In chemistry, an atomic orbital is the region in which an electron may be found around a single atom.^[1] Specificaly, atomic orbitals are the quantum states of the individual electrons in the electron cloud around a single atom. Classically, the electrons were thought to orbit the atomic nucleus, much like the planets around the Sun (or more accurately, a moth orbiting very quickly around a lamp). However electrons can not be described as solid particles (as a planet or a moth), so a more accurate comparison would be that of a (huge) atmosphere (the spatially distributed electron) around a (tiny) planet (the nucleus). Hence the term "orbit" had to be substituted with something else: orbital. Chemistry (from the Greek word χημεία (chemeia) meaning cast together or pour together) is the science of matter at the atomic to molecular scale, dealing primarily with collections of atoms (such as molecules, crystals, and metals). ... Properties The electron is a lightweight fundamental subatomic particle that carries a negative electric charge. ... Properties For other uses, see Atom (disambiguation). ... A quantum state is any possible state in which a quantum mechanical system can be. ... Electron cloud is a term used for introducing the concept of wavefunction in low-level pedagogical introductions to atomic physics, molecular physics, chemistry or quantum chemistry. ...

Explaining the behaviour of the electrons that "orbit" an atom was one of the driving forces behind quantum mechanics. In quantum mechanics, the atomic orbitals are the quantum states that electrons surrounding an atom may exist in. These can be described as a wave function over space, as shown in the diagram on the right, by the n, l, and m quantum numbers of the orbital, or by the names of the orbitals, as used in electron configurations. Fig. ... In the most restricted usage in quantum mechanics, the wavefunction associated with a particle such as an electron, is a complex-valued square integrable function ψ defined over a portion of space normalized in such a way that In Max Borns probabilistic interpretation of the wavefunction, the amplitude squared... A quantum number is a number used to parametrise certain properties of particles or other systems in quantum mechanics. ... Electron atomic and molecular orbitals In atomic physics and quantum chemistry, the electron configuration is the arrangement of electrons in an atom, molecule or other body. ...

Electron atomic and molecular orbitals

Image File history File links Electron_orbitals. ... Image File history File links Electron_orbitals. ... Properties The electron is a lightweight fundamental subatomic particle that carries a negative electric charge. ... Electron atomic and molecular orbitals In quantum chemistry (electronic structure theory), the molecular electronic states, i. ...

Orbital names

Orbitals are given names in the form:

where X is the energy level corresponding to the principal quantum number , type is a lower-case letter denoting the shape or subshell of the orbital and it corresponds to the angular quantum number , and y is the number of electrons in that orbital. A quantum number describes the energies of electrons in atoms. ... In atomic physics, an electron subshell is a group of atomic orbitals with the same values of the principal quantum number n and the angular momentum quantum number l. ... The Azimuthal quantum number (or orbital angular momentum quantum number) l is a quantum number for an atomic orbital which determines its orbital angular momentum. ...

For example, the orbital 1s² (pronounced "one s two") has two electrons and is the lowest energy level (n = 1) and has an angular quantum number of l = 0. In some cases, the principal quantum number is given a letter associated with it. For n = 1, 2, 3, 4, 5 ....., the letters associated with those number are K, L, M, N, O .... respectively.

Formal quantum mechanical definition

In quantum mechanics, the state of an atom, i.e. the eigenstates of the atomic Hamiltonian, is expanded (see configuration interaction expansion and basis (linear algebra)) into linear combinations of anti-symmetrized products (Slater determinants) of one-electron functions. The spatial components of these one-electron functions are called atomic orbitals. (When one considers also their spin component, one speaks of atomic spin orbitals.) Fig. ... In linear algebra, the eigenvectors (from the German eigen meaning inherent, characteristic) of a linear operator are non-zero vectors which, when operated on by the operator, result in a scalar multiple of themselves. ... The quantum Hamiltonian is the physical state of a system, which may be characterized as a ray in an abstract Hilbert space (or, in the case of ensembles, as a trace class operator with trace 1). ... Configuration interaction (CI) is a post Hartree-Fock linear variational method for solving the nonrelativistic Schrödinger equation within the Born-Oppenheimer approximation for a quantum chemical multi-electron system. ... In linear algebra, a basis is a minimum set of vectors that, when combined, can address every vector in a given space. ... In mathematics, linear combinations are a concept central to linear algebra and related fields of mathematics. ... A Slater determinant (named after the physicist John C. Slater) is an expression in quantum mechanics for the wavefunction of a many-fermion system, which by construction satisfies the Pauli principle. ... Properties The electron is a lightweight fundamental subatomic particle that carries a negative electric charge. ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is generated by the motion of its center of mass about an external point. ...

