# Structure and bonding
## Introduction

Structural theory plays an essentially central role in the study of organic molecules. Atoms can form certain number of bonds in order to fulfill their valence by sharing electrons. Carbon, the most prevalent element in organic compounds, is tetravalent and can form up to four covalent bonds with other atoms of similar electronegativity (large differences in electronegativities result in ionic bond formation). This is because of the tendency of the carbon atom to attain an electron configuration to complete its octet of electrons. Similarly, oxygen can form two covalent bonds and hence it is divalent and halogens as well as hydrogen (with a few exceptions) are monovalent. Carbon virtually always forms 4 bonds. The bonds can be single, double or triple bonds. The bond can therefor create intricate chains of carbon and other atoms. These often produce extremely large and complex molecules. In biological systems the important elements are carbon, hydrogen, oxygen, nitrogen, sulfur and phosphorus. These are the elements which hold the greatest interest in bonding with carbon. The single bonds form a tetrahedron shape (a three sided pyramid) with the carbon atom at the center whereas a double bond (with two single bonds) forms a y shape with the carbon at the center and a triple bond or two double bonds form straight lines. Thus depending upon the type of bond, carbon forms predictable shapes

## The Octet Rule

As described in most general chemistry courses, atoms have a tendency of forming an octet of electrons about themselves. In 1916,G.N. Lewis and W. Kössel described this phenomenon by claiming that atoms react to form a valence shell with eight electrons, like that of noble gases (except Helium which only has two valence electrons), due to their high stability. This generalized rule is commonly referred to as the octet rule.
However, this rule can only be truly applied to the second period elements of the periodic table since they have one s and three p orbitals available for bonding. Elements in periods below the second have higher d orbitals available for bonding and hence these atoms can form more than four bonds. The most often used example is the octahedral molecule SF$_6$.
On the other hand, some unstable molecules can actually form fewer than four bonds. An example that will be used later in hydroboration reactions is the molecule trigonal planar BH$_3$ which has a valence of six electrons. Note that ammonia (NH$_3$) also has three bonds as such:
But is this molecule an exception?
If you think about it, the answer should clearly be no! This is because nitrogen has a valence of five electrons in the ground state, therefore forming three bonds fulfills its octet valence because it has a free electron pair and six electrons around it in covalent bonds. A more faithful rendition of ammonia would be more like (more on structural formulas below)
If you cannot see why, you might want to review relevant material from a general chemistry text or notes.

## Lewis Structures

As an aspiring organic chemist, or perhaps a perplexed student, you will find that Lewis structures are of vital importance to understanding many principles behind organic chemistry. When writing Lewis structures, we generally try to give each atom an octet matching the closest noble gas. Carbon, Nitrogen, Oxygen, and Fluorine all are drawn with a configuration of Neon. However, it is important to note how many valence electrons each atom has, the number of valance electrons can be attained by simply looking at what group (column) in the periodic table a particular element belongs to. For example, carbon belongs to Group 4A (or IVA), therefore it has 4 valence electrons and all halogens (Group 7A) have 7 valence electrons.
If the structure is ionic, then we add or subtract electrons from individual atoms, such as in the case of LiBr:
If the structure is covalent, then we use covalent bonds for electron pairs shared between atoms. At times, multiple bonds may be needed to complete the octet of atoms. A number of simple examples of Lewis structures are shown below:

## Formal Charges

Formal charge on an atom refers to its net electrostatic charge due to the electrons directly acting upon that atom. For example, the oxygen in a stardard divalent water molecule is zero. You should be able to recall the structure of H$_2$O and remember that it has no net charge. However, a hydronium ion H$_3$O$^+$ has a net positive charge of +1. To find the formal charge on each respective atom in a molecule, you can simply follow the steps given below:
* Set up a Lewis structure of the molecule if it is not given
* Identify the number of valence electrons of the element in question from a periodic table (remember, number of valence electrons are equal to the group number) -- let's call this number v.
* Identify the number of free electrons (keeping in mind that in non-radical species, they come in pairs) on the atom -- lets call this number f.
* Identify the number of bonds formed by the atom -- lets call this number b
* Now we can figure out the formal charge on that particular atom by substituting the values of v,f, and b into the equation
c = v - f - b
where c is the formal charge on that particular atom.
Looking at the two molecules given above, H$_2$O and H$_3$O$^+$, we can calculate the formal charge on each atom of the molecule and determine the net charge (if any) of the entire molecule:
| H$_2$O Formal charge calculation for H: v = 1 f = 0 b = 1 c = (1) - (0) - (1) = 0 Note that both hydrogens are chemically equivalent Formal charge calculation for O: v = 6 f = 4 b = 2 c = (6) - (4) - (2) = 0 Net Molecular Charge = 0 | H$_3$O$^+$ Formal charge calculation for H: v = 1 f = 0 b = 1 c = (1) - (0) - (1) = 0 Note that all three hydrogens are chemically equivalent Formal charge calculation for O: v = 6 f = 2 b = 3 c = (6) - (2) - (3) = +1 Net Molecular Charge = +1 |
A few other examples are also given in figure 1.2.1. For example, we can look at the structure of oxaloacetate, an important metabolite of gluconeogenesis and the Krebs Cycle, and determine by inspection that all atoms on the molecule are uncharged with exception of the two terminal oxygen atoms. This can be justified by preforming the formal charge calculation or by reasoning that since divalent oxygens are uncharged, such as those present in H$_2$O, all divalent oxygen atoms do not contribute to the molecule's net charge, and hence they have a formal charge of 0 or no net charge. Also as calculated above, we noticed that monovalent Hydrogens also have a net charge of zero, therefore oxaloacetate's hydrogens do not contribute to the net charge. Now looking at the molecule's carbon atoms, would these atoms contribute to charge? Well, since carbon atoms are tetravalent and therefore have the tendency to form four covalent bonds in order to attain a noble gas-like electron configuration we can deduce that all tetravalent carbons in oxaloacetate have a formal charge of 0 (for example, the molecule methane, CH$_4$, has a neutral charge). Otherwise formal charges can be calculated for each carbon atom where each has four valence electrons (v), each has zero free electrons (f), and each has four bonds (b). Therefore each has a charge of (4 - 0 - 4 =) 0. All that is left now are the two terminal oxygen atoms that were exepmt from the earlier condition. Since each oxygen is monovalent, we can reason that each atom will bear a charge of -1 (just like the monovalent analogue hydroxide -- OH$^-$). Thus the molecule has a net charge of -2 due to the two formal charges.

## Isomers

Isomer is a term applied to compounds that have the same empirical formula as one another but are structurally unique. Note, however, that these isomers ought not to be confused with isomers.There are several types of isomers that will be analyzed:

## Constitutional (Structural) Isomers

These isomers differ from one another in terms of the connectivity of its constituent atoms. For example, 2-chloropropane (isobutyl chloride) and 1-chloropropane (n-propyl chloride) are structural isomers because they have the same empirical formula but differ in their connectivity.

## Hybridization and the VSEPR Theory

hybridization is the mixing of atomic orbitals to form new hybrid orbitals with new directional properties (degenerate)