Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
Concept
Hartree
Summary
The hartree (symbol: Eh or Ha), also known as the Hartree energy, is the unit of energy in the Hartree atomic units system, named after the British physicist Douglas Hartree. Its CODATA recommended value is =
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 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.
= 2 Ry = 2 R∞hc
≜ 27.211386245988eV
≜ 4.3597447222071e-18J
≜ 4.3597447222071e-11erg
≜ 2625.4996394799kJ/mol
≜ 627.5094740631kcal/mol
≜ 219474.63136320cm-1
≜ 6579.683920502THz
≜ 315775.02480407K
where:
ħ is the reduced Planck constant,
me 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 is defined as , one may write the Hartree energy as in Gaussian units where .
Effective hartree units are used in semiconductor physics where is replaced by and is the static dielectric constant. Also, the electron mass is replaced by the effective band mass . The effective hartree in semiconductors becomes small enough to be measured in millielectronvolts (meV).
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Ontological neighbourhood
Related courses (1)
CH-244: Quantum chemistry
Introduction to Quantum Mechanics with examples related to chemistry
Related lectures (7)
Perturbation Theory and Variational Principle
Covers perturbation theory, variational principle, and systematic approaches to determining true energy levels.
Quantum Mechanics Basics: Atomic Units and Operators
Introduces atomic units, operators, and the postulates of quantum mechanics.
Symmetry and Group Theory
Explores symmetry and group theory applications in chemistry, covering matrix representations, normal modes, and harmonic oscillators.
Related publications (2)
Related concepts (6)
Hartree atomic units
The Hartree atomic units are a system of natural units of measurement which is especially convenient for calculations in atomic physics and related scientific fields, such as computational chemistry and atomic spectroscopy. They are named after the physicist Douglas Hartree. Atomic units are often abbreviated "a.u." or "au", not to be confused with the same abbreviation used also for astronomical units, arbitrary units, and absorbance units in other contexts.
Unit of measurement
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multiple of the unit of measurement. For example, a length is a physical quantity. The metre (symbol m) is a unit of length that represents a definite predetermined length. For instance, when referencing "10 metres" (or 10 m), what is actually meant is 10 times the definite predetermined length called "metre".
Natural units
In physics, natural units are physical units of measurement in which only universal physical constants are used as defining constants, such that each of these constants acts as a coherent unit of a quantity. For example, the elementary charge e may be used as a natural unit of electric charge, and the speed of light c may be used as a natural unit of speed. A purely natural system of units has all of its units defined such that each of these can be expressed as a product of powers of defining physical constants.