Trystan Casey
The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, and is used to understand the behaviour of substances in the presence of external electric fields. While the dipole moment of a molecule can be calculated based on its molecular structure, a permanent electric dipole moment of a fundamental particle violates both parity (P) and time-reversal (T) symmetries. This violation can be understood by examining the neutron's magnetic dipole moment and hypothetical electric dipole moment. Under time reversal, the magnetic dipole moment changes direction, while the electric dipole moment remains unchanged. Under parity, the electric dipole moment changes direction, but not the magnetic dipole moment. These asymmetries have led to ongoing experimental searches for an electric dipole moment in atoms and molecules.
| Characteristics | Values |
|---|---|
| Electric dipole moment | A measure of the separation of positive and negative electrical charges within a system, i.e., a measure of the system's overall polarity |
| SI unit | Coulomb-metre (C⋅m) |
| Other units | Debye (D) in atomic physics and chemistry |
| Parity (P) and time-reversal (T) symmetries | Violated by electric dipole moments (EDMs) |
| CP-violation | EDM values yield a model-independent measure, providing strong constraints on the scale of CP-violation beyond the Standard Model |
| Experiments | Designed to be sensitive to supersymmetry range of EDMs, complementing LHC experiments |
| Theories | Many theories are inconsistent with current limits, while others predict a nonzero electric dipole moment |
| Neutron electric dipole moment | A non-zero value would violate T symmetry |
| Proton electric dipole moment | Experiments aim to measure the EDM of the proton |
| Electron electric dipole moment | Should exist but is likely too small to be measured |
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What You'll Learn
Electric dipole moment and the separation of charge
The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, or the system's overall polarity. It is defined by two equal and opposite charges that are infinitesimally close together, although real dipoles have separated charges. The simplest approximation of an electric dipole is a model of ideal, infinitesimally spaced dipoles.
The electric dipole moment is calculated as the product of the magnitude of the charges multiplied by the distance between them. It is a vector quantity with a defined direction from the negative charge to the positive charge, although the convention is reversed in chemistry. The dipole direction tends to align itself with an external electric field.
The dipole moment of a molecule can be calculated based on its molecular structure using group contribution methods. It can also be calculated from electronic structure theory, either as a response to constant electric fields or from the density matrix.
Theoretically, an electric dipole is defined by the first-order term of the multipole expansion. As the distance between the two charges decreases, the dipole term becomes the only significant term, and in the limit of infinitesimal separation, it is the only term that matters. This limiting process results in a "point dipole".
Atoms and molecules cannot have a permanent electric dipole moment unless fundamental symmetries, namely time-reversal (T) and parity (P), are violated. This is because under time reversal, the electric dipole moment remains unchanged, while under parity, it changes direction. As the resulting system under P and T is not symmetric with respect to the initial system, these symmetries are violated in the case of the existence of an electric dipole moment.
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Parity (P) and time-reversal (T) symmetries
Time-reversal symmetry, on the other hand, involves reversing the direction of time. This means that any operation that changes the sign of i, which represents the square root of -1, will turn positive energies into negative energies unless it also changes the direction of time. In quantum mechanics, time reversal is represented by an anti-unitary operator, which means it does not behave in the same way as parity transformations.
The violation of these symmetries by a permanent electric dipole moment (EDM) can be understood by examining the behaviour of magnetic and electric dipole moments under P and T transformations. Under time reversal (T), the magnetic dipole moment changes its direction, but the electric dipole moment remains unchanged. On the other hand, under parity (P), the electric dipole moment changes direction while the magnetic dipole moment does not. Therefore, the presence of a permanent EDM in a system violates both P and T symmetries, as the resulting system is not symmetric with respect to the initial configuration.
The relationship between P and T symmetries is complex and has been the subject of much discussion. While P and T are often considered separately, their combination (PT) is also important in understanding certain physical phenomena. In some cases, PT transformations are considered rotations in spacetime rather than reflections, which has led to debates about how to generalize the concept of parity to include time.
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Molecular dipole moment and charge transfer
A molecular dipole moment is a measure of the overall polarity of a molecule, which is determined by the distribution of charges within it. It is influenced by the structure of the molecule, chemical bonding, and charge transfer between atoms. The polarity of a molecule arises from differences in electronegativity between atoms, where the greater the difference, the larger the dipole moment. The distance between the charged atoms also affects the size of the dipole moment.
The dipole moment of a molecule can be calculated using Equation \(\vec{\mu} = \sum_i q_i \, \vec{r}_i \), where \(\vec{\mu}\) represents the dipole moment, \(q_i\) is the charge, and \(\vec{r}_i\) is the distance between the charges. The dipole moment acts in the direction of the vector quantity.
In the context of charge transfer, the transition dipole moment plays a crucial role. The transition dipole moment relates to the movement of electrons from one atom to another within a molecule. This movement of electrons results in a change in the distribution of charges within the molecule, thereby affecting its dipole moment.
The study of transition dipole moments in one-component molecular crystals, such as oligothiophene crystals, has revealed the dominance of charge transfer states in their low-energy b-polarized spectra. By applying the Mulliken theory of charge transfer transitions, researchers can estimate the transition dipole moments of these crystals.
