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Atomic orbital

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In quantum mechanics, 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]

135 relations: Absolute value, Absorption spectroscopy, Albert Einstein, Alkali metal, Angular momentum, Argon, Atom, Atomic electron transition, Atomic nucleus, Atomic number, Atomic physics, Aufbau principle, 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, 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, Particle, Pauli exclusion principle, Periodic table, Philosophical Magazine, Photoelectric effect, Photon, Physical Review, Planck constant, Plum pudding model, Principal quantum number, Probability, Probability distribution, Quantum chemistry, Quantum electrodynamics, Quantum mechanics, Quantum number, Quantum state, Quantum superposition, 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, Wave function, Wave function collapse, Wave interference, Wave packet, Wave–particle duality, Werner Heisenberg, X-ray notation, Zeitschrift für Physik. Expand index (85 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 who developed the theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics).

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Alkali metal

The alkali metals are a group (column) in the periodic table consisting of the chemical elements lithium (Li), sodium (Na), potassium (K),The symbols Na and K for sodium and potassium are derived from their Latin names, natrium and kalium; these are still the names for the elements in some languages, such as German and Russian.

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Angular momentum

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

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Argon

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

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Atom

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 energy level to another within an atom or artificial atom.

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Atomic nucleus

The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment.

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Atomic number

The atomic number or proton number (symbol Z) of a chemical element is the number of protons found in the nucleus of an atom.

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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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Aufbau principle

The aufbau principle states that in the ground state of an atom or ion, electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels.

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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 bounded by 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) that is used to represent the electronic wave function in the Hartree–Fock method or density-functional theory in order to turn the partial differential equations of the model into algebraic equations suitable for efficient implementation on a computer.

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Beryllium

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 or Bohr diagram, introduced by Niels Bohr and Ernest Rutherford in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar to the structure of 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

Caesium (British spelling and IUPAC spelling) or cesium (American spelling) 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 to the point from two fixed perpendicular directed lines, measured in the same unit of length.

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Chemical element

A chemical element is a species of atoms having the same number of protons in their atomic nuclei (that is, the same atomic number, or 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 a solution of the equation.

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Condensed matter physics

Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties 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 isocline, isopleth, isarithm, or equipotential curve) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal 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 the points or other geometric elements 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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Dumbbell

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 linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.

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Electron

The electron is a subatomic particle, symbol or, whose electric charge is negative one elementary 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)

This page shows the electron configurations of the neutral gaseous atoms in their ground states.

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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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Ellipsoid

An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation.

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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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Energy

In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object.

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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, HFRSE LLD (30 August 1871 – 19 October 1937) was a New Zealand-born British physicist who came to be 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.

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Exponential function

In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.

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Extended periodic table

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

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Fermion

In particle physics, a fermion is a particle that follows Fermi–Dirac statistics.

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Fine-structure constant

In physics, the fine-structure constant, also known as Sommerfeld's constant, commonly denoted (the Greek letter ''alpha''), 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 was originally the idealization of how a varying quantity depends on another quantity.

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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

Gold is a chemical element with symbol Au (from aurum) and atomic number 79, making it one of the higher atomic number elements that occur naturally.

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Hamiltonian (quantum mechanics)

In quantum mechanics, a Hamiltonian is an 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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Harmonic

A harmonic is any member of the harmonic series, a divergent infinite 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

Helium (from lit) 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

Hydrogen is a chemical element with 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 which has one electron and thus is isoelectronic with hydrogen.

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Ion

An ion is an atom or molecule that has a non-zero net electrical charge (its total number of electrons is not equal to its total number of protons).

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J. J. Thomson

Sir Joseph John Thomson (18 December 1856 – 30 August 1940) was an English physicist and Nobel Laureate in Physics, credited with the discovery and identification of the electron; and with the discovery of the first subatomic particle.

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Kepler orbit

In celestial mechanics, a Kepler orbit (or Keplerian orbit) is the motion of one body relative to another, 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, is a difference in energy between two energy levels 2S1/2 and 2P1/2 (in term symbol notation) of the hydrogen atom which was not predicted by the Dirac equation, according to which these states should have the same energy.

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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, educator, and husband of American human rights activist Ava Helen Pauling.

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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

Lithium (from lit) 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 de Broglie, duke 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

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, designated by the letter ml, is the third in a set of four 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.

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Matter wave

Matter waves are a central part of the theory of quantum mechanics, being an example of wave–particle duality.

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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 (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 are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

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Neon

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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Particle

In the physical sciences, a particle (or corpuscule in older texts) is a small localized object to which can be ascribed several physical or chemical properties such as volume, density or mass.

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Pauli exclusion principle

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

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Periodic table

The periodic table is a tabular arrangement of the chemical elements, ordered by their atomic number, electron configuration, and recurring chemical properties, whose structure shows periodic trends.

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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 emission of electrons or other free carriers when light shines on a material.

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Photon

The photon is a type of elementary particle, the quantum of the electromagnetic field including electromagnetic radiation such as light, and the force carrier for the electromagnetic force (even when static via virtual particles).

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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, central in quantum mechanics.

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Plum pudding model

The plum pudding model is one of several scientific models of the atom.

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Principal quantum number

In quantum mechanics, the principal quantum number (symbolized n) is one of four quantum numbers which are assigned to all electrons in an atom to describe that electron's state.

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Probability

Probability is the measure of the likelihood that an event will occur.

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Probability distribution

In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

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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, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.

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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 an isolated quantum system.

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Quantum superposition

Quantum superposition is a fundamental principle of quantum mechanics.

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Radium

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 mathematical equation that describes the changes over time of a physical system in which quantum effects, such as wave–particle duality, are significant.

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Slater determinant

In quantum mechanics, a Slater determinant is an expression that describes the wave function 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

Sodium is a chemical element with symbol Na (from 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

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 and physical science, spherical harmonics are special functions defined on the surface of a sphere.

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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 which oscillates in time but whose peak amplitude profile does not move in space.

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Stern–Gerlach experiment

The Stern–Gerlach experiment demonstrated that the spatial orientation of angular momentum is quantized.

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Tangent

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 (total) angular momentum quantum numbers in a multi-electron atom (however, even a single electron can be described by a term symbol).

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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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Torus

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.

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Valence electron

In chemistry, a valence electron is an outer shell electron that is associated with an atom, and that can participate in the formation of a chemical bond if the outer shell is not closed; 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

In physics, a wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport.

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Wave function

A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system.

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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 interference

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

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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 concept in quantum mechanics that every particle or quantic entity may be partly described in terms not only of particles, but also of 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 (English: Journal for physics) 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 cloud model, Electron clouds, Empty orbital, F 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.

References

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

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