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Hartree
Unit of energy in the atomic units system
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 = The name "hartree" was suggested for this unit of energy.
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
:: =
:: =
:: =
:: ≘
:: ≘
:: ≘
:: ≘
where:
- ħ is the reduced Planck constant,
- me 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).
References
References
- (1959). "Atomic Units". Nature Publishing Group.
- (May 1973). "Natural Units in Atomic and Molecular Physics". Nature.
- Tsuneya Ando, Alan B. Fowler, and Frank Stern Rev. Mod. Phys. '''54''', 437 (1982)
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