Molecular dipole: Difference between revisions
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Being a charge distribution consisting of [[electron]]s and [[nucleus|nuclei]], a molecule may possess a permanent [[electric dipole]], called a '''molecular dipole'''. | {{subpages}} | ||
Being a charge distribution consisting of [[electron]]s and [[nucleus|nuclei]], a [[molecule]] may possess a permanent [[electric dipole]], called a '''molecular dipole'''. | |||
Whether or not a molecule has a non-zero permanent dipole depends on the [[molecular symmetry|symmetry]] of the molecule and the symmetry species of the molecular state under consideration. Usually one considers molecules in their ground (lowest energy) state and this state is almost always totally symmetric, i.e., invariant under all symmetry operations. For a molecule that is in a totally symmetric state, it can be shown that any of the three components of the molecular dipole (a vector) that are totally symmetric (invariant under all symmetry operations) are the only ones that are non-vanishing. If a dipole component changes under the action of one or more symmetry operations, it is zero. | |||
This rule can be proved formally, but also understood intuitively. By definition a symmetry operation changes a molecule to a conformation that is indistinguishable from the original conformation. If a dipole component would change under a symmetry operation, it would give a handle for distinguishing the old from the new conformation, so that the two conformations would be distinguishable. This is a contradiction and, hence, either a dipole component is zero or it is invariant (does not change). | This rule can be proved formally, but also understood intuitively. By definition a symmetry operation changes a molecule to a conformation that is indistinguishable from the original conformation. If a dipole component would change under a symmetry operation, it would give a handle for distinguishing the old from the new conformation, so that the two conformations would be distinguishable. This is a contradiction and, hence, either a dipole component is zero or it is invariant (does not change). | ||
More technically: the symmetry operations of a rigid molecule—the nuclei are clamped in space, but the electrons "move" in the quantum mechanical sense of the word—form a [[group]], the ''[[point group]]'' of the molecule. This point group has [[irreducible representations]] among which the totally symmetric one, commonly denoted by ''A''<sub>1</sub>. Most molecular ground states transform as ''A''<sub>1</sub> (the symmetry species of the ground state is ''A''<sub>1</sub>). Only the components of the dipole that | More technically: the symmetry operations of a rigid molecule—the nuclei are clamped in space, but the electrons "move" in the quantum mechanical sense of the word—form a [[group]], the ''[[point group]]'' of the molecule. This point group has [[irreducible representations]] among which is the totally symmetric one, commonly denoted by ''A''<sub>1</sub>. Most molecular ground states transform as ''A''<sub>1</sub> (alternatively expressed as: "the symmetry species of the ground state is ''A''<sub>1</sub>"). Only the components of the dipole that transform according to ''A''<sub>1</sub> are non-vanishing. This is true not only for molecules in an ''A''<sub>1</sub> state, but for molecules in any non-degenerate state (a state that transforms according to a one-dimensional irreducible representation of the point group). | ||
An electric dipole moment has the dimension charge times length. The [[SI]] unit of dipole is | ==Units and order of magnitude== | ||
An electric dipole moment has the dimension charge times length. The [[SI]] unit of dipole is accordingly [[coulomb]] times [[meter]]. However, this unit is unwieldly large and therefore hardly used in chemistry and molecular physics. The [[Gaussian unit]] of [[debye]] (D) is most widely applied. It is 10<sup>−10</sup> esu times [[ångstrom]]. An ångstrom is 10<sup>−8</sup> cm = 10<sup>−10</sup> m. An esu (electrostatic unit of charge, now called [[statcoulomb]]) is C/(10⋅''c'') ≈ 3.335 640 95⋅10<sup>−10</sup> C, where C is coulomb and ''c'' is [[speed of light]]. Hence, | |||
:<math> | :<math> | ||
