The hartree (symbol: ''E''_h), also known as the Hartree energy, is the

unit Unit may refer to: General measurement * Unit of measurement, a definite magnitude of a physical quantity, defined and adopted by convention or by law **International System of Units (SI), modern form of the metric system **English units, histo ...

energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...

in the

atomic units The atomic units are a system of natural units of measurement that is especially convenient for calculations in atomic physics and related scientific fields, such as computational chemistry and atomic spectroscopy. They were originally suggested ...

system, named after the British physicist

Douglas Hartree Douglas Rayner Hartree (27 March 1897 – 12 February 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree–Fock equations of atomic physics and the c ...

. Its

CODATA The Committee on Data of the International Science Council (CODATA) was established in 1966 as the Committee on Data for Science and Technology, originally part of the International Council of Scientific Unions, now part of the International ...

recommended value is = The hartree is approximately the negative

electric potential energy Electric potential energy is a potential energy (measured in joules) that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system. An ''object'' may be sa ...

of the electron in a

hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...

atom Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...

in its

ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state ...

and, by the

virial theorem In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by a conservative force (where the work done is independent of path), with ...

, approximately twice its

ionization energy In physics and chemistry, ionization energy (IE) is the minimum energy required to remove the most loosely bound electron of an isolated gaseous atom, Ion, positive ion, or molecule. The first ionization energy is quantitatively expressed as : ...

; the relationships are not exact because of the finite

mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...

of the

nucleus Nucleus (: nuclei) is a Latin word for the seed inside a fruit. It most often refers to: *Atomic nucleus, the very dense central region of an atom *Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA Nucleu ...

of the hydrogen atom and relativistic corrections. The hartree is usually used as a unit of energy in

atomic physics Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned wit ...

and

computational chemistry Computational chemistry is a branch of chemistry that uses computer simulations to assist in solving chemical problems. It uses methods of theoretical chemistry incorporated into computer programs to calculate the structures and properties of mol ...

: for experimental measurements at the atomic scale, the

electronvolt In physics, an electronvolt (symbol eV), also written electron-volt and electron volt, is the measure of an amount of kinetic energy gained by a single electron accelerating through an Voltage, electric potential difference of one volt in vacuum ...

(eV) or the

reciprocal centimetre Reciprocal length or inverse length is a quantity or measurement used in several branches of science and mathematics, defined as the reciprocal of length. Common units used for this measurement include the reciprocal metre or inverse metre (symbol ...

(cm⁻¹) are much more widely used.

Other relationships

E_\mathrm =  = m_\mathrm\left(\frac\right)^2 = m_\mathrm c^2 \alpha^2 =

:: = 2 Ry = 2 ''R''_∞''hc'' :: = :: = :: = :: ≘ :: ≘ :: ≘ :: ≘ where: * ''ħ'' is the

reduced Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...

, * ''m''_e is the

electron mass In particle physics, the electron mass (symbol: ) is the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about or about , which has an energy ...

, * ''e'' is the

elementary charge The elementary charge, usually denoted by , is a fundamental physical constant, defined as the electric charge carried by a single proton (+1 ''e'') or, equivalently, the magnitude of the negative electric charge carried by a single electron, ...

, * ''a''₀ is the

Bohr radius The Bohr radius () is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an at ...

, * ''ε''₀ is the

electric constant Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric const ...

, * ''c'' is the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...

in vacuum, and * ''α'' is the

fine-structure constant In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Alpha, Greek letter ''alpha''), is a Dimensionless physical constant, fundamental physical constant that quantifies the strength of the el ...

. Effective hartree units are used in semiconductor physics where

e^2

is replaced by

e^2/\varepsilon

and

\varepsilon

is the static dielectric constant. Also, the electron mass is replaced by the effective band mass

m^*

. The effective hartree in semiconductors becomes small enough to be measured in

millielectronvolt In physics, an electronvolt (symbol eV), also written electron-volt and electron volt, is the measure of an amount of kinetic energy gained by a single electron accelerating through an electric potential difference of one volt in vacuum. When us ...

s (meV). Tsuneya Ando, Alan B. Fowler, and Frank Stern Rev. Mod. Phys. 54, 437 (1982)

References

{{reflist Units of energy Physical constants