General formula to design a freeform singlet free of spherical aberration and astigmatism

A chemical formula presents information about the proportions of atoms constituting a particular chemical compound or molecule, mainly using symbols of elements and numbers. At times other symbols, such as dashes, parentheses, brackets, commas, plus, and minus signs, are also used. A chemical formula can be one of three types – molecular, empirical, and structural.

Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...

An element composed of atoms that readily lose electrons (a metal) can react with an element composed of atoms that readily gain electrons (a nonmetal) to produce ions through complete electron transfer. The compound formed by this transfer is stabilized by the electrostatic attractions (ionic bonds) between the oppositely charged ions.

Molecular compounds or covalent compounds result when atoms share electrons to form covalent bonds. Since there is no electron transfer, molecular compounds do not contain ions; instead, they consist of discrete, neutral molecules. 

The elemental makeup of a compound defines its chemical identity, and chemical formulas are the most concise way of representing this elemental makeup. When a compound’s formula is unknown, measuring the mass of its constituent elements is often the first step in determining the formula experimentally.

Formula Mass of Covalent Compounds