A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen constitutes about 75% of the baryonic mass of the universe.
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 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.
In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter.
A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The term is commonly used for the energy levels of the electrons in atoms, ions, or molecules, which are bound by the electric field of the nucleus, but can also refer to energy levels of nuclei or vibrational or rotational energy levels in molecules. The energy spectrum of a system with such discrete energy levels is said to be quantized.
In classical and quantum mechanics, geometric phase is a phase difference acquired over the course of a cycle, when a system is subjected to cyclic adiabatic processes, which results from the geometrical properties of the parameter space of the Hamiltonian. The phenomenon was independently discovered by S. Pancharatnam (1956), in classical optics and by H. C. Longuet-Higgins (1958) in molecular physics; it was generalized by Michael Berry in (1984). It is also known as the Pancharatnam–Berry phase, Pancharatnam phase, or Berry phase. It can be seen in the conical intersection of potential energy surfaces and in the Aharonov–Bohm effect. Geometric phase around the conical intersection involving the ground electronic state of the C6H3F3+ molecular ion is discussed on pages 385–386 of the textbook by Bunker and Jensen. In the case of the Aharonov–Bohm effect, the adiabatic parameter is the magnetic field enclosed by two interference paths, and it is cyclic in the sense that these two paths form a loop. In the case of the conical intersection, the adiabatic parameters are the molecular coordinates. Apart from quantum mechanics, it arises in a variety of other wave systems, such as classical optics. As a rule of thumb, it can occur whenever there are at least two parameters characterizing a wave in the vicinity of some sort of singularity or hole in the topology; two parameters are required because either the set of nonsingular states will not be simply connected, or there will be nonzero holonomy.
In chemistry, a lone pair refers to a pair of valence electrons that are not shared with another atom in a covalent bond and is sometimes called an unshared pair or non-bonding pair. Lone pairs are found in the outermost electron shell of atoms. They can be identified by using a Lewis structure. Electron pairs are therefore considered lone pairs if two electrons are paired but are not used in chemical bonding. Thus, the number of electrons in lone pairs plus the number of electrons in bonds equals the number of valence electrons around an atom.
In atomic physics, hyperfine structure is defined by small shifts in otherwise degenerate energy levels and the resulting splittings in those energy levels of atoms, molecules, and ions, due to electromagnetic multipole interaction between the nucleus and electron clouds.
In quantum physics and chemistry, quantum numbers are quantities that characterize the possible states of the system. Quantum numbers are closely related to eigenvalues of observables. When the corresponding observable commutes with the Hamiltonian, the quantum number is said to be "good", and acts as a constant of motion in the quantum dynamics.
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 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 numberms 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 ms 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.
In group theory, a branch of abstract algebra, a character table is a two-dimensional table whose rows correspond to irreducible representations, and whose columns correspond to conjugacy classes of group elements. The entries consist of characters, the traces of the matrices representing group elements of the column's class in the given row's group representation. In chemistry, crystallography, and spectroscopy, character tables of point groups are used to classify e.g. molecular vibrations according to their symmetry, and to predict whether a transition between two states is forbidden for symmetry reasons. Many university level textbooks on physical chemistry, quantum chemistry, spectroscopy and inorganic chemistry devote a chapter to the use of symmetry group character tables.
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates :
The Jahn–Teller effect is an important mechanism of spontaneous symmetry breaking in molecular and solid-state systems which has far-reaching consequences in different fields, and is responsible for a variety of phenomena in spectroscopy, stereochemistry, crystal chemistry, molecular and solid-state physics, and materials science. The effect is named for Hermann Arthur Jahn and Edward Teller, who first reported studies about it in 1937.
A molecular orbital diagram, or MO diagram, is a qualitative descriptive tool explaining chemical bonding in molecules in terms of molecular orbital theory in general and the linear combination of atomic orbitals (LCAO) method in particular. A fundamental principle of these theories is that as atoms bond to form molecules, a certain number of atomic orbitals combine to form the same number of molecular orbitals, although the electrons involved may be redistributed among the orbitals. This tool is very well suited for simple diatomic molecules such as dihydrogen, dioxygen, and carbon monoxide but becomes more complex when discussing even comparatively simple polyatomic molecules, such as methane. MO diagrams can explain why some molecules exist and others do not. They can also predict bond strength, as well as the electronic transitions that can take place.
