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The electron's electric dipole moment (EDM) must be collinear with the direction of the electron's magnetic moment (spin). [1] Within the Standard Model , such a dipole is predicted to be non-zero but very small, at most 10 −38 e ⋅cm , [ 2 ] where e stands for the elementary charge .
A stronger mathematical definition is to use vector algebra, since a quantity with magnitude and direction, like the dipole moment of two point charges, can be expressed in vector form = where d is the displacement vector pointing from the negative
In atomic physics, the electron magnetic moment, or more specifically the electron magnetic dipole moment, is the magnetic moment of an electron resulting from its intrinsic properties of spin and electric charge. The value of the electron magnetic moment (symbol μ e) is −9.284 764 6917 (29) × 10 −24 J⋅T −1. [1]
The method of image charges (also known as the method of images and method of mirror charges) is a basic problem-solving tool in electrostatics.The name originates from the replacement of certain elements in the original layout with fictitious charges, which replicates the boundary conditions of the problem (see Dirichlet boundary conditions or Neumann boundary conditions).
Let's say we want to calculate transition dipole moments for an electron transition from a 4d to a 2p orbital of a hydrogen atom, i.e. the matrix elements of the form , | |, , where r i is either the x, y, or z component of the position operator, and m 1, m 2 are the magnetic quantum numbers that distinguish different orbitals within the 2p or 4d subshell.
For example, the transition from a bonding orbital to an antibonding orbital is allowed because the integral defining the transition dipole moment is nonzero. Such a transition occurs between an even and an odd orbital; the dipole operator, μ → {\displaystyle {\vec {\mu }}} , is an odd function of r {\displaystyle \mathbf {r} } , hence the ...
Maintenance of the minimum-image convention also generally requires that a spherical cutoff radius for nonbonded forces be at most half the length of one side of a cubic box. Even in electrostatically neutral systems, a net dipole moment of the unit cell can introduce a spurious bulk-surface energy, equivalent to pyroelectricity in polar ...
Typical dipole moments for simple diatomic molecules are in the range of 0 to 11 D. Molecules with symmetry point groups or containing inversion symmetry will not have a permanent dipole moment, while highly ionic molecular species have a very large dipole moment, e.g. gas-phase potassium bromide, KBr, with a dipole moment of 10.41 D. [3] A proton and an electron 1 Å apart have a dipole ...