Atomic orbital in the context of Probability density

The electron (e
, or β
in nuclear reactions) is a subatomic particle whose electric charge is negative one elementary charge. It is an elementary particle that comprises the ordinary matter that makes up the universe, along with up and down quarks.

Electrons are extremely lightweight particles. In atoms, an electron's matter wave occupies atomic orbitals around a positively charged atomic nucleus. The configuration and energy levels of an atom's electrons determine the atom's chemical properties. Electrons are bound to the nucleus to different degrees. The outermost or valence electrons are the least tightly bound and are responsible for the formation of chemical bonds between atoms to create molecules and crystals. These valence electrons also facilitate all types of chemical reactions by being transferred or shared between atoms. The inner electron shells make up the atomic core.

In chemistry, a hydrogen bond (H-bond) is a specific type of molecular interaction that exhibits partial covalent character and cannot be described as a purely electrostatic force. It occurs when a hydrogen (H) atom, covalently bonded to a more electronegative donor atom or group (Dn), interacts with another electronegative atom bearing a lone pair of electrons—the hydrogen bond acceptor (Ac). Unlike simple dipole–dipole interactions, hydrogen bonding arises from charge transfer (nB → σ*AH), orbital interactions, and quantum mechanical delocalization, making it a resonance-assisted interaction rather than a mere electrostatic attraction.

The general notation for hydrogen bonding is Dn−H···Ac, where the solid line represents a polar covalent bond, and the dotted or dashed line indicates the hydrogen bond. The most frequent donor and acceptor atoms are nitrogen (N), oxygen (O), and fluorine (F), due to their high electronegativity and ability to engage in stronger hydrogen bonding.

In quantum mechanics, the Pauli exclusion principle (German: Pauli-Ausschlussprinzip) states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously occupy the same quantum state within a system that obeys the laws of quantum mechanics. This principle was formulated by Austrian physicist Wolfgang Pauli in 1925 for electrons, and later extended to all fermions with his spin–statistics theorem of 1940.

In the case of electrons in atoms, the exclusion principle can be stated as follows: in a poly-electron atom it is impossible for any two electrons to have the same two values of all four of their quantum numbers, which are: n, the principal quantum number; ℓ, the azimuthal quantum number; m_ℓ, the magnetic quantum number; and m_s, the spin quantum number. For example, if two electrons reside in the same orbital, then their values of n, ℓ, and m_ℓ are equal. In that case, the two values of m_s (spin) pair must be different. Since the only two possible values for the spin projection m_s are +1/2 and −1/2, it follows that one electron must have m_s = +1/2 and one m_s = −1/2.

The alkaline earth metals are six chemical elements in group 2 of the periodic table. They are beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), barium (Ba), and radium (Ra). The elements have very similar properties: they are all shiny, silvery-white, somewhat reactive metals at standard temperature and pressure.

Together with helium, these elements have in common an outer s orbital which is full—that is, this orbital contains its full complement of two electrons, which the alkaline earth metals readily lose to form cations with charge +2, and an oxidation state of +2. Helium is grouped with the noble gases and not with the alkaline earth metals, but it is theorized to have some similarities to beryllium when forced into bonding and has sometimes been suggested to belong to group 2.

Organolead chemistry is the scientific study of the synthesis and properties of organolead compounds, which are organometallic compounds containing a chemical bond between carbon and lead. The first organolead compound was hexaethyldilead (Pb₂(C₂H₅)₆), first synthesized in 1858. Sharing the same group with carbon, lead is tetravalent.

Going down the carbon group the C–X (X = C, Si, Ge, Sn, Pb) bond becomes weaker and the bond length larger. The C–Pb bond in tetramethyllead is 222 pm long with a dissociation energy of 49 kcal/mol (204 kJ/mol). For comparison the C–Sn bond in tetramethyltin is 214 pm long with dissociation energy 71 kcal/mol (297 kJ/mol). The dominance of Pb(IV) in organolead chemistry is remarkable because inorganic lead compounds tend to have Pb(II) centers. The reason is that with inorganic lead compounds elements such as nitrogen, oxygen and the halides have a much higher electronegativity than lead itself and the partial positive charge on lead then leads to a stronger contraction of the 6s orbital than the 6p orbital making the 6s orbital inert; this is called the inert-pair effect.

The subatomic scale is the domain of physical size that encompasses objects smaller than an atom. It is the scale at which the atomic constituents, such as the nucleus containing protons and neutrons, and the electrons in their orbitals, become apparent.

The subatomic scale includes the many thousands of times smaller subnuclear scale, which is the scale of physical size at which constituents of the protons and neutrons—particularly quarks—become apparent.

In quantum mechanics, the azimuthal quantum number ℓ is a quantum number for an atomic orbital that determines its orbital angular momentum and describes aspects of the angular shape of the orbital. The azimuthal quantum number is the second of a set of quantum numbers that describe the unique quantum state of an electron (the others being the principal quantum number n, the magnetic quantum number m_ℓ, and the spin quantum number m_s).

For a given value of the principal quantum number n (electron shell), the possible values of ℓ are the integers from 0 to n − 1. For instance, the n = 1 shell has only orbitals with ${\displaystyle \ell =0}$, and the n = 2 shell has only orbitals with ${\displaystyle \ell =0}$, and ${\displaystyle \ell =1}$.

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).

Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, diamagnetic materials are repelled by magnetic fields and form induced magnetic fields in the direction opposite to that of the applied magnetic field. Paramagnetic materials include most chemical elements and some compounds; they have a relative magnetic permeability slightly greater than 1 (i.e., a small positive magnetic susceptibility) and hence are attracted to magnetic fields. The magnetic moment induced by the applied field is linear in the field strength and rather weak. It typically requires a sensitive analytical balance to detect the effect and modern measurements on paramagnetic materials are often conducted with a SQUID magnetometer.

Paramagnetism is due to the presence of unpaired electrons in the material, so most atoms with incompletely filled atomic orbitals are paramagnetic, although exceptions such as copper exist. Due to their spin, unpaired electrons have a magnetic dipole moment and act like tiny magnets. An external magnetic field causes the electrons' spins to align parallel to the field, causing a net attraction. Paramagnetic materials include aluminium, oxygen, titanium, and iron oxide (FeO). Therefore, a simple rule of thumb is used in chemistry to determine whether a particle (atom, ion, or molecule) is paramagnetic or diamagnetic: if all electrons in the particle are paired, then the substance made of this particle is diamagnetic; if it has unpaired electrons, then the substance is paramagnetic.

In atomic physics, a magnetic quantum number is a quantum number used to distinguish quantum states of an electron or other particle according to its angular momentum along a given axis in space. The orbital magnetic quantum number (m_l or m) distinguishes the orbitals available within a given subshell of an atom. It specifies the component of the orbital angular momentum that lies along a given axis, conventionally called the z-axis, so it describes the orientation of the orbital in space. The spin magnetic quantum number m_s specifies the z-axis component of the spin angular momentum for a particle having spin quantum number s. For an electron, s is 1⁄2, and m_s is either +1⁄2 or −1⁄2, often called "spin-up" and "spin-down", or α and β. The term magnetic in the name refers to the magnetic dipole moment associated with each type of angular momentum, so states having different magnetic quantum numbers shift in energy in a magnetic field according to the Zeeman effect.

The four quantum numbers conventionally used to describe the quantum state of an electron in an atom are the principal quantum number n, the azimuthal (orbital) quantum number ${\displaystyle \ell }$, and the magnetic quantum numbers m_l and m_s. Electrons in a given subshell of an atom (such as s, p, d, or f) are defined by values of ${\displaystyle \ell }$ (0, 1, 2, or 3). The orbital magnetic quantum number takes integer values in the range from ${\displaystyle -\ell }$ to ${\displaystyle +\ell }$, including zero. Thus the s, p, d, and f subshells contain 1, 3, 5, and 7 orbitals each. Each of these orbitals can accommodate up to two electrons (with opposite spins), forming the basis of the periodic table.

Internal conversion (often abbreviated IC) is an atomic decay process where an excited nucleus interacts electromagnetically with one of the orbital electrons of an atom. This causes the electron to be emitted (ejected) from the atom. Thus, in internal conversion, a high-energy electron is emitted from the excited atom, but not from the nucleus. For this reason, the high-speed electrons resulting from internal conversion are not called beta particles, since the latter come from beta decay, where they are newly created in the nuclear decay process.

IC is possible whenever gamma decay is possible, except if the atom is fully ionized. In IC, the atomic number does not change, and thus there is no transmutation of one element to another. Also, neutrinos and the weak force are not involved in IC.

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 chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The terms atomic orbital and molecular orbital were introduced by Robert S. Mulliken in 1932 to mean one-electron orbital wave functions. At an elementary level, they are used to describe the region of space in which a function has a significant amplitude.

In an isolated atom, the orbital electrons' location is determined by functions called atomic orbitals. When multiple atoms combine chemically into a molecule by forming a valence chemical bond, the electrons' locations are determined by the molecule as a whole, so the atomic orbitals combine to form molecular orbitals. The electrons from the constituent atoms occupy the molecular orbitals. Mathematically, molecular orbitals are an approximate solution to the Schrödinger equation for the electrons in the field of the molecule's atomic nuclei. They are usually constructed by combining atomic orbitals or hybrid orbitals from each atom of the molecule, or other molecular orbitals from groups of atoms. They can be quantitatively calculated using the Hartree–Fock or self-consistent field (SCF) methods.

In chemistry, an unpaired electron is an electron that occupies an orbital of an atom singly, rather than as part of an electron pair. Each atomic orbital of an atom (specified by the three quantum numbers n, l and m) has a capacity to contain two electrons (electron pair) with opposite spins. As the formation of electron pairs is often energetically favourable, either in the form of a chemical bond or as a lone pair, unpaired electrons are relatively uncommon in chemistry, because an entity that carries an unpaired electron is usually rather reactive. In organic chemistry they typically only occur briefly during a reaction on an entity called a radical; however, they play an important role in explaining reaction pathways.

Radicals are uncommon in s- and p-block chemistry, since the unpaired electron occupies a valence p orbital or an sp, sp or sp hybrid orbital. These orbitals are strongly directional and therefore overlap to form strong covalent bonds, favouring dimerisation of radicals. Radicals can be stable if dimerisation would result in a weak bond or the unpaired electrons are stabilised by delocalisation. In contrast, radicals in d- and f-block chemistry are very common. The less directional, more diffuse d and f orbitals, in which unpaired electrons reside, overlap less effectively, form weaker bonds and thus dimerisation is generally disfavoured. These d and f orbitals also have comparatively smaller radial extension, disfavouring overlap to form dimers.

In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals. For example, the electron configuration of the neon atom is 1s 2s 2p, meaning that the 1s, 2s, and 2p subshells are occupied by two, two, and six electrons, respectively.

Electronic configurations describe each electron as moving independently in an orbital, in an average field created by the nuclei and all the other electrons. Mathematically, configurations are described by Slater determinants or configuration state functions.

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.