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Atomic orbital

An atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. [1]

131 relations: Absolute value, Absorption spectroscopy, Albert Einstein, Angular momentum, Argon, Atom, Atomic electron transition, Atomic nucleus, Atomic number, Atomic physics, Azimuthal quantum number, Ball (mathematics), Basis set (chemistry), Beryllium, Block (periodic table), Bohr model, Bounded function, Caesium, Cartesian coordinate system, Chemical element, Complex number, Condensed matter physics, Configuration interaction, Contour line, Coordinate system, Cubic harmonic, Dirac equation, Dumbbell, Eigenvalues and eigenvectors, Electron, Electron configuration, Electron configurations of the elements (data page), Electron shell, Electronic correlation, Ellipsoid, Emission spectrum, Energy, Energy level, Ernest Rutherford, Erwin Schrödinger, Euclidean vector, Exponential function, Extended periodic table, Fermion, Fine-structure constant, Function (mathematics), Fundamental frequency, Gaussian orbital, Gold, Hamiltonian (quantum mechanics), ..., Hantaro Nagaoka, Harmonic, Hartree–Fock method, Helium, Hund's rules, Hydrogen, Hydrogen atom, Hydrogen-like atom, Interference (wave propagation), Ion, J. J. Thomson, Kepler orbit, Lamb shift, Limit (mathematics), Linear combination, Linear combination of atomic orbitals, Linus Pauling, List of quantum chemistry and solid-state physics software, Lithium, London dispersion force, Louis de Broglie, Magnesium, Magnetic quantum number, Matter wave, Max Born, Mercury (element), Molecular orbital, Molecular orbital theory, Natural number, Neon, Niels Bohr, Node (physics), Orbital eccentricity, Orbital resonance, Particle, Pauli exclusion principle, Periodic table, Philosophical Magazine, Photoelectric effect, Photon, Physical Review, Planck constant, Plum pudding model, Principal quantum number, Probability distribution, Quantum chemistry, Quantum electrodynamics, Quantum mechanics, Quantum number, Quantum state, Radium, Richard Feynman, Robert S. Mulliken, Roger Penrose, Schrödinger equation, Slater determinant, Slater-type orbital, Sodium, Solid-state physics, Spectral line, Spectroscopy, Spherical coordinate system, Spherical harmonics, Spin (physics), Spin quantum number, Standing wave, Stern–Gerlach experiment, Tangent, Term symbol, The Road to Reality, Torus, Uncertainty principle, Valence electron, Vibrations of a circular membrane, Wave function, Wave function collapse, Wave packet, Wave–particle duality, Werner Heisenberg, X-ray notation, Zeitschrift für Physik. Expand index (81 more) »

Absolute value

In mathematics, the absolute value (or modulus) of a real number is the non-negative value of without regard to its sign.

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Absorption spectroscopy

Absorption spectroscopy refers to spectroscopic techniques that measure the absorption of radiation, as a function of frequency or wavelength, due to its interaction with a sample.

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Albert Einstein

Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist.

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Angular momentum

In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum.

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Argon is a chemical element with symbol Ar and atomic number 18.

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An atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element.

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Atomic electron transition

Atomic electron transition is a change of an electron from one quantum state to another within an atom or artificial atom.

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Atomic nucleus

The nucleus is the small, dense region consisting of protons and neutrons at the center of an atom.

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Atomic number

In chemistry and physics, the atomic number of a chemical element (also known as its proton number) is the number of protons found in the nucleus of an atom of that element, and therefore identical to the charge number of the nucleus.

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Atomic physics

Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus.

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Azimuthal quantum number

The azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital.

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Ball (mathematics)

In mathematics, a ball is the space inside a sphere.

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Basis set (chemistry)

A basis set in theoretical and computational chemistry is a set of functions (called basis functions) which are combined in linear combinations (generally as part of a quantum chemical calculation) to create molecular orbitals.

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Beryllium is a chemical element with symbol Be and atomic number 4.

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Block (periodic table)

A block of the periodic table of elements is a set of adjacent groups.

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Bohr model

In atomic physics, the Rutherford–Bohr model or Bohr model, introduced by Niels Bohr in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with attraction provided by electrostatic forces rather than gravity.

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Bounded function

In mathematics, a function f defined on some set X with real or complex values is called bounded, if the set of its values is bounded.

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Caesium or cesium is a chemical element with symbol Cs and atomic number 55.

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Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length.

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Chemical element

A chemical element (or element) is a chemical substance consisting of atoms having the same number of protons in their atomic nuclei (i.e. the same atomic number, Z).

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers and is the imaginary unit, that satisfies the equation.

