hartree

The hartree (symbol: E_h), 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 {{physconst|Eh|symbol=yes}} = {{physconst|Eh_eV|after=.}}

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

: $E_\mathrm{h} = {\hbar^2 \over {m_\mathrm{e} a^2_0}} = m_\mathrm{e}\left(\frac{e^2}{4\pi\varepsilon_0\hbar}\right)^2 = m_\mathrm{e} c^2 \alpha^2 = {\hbar c \alpha \over {a_0}}$

:: = 2 Ry = 2 R_∞hc

:: = {{physconst|Eh_eV|unit={{val|ul=eV}}}}

:: = {{physconst|Eh|unit={{val|ul=J}}}}

:: = {{val|4.3597447222060|(48)|e=-11|ul=erg}}

:: ≘ {{val|2625.4996394799|(50)|ul=kJ/mol}}

:: ≘ {{val|627.5094740631|(12)|ul=kcal/mol}}

:: ≘ {{val|219474.63136320|(43)|ul=cm-1}}

:: ≘ {{val|6579.683920502|(13)|ul=THz}}

where:

ħ is the reduced Planck constant,
m_e is the electron 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.

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

References

Category:Units of energy

Category:Physical constants