Electron density in the context of Mössbauer spectroscopy

Electronegativity, symbolized as χ, is the tendency for an atom of a given chemical element to attract shared electrons (or electron density) when forming a chemical bond. An atom's electronegativity is affected by both its atomic number and the distance at which its valence electrons reside from the charged nucleus. The higher the associated electronegativity, the more an atom or a substituent group attracts electrons. Electronegativity serves as a simple way to quantitatively estimate the bond energy, and the sign and magnitude of a bond's chemical polarity, which characterizes a bond along the continuous scale from covalent to ionic bonding. The loosely defined term electropositivity is the opposite of electronegativity: it characterizes an element's tendency to donate valence electrons.

On the most basic level, electronegativity is determined by factors like the nuclear charge (the more protons an atom has, the more "pull" it will have on electrons) and the number and location of other electrons in the atomic shells (the more electrons an atom has, the farther from the nucleus the valence electrons will be, and as a result, the less positive charge they will experience—both because of their increased distance from the nucleus and because the other electrons in the lower energy core orbitals will act to shield the valence electrons from the positively charged nucleus).

In theoretical chemistry, the bonding orbital is used in molecular orbital (MO) theory to describe the attractive interactions between the atomic orbitals of two or more atoms in a molecule. In MO theory, electrons are portrayed to move in waves. When more than one of these waves come close together, the in-phase combination of these waves produces an interaction that leads to a species that is greatly stabilized. The result of the waves' constructive interference causes the density of the electrons to be found within the binding region, creating a stable bond between the two species.

In theoretical chemistry, an antibonding orbital is a type of molecular orbital that weakens the chemical bond between two atoms and helps to raise the energy of the molecule relative to the separated atoms. Such an orbital has one or more nodes in the bonding region between the nuclei. The density of the electrons in the orbital is concentrated outside the bonding region and acts to pull one nucleus away from the other and tends to cause mutual repulsion between the two atoms. This is in contrast to a bonding molecular orbital, which has a lower energy than that of the separate atoms, and is responsible for chemical bonds.

In chemistry, sigma bonds (σ bonds) or sigma overlap are the strongest type of covalent chemical bond. They are formed by head-on overlapping between atomic orbitals along the internuclear axis. Sigma bonding is most simply defined for diatomic molecules using the language and tools of symmetry groups. In this formal approach, a σ-bond is symmetrical with respect to rotation about the bond axis. By this definition, common forms of sigma bonds are s+s, p_z+p_z, s+p_z and d_z+d_z (where z is defined as the axis of the bond or the internuclear axis).Quantum theory also indicates that molecular orbitals (MO) of identical symmetry actually mix or hybridize. As a practical consequence of this mixing of diatomic molecules, the wavefunctions s+s and p_z+p_z molecular orbitals become blended. The extent of this mixing (or hybridization or blending) depends on the relative energies of the MOs of like symmetry.

For homodiatomics (homonuclear diatomic molecules), bonding σ orbitals have no nodal planes at which the wavefunction is zero, either between the bonded atoms or passing through the bonded atoms. The corresponding antibonding, or σ* orbital, is defined by the presence of one nodal plane between the two bonded atoms.

In chemistry, pi bonds (π bonds) are covalent chemical bonds, in each of which two lobes of an orbital on one atom overlap with two lobes of an orbital on another atom, and in which this overlap occurs laterally. Each of these atomic orbitals has an electron density of zero at a shared nodal plane that passes through the two bonded nuclei. This plane also is a nodal plane for the molecular orbital of the pi bond. Pi bonds can form in double and triple bonds but do not form in single bonds in most cases.

The Greek letter π in their name refers to p orbitals, since the orbital symmetry of the pi bond is the same as that of the p orbital when seen down the bond axis. One common form of this sort of bonding involves p orbitals themselves, though d orbitals also engage in pi bonding. This latter mode forms part of the basis for metal-metal multiple bonding.