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Condensed matter physics

Condensed matter physics is a branch of physics that deals with the physical properties of condensed phases of matter.

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Configuration interaction

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.

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Contour line

A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value.

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Coordinate system

In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element on a manifold such as Euclidean space.

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Cubic harmonic

In fields like computational chemistry and solid-state and condensed matter physics the so-called atomic orbitals, or spin-orbitals, as they appear in textbooks on quantum physics, are often partially replaced by cubic harmonics for a number of reasons.

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Dirac equation

In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928.

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The dumbbell, a type of free weight, is a piece of equipment used in weight training.

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Eigenvalues and eigenvectors

In linear algebra, an eigenvector or characteristic vector of a square matrix is a vector that does not change its direction under the associated linear transformation.

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The electron is a subatomic particle, symbol or, with a negative elementary electric charge.

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Electron configuration

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.

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Electron configurations of the elements (data page)

Electron configurations of the neutral gaseous atoms in the ground state.

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Electron shell

In chemistry and atomic physics, an electron shell, or a principal energy level, may be thought of as an orbit followed by electrons around an atom's nucleus.

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Electronic correlation

Electronic correlation is the interaction between electrons in the electronic structure of a quantum system.

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An ellipsoid is a closed quadric surface that is a three-dimensional analogue of an ellipse.

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Emission spectrum

The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to an atom or molecule making a transition from a high energy state to a lower energy state.

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In physics, energy is a property of objects which can be transferred to other objects or converted into different forms, but cannot be created or destroyed.

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Energy level

A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy.

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Ernest Rutherford

Ernest Rutherford, 1st Baron Rutherford of Nelson, (30 August 1871 – 19 October 1937) was a New Zealand-born British physicist who became known as the father of nuclear physics.

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Erwin Schrödinger

Erwin Rudolf Josef Alexander Schrödinger (12 August 1887 – 4 January 1961), sometimes written as or, was a Nobel Prize-winning Austrian physicist who developed a number of fundamental results in the field of quantum theory, which formed the basis of wave mechanics: he formulated the wave equation (stationary and time-dependent Schrödinger equation) and revealed the identity of his development of the formalism and matrix mechanics.

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Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction and can be added to other vectors according to vector algebra.

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Exponential function

In mathematics, an exponential function is a function of the form The input variable x occurs as an exponent – hence the name.

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Extended periodic table

An extended periodic table theorizes about elements beyond element 118 (beyond period 7, or row 7).

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In particle physics, a fermion (a name coined by Paul Dirac from the surname of Enrico Fermi) is any particle characterized by Fermi–Dirac statistics.

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Fine-structure constant

In physics, the fine-structure constant, also known as Sommerfeld's constant, commonly denoted α (the Greek letter α), is a fundamental physical constant characterizing the strength of the electromagnetic interaction between elementary charged particles.

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Function (mathematics)

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

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Fundamental frequency

The fundamental frequency, often referred to simply as the fundamental, is defined as the lowest frequency of a periodic waveform.

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Gaussian orbital

In computational chemistry and molecular physics, Gaussian orbitals (also known as Gaussian type orbitals, GTOs or Gaussians) are functions used as atomic orbitals in the LCAO method for the representation of electron orbitals in molecules and numerous properties that depend on these.

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Gold is a chemical element with symbol Au (from aurum) and atomic number 79.

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Hamiltonian (quantum mechanics)

In quantum mechanics, the Hamiltonian is the operator corresponding to the total energy of the system in most of the cases.

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Hantaro Nagaoka

was a Japanese physicist and a pioneer of Japanese physics during the Meiji period.

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The term harmonic in its strictest sense is any member of the harmonic series.

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Hartree–Fock method

In computational physics and chemistry, the Hartree–Fock (HF) method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system in a stationary state.

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Helium is a chemical element with symbol He and atomic number 2.

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Hund's rules

In atomic physics, Hund's rules refers to a set of rules that German physicist Friedrich Hund formulated around 1927, which are used to determine the term symbol that corresponds to the ground state of a multi-electron atom.

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Hydrogen is a chemical element with chemical symbol H and atomic number 1.

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Hydrogen atom

A hydrogen atom is an atom of the chemical element hydrogen.

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Hydrogen-like atom

A hydrogen-like ion is any atomic nucleus with one electron and thus is isoelectronic with hydrogen.

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Interference (wave propagation)

In physics, interference is a phenomenon in which two waves superpose to form a resultant wave of greater or lower amplitude.

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An ion is an atom or a molecule in which the total number of electrons is not equal to the total number of protons, giving the atom or molecule a net positive or negative electrical charge.