Superexchange or Kramers–Anderson superexchange interaction, is a prototypical indirect exchange coupling between neighboring magnetic moments by virtue of exchanging electrons through a non-magnetic anion known as the superexchange center. In this way, it differs from direct exchange, in which there is direct overlap of electron wave function from nearest neighboring cations not involving an intermediary anion or exchange center. While direct exchange can be either ferromagnetic or antiferromagnetic, the superexchange interaction is usually antiferromagnetic, preferring opposite alignment of the connected magnetic moments. Similar to the direct exchange, superexchange calls for the combined effect of Pauli exclusion principle and Coulomb's repulsion of the electrons. If the superexchange center and the magnetic moments it connects to are non-collinear, namely the atomic bonds are canted, the superexchange will be accompanied by the antisymmetric exchange known as the Dzyaloshinskii–Moriya interaction, which prefers orthogonal alignment of neighboring magnetic moments. In this situation, the symmetric and antisymmetric contributions compete with each other and can result in versatile magnetic spin textures such as magnetic skyrmions.
In computational chemistry, spin contamination is the artificial mixing of different electronic spin-states. This can occur when an approximate orbital-based wave function is represented in an unrestricted form – that is, when the spatial parts of α and β spin-orbitals are permitted to differ. Approximate wave functions with a high degree of spin contamination are undesirable. In particular, they are not eigenfunctions of the total spin-squared operator, Ŝ2, but can formally be expanded in terms of pure spin states of higher multiplicities.
The Flippin–Lodge angle is one of two angles used by organic and biological chemists studying the relationship between a molecule's chemical structure and ways that it reacts, for reactions involving "attack" of an electron-rich reacting species, the nucleophile, on an electron-poor reacting species, the electrophile. Specifically, the angles—the Bürgi–Dunitz, , and the Flippin–Lodge, —describe the "trajectory" or "angle of attack" of the nucleophile as it approaches the electrophile, in particular when the latter is planar in shape. This is called a nucleophilic addition reaction and it plays a central role in the biological chemistry taking place in many biosyntheses in nature, and is a central "tool" in the reaction toolkit of modern organic chemistry, e.g., to construct new molecules such as pharmaceuticals. Theory and use of these angles falls into the areas of synthetic and physical organic chemistry, which deals with chemical structure and reaction mechanism, and within a sub-specialty called structure correlation.
Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms. Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or quantum field theory.
Magnetochemistry is concerned with the magnetic properties of chemical compounds. Magnetic properties arise from the spin and orbital angular momentum of the electrons contained in a compound. Compounds are diamagnetic when they contain no unpaired electrons. Molecular compounds that contain one or more unpaired electrons are paramagnetic. The magnitude of the paramagnetism is expressed as an effective magnetic moment, μeff. For first-row transition metals the magnitude of μeff is, to a first approximation, a simple function of the number of unpaired electrons, the spin-only formula. In general, spin–orbit coupling causes μeff to deviate from the spin-only formula. For the heavier transition metals, lanthanides and actinides, spin–orbit coupling cannot be ignored. Exchange interaction can occur in clusters and infinite lattices, resulting in ferromagnetism, antiferromagnetism or ferrimagnetism depending on the relative orientations of the individual spins.
Molecular symmetry in physics and chemistry describes the symmetry present in molecules and the classification of molecules according to their symmetry. Molecular symmetry is a fundamental concept in the application of Quantum Mechanics in physics and chemistry, for example it can be used to predict or explain many of a molecule's properties, such as its dipole moment and its allowed spectroscopic transitions, without doing the exact rigorous calculations. To do this it is necessary to classify the states of the molecule using the irreducible representations from the character table of the symmetry group of the molecule. Among all the molecular symmetries, diatomic molecules show some distinct features and they are relatively easier to analyze.
In applied mathematics, finite subgroups of SU(2) are groups composed of rotations and related transformations, employed particularly in the field of physical chemistry. The symmetry group of a physical body generally contains a subgroup of the 3D rotation group. It may occur that the group {±1} with two elements acts also on the body; this is typically the case in magnetism for the exchange of north and south poles, or in quantum mechanics for the change of spin sign. In this case, the symmetry group of a body may be a central extension of the group of spatial symmetries by the group with two elements. Hans Bethe introduced the term "double group" (Doppelgruppe) for such a group, in which two different elements induce the spatial identity, and a rotation of 2π may correspond to an element of the double group that is not the identity.
![Structure of a square-planar complex ion such as [AgF4] Square-planar-3D-balls.png](http://upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Square-planar-3D-balls.png/170px-Square-planar-3D-balls.png)
