sp3d and sp3d 2 Hybridization

The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...

According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...

Molecular Orbital Energy Diagrams

Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...

In an NMR sample, precise measurement of the absolute absorption frequencies of nuclei is difficult. A standard internal reference compound is added, and the frequency difference between the reference signal and sample signals is measured.
The internal reference compound generally used in NMR spectroscopy is tetramethylsilane (TMS). TMS is preferred because it is chemically inert, soluble in NMR solvents, and easily removable. Also, the highly shielded methyl protons in TMS yield an intense...