# Electric dipole moment

Physical size
Surname Electric dipole moment
Formula symbol ${\ displaystyle {\ vec {p}}, {\ vec {d}}}$
Size and
unit system
unit dimension
SI A · m · s I · L · T
Gauss ( cgs ) D = 10 -18 · StatC · cm L 5/2 · M ½ · T −1
esE ( cgs ) D = 10 -18 · StatC · cm L 5/2 · M ½ · T −1
emE ( cgs ) abC · cm L 3/2 x M ½
Dipole moment of an H 2 O molecule.
red: negative partial charge
blue: positive partial charge
green: directional dipole

The electric dipole moment characterizes a spatial charge separation. Has one in a body, e.g. B. a molecule , an electrical charge of different sign in different places so that the center of gravity of the negative charges ( electrons ) and the center of gravity of the positive charges ( atomic nuclei ) do not coincide, then this body has an electrical dipole moment. ${\ displaystyle {\ vec {p}}}$

In chemistry , the dipole moment is a measure of the strength of a dipole molecule and thus the polarity of a molecule . This is caused by polar atomic bonds or in extreme cases by ionic bonds .

Other dipoles (e.g. magnetic dipoles ) are also possible, which consequently also develop other dipole moments .

## calculation

Electric dipole moment of selected molecules
molecule Dipole moment
in Debye
Dipole moment
in 10 −30  C m
CO 0.11 0.367
HF 1.826178 6.0915
HCl 1.109 3,700
HBr 0.827 2.759
HI 0.448 1.495
NH 3 1.471 4.907
PF 3 1.025 3.419
H 2 O 1.84 6,152
H 2 S 0.97 3.236
CH 2 O 2.34 7.806
NaCl 8.5 28,356
Theatrical Version 7.33 28.690
KCl 10.48 34.261
KBr 10.41 34.728
AI 11.05 30.825
CsCl 10.387 34.647

If there is a positive charge   with the normalized connection vector at a distance from a negative charge  (this points from the negative charge in the direction of the positive charge) and these charges are rigidly connected to one another, this structure has a dipole moment of the size: ${\ displaystyle -q}$${\ displaystyle l}$${\ displaystyle q}$${\ displaystyle {\ vec {e}} _ {l}}$

${\ displaystyle {\ vec {p}} = q \ cdot l \ cdot {\ vec {e}} _ {l}}$

The larger the charge  , the higher the dipole moment. Even if the charges move further apart (increasing amount of ), the dipole moment increases. ${\ displaystyle q}$${\ displaystyle {\ vec {l}}}$

If, with a discrete charge distribution, there are charges at the locations relative to the center of gravity of the charge distribution, the total dipole moment is made up of the individual dipole moments : ${\ displaystyle n}$${\ displaystyle q_ {i}}$${\ displaystyle {\ vec {r}} _ {i}}$${\ displaystyle {\ vec {p}}}$${\ displaystyle {\ vec {p}} _ {i}}$

${\ displaystyle {\ vec {p}} = \ sum _ {i = 1} ^ {n} {\ vec {p}} _ {i} = \ sum _ {i = 1} ^ {n} q_ {i } \, {\ vec {r}} _ {i}.}$

In the general case of a continuous charge distribution, the dipole moment is calculated using the charge density : ${\ displaystyle \ rho ({\ vec {r}})}$

${\ displaystyle {\ vec {p}} = \ int _ {V} \ rho ({\ vec {r}}) \ cdot {\ vec {r}} \, \ mathrm {d} ^ {3} r}$

The discrete case emerges from the general, if the charge density is represented by the individual charges and the delta distribution : ${\ displaystyle \ rho ({\ vec {r}})}$${\ displaystyle q_ {i}}$ ${\ displaystyle \ delta ({\ vec {r}} - {\ vec {r}} _ {i})}$

${\ displaystyle \ rho ({\ vec {r}}) = \ sum _ {i = 1} ^ {n} q_ {i} \, \ delta ({\ vec {r}} - {\ vec {r} } _ {i}).}$

The volume integral then only provides contributions at the locations of the charges, so that we get: ${\ displaystyle {\ vec {r}} _ {i}}$

${\ displaystyle {\ vec {p}} = \ int _ {V} \ sum _ {i = 1} ^ {n} q_ {i} \, \ delta ({\ vec {r}} - {\ vec { r}} _ {i}) \, {\ vec {r}} \, \ mathrm {d} ^ {3} r = \ sum _ {i = 1} ^ {n} q_ {i} \, {\ vec {r}} _ {i}}$

In general, a potential can be developed into a constant part and multipole parts , including the dipole moment.

## unit

Despite the change to the International System of Units (SI) , the cgs unit Debye is still used as the unit of dipole moment, named after the Dutch physicist Peter Debye . The reason for this is that when using the SI units coulomb and meter one would have to deal with very small numbers:

${\ displaystyle [p] = 1 \, \ mathrm {Debye} = 3 {,} 33564 \ cdot 10 ^ {- 30} \, \ mathrm {Coulomb} \ cdot \ mathrm {Meter}}$

For molecules, the dipole moment is usually in the range from 0 Debye to 12 Debye. The most polar non-ionic, fully saturated compound is Debye all- cis -1,2,3,4,5,6-hexafluorocyclohexane with a dipole moment of 6.2 . With 14.1 Debye, the likewise nonionic but unsaturated compound 5,6-diaminobenzo-1,2,3,4-tetracarbonitrile is again significantly more polar.

