Debye

The debye (symbol: D) is a CGS unit^[1] (a non-SI metric unit) of electric dipole moment^{[note 1]} named in honor of the physicist Peter J. W. Debye. It is defined as 1 × 10⁻¹⁸ statcoulomb-centimeter.^{[note 2]} Historically the debye was defined as the dipole moment resulting from two charges of opposite sign but an equal magnitude of 10^-10 statcoulomb^{[note 3]} (generally called e.s.u. (electrostatic unit) in older literature), which were separated by 1 ångström.^{[note 4]} This gave a convenient unit for molecular dipole moments.

1 D	= 10-18 statC·cm
	= 10-10 esu·Å[note 2]
	= 1⁄299,792,458 × 10−21 C·m[note 5]
	≈ 3.33564 × 10−30 C·m
	≈ 1.10048498 × 1023 qPlP
	≈ 0.393430307 ea0[2]

Typical dipole moments for simple diatomic molecules are in the range of 0 to 11 D. Symmetric homoatomic species, e.g. chlorine, Cl₂, have zero dipole moment and highly ionic molecular species have a very large dipole moment, e.g. gas phase potassium bromide, KBr, with a dipole moment of 10.5 D.^[3]

The debye is still used in atomic physics and chemistry because SI units are inconveniently large. The smallest SI unit of electric dipole moment is the yoctocoulomb-meter, which is roughly 300,000 D.^{[note 6]} There is currently no satisfactory solution to this problem of notation without resorting to the use of scientific notation.

Notes

1. ^ Electric dipole moment is defined as charge times displacement:

   p = qr

2. ^ ^{a b} The statcoulomb is also known as the franklin or electrostatic unit of charge.

   1 statC	=1 Fr
   	=1 esu

3. ^ 10^-10 statcoulomb is approximately 0.2083 units of elementary charge.
4. ^ The ångström is of an order of magnitude close to that of a typical covalent bond.

   1 Å	= 100 pm
   	= 10-8 cm
   	= 10-10 m

5. ^ One debye equals 1 × 10⁻²¹ C·m²/s divided by the speed of light in vacuum. Conversely 1 C·m = 2.99792458 × 10²⁹ D.
6. ^ Yocto-, with a value of 10⁻²⁴, is the smallest SI prefix. Note that SI disallows the application of prefixes to both members of a compound unit or the compounding of prefixes, thus ruling out such units as the femtocoulomb-femtometer or the microyoctocoulomb-meter (both approximately 0.3 D) respectively.

References

1. ^ CGS units R. Rowlett (University of North Carolina at Chapel Hill)
2. ^ Atomic unit of electric dipole moment NIST
3. ^ Physical chemistry 2d Edition (1966) G.M. Barrow McGraw Hill