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J. J. Thomson

Sir Joseph John "J.

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Kepler orbit

In celestial mechanics, a Kepler orbit (or Keplerian orbit) describes the motion of an orbiting body as an ellipse, parabola, or hyperbola, which forms a two-dimensional orbital plane in three-dimensional space.

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Lamb shift

In physics, the Lamb shift, named after Willis Lamb (1913–2008), is a small difference in energy between two energy levels 2S1/2 and 2P1/2 (in term symbol notation) of the hydrogen atom in quantum electrodynamics (QED).

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Limit (mathematics)

In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value.

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Linear combination

In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).

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Linear combination of atomic orbitals

A linear combination of atomic orbitals or LCAO is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum chemistry.

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Linus Pauling

Linus Carl Pauling (February 28, 1901 – August 19, 1994) was an American chemist, biochemist, peace activist, author, and educator.

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List of quantum chemistry and solid-state physics software

Quantum chemistry computer programs are used in computational chemistry to implement the methods of quantum chemistry.

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Lithium (from λίθος lithos, "stone") is a chemical element with symbol Li and atomic number 3.

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London dispersion force

London dispersion forces (LDF, also known as dispersion forces, London forces, instantaneous dipole–induced dipole forces, or loosely van der Waals forces) are a type of force acting between atoms and molecules.

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Louis de Broglie

Louis-Victor-Pierre-Raymond, 7th duc de Broglie (or; 15 August 1892 – 19 March 1987) was a French physicist who made groundbreaking contributions to quantum theory.

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Magnesium is a chemical element with symbol Mg and atomic number 12.

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Magnetic quantum number

In atomic physics, the magnetic quantum number is the third of a set of quantum numbers (the principal quantum number, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number) which describe the unique quantum state of an electron and is designated by the letter m. The magnetic quantum number denotes the energy levels available within a subshell.

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Matter wave

All matter can exhibit wave-like behaviour.

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Max Born

Max Born (11 December 1882 – 5 January 1970) was a German physicist and mathematician who was instrumental in the development of quantum mechanics.

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Mercury (element)

Mercury is a chemical element with symbol Hg and atomic number 80.

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Molecular orbital

In chemistry, a molecular orbital (or MO) is a mathematical function describing the wave-like behavior of an electron in a molecule.

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Molecular orbital theory

In chemistry, molecular orbital (MO) theory is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule.

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Natural number

In mathematics, the natural numbers (sometimes called the whole numbers): "whole number An integer, though sometimes it is taken to mean only non-negative integers, or just the positive integers." give definitions of "whole number" under several headwords: INTEGER … Syn. whole number.

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Neon is a chemical element with symbol Ne and atomic number 10.

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Niels Bohr

Niels Henrik David Bohr (7 October 1885 – 18 November 1962) was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922.

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Node (physics)

A node is a point along a standing wave where the wave has minimum amplitude.

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Orbital eccentricity

The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle.

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Orbital resonance

In celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers.

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A particle is a minute fragment or quantity of matter.

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Pauli exclusion principle

The Pauli exclusion principle is the quantum mechanical principle that states that two identical fermions (particles with half-integer spin) cannot occupy the same quantum state simultaneously.

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Periodic table

The periodic table is a tabular arrangement of the chemical elements, ordered by their atomic number (number of protons in the nucleus), electron configurations, and recurring chemical properties.

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Philosophical Magazine

The Philosophical Magazine is one of the oldest scientific journals published in English.

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Photoelectric effect

The photoelectric effect is the observation that many metals emit electrons when light shines upon them.

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No description.

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Physical Review

Physical Review is an American peer-reviewed scientific journal established in 1893 by Edward Nichols.

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Planck constant

The Planck constant (denoted, also called Planck's constant) is a physical constant that is the quantum of action in quantum mechanics.

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Plum pudding model

The plum pudding model is an obsolete scientific model of the atom proposed by J. J. Thomson in 1904.

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Principal quantum number

The principal quantum number, symbolized as n, is the first of a set of quantum numbers (which includes the principal quantum number, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number) of an atomic orbital.

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Probability distribution

In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.

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Quantum chemistry

Quantum chemistry is a branch of chemistry whose primary focus is the application of quantum mechanics in physical models and experiments of chemical systems.

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Quantum electrodynamics

In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics.

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Quantum mechanics

Quantum mechanics (QM; also known as quantum physics, or quantum theory), including quantum field theory, is a fundamental branch of physics concerned with processes involving, for example, atoms and photons.

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Quantum number

Quantum numbers describe values of conserved quantities in the dynamics of a quantum system.

