Hartree

Hartree is a unit of energy used primarily within the field of quantum mechanics and atomic physics. It is named after the British physicist Douglas Hartree. The Hartree energy (symbol: E_h) is defined as the kinetic energy of an electron moving in a Bohr orbit around the proton in a hydrogen atom in its ground state. The Hartree energy is a fundamental quantity in atomic units, a system of natural units that is especially convenient for atomic physics and quantum chemistry calculations.

Definition

The Hartree energy is defined as:

E_h = \frac{e^2}{4\pi\epsilon_0 a_0}

where:

• e is the elementary charge,
• \(\epsilon_0\) is the vacuum permittivity,
• \(a_0\) is the Bohr radius.

In terms of physical constants, the Hartree energy can also be expressed as:

E_h = \frac{\hbar^2}{m_e a_0^2}

where:

• \(\hbar\) is the reduced Planck's constant,
• \(m_e\) is the electron mass.

Value

The value of the Hartree energy is approximately 4.359744650(54) × 10⁻¹⁸ joules or 27.21138602(17) electronvolts (eV).

Usage

The Hartree energy is widely used in quantum chemistry and atomic physics as it simplifies many equations and calculations. It is the natural energy unit in the system of atomic units, where it is set to 1 Hartree (1 E_h). This makes it particularly useful for computational methods in quantum mechanics, such as Hartree-Fock and Density Functional Theory (DFT), where energies are often reported in units of E_h.

Relation to Other Units

The Hartree energy is related to other units of energy through the fundamental constants. For example, converting Hartree to electronvolts (eV) involves the elementary charge, and converting to joules involves additional constants like the Planck constant and the speed of light.

See Also

• Quantum mechanics
• Atomic units
• Bohr radius
• Electronvolt
• Hartree-Fock method
• Density Functional Theory