can change by any amount. The allowed transitions of the electrons can be compiled in term series in which the principal quantum number n precedes the term symbol as a number. The series in which l=0, 1, 2, 3 are designed by the letters s, p, d, f. Through the spin of the electrons and the associated magnetic field, splitting of the energy levels takes place, described by the inner quantum number j, which results in a fine multiplet structure of the spectral lines.

The energy levels can only absorb well-defined amounts of energy, i.e., they are quantized according to the symmetry rules. The most stable electronic configuration of an atom that has the lowest energy is the ground state. For example, the electronic configuration of the sodium atom is 1s22s22p63s1 (ground state with energy E0). The transition between the 3s orbital and a p orbital can be realized by absorption of light of definite wavelength, as illustrated in the partial term (Grotrian) diagram of sodium shown in Figure 1. For the sake of clarity, many of the upper-state transitions are omitted.


Guilherme Bresciani, ... Javier González-Gallego, in Advances in Clinical Chemistry, 2015

1 Introduction

During the last few decades, researchers in biochemistry, biology, chemistry, and physiology have studied the self-regulating modulation of the bioenergetics of aerobes, i.e., “oxidative stress.” The growing interest in this phenomenon is due to the peculiar characteristics presented by oxidative stress that change the way we perceive this vital molecule, oxygen (O2). O2 is essential for aerobic survival in our oxygen-rich atmosphere has played a major role in aerobic evolution due to its unique properties as the final electron acceptor of the mitochondrial electron transport chain (ETC) <1>. Without O2, organisms would have been unable to evolve into more complex multicellular life forms. Bioenergetics would be decreased and less effective, thus directly affecting reproduction and dampening propagation of varieties and species.

Nevertheless, O2 metabolism also presented aerobes with a challenge. It is well known that more than 90% of the body's O2 is consumed by the ETC in mitochondria <2>. O2 reduction is, however, complex, i.e., the molecule has two parallel spinning unpaired electrons in its outermost orbital <3>. According to Pauli's Exclusion Principle, it is impossible to reduce O2 in one step. Consequently, it undergoes a one-electron reduction to produce the first free radical found in aerobes, the superoxide anion (O2•−) <4>. Intermediates in the O2 reduction process are called free radicals—molecules that contain an unpaired electron (radical) and are capable of independent existence (free) <3>. Free radicals derived from O2 metabolism are also known as reactive oxygen species (ROS) <5>.

The relevance of the ROS relies on their dual role in aerobes (Fig. 1). At physiologic concentration, ROS have been implicated in modulation of gene expression and cellular signaling <6>. First recognized as toxic metabolites of O2 metabolism, ROS are now known to be significant modulators of different signaling pathways <7,8>. In addition, they play a key role in inflammation via adhesion and chemotaxic molecules. Uncontrolled ROS release, however, leads to oxidation of cellular components, such as proteins, lipids, and deoxyribonucleic acid (DNA). As such, uncontrolled ROS production by oxidative metabolism and other sources may cause distress leading to cellular damage <9>. Therefore, ROS are linked to physiologic and pathophysiologic conditions depending on the balance of production and clearance. Equilibrium between oxidants and antioxidants is required to reach homeostasis. Oxidative imbalance may result in pathologic response and lead to important functional disruptions and associated diseases.

Over the last few decades, oxidative stress and its role in pathology have been extensively studied. A few ROS-related molecular pathways have been identified and subsequently linked to metabolic-related diseases. Harman was the first scientist to propose a link between free radicals and deleterious effects to the organism, stating that aging was a process that was at least in part caused by free radicals <10>. Among the most studied and well-described oxidative stress-related diseases are cardiovascular diseases (CADs) <11>, metabolic-related <12>, and neurodegenerative conditions <13>. Nevertheless, the exact role of oxidative stress as a disease cause or consequence has yet to be fully clarified. Epidemiologic and associative studies established a potential relationship between genetics and diseases in the early 1990s. Research has evaluated the effects of genes and single nucleotide polymorphisms (SNPs) on the expression of proteins’ key to oxidative stress control, i.e., antioxidant enzymes. Therefore, elucidation of the molecular biology and the genetics of key antioxidant proteins have achieved more prominence in recent years.