In atomic physics, the atomic spectral lines correspond to transitions (quantum leaps) between quantum states of an atom. These states are labelled by a set of quantum numbers summarized in the term symbol and usually associated to particular electron configurations, i.e. by occupations schemes of atomic orbitals (e.g. for the ground state of neon -- term symbol: ). Atomic physics (or atom physics) is the field of physics that studies atoms as isolated systems comprised of electrons and an atomic nucleus. ... In physics, atomic spectral lines are formed when an electron makes a transition from a particular energy level of an atom, to a lower energy state. ... Quantum Leap was a science fiction television series that ran for 97 episodes from March 1989 to May 1993 on NBC. It follows the adventures of Dr. Samuel Beckett (played by Scott Bakula), a brilliant scientist who finds himself abruptly and uncontrollably leaping through time, temporarily switching places with diverse... A quantum state is any possible state in which a quantum mechanical system can be. ... Properties For other uses, see Atom (disambiguation). ... A quantum number describes the energies of electrons in atoms. ... In quantum mechanics, the term symbol is an abbreviated description of the angular momentum quantum numbers in a multi-electron atom. ... Electron atomic and molecular orbitals In atomic physics and quantum chemistry, the electron configuration is the arrangement of electrons in an atom, molecule or other body. ... General Name, Symbol, Number neon, Ne, 10 Chemical series noble gases Group, Period, Block 18, 2, p Appearance colorless Atomic mass 20. ...

This notation means that the corresponding Slater determinants have a clear higher weight in the configuration interaction expansion. The atomic orbital concept is therefore a key concept for visualizing the excitation process associated to a given transition. For example, one can say for a given transition that it corresponds to the excitation of an electron from an occupied orbital to a given unoccupied orbital. Nevertheless one has to keep in mind that electrons are fermions ruled by Pauli exclusion principle and cannot be distinguished from the other electrons in the atom. Moreover, it sometimes happens that the configuration interaction expansion converges very slowly and that one cannot speak about simple one-determinantal wave function at all. This is the case when electron correlation is large. A Slater determinant (named after the physicist John C. Slater) is an expression in quantum mechanics for the wavefunction of a many-fermion system, which by construction satisfies the Pauli principle. ... Configuration interaction (CI) is a post Hartree-Fock linear variational method for solving the nonrelativistic Schrödinger equation within the Born-Oppenheimer approximation for a quantum chemical multi-electron system. ... In particle physics, fermions, (named after Enrico Fermi), are particles with semi-integer spin. ... The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925, which states that no two identical fermions may occupy the same quantum state simultaneously. ... Electronic correlation refers to the interaction between electrons in a quantum system whose electronic structure is being considered. ...

Fundamentally, an atomic orbital is a one-electron wavefunction. Don't forget that when thinking about orbitals, we are often bombarded (even if we don't know it) by the Hartree-Fock vision of molecular orbital theory. In computational physics and computational chemistry, the Hartree-Fock (HF) or self-consistent field (SCF) calculation scheme is a self-consistent iterative variational procedure to calculate the Slater determinant (or the molecular orbitals which it is made of) for which the expectation value of the electronic molecular Hamiltonian is minimum. ...

Hydrogen-like atoms

Main article: Hydrogen-like atom

The simplest atomic orbitals are those that occur in an atom with a single electron, such as the hydrogen atom. In this case the atomic orbitals are the eigenstates of the hydrogen Hamiltonian. They can be obtained analytically (see Hydrogen atom). An atom of any other element ionized down to a single electron is very similar to hydrogen, and the orbitals take the same form. Hydrogen-like atoms are atoms with one single electron. ... depiction of a hydrogen-1 atom showing the Van der Waals radius and the proton nucleus. ... depiction of a hydrogen-1 atom showing the Van der Waals radius and the proton nucleus. ... An ion is an atom, group of atoms, or subatomic particle that normally is electrically neutral and achieve their status as an ion by loss (and addition) of an electron. ...

