Atomic bonding rules

**Atomic bonding rules** refer to the rules by which atoms bond.

## Electron configurations

Every atom is made up of three basic types of entities: neutrons, protons, and electrons. The neutrons and protons are bound up in the nucleus while the electrons "orbit" around the nucleus. Due to the Heisenberg uncertainty principle there is actually uncertainty about where exactly an electron will be, so instead of having well-defined orbits, there are *regions* where the electrons may be. The situation can be compared to throwing a tennis bowl at a piano with a blindfold on. By seeing whether the pitch of the tone cluster is relatively high or low you can determine the general region, or orbital, the tennis ball is bound to be in relative to the piano. But the exact notes it struck may be impossible to tell (unless you are pitch perfect and extraordinarily gifted).

In the same way, electrons have regions where they're more likely to be around the nucleus of an atom. These are divided into shells and sub-shells, or orbitals. Atoms which are not ions prefer to have all their lower energy shells filled first before their outer shells are filled, and in general the nth shell can hold 2n2 electrons. Shells are made up of a number of orbitals, which for the beginning elements only come in two types: *s-orbitals* and *p-orbitals*. The s-orbitals are spherical while the p-orbitals are shaped like two teardrops with their pointy ends touching. Each orbital can hold two electrons.

### Notation

The number of electrons in an orbital is denoted in the form Mtn, where M is the electron shell, t is the orbital type (either s or p so far), and n is the number of electrons. So for example, a hydrogen atom with one electron will have that electron occupy the first energy shell in the first orbital, which happens to be an s-orbital. Thus the electronic configuration of a hydrogen atom is denoted 1s1. - You know when to switch to another orbital type by using the Aufbau (German: "building") electron configuration ordering schema, depicted in the following table:

Aufbau Electron Configuration Schema

In the Aufbau table, orbitals are filled in the direction the color gets darker, starting from a dark cyan.

By the Aufbau ordering schema, the electronic configurations of the first few elements would be 1s1, 1s2, 1s22s1, 1s22s2, 1s22s22p1 which correspond to hydrogen, helium, lithium, beryllium, and boron respectively. Past this point however things get interesting - how so?

You may have noticed that the second electron shell only has one s-orbital and thus two electron slots, yet there are six more electrons to make eight. This is because there are three p-orbitals, which are oriented perpendicular to each other along the X,Y,Z axis. The shells are denoted 2px, 2py, and 2pz. According to *Hund's rule*, when you have multiple of the same type of orbital still available with a number of electrons that won't completely fill the electron shell, you distribute them as evenly as possible among the remaining orbitals. Thus the electronic configuration for carbon is not 1s22s22px22py02pz0 but actually 1s22s22px12py12pz0.

The electronic configuration of an atom is highly influential in how the atom bonds. Electronic configurations are the most important thing about bonding, and hence chemistry. As a case in point, consider helium with a configuration of 1s2. Because all the shells are filled helium tends to be non-reactive. Yet by substituting one of the electrons in a helium atom with a muon, the muon will orbit the helium so much closer due to its higher mass that the net result will be a helium nucleus and muon that behaves as if there were only one proton, since the muon cancels out of the charge of one of the protons. In turn this means that the remaining electron will treat this as a hydrogen nucleus. By cleverly altering electronic configuration you can turn helium into an atom as reactive as hydrogen.

## Covalent v. Ionic bonding

In chemistry there are two main types of bonds: *covalent* and *ionic* bonding. In covalent bonding, two or more atoms *share* electrons. In ionic bonding, atoms *steal* electrons for themselves, and they are bonded by the fact that when an atom steals or gives up electrons it becomes an ion, which can attract other ions through electromagnetism. Water is an example of a covalently bonded molecule. In H2O, the hydrogen shares two electrons from the oxygen atom while contributing their electrons to complete the oxygen atom's second electronic shell. An example of ionic bonding is ordinary table salt, or Na+Cl-. By giving up an electron the sodium atom (Na) gains a positive charge and the chlorine atom (Cl) gains a negative charge. This charge between them attracts them.

### Electronegativity

The "desire" of an atom to steal electrons from another atom is called electronegativity. By looking at a table of elemental electronegativity values and finding the difference between these elements, you can determine the type of bond that will be formed:

* If the electronegativity difference is 0, the bond will be purely covalent. (I.e. H-H and O=O)
* If the electronegativity difference is between 0 and 2 the bond is polar covalent, which means one of the atoms tends to have more of the electrons, and thus the sharing of electrons is less equal. (I.e. the H-O bond in H2O)
* If the electronegaitvity difference is greater than 2, the bond is ionic. (I.e. Na+Cl-)

### Dipole moments

If more electrons are clustered around an atom in a polar covalent or ionic bond, then that atom becomes more negatively charged, and the other atom is more positively charged. The dipole moment of the bond is the direction and amount of charge this bonding accumulates, and is usually denoted with an arrow. The plus sign is on the side of the positive atom while the arrowhead is on the side of the negative atom.

To calculate the dipole moment of an entire molecule, sum up the vectors associated with the dipole moment of each individual bond. For example, CO2 is shaped like O=C=O, and the oxygen has higher electronegativity, so the dipole vectors would be O<-+C+->O. These cancel each other out and so the dipole moment of carbon dioxide is 0.

In the case of water however, the molecule is not in a straight line and is more "Micky Mouse" shaped. Since the dipole moment bond vectors point towards the oxygen, it means a water molecule has an overall dipole moment negatively charged towards the oxygen side and positively charged towards the hydrogen side.

## Orbitals and atomic hybridization

Because electrons repel each other, bonds to a single atom tend to be distributed around as far apart as possible, so that bonds with two, three, and four substituents (connected atoms) will tend to assume a linear, planar trigonal, and tetrahedral geometry respectively. This poses an issue however, because the s-orbital is only linear, and the p-orbitals are perpendicular. How can an atom such as methane (CH4) have tetrahedral symmetry when carbon's p-orbitals are perpendicular?

The solution is through some clever electron shuffling. Carbon brings up one electron from the 2s orbital to a 2p orbital leaving four open orbitals, one 2s and three 2p. These then *merge* with eachother to form a hybrid type of orbital called a sp3 orbital, which assumes a tetrahedral geometry and thus allows methane to form. While pulling up an electron from the 2s orbital to a 2p orbital does cost energy, it is made more efficient by the bonding into a stable configuration.

The three main types of hybridized orbitals are sp, sp2, and sp3, allowing for linear, planar trigonal, and tetrahedral symmetries respectively.

### Pi and sigma bonding

Between orbitals, there are two main types of bonding: pi and sigma. Sigma bonds are bonds such that a line drawn between the two nuclei of the atoms always passes through an orbital zone, while pi bonds are bonds such that a line drawn between the two nuclei of the atoms does *not* pass through an orbital zone.

An example of a sigma bond is H-H while an example of a pi bond is the C-C bond in ethylene H2C=CH2 (of the carbon bond, one is a sigma bond between sp2-orbitals while the other is pi type between the p-orbitals).

The type of bond (pi v. sigma) is useful in determining the reactivity of a molecule, thus affecting chemistry and bonding. Sigma bonds are stronger due to the greater overlap in orbitals.

### Resonance structures

Resonance structures are alternate valid ways to write out a molecule's structure such that the atoms never change and each atom maintains the same number of electrons in bonding. In benzene (C6H6), for instance, there are two ways to write the ring structure, corresponding to two resonance structures. These are correlated through the double-headed arrow, specially reserved for such resonance equivalences.