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Here is the internuclear distance between two atoms.
For , there is no generally applicable expression for the internuclear potential.
In this case, we take and and assume precesses quickly around the internuclear axis.
Exchange energy splittings are very elusive to calculate for molecular systems at large internuclear distances.
This means that rotation of the MO about the internuclear axis does not result in a phase change.
The process is driven by dipolar coupling, and is therefore related to internuclear distances.
Internuclear ophthalmoplegia is a disorder of conjugate lateral gaze.
Instead and combine to form , which has a projection along the internuclear axis of magnitude .
The most direct measure of the atomic radius is 1/2 the internuclear distance of the diatomic molecule.
Consequently this denominator is almost unity for sufficiently large internuclear distances and only the surface integral of the numerator need be considered.
The minimum in the potential function will therefore be at a shorter internuclear distance, and the vibration frequency will be higher than for the molecule.
If we remove an electron from a non-bonding level, the potential functions of ion and molecule should have minima at very similar internuclear distances.
Although the exchange energy becomes elusive at large internuclear systems, it is of prominent importance in theories of molecular binding and magnetism.
A new set of operators have to be used instead: , where the z-axis is defined along the internuclear axis of the molecule.
White matter tracts connecting these nuclei, as in internuclear ophthalmoplegia, an occasional finding in multiple sclerosis.
Since the orientation of the target molecules relative to the electron beams is random, the internuclear distance information obtained is one-dimensional.
In cyclopropane the maximum electron density between two carbon atoms does not correspond to the internuclear axis hence the name bent bond.
An MO will have π symmetry if the orbital is asymmetrical with respect to rotation about the internuclear axis.
In case (d), the rotational coupling between and is much stronger than the electrostatic coupling of to the internuclear axis.
This overlap leads to the formation of a bonding molecular orbital with two nodal planes which contain the internuclear axis and go through both atoms.
In case (a), is electrostatically coupled to the internuclear axis, and is coupled to by spin-orbit coupling.
For the ground-state molecule, the spread of internuclear distances is represented by the ground-state wavefunction, with a maximum probability near the center.
(6), is negative, Heisenberg first suggested that it changes sign at some critical ratio of internuclear distance to mean radial extension of the atomic orbital.
The direct dipole-dipole coupling is very useful for molecular structural studies, since it depends only on known physical constants and the inverse cube of internuclear distance.
One problem with using dipolar couplings in structure determination is that a dipolar coupling does not uniquely describe an internuclear vector orientation.