Furthermore, the concept of electric dipole moments is closely related to symmetry. According to fundamental symmetries, molecules cannot possess a permanent electric dipole moment unless time-reversal (T) and parity (P) symmetries are violated. This is because the dipole moment vector, which represents the separation of positive and negative charges, is incompatible with the center of symmetry.
Experiments aimed at measuring the electric dipole moment of particles, such as the electron and neutron, have been conducted to investigate the violation of T and P symmetries. These experiments provide valuable insights into the nature of CP-violation and constrain theories beyond the Standard Model of particle physics.
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Permanent electric dipole moment and particle interactions
The permanent electric dipole moment (EDM) of a particle or system is a separation of charge along the direction of the total angular momentum of the system. It arises from elementary particle interactions that directly violate parity and time-reversal symmetry.
The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, or the system's overall polarity. It is defined by the first-order term of the multipole expansion, consisting of two equal and opposite charges that are infinitesimally close together. Real dipoles, however, have separated charges.
Atoms and molecules cannot possess a permanent electric dipole moment unless fundamental symmetries, namely time-reversal (T) and parity (P), are violated. This is because, under time reversal, the magnetic dipole moment changes direction, while the electric dipole moment remains unchanged. In contrast, under parity, the electric dipole moment changes direction, but not the magnetic dipole moment. As a result, the system under P and T is not symmetric with respect to the initial system, leading to a violation of these symmetries.
The existence of a permanent electric dipole moment in a particle or system indicates the violation of charge-conjugation and parity symmetry (CP violation). This violation is significant as it probes very weak interactions in the background of stronger interactions that bind atoms and their nuclei. The CP violation is an essential component of Sakharov's mechanism of baryogenesis, but the Standard Model does not account for CP violation strong enough to explain the observed baryon asymmetry.
Experiments have been conducted to measure the electric dipole moments of various particles, such as electrons, neutrons, protons, and molecules. These experiments aim to detect a linear dependence of energy on an applied electric field, indicating the presence of an electric dipole moment. The results obtained so far have been null, placing upper bounds on the possible electric dipole moment.
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Electric dipole moment in multiatomic molecules
The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, essentially measuring the system's overall polarity. The SI unit for the electric dipole moment is the coulomb-metre (C·m), while the debye (D) is another unit of measurement used in atomic physics and chemistry.
The dipole moment of a molecule can be calculated based on its molecular structure using group contribution methods. The dipole moment of a single bond in a polyatomic molecule is known as the bond dipole moment, which is different from the dipole moment of the molecule as a whole. The dipole moment of a molecule is the vector sum of all the present bond dipoles in the molecule.
The polarity of multiatomic molecules depends on the polarity of a given chemical bond and their mutual arrangement. The electric dipole moment of a multiatomic molecule can be considered the result of the geometrical summation of the individual moments of each bond. The dipole moment is the specific property of a chemical bond, irrespective of the molecule in which it participates.
The molecular dipole moment depends on the charge transfer from one atom to another. Diatomic molecules consisting of identical atoms, due to the symmetry of the electron pair arrangement, are not polar and have an electric dipole moment equal to zero. On the other hand, diatomic molecules consisting of different atoms are usually polar. The polarity of the bond is determined by the electron affinity of the atoms, with the difference in electron density determining the polarity of the bond. The greater the difference in electron density, the more polar the bond.
Theoretically, an electric dipole consists of two equal and opposite charges that are infinitesimally close together, although real dipoles have separated charges. The dipole moment is a vector quantity, with magnitude and direction. It is represented by an arrow pointing from the negative charge towards the positive charge.
Experiments have been conducted to measure the electric dipole moment of particles like the electron and neutron. These experiments are designed to detect a linear dependence of energy on an applied electric field in a paramagnetic atom or molecule with one or more unpaired electrons. The results obtained so far indicate that atoms and molecules cannot have a permanent electric dipole moment unless fundamental symmetries, specifically time-reversal (T) and parity (P), are violated. This is because the dipole moment vector must transform equally under P and T for non-zero dipole moments. However, under P, the dipole moment vector changes sign, while under T, it does not, implying that the dipole moment must vanish for there to be symmetry.
Theoretically, elementary particles may possess tiny electric dipole moments, but these have not been observed in experiments.
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Frequently asked questions
The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, or a measure of the system's overall polarity.
A permanent electric dipole moment of a fundamental particle violates both parity (P) and time-reversal symmetry (T). Under time reversal, the magnetic dipole moment changes its direction, whereas the electric dipole moment stays unchanged. Under parity, the electric dipole moment changes its direction but not the magnetic dipole moment.
Precise measurement of the EDMs of fundamental charged particles would provide a significant probe of physics beyond the Standard Model. Any measurably large EDM would imply a violation of both time reversal and parity conservation, with implications for the matter/anti-matter imbalance of the universe. Additionally, measuring the EDM of particles like the neutron would improve our understanding of CP-violating processes and CPT symmetry.
