Hybridization and Resonance

Hybridization and Resonance 

 Hybridization:

 In chemistry, hybridisation (or hybridization) is the idea of mixing atomic orbitals to form new hybrid orbitals suitable for the qualitative description of atomic bonding properties. Hybridised orbitals are very useful in the explanation of the shape of molecular orbitals for molecules. It is an essential part of valence bond theory. Although sometimes taught together with the valence shell electron-pair repulsion (VSEPR) theory, valence bond and hybridization are in fact not related to the VSEPR model.

                        Types of Hybridizations
        There are Three types of hybridization which are given below:

• sp3 hybrids
• sp2 hybrids
• sp hybrids 

 sp3 hybrids: 

Hybridisation describes the bonding atoms from an atom's point of view. That is, for a tetrahedrally coordinated carbon (e.g., methane, CH4), the carbon should have 4 orbitals with the correct symmetry to bond to the 4 hydrogen atoms. The problem with the existence of methane is now this: carbon's ground-state configuration is 1s2 2s2 2px1 2py1 or more easily read:

 

The valence bond theory would predict, based on the existence of two half-filled p-type orbitals (the designations px py or pz are meaningless at this point, as they do not fill in any particular order), that C forms two covalent bonds, i.e., CH2 (methylene). However, methylene is a very reactive molecule (see also: carbene) and cannot live outside of a molecular system. Therefore, this theory alone cannot explain the survival of CH4.

Furthermore, ground state orbitals cannot be used for bonding in CH4. While exciting a 2s electron into a 2p orbital would, in theory, allow for four bonds according to the valence bond theory, (which has been proved experimentally accurate for systems like O2) this would imply that the various bonds of CH4 would have differing energies due to differing levels of orbital overlap. Once again, this has been experimentally disproved: any hydrogen can be removed from a carbon with equal ease.

To summarise, to explain the existence of CH4 (and many other molecules) a method by which as many as 12 bonds (for transition metals) of equal strength (and therefore equal length) was required.

The first step in hybridisation is the excitation of one (or more) electrons (we consider the carbon atom in methane, for simplicity of the discussion):

 

The proton that forms the nucleus of a hydrogen atom attracts one of the lower-energy valence electrons on carbon. This causes an excitation, moving a 2s electron into a 2p orbital. This, however, increases the influence of the carbon nucleus on the valence electrons by increasing the effective core potential (the amount of charge the nucleus exerts on a given electron = Charge of Core − Charge of all electrons closer to the nucleus). The effective core potential is also known as the effective nuclear charge, or Z_eff.

The solution to the Schrödinger equation for this configuration is a linear combination of the s and p wave functions, or orbitals, known as a hybridized orbital[3]. In the case of carbon attempting to bond with four hydrogens, four orbitals are required. Therefore, the 2s orbital (core orbitals are almost never involved in bonding) "mixes" with the three 2p orbitals to form four sp3 hybrids (read as s-p-three). See graphical summary below.

In CH4, four sp3 hybridised orbitals are overlapped by hydrogen's 1s orbital, yielding four σ (sigma) bonds (that is, four single covalent bonds). The four bonds are of the same length and strength. This theory fits our necessities.

 

 

If we now recombine these orbitals with the blank s-orbitals of 4 hydrogens (4 protons, H+) and allow maximum separation between the 4 hydrogens (i.e., tetrahedral surrounding of the carbon), we see that at any orientation of the p-orbitals, a single hydrogen has an overlap of 25% with the s-orbital of the C, and a total of 75% of overlap with the 3 p-orbitals (see that the relative percentages are the same as the character of the respective orbital in an sp3-hybridisation model, 25% s- and 75% p-character).

According to the orbital hybridisation theory, the valence electrons in methane should be equal in energy but its photoelectron spectrum [4] shows two bands, one at 12.7 eV (one electron pair) and one at 23 eV (three electron pairs). This visible inconsistency can be explained when one considers additional orbital mixing taking place when the sp3 orbitals mix with the 4 hydrogen orbitals.

sp2 hybrids: 

Other carbon based compounds and other molecules may be explained in a similar way as methane. Take, for example, ethene (C2H4). Ethene has a double bond between the carbons.

