Valence shell electron pair repulsion (VSEPR) theory is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms. It is also named the Gillespie-Nyholm theory after its two main developers. The acronym "VSEPR" is pronounced either "ves-per" or "vuh-seh-per" by some chemists. The premise of VSEPR is that the valence electron pairs surrounding an atom tend to repel each other, and will therefore adopt an arrangement that minimizes this repulsion, thus determining the molecule's geometry. Gillespie has emphasized that...

This is a table of orthonormalized spherical harmonics that employ the Condon-Shortley phase up to degree l = 10. Some of these formulas give the "Cartesian" version. This assumes x, y, z, and r are related to θ {\displaystyle \theta } and φ {\displaystyle \varphi \,} through the usual spherical-to-Cartesian coordinate transformation: x = r ...

The term harmonic in its strictest sense describes any member of the harmonic series. The term is employed in various disciplines, including music and acoustics, electronic power transmission, radio technology, etc. It is typically applied to repeating signals, such as sinusoidal waves. A harmonic of such a wave is a wave with a frequency that is a positive integer multiple of the frequency of the original wave, known as the fundamental frequency. The original wave is also called 1st harmonic, the following harmonics are known as higher harmonics. As all harmonics are periodic at the fundamental...