For atoms with two or more electrons, the governing equations can only be solved with the use of methods of iterative approximation. Orbitals of multi-electron atoms are qualitatively similar to those of hydrogen, and in the simplest models, they are taken to have the same form. For more rigorous and precise analysis, the numerical approximations must be used.

A given (hydrogen-like) atomic orbital is identified by unique values of three quantum numbers: n, l, and m_l. The rules restricting the values of the quantum numbers, and their energies (see below), explain the electron configuration of the atoms and the periodic table. A quantum number describes the energies of electrons in atoms. ... In atomic physics, the principal quantum number symbolized as n is the first quantum number of an atomic orbital. ... The Azimuthal quantum number (or orbital angular momentum quantum number) symbolized as l is a quantum number for an atomic orbital which determines its orbital angular momentum. ... By virtue of its charge and spin motion, an electron develops a magnetic field. ... Electron atomic and molecular orbitals In atomic physics and quantum chemistry, the electron configuration is the arrangement of electrons in an atom, molecule or other body. ... The periodic table of the chemical elements is a tabular method of displaying the chemical elements, first devised in 1869 by the Russian chemist Dmitri Mendeleev. ...

The stationary states (quantum states) of the hydrogen-like atoms are its atomic orbital. However, in general, an electron's behavior is not fully described by a single orbital. Electron states are best represented by time-depending "mixtures" (linear combinations) of multiple orbitals. See Linear combination of atomic orbitals molecular orbital method. A quantum state is any possible state in which a quantum mechanical system can be. ... In mathematics, linear combinations are a concept central to linear algebra and related fields of mathematics. ... This article may be too technical for most readers to understand. ...

The quantum number n first appeared in the Bohr model. It determines, among other things, the distance of the electron from the nucleus; all electrons with the same value of n lay at the same distance. Modern quantum mechanics confirms that these orbitals are closely related. For this reason, orbitals with the same value of n are said to comprise a "shell". Orbitals with the same value of n and also the same value of l are even more closely related, and are said to comprise a "subshell". The Bohr model of the atom In 1913, Niels Bohr introduced what has become known as the Bohr model of the atom to atomic physics. ... In atomic physics, an electron shell, also known as a main energy level, is a group of atomic orbitals with the same value of the principal quantum number n. ... In atomic physics, an electron subshell is a group of atomic orbitals with the same values of the principal quantum number n and the angular momentum quantum number l. ...

Qualitative characterization

Limitations on the quantum numbers

An atomic orbital is uniquely identified by the values of the three quantum numbers, and each set of the three quantum numbers corresponds to exactly one orbital, but the quantum numbers only occur in certain combinations of values. The rules governing the possible values of the quantum numbers are as follows:

The principal quantum number n is always a positive integer. In fact, it can be any positive integer, but for reasons discussed below, large numbers are seldom encountered. Each atom has, in general, many orbitals associated with each value of n; these orbitals together are sometimes called a shell. In atomic physics, the principal quantum number symbolized as n is the first quantum number of an atomic orbital. ... Natural number can mean either a positive integer (1, 2, 3, 4, ...) or a non-negative integer (0, 1, 2, 3, 4, ...). Natural numbers have two main purposes: they can be used for counting (there are 3 apples on the table), or they can be used for ordering (this is... In atomic physics, an electron shell, also known as a main energy level, is a group of atomic orbitals with the same value of the principal quantum number n. ...

The azimuthal quantum number is a non-negative integer. Within a shell where n is some integer n₀, ranges across all (integer) values satisfying the relation . For instance, the n = 1 shell has only orbitals with , and the n = 2 shell has only orbitals with , and . The set of orbitals associated with a particular value of are sometimes collectively called a subshell. The Azimuthal quantum number (or orbital angular momentum quantum number) symbolized as l is a quantum number for an atomic orbital which determines its orbital angular momentum. ...

The magnetic quantum number is also always an integer. Within a subshell where is some integer , ranges thus: . By virtue of its charge and spin motion, an electron develops a magnetic field. ...

