internuclear axis

(noun)

The space between the nuclei of two atoms bonded to each other.

Related Terms

Examples of internuclear axis in the following topics:

  • Explanation of Valence Bond Theory

    • $\sigma$ bonds occur when orbitals overlap between the nuclei of two atoms, also known as the internuclear axis.
    • Atomic orbitals from two atoms overlap in the region between the nuclei (internuclear axis).

  • Bonding and Antibonding Molecular Orbitals

    • A bond involving molecular orbitals that are symmetric with respect to rotation around the bond axis is called a sigma bond (σ-bond).
    • In this anti-bonding MO, with energy much higher than the original AOs, any electrons present are located in lobes pointing away from the central internuclear axis.
    • For a π-bond, corresponding bonding and antibonding orbitals would not have such symmetry around the bond axis, and are designated π and π* respectively.

  • The Phase of Orbitals

    • A bond involving molecular orbitals that are symmetric with respect to rotation around the bond axis is called a sigma bond (σ-bond).
    • In this anti-bonding molecular orbital with energy much higher than the original atomic orbitals, any electrons present are located in lobes pointing away from the central internuclear axis.
    • For a π-bond, corresponding bonding and antibonding orbitals would not have such symmetry around the bond axis and would be designated π and π*, respectively.

  • Double and Triple Covalent Bonds

    • Similar to double bonds, no rotation around the triple bond axis is possible.
    • The electron density corresponding to the shared electrons is not concentrated along the internuclear axis (i.e., between the two atoms), unlike in sigma bonds.

  • Molecular Excitations

    • Morse found that the internuclear potential can often be well approximated by a function of the form
    • We can change the vibrational level by $\Delta v=\pm 1$ and we must also have $\Delta L=L_\textrm{lower}-L_\textrm{upper}=+1$ ($P$ branch) or $\Delta L=-1$ ($R$ branch) or if there is an component of electronic orbital or spin angular momentum along the internuclear axis $L$ ($Q$ branch).

  • Bond Energy

    • A Morse curve shows how the energy of a two atom system changes as a function of internuclear distance.
    • At internuclear distances in the order of an atomic diameter, attractive forces dominate.
    • The internuclear distance at which the energy minimum occurs defines the equilibrium bond length.

  • Regional Terms and Axes

    • The Dorsoventral axis (DV axis): is the axis formed by the connection of the dorsal and ventral points of a region.
    • The Anterioposterior axis (AP axis): is the axis formed by the connection of the anterior (top) and posterior (bottom) ends of a region.
    • The AP axis of a region is by definition perpendicular to the DV axis, and vice-versa.
    • The Left-to-right axis: is the axis that connects the left and right hand sides of a region.
    • Axis (A) (in red) shows the AP axis of the tail, (B) shows the AP axis of the neck, and (C) shows the AP axis of the head.

  • Symmetry of Functions

    • Functions and relations can be symmetric about a point, a line, or an axis.  
    • The image below shows an example of a function and its symmetry over the $x$-axis (vertical reflection) and over the $y$-axis (horizontal reflection).  
    • The axis splits the U-shaped curve into two parts of the curve which are reflected over the axis of symmetry.  
    • Notice that the $x$-intercepts are reflected points over the axis of symmetry and are equidistant from the axis.
    • This type of symmetry is a translation over an axis.

  • Standard Equations of Hyperbolas

    • Consistent with the symmetry of the hyperbola, if the transverse axis is aligned with the x-axis, the slopes of the asymptotes are equal in magnitude but opposite in sign, ±b⁄a, where b=a×tan(θ) and where θ is the angle between the transverse axis and either asymptote.
    • A conjugate axis of length 2b, corresponding to the minor axis of an ellipse, is sometimes drawn on the non-transverse principal axis; its endpoints ±b lie on the minor axis at the height of the asymptotes over/under the hyperbola's vertices.
    • If the transverse axis of any hyperbola is aligned with the x-axis of a Cartesian coordinate system and is centered on the origin, the equation of the hyperbola can be written as:
    • The perpendicular thin black line through the center is the conjugate axis.
    • The two thick black lines parallel to the conjugate axis (thus, perpendicular to the transverse axis) are the two directrices, D1 and D2.

  • The Cartesian System

    • The horizontal axis is known as the x-axis and the vertical axis is known as the y-axis.
    • The non-integer coordinate, $(-1.5,-2.5)$ is in the middle of -1 and -2 on the x-axis and -2 and -3 on the y-axis.
    • The revenue is plotted on the y-axis and the number of cars washed is plotted on the x-axis.  
    • Point $(4,0)$ is on the x-axis and not in a quadrant.  
    • Point $(0,-2)$ is on the y-axis and also not in a quadrant.