Physics:Hartree

From HandWiki
Short description: Unit of energy in the atomic units system

The hartree (symbol: Eh), also known as the Hartree energy, is the unit of energy in the atomic units system, named after the British physicist Douglas Hartree. Its CODATA recommended value is Eh = 4.3597447222071(85)×10−18 J[1] = .

The hartree is approximately the negative electric potential energy of the electron in a 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 as 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 relationships

[math]\displaystyle{ E_\mathrm{h} = {\hbar^2 \over {m_\mathrm{e} a^2_0}} = m_\mathrm{e}\left(\frac{e^2}{4\pi\varepsilon_0\hbar}\right)^2 = m_\mathrm{e} c^2 \alpha^2 = {\hbar c \alpha \over {a_0}} }[/math]
= 2 Ry = 2 Rhc
= 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

where:

Effective hartree units are used in semiconductor physics where [math]\displaystyle{ e^2 }[/math] is replaced by [math]\displaystyle{ e^2/\varepsilon }[/math] and [math]\displaystyle{ \varepsilon }[/math] is the static dielectric constant. Also, the electron mass is replaced by the effective band mass [math]\displaystyle{ m^* }[/math]. The effective hartree in semiconductors becomes small enough to be measured in millielectronvolts (meV).[2]

References

  1. "2018 CODATA Value: Hartree energy". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. http://physics.nist.gov/cgi-bin/cuu/Value?hr. Retrieved 2019-05-20. 
  2. Tsuneya Ando, Alan B. Fowler, and Frank Stern Rev. Mod. Phys. 54, 437 (1982)