The above results may be summarized in the following table. Each cell represents a subshell, and lists the values of available in that subshell. Empty cells represent subshells that do not exist.

Subshells are usually identified by their n- and -values. n is represented by its numerical value, but is represented by a letter as follows: 0 is represented by 's', 1 by 'p', 2 by 'd', 3 by 'f', and 4 by 'g'. For instance, one may speak of the subshell with n = 2 and as a '2s subshell'.

The Shapes of Orbitals

The shapes of the first five atomic orbitals

Any discussion of the shapes of electron orbitals is necessarily imprecise, because a given electron, regardless of which orbital it occupies, can at any moment be found at any distance from the nucleus and in any direction due to the Uncertainty Principle. Image File history File links Download high resolution version (2000x1106, 591 KB) File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Atomic orbital ... Image File history File links Download high resolution version (2000x1106, 591 KB) File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Atomic orbital ... In quantum physics, the Heisenberg uncertainty principle or the Heisenberg indeterminacy principle — the latter name given to it by Niels Bohr — states that one cannot measure values (with arbitrary precision) of certain conjugate quantities, which are pairs of observables of a single elementary particle. ...

However, the electron is much more likely to be found in certain regions of the atom than in others. Given this, a boundary surface can be drawn so that the electron has a high probability to be found anywhere within the surface, and all regions outside the surface have low values. The precise placement of the surface is arbitrary, but any reasonably compact determination must follow a pattern specified by the behavior of ψ², the square of the wavefunction. This boundary surface is what is meant when the "shape" of an orbital is mentioned. An open surface with X-, Y-, and Z-contours shown. ... This article discusses the concept of a wavefunction as it relates to quantum mechanics. ...

Generally speaking, the number n determines the size and energy of the orbital: as n increases, the size of the orbital increases.

Also in general terms, determines an orbital's shape, and its orientation. However, since some orbitals are described by equations in complex numbers, the shape sometimes depends on also. s-orbitals () are shaped like spheres. p-orbitals have the form of two ellipsoids with a point of tangency at the nucleus (sometimes referred to as a dumbbell). The three p-orbitals in each shell are oriented at right angles to each other, as determined by their respective values of . In mathematics, a complex number is a number of the form where a and b are real numbers, and i is the imaginary unit, with the property i 2 = −1. ... 3D rendering of an ellipsoid In mathematics, an ellipsoid is a type of quadric that is a higher dimensional analogue of an ellipse. ... In mathematics, the word tangent has two distinct, but etymologically related meanings: one in geometry, and one in trigonometry. ... A semi-accurate depiction of the helium atom. ... In atomic physics, an electron shell, also known as a main energy level, is a group of atomic orbitals with the same value of the principal quantum number n. ...

Orbitals of hydrogen atom, calculated by quantum mechanics

Four of the five d-orbitals look similar, each with four pear-shaped balls, each ball tangent to two others, and the centers of all four lying in one plane, between a pair of axes. Three of these planes are the xy-, xz-, and yz-planes, and the fourth has the centres on the x and y axes. The fifth and final d-orbital consists of three regions of high probability density: a torus with two pear-shaped regions placed symmetrically on its z axis. Image File history File links HAtomOrbitals. ... Image File history File links HAtomOrbitals. ... A torus. ...

There are seven f-orbitals, each with shapes more complex than those of the d-orbitals.

The shapes of atomic orbitals in one-electron atom are related to 3-dimensional spherical harmonics. In mathematics, the spherical harmonics are an orthogonal set of solutions to Laplaces equation represented in a system of spherical coordinates. ...

Orbital energy

In atoms with a single electron (essentially the hydrogen atom), the energy of an orbital (and, consequently, of any electrons in the orbital) is determined exclusively by n. The n = 1 orbital has the lowest possible energy in the atom. Each successively higher value of n has a higher level of energy, but the difference decreases as n increases. For high n, the level of energy becomes so high that the electron can easily escape from the atom. depiction of a hydrogen-1 atom showing the Van der Waals radius and the proton nucleus. ...

