Hartree

The Hartree E_h, also known as the Hartree energy, is a physical constant, which is used in the Hartree atomic units system and named after the British physicist Douglas Hartree. It is defined as 2R_∞hc, where R_∞ is the Rydberg constant, h is the Planck constant and c is the speed of light. Its CODATA recommended value is E_h = 4.3597447222071(85)×10⁻¹⁸ J^[1] = 27.211386245988(53) eV.^[2]

The Hartree energy is approximately the electric potential energy of the hydrogen atom in its ground state and, by the virial theorem, approximately twice its ionization energy; the relationships are not exact because of the finite mass of the nucleus of the hydrogen atom and relativistic corrections.

The Hartree is usually used like a unit of energy in atomic physics and computational chemistry: for experimental measurements at the atomic scale, the electronvolt (eV) or the reciprocal centimetre (cm⁻¹) are much more widely used.

Other relationshipsEdit

${\displaystyle E_{\mathrm {h} }={\hbar ^{2} \over {m_{\mathrm {e} }a_{0}^{2}}}=m_{\mathrm {e} }\left({\frac {e^{2}}{4\pi \epsilon _{0}\hbar }}\right)^{2}=m_{\mathrm {e} }c^{2}\alpha ^{2}={\hbar c\alpha \over {a_{0}}}}$

= 2 Ry

≜ 27.211386245988(53) eV

≜ 4.3597447222071(85)×10⁻¹⁸ J

≜ 4.3597447222071(85)×10⁻¹¹ erg

≜ 2625.4996394799(50) kJ/mol

≜ 627.5094740631(12) kcal/mol

≜ 219474.63136320(43) cm⁻¹

≜ 6579.683920502(13) THz

≜ 315775.02480407(61) K

where:

ħ is the reduced Planck constant,

m_e is the electron rest mass,

e is the elementary charge,

a₀ is the Bohr radius,

ε₀ is the electric constant,

c is the speed of light in vacuum, and

α is the fine structure constant.

Note that since the Bohr radius ${\displaystyle a_{0}}$ is defined as ${\displaystyle a_{0}={\frac {4\pi \varepsilon _{0}\hbar ^{2}}{m_{\mathrm {e} }e^{2}}}={\frac {\hbar }{m_{\mathrm {e} }c\alpha }}}$, one may write the Hartree energy as ${\displaystyle E_{\mathrm {h} }=e^{2}/a_{0}}$ in Gaussian units where ${\displaystyle 4\pi \varepsilon _{0}=1}$. Effective Hartree units are used in semiconductor physics where ${\displaystyle e^{2}}$ is replaced by ${\displaystyle e^{2}/\epsilon }$ and ${\displaystyle \epsilon }$ is the static dielectric constant. Also, the electron mass is replaced by the effective band mass ${\displaystyle m^{*}}$. The effective Hartree in semiconductors becomes small enough to be measured in millielectronvolts (meV).

This article uses material from the Wikipedia article  Metasyntactic variable, which is released under the  Creative Commons Attribution-ShareAlike 3.0 Unported License.