What is meant by a unified atomic unit?

A unified atomic unit is a system of natural units commonly used in quantum chemistry and physics to simplify calculations. In this system, fundamental physical constants such as the electron charge, electron mass, and Planck's constant are set to unity, making calculations easier and more intuitive. This system allows for easier comparison of different physical quantities and simplifies the equations used in quantum mechanics.

A unified atomic unit (u.a.u.) is a system of units that is based on the fundamental constants of nature, including the speed of light, the elementary charge, and the Planck constant. It is a convenient system of units for use in atomic and molecular physics, as it eliminates the need to use conversion factors between different units.

The u.a.u. system is defined by the following equations:

- Length: The u.a.u. of length is the Bohr radius, which is the average distance between the nucleus and an electron in the hydrogen atom.
- Mass: The u.a.u. of mass is the electron mass.
- Time: The u.a.u. of time is the atomic unit of time, which is the time it takes for an electron to orbit the nucleus of a hydrogen atom once.
- Charge: The u.a.u. of charge is the elementary charge.
- Energy: The u.a.u. of energy is the Hartree, which is the energy of an electron in the lowest energy level of a hydrogen atom.

The u.a.u. system is a consistent system of units that can be used to describe a wide range of atomic and molecular phenomena. It is a convenient system of units for use in theoretical calculations, as it eliminates the need to use conversion factors between different units.