Ab initio

Calculations based on first principles, which are often used in computational or theoretical chemistry.

Biological chromophore

A light absorbing moiety of a biological molecule.


Term describing the interaction between biology and photonics or the science and technology of generation, manipulation, and detection of photons.

Brillouin's theorem

Theorem that states that single excited determinants will not interact directly with the ground-state Hartree-Fock determinant.


Organic pigments found in chloroplasts and chromoplasts and photosynthetic organisms.

Closed shell

An atomic shell that contains the maximum number of electrons allowed by the Pauli exclusion principle.


Complete neglect of differential overlap. An approximation to the Hamiltonian, which neglects all two-center integrals.

Configuration interaction

A mathematical treatment implemented to include the effects of electron correlation.

Coupled cluster

Theoretical method used to calculate the correlation effects in nuclear matter while providing size consistency where electron configuration fails.

Electron correlation

The mixing of electron configurations.

Excited state

A state with an energy above the ground state in a quantum mechanical system.

Ground state

The lowest energy state in a quantum mechanical system.


A Hermitian mathematical operator, which operates on a wavefunction to yield the energy of the particle the wavefunction describes.


Intermediate neglect of differential overlap. An approximation to the Hamiltonian, which neglects all two-center terms.


Modified neglect of differential overlap with partial single and double configuration interaction. This is a method for studying the excited states of molecules with a high degree of π conjugation. The Hamiltonian makes the MNDO approximation and the excited-state energies are derived from a configuration interaction calculation.

Molecular orbital

A theoretical spatial confinement for an electron of a given energy.

Open shell

A valence shell that is not completely filled with electrons.

Pariser-Parr-Pople theory

Semiempirical method developed by Rudolph Pariser, Robert Parr, and John Pople that uses an SCF-LCAO-MO approximation to predict molecular electronic structures and spectra quantitatively.


Polyunsaturated organic compounds that contain one or more sequences of alternating double and single carbon-carbon bonds.

Quantum physics

Method used to study individual units of energy called quanta.


A biological chromophore found in rhodopsin, which is the agonist of the peptide. The agonist is covalently bound in the inactive form until it absorbs a photon of light, resulting in the active form.


A protein found in the retina of the eye, responsible for the formation of the photoreceptor cells and the first photo events of the messenger cascade that transmits signals along the optic nerve resulting in the perception of light.


Symmetry adapted cluster configuration interaction. Size consistent method for studying excited states.

Self-consistent field

An iterative procedure used to minimize electron density about a set of fixed nuclei.

Semiempirical method

Method used in quantum chemistry, which is based on the Hartree-Fock formalism that uses parameters based on experimental observation.


The study of the interaction of light with a molecule.

Transition energy

The energy between the ground state and one of the excited state of a molecule. The energy required for the molecule to transfer electron density from and occupied orbital to an unoccupied orbital.

Visual pigments

A class of biological chromophores found in the eyes of vertebrates.


A mathematical equation describing the motion of a subatomic particle.

Zero differential overlap

Approximation used to simplify the computation of wavefunctions in a Hartree-Fock treatment. In this approximation electron repulsion integrals involving overlap distributions are assumed insignificant and neglected, while the core integrals involved in overlap are treated semiempirically.


Zerner's intermediate neglect of differential overlap. This method, based on the INDO approximations of Pople, Santry, and Segal is a semiempirical method used to predict electronic spectra, in addition to modeling transition metal systems.

In order to interpret these experiments one needs to bear in mind the different types of forces that can act between the tip and the sample.

At large distances the force most commonly present is the Van der Waals force. Between two atoms the Van der Waals force energy decays with separation z according to the well-known z−7 law, but for a sphere above a planar surface (one simple model for the tip–surface system) the decay is only as z−2. This relatively slow fall-off tells us that in SFM, unlike STM, the large-scale structure of the tip is important.

If the sample is an insulator, it may be locally charged. The interaction between these local ‘patch charges’ and the tip also decays like a power law in the tip–sample separation. The patch charges are difficult to control; the highest-resolution SFM results are generally obtained on conducting samples.

At smaller distances (of the order of 3–5 Å separation) local interactions between the closest atoms of the tip and sample start to become important. These include the onset of covalent bonding, and local electrostatic forces.