1\; \mathrm{D} = 10^{-10}\; \frac{10^{-10}}{10 c}\; \mathrm{C\,m} \approx 3.335\,640\,95\cdot 10^{-30}\;\; \mathrm{C\,m} | 1\; \mathrm{D} = 10^{-10}\; \frac{10^{-10}}{10 c}\; \mathrm{C\,m} \approx 3.335\,640\,95\cdot 10^{-30}\;\; \mathrm{C\,m} . | ||
</math> | </math> | ||
In quantum chemistry and molecular physics a common unit of dipole moment is the [[atomic unit]]: | |||
the charge ''e'' of an electron times the [[bohr radius]] ''a''<sub>0</sub>. | |||
Since 1 ''e'' = 1.602 176 487 ⋅ 10<sup>−19</sup> C and ''a''<sub>0</sub> = 0.529 177 208 59 ⋅ 10<sup>−10</sup> m, it follows that | |||
:<math> | |||
1\; \mathrm{au} = 8.4783528106\cdot10^{-30} \; \mathrm{C\cdot m} = 2.54174623039\; \mathrm{D} | |||
</math> | |||
The debye is of such magnitude that most molecules have dipole moments on the order of 1 to 10 D. For instance, water has an electric dipole moment of 1.85 D and HCl has 1.09 D. In both cases the direction of the dipole is determined by the fact that the hydrogen atom(s) is(are) slightly positive. In the case of the bend molecule H<sub>2</sub>O the dipole bisects the H-O-H angle and in the case of HCl the dipole points from Cl to H (in the physics convention). | |||
Revision as of 07:20, 29 August 2009
Being a charge distribution consisting of electrons and nuclei, a molecule may possess a permanent electric dipole, called a molecular dipole.
Whether or not a molecule has a non-zero permanent dipole depends on the symmetry of the molecule and the symmetry species of the molecular state under consideration. Usually one considers molecules in their ground (lowest energy) state and this state is almost always totally symmetric, i.e., invariant under all symmetry operations. For a molecule that is in a totally symmetric state, it can be shown that any of the three components of the molecular dipole (a vector) that are totally symmetric (invariant under all symmetry operations) are the only ones that are non-vanishing. If a dipole component changes under the action of one or more symmetry operations, it is zero.
This rule can be proved formally, but also understood intuitively. By definition a symmetry operation changes a molecule to a conformation that is indistinguishable from the original conformation. If a dipole component would change under a symmetry operation, it would give a handle for distinguishing the old from the new conformation, so that the two conformations would be distinguishable. This is a contradiction and, hence, either a dipole component is zero or it is invariant (does not change).
More technically: the symmetry operations of a rigid molecule—the nuclei are clamped in space, but the electrons "move" in the quantum mechanical sense of the word—form a group, the point group of the molecule. This point group has irreducible representations among which is the totally symmetric one, commonly denoted by A1. Most molecular ground states transform as A1 (alternatively expressed as: "the symmetry species of the ground state is A1"). Only the components of the dipole that transform according to A1 are non-vanishing. This is true not only for molecules in an A1 state, but for molecules in any non-degenerate state (a state that transforms according to a one-dimensional irreducible representation of the point group).
Units and order of magnitude
An electric dipole moment has the dimension charge times length. The SI unit of dipole is accordingly coulomb times meter. However, this unit is unwieldly large and therefore hardly used in chemistry and molecular physics. The Gaussian unit of debye (D) is most widely applied. It is 10−10 esu times ångstrom. An ångstrom is 10−8 cm = 10−10 m. An esu (electrostatic unit of charge, now called statcoulomb) is C/(10⋅c) ≈ 3.335 640 95⋅10−10 C, where C is coulomb and c is speed of light. Hence,
In quantum chemistry and molecular physics a common unit of dipole moment is the atomic unit: the charge e of an electron times the bohr radius a0. Since 1 e = 1.602 176 487 ⋅ 10−19 C and a0 = 0.529 177 208 59 ⋅ 10−10 m, it follows that
The debye is of such magnitude that most molecules have dipole moments on the order of 1 to 10 D. For instance, water has an electric dipole moment of 1.85 D and HCl has 1.09 D. In both cases the direction of the dipole is determined by the fact that the hydrogen atom(s) is(are) slightly positive. In the case of the bend molecule H2O the dipole bisects the H-O-H angle and in the case of HCl the dipole points from Cl to H (in the physics convention).