In organic chemistry, a bent bond, also known as a banana bond, is a type of covalent chemical bond with a geometry somewhat reminiscent of a banana. The term itself is a general representation of electron density or configuration resembling a similar "bent" structure within small ring molecules, such as cyclopropane (C₃H₆) or as a representation of double or triple bonds within a compound that is an alternative to the sigma and pi bond model.

Immunogold labeling or immunogold staining (IGS) is a staining technique used in electron microscopy. This staining technique is an equivalent of the indirect immunofluorescence technique for visible light. Colloidal gold particles are most often attached to secondary antibodies which are in turn attached to primary antibodies designed to bind a specific antigen or other cell component. Gold is used for its high electron density which increases electron scatter to give high contrast 'dark spots'.

First used in 1971, immunogold labeling has been applied to both transmission electron microscopy and scanning electron microscopy, as well as brightfield microscopy. The labeling technique can be adapted to distinguish multiple objects by using differently-sized gold particles.

Incoherent scatter radar is a ground-based radar technique for studying the Earth's ionosphere, first proposed by Professor William E. Gordon in 1958. It is based on radio waves being scattered incoherently by random fluctuations in a plasma.

A radar beam scattering off electrons in the ionosphere creates an incoherent scatter return. When an electromagnetic wave is transmitted through the atmosphere, each of the electrons in the ionospheric plasma essentially acts as an antenna excited by the incoming wave, and the wave is re-radiated from the electron. Since the electrons are all moving at varying speeds as a result of ionospheric dynamics and random thermal motion, the reflection from each electron is also Doppler shifted. The receiver on the ground then receives a signal composed of the superposition of the re-radiated waves from all the electrons in the path of the incoming wave. Since the positively-charged ions also present in the ionosphere are orders of magnitude more massive, they are not as readily excited by the incoming electromagnetic wave in the way that the electrons are, so they do not re-radiate the signal. However, the electrons tend to remain close to the positively-charged ions. As a result, the distribution function of the ionospheric electrons is modified by the much slower and more massive positive ions — electron density fluctuations relate to ion temperature, mass distribution, and motion. The incoherent scatter signal allows measurement of electron density, ion temperature and electron temperatures, ion composition and plasma velocity.

In chemistry, a chalcogen bond (ChB) is an attractive interaction in the family of σ-hole interactions, along with halogen bonds. Electrostatic, charge-transfer (CT) and dispersion terms have been identified as contributing to this type of interaction. In terms of CT contribution, this family of attractive interactions has been modeled as an electron donor (the bond acceptor) interacting with the σ* orbital of a C-X bond (X= hydrogen, halogen, chalcogen, pnictogen, etc.) of the bond donor. In terms of electrostatic interactions, the molecular electrostatic potential (MEP) maps is often invoked to visualize the electron density of the donor and an electrophilic region on the acceptor, where the potential is depleted, referred to as a σ-hole. ChBs, much like hydrogen and halogen bonds, have been invoked in various non-covalent interactions, such as protein folding, crystal engineering, self-assembly, catalysis, transport, sensing, templation, and drug design.

In quantum chemistry, the quantum theory of atoms in molecules (QTAIM), sometimes referred to as atoms in molecules (AIM), is a model of molecular and condensed matter electronic systems (such as crystals) in which the principal objects of molecular structure - atoms and bonds - are natural expressions of a system's observable electron density distribution function. An electron density distribution of a molecule is a probability distribution that describes the average manner in which the electronic charge is distributed throughout real space in the attractive field exerted by the nuclei. According to QTAIM, molecular structure is revealed by the stationary points of the electron density together with the gradient paths of the electron density that originate and terminate at these points.

QTAIM was primarily developed by Professor Richard Bader and his research group at McMaster University over the course of decades, beginning with analyses of theoretically calculated electron densities of simple molecules in the early 1960s and culminating with analyses of both theoretically and experimentally measured electron densities of crystals in the 90s. The development of QTAIM was driven by the assumption that, since the concepts of atoms and bonds have been and continue to be so ubiquitously useful in interpreting, classifying, predicting and communicating chemistry, they should have a well-defined physical basis.