The dipole moment can be determined with the help of the Debye equation by measuring the dielectric constant . Furthermore, measurements of the Stark effect provide information about the dipole moment of a substance.

## Dipole moments of excited states

Knowledge of the change in molecular dipole moments with electronic excitation is essential for understanding important natural photo-induced processes such as photosynthesis or the process of vision . The measurement of solvatachromic or thermochromic wavelength shifts in solutions can be used to determine the dipole moments of excited states .

The dipole moments

• μ G in the ground state of the molecule as well
• μ E in the excited state of the molecule

can be calculated using the Lippert-Mataga equation :

${\ displaystyle {\ overline {\ nu}} _ {A} - {\ overline {\ nu}} _ {E} = {\ frac {2} {hc}} {\ biggl (} {\ frac {\ varepsilon -1} {2 \ varepsilon +1}} - {\ frac {n ^ {2} -1} {2n ^ {2} +1}} {\ biggr)} {\ frac {(\ mu _ {G}) - \ mu _ {E}) ^ {2}} {a ^ {3}}} + const.}$

With

• the Stokes shift ${\ textstyle {\ overline {\ nu}} _ {A} - {\ overline {\ nu}} _ {E}}$
• the Planck's constant ${\ displaystyle h}$
• the speed of light in a vacuum${\ displaystyle c}$
• the permittivity  ε of the solvent
• the refractive index  n of the solvent
• the radius  a of the solvent cavity .

Dipole moments of molecules in the gas phase can be determined much more precisely by electronic Stark spectroscopy.

## Individual evidence

1. At a temperature of 20 ° C and a pressure of 101.325 kPa.
2. David R. Lide: CRC Handbook of Chemistry and Physics . 87th edition. B&T, 2006, ISBN 0-8493-0487-3 .
3. ^ David Frank Eggers: Physical chemistry . Wiley, 1964, ISBN 978-0-471-23395-4 , pp. 572 ( limited preview in Google Book search).
4. BI Bleaney, Betty Isabelle Bleaney, Brebis Bleaney: Electricity and Magnetism . 3. Edition. Vol. 2. OUP Oxford, 2013, ISBN 978-0-19-964543-5 , pp. 303 ( limited preview in Google Book search).
5. ^ Jean-Marie André, Joseph Delhalle, Jean Luc Brédas: Quantum Chemistry Aided Design of Organic Polymers An Introduction to the Quantum Chemistry of Polymers and Its Applications . World Scientific, 1991, ISBN 978-981-02-0004-6 , pp. 89 ( limited preview in Google Book search).
6. Jacob N. Israelachvili: Intermolecular and Surface Forces Revised Third Edition . Academic Press, 2011, ISBN 978-0-12-391927-4 , pp. 72 ( limited preview in Google Book search).
7. ^ Paul A. Tipler, Gene Mosca ,: Physics . Ed .: Peter Kersten, Jenny Wagner. 8th edition. Springer Spectrum, ISBN 978-3-662-58281-7 , p. 684 .
8. ^ A b Ernst Wilhelm Otten: Repetitorium Experimentalphysik . Springer-Verlag, 2008, ISBN 978-3-540-85788-4 , p. 464 ( limited preview in Google Book search).
9. ^ Armin Wachter, Henning Hoeber: Repetitorium Theoretische Physik . Springer-Verlag, 2013, ISBN 978-3-662-09755-7 , pp. 175 ( limited preview in Google Book search).
10. Ralf Steudel: Chemistry of the non-metals with atomic structure, molecular geometry and bond theory . Walter de Gruyter, 1998, ISBN 978-3-11-015902-8 , pp. 137 ( limited preview in Google Book search).
11. ^ Neil S. Keddie, Alexandra MZ Slawin, Tomas Lebl, Douglas Philp, David O'Hagan: All-cis 1,2,3,4,5,6-hexafluorocyclohexane is a facially polarized cyclohexane. In: Nature Chemistry . 7, 2015, pp. 483-488, doi: 10.1038 / nchem.2232 , PMID 25991526 .
12. Stephen K. Ritter: Molecule Claims Most Polar Title . In: Chemical & Engineering News . 93 (13), 2015, p. 5.
13. Stephen K. Ritter: Lopsided Benzene Sets A New Polarity Record . In: Chemical & Engineering News. 94 (7), 2016, p. 23.
14. Jakob Wudarczyk, George Papamokos, Vasilis Margaritis, Dieter Schollmeyer, Felix Hinkel, Martin Baumgarten, George Floudas, Klaus Müllen: Hexasubstituted Benzenes with Ultrastrong Dipole Moments. In: Angewandte Chemie International Edition. 55, 2016, pp. 3220–3223, doi: 10.1002 / anie.201508249 .
15. E. Lippert: Spectroscopic determination of the dipole moment of aromatic compounds in the first excited singlet state . In: Z. Electrochem. tape 61 , 1957, pp. 962 .
16. N. Mataga, Y. Kaifu, M. Koizumi: Solvent effects upon fluorescence spectra and the dipole moments of excited molecules . In: Bull. Chem. Soc. Jpn . tape 29 , 1956, pp. 465 .
17. Josefin Wilke, Martin Wilke, W. Leo Meerts, Michael Schmitt: Determination of ground and excited state dipole moments via electronic Stark spectroscopy: 5-methoxyindole . In: The Journal of Chemical Physics . tape 144 , no. 4 , January 28, 2016, ISSN  0021-9606 , p. 044201 , doi : 10.1063 / 1.4940689 .