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Quantum state

In quantum physics, quantum state refers to the state of a quantum system.

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Radium is a chemical element with symbol Ra and atomic number 88.

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Richard Feynman

Richard Phillips Feynman, (May 11, 1918 – February 15, 1988) was an American theoretical physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics for which he proposed the parton model.

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Robert S. Mulliken

Robert Sanderson Mulliken (June 7, 1896 – October 31, 1986) was an American physicist and chemist, primarily responsible for the early development of molecular orbital theory, i.e. the elaboration of the molecular orbital method of computing the structure of molecules.

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Roger Penrose

Sir Roger Penrose (born 8 August 1931) is an English mathematical physicist, mathematician and philosopher of science.

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Schrödinger equation

In quantum mechanics, the Schrödinger equation is a partial differential equation that describes how the quantum state of a physical system changes with time.

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Slater determinant

In quantum mechanics, a Slater determinant is an expression that describes the wavefunction of a multi-fermionic system that satisfies anti-symmetry requirements and consequently the Pauli principle by changing sign upon exchange of two electrons (or other fermions).

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Slater-type orbital

Slater-type orbitals (STOs) are functions used as atomic orbitals in the linear combination of atomic orbitals molecular orbital method.

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Sodium is a chemical element with symbol Na (from New Latin natrium) and atomic number 11.

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Solid-state physics

Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy.

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Spectral line

A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies.

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Spectroscopy is the study of the interaction between matter and electromagnetic radiation.

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Spherical coordinate system

In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.

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Spherical harmonics

In mathematics, spherical harmonics are a series of special functions defined on the surface of a sphere used to solve some kinds of differential equations.

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Spin (physics)

In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles (hadrons), and atomic nuclei.

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Spin quantum number

In atomic physics, the spin quantum number is a quantum number that parameterizes the intrinsic angular momentum (or spin angular momentum, or simply spin) of a given particle.

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Standing wave

In physics, a standing wave – also known as a stationary wave – is a wave in a medium in which each point on the axis of the wave has an associated constant amplitude.

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Stern–Gerlach experiment

The Stern–Gerlach experiment famously demonstrates the quantization of spatial orientation of angular momentum.

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In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.

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Term symbol

In quantum mechanics, the term symbol is an abbreviated description of the angular momentum quantum numbers in a multi-electron atom.

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The Road to Reality

The Road to Reality: A Complete Guide to the Laws of the Universe is a book on modern physics by the British mathematical physicist Roger Penrose, published in 2004.

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In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

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Uncertainty principle

In quantum mechanics, the uncertainty principle, also known as Heisenberg's uncertainty principle, is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known simultaneously.

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Valence electron

In chemistry, a valence electron is an electron that is associated with an atom, and that can participate in the formation of a chemical bond; in a single covalent bond, both atoms in the bond contribute one valence electron in order to form a shared pair.

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Vibrations of a circular membrane

A two-dimensional elastic membrane under tension can support transverse vibrations.

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Wave function

A wave function in quantum mechanics describes the quantum state of an isolated system of one or more particles.

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Wave function collapse

In quantum mechanics, wave function collapse is said to occur when a wave function—initially in a superposition of several eigenstates—appears to reduce to a single eigenstate (by "observation").

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Wave packet

In physics, a wave packet (or wave train) is a short "burst" or "envelope" of localized wave action that travels as a unit.

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Wave–particle duality

Wave–particle duality is the fact that every elementary particle or quantic entity exhibits the properties of not only particles, but also waves.

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Werner Heisenberg

Werner Karl Heisenberg (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the key pioneers of quantum mechanics.

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X-ray notation

X-ray notation is a method of labeling atomic orbitals that grew out of X-ray science.

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Zeitschrift für Physik

Zeitschrift für Physik is a defunct series of German peer-reviewed German scientific journal of physics established in 1920 by Springer Berlin Heidelberg.

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1s electron, 1s orbital, 1s1s, 2p electron, 2s electron, 2s shell, Atomic Orbital, Atomic orbital model, Atomic orbitals, Atomic shell, Bohr orbital, D orbital, D orbitals, D-Orbitals, D-orbital, Dalton model, Electron Cloud Model, Electron cloud, Electron clouds, Empty orbital, F-orbital, H-orbital, Inner-shell electrons, Orbital atom model, P orbital, P-orbital, P-orbitals, Parabola Orbital, S P D F G, S orbital, S-orbital, SPDFG orbitals, Sp orbital, Spin orbital, Spin-orbital.


[1] https://en.wikipedia.org/wiki/Atomic_orbital

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