For this molecule, carbon will sp2 hybridise, because one π (pi) bond is required for the double bond between the carbons, and only three σ bonds are formed per carbon atom. In sp2 hybridisation the 2s orbital is mixed with only two of the three available 2p orbitals

forming a total of 3 sp2 orbitals with one p-orbital remaining. In ethylene (ethene) the two carbon atoms shape a σ bond by overlapping two sp2 orbitals and each carbon atom forms two covalent bonds with hydrogen by s–sp2 overlap all with 120° angles. The π bond between the carbon atoms perpendicular to the molecular plane is formed by 2p–2p overlap. The hydrogen-carbon bonds are all of equal strength and length, which agrees with experimental data.

The amount of p-character is not restricted to integer values; i.e., hybridisations like sp2.5 are also willingly described. In this case the geometries are somewhat distorted from the ideally hybridised picture. For example, as stated in Bent's rule, a bond tends to have higher p-character when directed toward a more electronegative substituen

 sp3 hybrids: 

The chemical bonding in compounds such as alkynes with triple bonds is explained by sp hybridization.

 

 In this model, the 2s orbital mixes with only one of the three p-orbitals resulting in two sp orbitals and two remaining unchanged p orbitals. The chemical bonding in acetylene (ethyne) (C2H2) consists of sp–sp overlap between the two carbon atoms forming a σ bond and two additional π bonds formed by p–p overlap. Each carbon also bonds to hydrogen in a sigma s–sp overlap at 180° angles.

Resonance : 

In chemistry, resonance or mesomerism  is a way of describing delocalized electrons within certain molecules or polyatomic ions wherever the bonding cannot be expressed by one single Lewis formula. A molecule or ion with such delocalized electrons is represented by several contributing structures  (also called resonance structures or canonical forms).

Every contributing structure can be represented by a Lewis structure, with only an integer number of covalent bonds between each pair of atoms within the structure. These individual contributors cannot be observed in the actual resonance-stabilized molecule; resonance is not a rapidly-interconverting set of contributors. Several Lewis structures are used collectively to describe the actual molecular structure. The actual structure is an approximate intermediate between the canonical forms, but its overall energy is lower than each of the contributors. This intermediate form between different contributing structures is called a resonance hybrid. Contributing structures differ only in the position of electrons, not in the position of nuclei.

Resonance is a key component of valence bond theory.

Electron delocalization lowers the potential energy of the substance and thus makes it more stable than any of the contributing structures. The difference between the potential energy of the real structure and that of the contributing structure with the lowest potential energy is called the resonance energy or delocalization energy.

              General characteristics of resonance:

• They can be represented by several correct Lewis formulas, called "contributing structures", "resonance structures" or "canonical forms". However, the real structure is not a rapid interconversion of contributing structures. Several Lewis structures are used together, because none of them exactly represents the actual structure. To represent the intermediate, a resonance hybrid is used instead.
• The contributing structures are not isomers. They differ only in the position of electrons, not in the position of nuclei. When transforming from one Lewis structure into another, eventually no sigma bonds are broken (except in the case of hyperconjugation). Only pi bonds differ.
• Each Lewis formula must have the same number of valence electrons (and thus the same total charge), and the same number of unpaired electrons, if any. [6]
• Bonds that have different bond orders in different contributing structures do not have typical bond lengths. Measurements reveal intermediate bond lengths.
• The real structure has a lower total potential energy than each of the contributing structures would have. This means that it is more stable than each separate contributing structure would be.

Resonance Energy:

 Each structure is associated with a certain quantity of energy, which determines the stability of the molecule or ion (the lower energy, the greater stability). A resonance hybrid has a structure that is intermediate between the contributing structures; the total quantity of potential energy, however, is lower than the intermediate. Hybrids are therefore always more stable than any of the contributing structures would be.[ The molecule is sometimes said to be "stabilized by resonance" or "resonance-stabilized," but the stabilization derives from electron delocalization, of which "resonance" is only a description. Delocalization of the π-electrons lowers the orbital energies, imparting this stability. The difference between the potential energy of the actual structure (the resonance hybrid) and that of the contributing structure with the lowest potential energy is called the "resonance energy".

Resonance energy of benzene: 

Resonance (or delocalization) energy is the amount of energy needed to convert the true delocalized structure into that of the most stable contributing structure. The empirical resonance energy can be estimated by comparing the heat of hydrogenation of the real substance with that estimated for the contributing structure.

The complete hydrogenation of benzene to cyclohexane via 1,3-cyclohexadiene and cyclohexene is exothermic; 1 mole benzene delivers 208.4 kJ (49.8 kcal)