As the tip-sample separation drops below the sum of the atomic radii of the atoms, the Pauli exclusion principle raises the energy of the overlapping electron distributions, producing a repulsive force. If the tip and sample are forced together beyond this point, atomic deformations (first elastic, then plastic) occur.

Of these interactions, the Van der Waals attraction and the Pauli repulsion are universal; the presence of the others depends on the nature of the material. The combination of Van der Waals and Pauli interactions is often captured by the simple ‘6-12’ Lennard-Jones interatomic potential

in which the attractive r−6 term represents the Van der Waals force and the repulsive r−12 term the Pauli force. Simulations of generic interatomic interactions are often performed using this potential, although it cannot be expected to be realistic for anything other than interactions between the simplest rare-gas solids. More realistic calculations include approximate forms for the electrostatic and covalent interactions between the atoms, or (better still) find these forces directly from the electronic structure of the materials involved.

With this in mind, let us examine the most common modes of SFM operation when high-resolution information about the surface is required.

. In this mode the tip is kept at a distance from the sample in the attractive part of the force–distance curve; usually it is then scanned across the sample, and the tip–sample distance adjusted to keep the cantilever displacement (and hence the force) constant. This procedure keeps the tip in the region where the tip–sample force is (relatively) well understood, but with the price that the force is determined by the cumulative effect of a large number of atoms – hence the resolution of individual atomic-scale features is seldom possible.

Contact mode. Here, by contrast, the tip is allowed to penetrate into the repulsive regime of Figure 5. This has the advantage that one expects a large component of the force to be determined by a relatively small number of atoms near the tip apex, but the disadvantage that the force becomes dependent on complex atomic processes involving the irreversible deformation of the tip–sample junction. Images with apparent atomic resolution can be seen in contact mode on simple crystalline materials such as alkali halides, but the conclusion of careful simulations is that the atomic-scale features are not, in fact, correlated with the positions of atoms in the surface. This theoretical conclusion is reinforced by the failure to resolve atomic defects (known to be present on the surface) in experiments.


One might think that a technique intermediate between contact and non-contact modes could be devised simply by bringing the tip close to the surface, but not in contact with it. In fact this is very difficult because of the ‘jump-to-contact’ phenomenon: a static tip held above a surface by a SFM cantilever with a given force constant kcant can be stable only as long as the force gradient from the tip–sample interaction is less than kcant (see Figure 5). The force gradient of a Van der Waals interaction between a tip and a flat surface diverges as the separation between them is reduced, so this condition is always violated and the tip snaps into contact with the sample. If the tip is pulled off the surface, a similar jump out of contact occurs (although between different values of tip–sample separation).

Since a very interesting range of tip–surface separations is rendered unavailable by the jump to contact, it would be desirable to eliminate it. To date, this has been done in two ways. First, a dynamical approach is used: the cantilever is vibrated above the surface with an amplitude of several hundred angströms, in such a way that its point of closest approach is only a few angströms from the surface. The difference from before is that the tip is accelerating rapidly away from the surface as it approaches; this suppresses the jump to contact. One way of expressing this is to say that the effective cantilever force constant is increased from kcant to kcant + Mtipω2, where Mtip is the total mass of the vibrating tip and ω is the angular frequency of vibration. The tip is usually scanned while keeping the vibrational period constant; this corresponds approximately to a scan of constant force gradient. Atomic resolution has been obtained using this technique, initially on the Si(111)–7 × 7 surface but now also on others. It seems this resolution can be understood in terms of the interaction between the tip and the surface near the point of closest approach, but the theory is complicated because the vibration of the tip samples all the different regions of the potential surface described above during a cycle, so a unified model containing all of them must be used.

A second approach is to control the force on the tip directly, generally by means of a small magnet mounted on the back. This removes the need to model a complicated tip oscillation, but imposes stringent demands on the response and stability of the electronics controlling the force. Direct measurements of tip–sample potential curves have now been reported using this technique, but comparison with theory is still in its infancy.

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Measurements of elastic properties

If local but not ultra-high-resolution measurements are required to probe the elastic properties of a hard material, there are advantages in using high-frequency measurements.