hartree

A unit of energy in the atomic system of units. The unit was proposed in 1926 and named in 1959.² In its rationalized form it is defined as

a fraction. The numerator is four times pi squared times m times e to the fourth power.  The denominator is h squared times the quantity four pi epsilon sub oh squared.

where

m the rest mass of the electron
e the electron charge
h the Planck constant
ε the rationalized permittivity of free space

According to the 2018 CODATA recommendations, 1 hartree equals 4.359 744 722 2071 × 10⁻¹⁸ joules with a one standard deviation uncertainty of ± 0.000 000 85 × 10⁻¹⁸ joules.³

The hartree is named for D.R. Hartree (1897–1958), who proposed an atomic system of units in 1928

1. D. R. Hartree.
The Wave Mechanics of an Atom with an Non-Coulomb Central Field. Part I. Theory and Methods.
Mathematical Proceedings of the Cambridge Philosophical Society, volume 24, issue 1, January 1928, pages 89 - 110 , (1928)
doi: https://doi.org/10.1017/S0305004100011919.

Page 91:

“Both in order to eliminate various universal constants from the equations and also to avoid high powers of ten in numerical work, it is convenient to express quantities in terms of units, which may be called ‘atomic units,’ defined as follows:

Unit of lengthequation,

on the orbital mechanics the radius of the 1-quantum circular orbit of the H-atom with fixed nucleus.

Unit of charge, e, the magnitude of the charge on the electron.

Unit of mass, m, the mass of the electron.

“Consistent with these are:

Unit of action, h2π.

Unit of energy, e²⁄a = potential energy of charge e at distance a from an equal charge = 2hcR = twice the ionization energy of the hydrogen atom with fixed nucleus.

Unit of time, ¼πrcR.”

2. H. Shull and G. G. Hall.
Atomic Units.
Nature, volume 184, no. 4698, page 1559 (Nov. 14, 1959).

Since the energy unit in this system is the one most generally needed, it seems appropriate that its name be simplified to the ‘Hartree’ and denoted by H. Thus we define:

equation

The conversion factor from Hartrees to cm.⁻¹ is then precisely twice as large as the infinite Rydberg, R.

3. https://physics.nist.gov/cgi-bin/cuu/Value?eqhr|search_for=hartree

resources

1

Hartree's atomic unit of energy, EH = ℏ²⁄(mea0²) = 27 eV, is the potential energy drawing the electron to the nucleus of the Bohr atom, and the unit of pressure is simply the energy density EHa0³ derived on dimensional grounds.

Raymond Jeanloz.
Calibrating experiments at atom-crushing pressures.
Science, vol 372, issue 6546, page 1038, footnote 7 (4 June 2021)

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