In atoms with multiple electrons, the energy of an electron depends not only on the intrinsic properties of its orbital, but also on its interactions with the other electrons. These interactions depend on the detail of its spatial probability distribution, and so the energy levels of orbitals depend not only on n but also on . Higher values of are associated with higher values of energy; for instance, the 2p state is higher than the 2s state. When = 3, the increase in energy of the orbital becomes so large as to push the energy of orbital above the energy of the s-orbital in the next higher shell; when = 4 the energy is pushed into the shell two steps higher. A quantum mechanical system can only be in certain states, so that only certain energy levels are possible. ...

The energy order of the first 24 subshells is given in the following table. Each cell represents a subshell with n and given by its row and column indices, respectively. The number in the cell is the subshell's position in the sequence. Empty cells represent subshells that do not exist.

Electron placement and the periodic table

Several rules govern the placement of electrons in orbitals (electron configuration). The first dictates that no two electrons in an atom may have the same set of values of quantum numbers (this is the Pauli exclusion principle). These quantum numbers include the three that define orbitals, as well as (the hitherto unmentioned) s. Thus, two electrons may occupy a single orbital, so long as they have different values of s. However, only two electrons, because of their spin, can be associated with each orbital. Electron atomic and molecular orbitals In atomic physics and quantum chemistry, the electron configuration is the arrangement of electrons in an atom, molecule or other body. ... The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925, which states that no two identical fermions may occupy the same quantum state simultaneously. ... In atomic physics, the spin quantum number is a quantum number that parametrizes the intrinsic angular momentum (or spin angular momentum, or simply spin) of a given particle. ...

Additionally, an electron always tries to occupy the lowest possible energy state. It is possible for it to occupy any orbital so long as it does not violate the Pauli exclusion principle, but if lower-energy orbitals are available, this condition is unstable. The electron will eventually lose energy (by releasing a photon) and drop into the lower orbital. Thus, electrons fill orbitals in the order specified by the energy sequence given above. In quantum physics, the photon (from Greek φως, phōs, meaning light) is the quantum of the electromagnetic field (light). ...

This behavior is responsible for the structure of the periodic table. The table may be divided into several rows (called 'periods'), numbered starting with 1 at the top. The presently known elements occupy seven periods. If a certain period has number i, it consists of elements whose outermost electrons fall in the ith shell. The periodic table of the chemical elements is a tabular method of displaying the chemical elements, first devised in 1869 by the Russian chemist Dmitri Mendeleev. ...

The periodic table may also be divided into several numbered rectangular 'blocks'. The elements belonging to a given block have this common feature: their highest-energy electrons all belong to the same -state (but the n associated with that -state depends upon the period). For instance, the leftmost two columns constitute the 's-block'. The outermost electrons of Li and Be respectively belong to the 2s subshell, and those of Na and Mg to the 3s subshell.

The number of electrons in a neutral atom increases with the atomic number. The electrons in the outermost shell, or valence electrons, tend to be responsible for an element's chemical behavior. Elements that contain the same number of valence electrons can be grouped together and display similar chemical properties. In chemistry and physics, the atomic number (Z) is the number of protons found in the nucleus of an atom. ... In chemistry, valence electrons are the electrons located within the outermost energy level of an atom. ...

See also

• List of Hund's rules
• Electron configuration
• Atomic electron configuration table
• Molecular orbital
• Energy level

In atomic physics, Hunds rules, discovered by Friedrich Hund, determine which is the term symbol that corresponds to the ground state of a multi-electron atom. ... Electron atomic and molecular orbitals In atomic physics and quantum chemistry, the electron configuration is the arrangement of electrons in an atom, molecule or other body. ... This is a table of electron configurations of atoms. ... Electron atomic and molecular orbitals In quantum chemistry (electronic structure theory), the molecular electronic states, i. ... A quantum mechanical system can only be in certain states, so that only certain energy levels are possible. ...

References

1. ^ Daintith, J. (2004). Oxford Dictionary of Chemistry. New York: Oxford University Press. ISBN 0198609183.

Further reading

• Tipler, Paul & Ralph Llewellyn (2003). Modern Physics (4th ed.). New York: W. H. Freeman and Company. ISBN 0-7167-4345-0

External links

• Guide to atomic orbitals
• Covalent Bonds and Molecular Structure
• The Orbitron, a visualization of all common and uncommon atomic orbitals, from 1s to 7g
• David Manthey's Orbital Viewer renders orbitals with n ≤ 30
• Java orbital viewer applet