- The advantage of atomic units is that if all calculations are directly expressed in such units, the results do not vary with any revision of the numerical values of the fundamental constants. Source: PAC, 1999, 71, 1919.
- We have listed here we know that carbon 12 is the most common isotope of carbon on earth ninety eight point eight nine percent of the carbon on earth is carbon-12 and we know that by definition its mass is exactly 12 atomic mass units now that's not the only isotope of carbon on earth there are other isotopes the next most frequent one is frequent one is carbon 13 one point one one percent of.
- Atomic masses are measured in terms of atomic mass units with the carbon-12 atom defined as having a mass of exactly 12 amu. It is also common practice to quote the rest mass energy E=m 0 c 2 as if it were the mass. The conversion to amu is: 1 u = 1.66054 x 10-27 kg = 931.494 MeV.
Atomic units (au or a.u.) form a system of natural units which is especially convenient for atomic physics calculations. Atomic units, like SI units, have a unit of mass, a unit of length, and so on. However, the use and notation is somewhat different from SI. Suppose a particle with a mass of m has 3.4 times the mass of electron. The value of mass (m) can be written in three ways:
- (m=3.4; m_e): This is the clearest notation (but least common), where the atomic unit is included explicitly as a symbol.
- (m=3.4; a.u.): This notation is ambiguous, but is common. Here, it means that the mass m is 3.4 times the atomic unit of mass. If considering a length L of 3.4 times the atomic unit of length, the equation would look the same, (L= 3.4 ;a.u.) The dimension needs to be inferred from context, which is sloppy.
- (m = 3.4): This notation is similar to the previous one, and has the same dimensional ambiguity. It comes from formally setting the atomic units to 1 (Table (PageIndex{1})).
This article deals with 'Hartree type' of atomic units, where the numerical values of the following four fundamental physical constants are all unity by definition:
Atomic units (au) form a system of units convenient for atomic physics, electromagnetism, and quantum electrodynamics, especially when the focus is on the properties of electrons. There are two different kinds of atomic units, which one might name Hartree atomic units and Rydberg atomic units, which differ in the choice of the unit of mass.
Dimension | Name | Symbol/Definition | Value in SI units | Value in Atomic Units |
---|---|---|---|---|
mass | electron rest mass | (m_e) | 9.109×10−31 kg | 1 |
charge | elementary charge | (e) | 1.602×10−19 C | 1 |
action | reduced Planck's constant | (hbar = dfrac{h}{2pi}) | 1.054×10−34 J·s | 1 |
electric constant−1 | Coulomb force constant | (displaystyle k_e = frac{1}{4 pi epsilon_o}) | 8.987 x 109 kg·m3·s−2·C−2 | 1 |
Use the atomic units definitions in Table (PageIndex{1}) to contrast the Hamiltonian for a Helium atom in Si units and in atomic units.
Solution
In SI units, the Hamiltonian for a Helium atom is
Atomic Units To Ev
[ hat {H} = -dfrac {hbar ^2}{2m_e} (nabla ^2_1 + nabla ^2_2) -dfrac {2e^2}{4 pi epsilon _0 r_1} - dfrac {2e^2}{4 pi epsilon _0 r_2} + dfrac {e^2}{4 pi epsilon _0 r_{12}} nonumber]
In atomic units, the same Hamiltonian
Atomic Units To Kj/mol
[ hat {H} = -dfrac {1}{2} (nabla ^2_1 + nabla ^2_2) - dfrac {2}{r_1} - dfrac {2}{r_2} + dfrac {1}{r_{12}} nonumber]
All the units that make the SI version of the Hamiltonian disappear to emphasize the key aspects of the operator.
Atomic units are derived from certain fundamental properties of the physical world, and are free of anthropocentric considerations. It should be kept in mind that atomic unites were designed for atomic-scale calculations in the present-day universe, with units normalize the reduced Planck constant and also mass and charge of the electron are set to 1, and, as a result, the speed of light in atomic units is a large value, (1/alpha approx 137). For example, the orbital velocity of an electron around a small atom is of the order of 1 in atomic units. Table (PageIndex{2}) give a few derived units. Some of them have proper names and symbols assigned, as indicated in the table.
Atomic Units Conversion
Dimension | Name | Symbol | Expression | Value in SI units | Value in more common units |
---|---|---|---|---|---|
length | bohr | (a_o) | (4pi epsilon_0 hbar^2 / (m_mathrm{e} e^2) = hbar / (m_mathrm{e} c alpha) ) | 5.291×10−11 m | 0.052 nm = 0.529 Å |
energy | hartree | (E_h) | (m_mathrm{e} e^4/(4piepsilon_0hbar)^2 = alpha^2 m_mathrm{e} c^2 ) | 4.359×10−18 J | 27.2 eV = 627.5 kcal·mol−1 |
time | (hbar / E_mathrm{h}) | 2.418×10−17 s | |||
velocity | ( a_0 E_mathrm{h} / hbar = alpha c) | 2.187×106 m·s−1 |