Ch 610a, 618a: Fall Semester, 2003

Professor Nathan L. Bauld



  1. Philosophy
  2. Definitions
  3. Structure
  4. AO's
  5. Ground_State_Electronic_Configurations_of_Atoms
  6. Rules_for_Ground_States
  7. Ionic_Bonding
  8. Covalent_Bonding
  9. MO_Picture_of_Covalent_Bonding
  10. Requirements_for_Strong_Covalent_Bonding
  11. Hybridization_States_of_Carbon
  12. The_Tetrahedral_Hybridization_State
  13. Hybridization_of_Noncarbon_Atoms
  14. Why_Hybridization_Occurs
  15. The_Trigonal_Hybridization_State
  16. The_Isoelectronic_Principle
  17. Hybridization_in_Carbocations
  18. Hybridization_in_Alkenes
  19. Sigma_Bonds
  20. Pi_Bonds
  21. Digonal Hybridization




Definition: ORGANIC CHEMISTRY--The chemistry of the compounds of Carbon. .

Review of Atomic Structure



ATOMIC STRUCTURE-- The distribution of electrons in the space around a nucleus.

MOLECULAR STRUCTURE--The specific, three-dimensional arrangement of atoms in a molecule.

General Principles:



It is reasonable to ask "Where do we get these AO's and how do we know their shapes and sizes?" The answer is--- we get them from quantum theory by solving the Schrodinger equation:

Hifi = Eifi

fi = the 1s AO = Nexp(-r/ao)

Where the only variable is r, the distance from the electron from the nucleus. The a0 is the so called Bohr radius, a constant, and the N is a constant, called the normalization factor. The key point to remember here is that the orbital is spherically symmetric, because its value does not depend on direction ( x, y, or z axis), but only on the distance from the nucleus.

2Px AO

X axis

Ground State Electronic Configurations of Atoms




The Hydrogen Atom


The Electronic Configuration of an Atom: A complete specification of the all the AO's of an atom which are occupied.


For the ground state H atom: 1s1

(This means that there is one electron ( the superscript gives the occupancy number) in the 1s AO) .

For the excited state depicted previously: 2s1

(This means that there is one electron in the 2s AO.)


The Linear Format:

He 1s2; Li 1s22s1; Be 1s22s2; B 1s22s22px1; C 1s22s22px12py1; N 1s22s22px12py12pz1 etc.

The Rules for Deriving Ground State Electron Configurations:



***Note: You should be able to do both energy level diagram and linear format representations of the electronic configurations of the ground states of all atoms from H through Ca.

Molecular Bonding: Ionic

Definition: IONIC BONDING: Bonding which arises from the electrostatic attraction of oppositely charged ions, as in Na+ F-.

***You should be able to illustrate, using either the linear or energy level diagram formats, the formation of an ionic bond between two atoms:

Na 1s22s22px22py22pz23s1 + F 1s22s22px22py22pz1

Na+ 1s2 2s22px22py22pz2 F- 1s22s22px22py22pz2

Question: Since both the sodium ion and the fluoride ion have the same electronic configuration, how do they differ?? (The larger nuclear charge for the sodium ion than the fluoride ion).


Molecular Bonding:Covalent

Definition: Covalent Bonding --- Bonding resulting from the sharing of electrons (usually two electrons).

Representations of Covalent Bonds:

A covalent bond may be represented as a pair of dots between two atoms (a Lewis structure)or as a line drawn between the two atoms (line or dash bonds).

An unshared electron pair can be represented as a pair of dots on a single atom.


Molecular Orbital Picture of the Covalent Bond


Molecular Orbital (MO): A wave function or orbital which extends over more than one atom, i.e., a wave function for a molecule. The symbol for a molecular orbital (wave function) is usually y , i.e., the Greek letter psi.

Bonding Molecular Orbital (BMO): An MO which is lower in energy than either of the AO's from which it is derived. The BMO of the hydrogen molecule is much lower in energy than the energy of a hydrogen 1s AO.

Antibonding Molecular Orbital (ABMO): An MO which is higher in energy than either of the AO's from which it is derived.

Description of the Energy Level Diagram: When two hydrogen atoms, each of which has a single electron in a 1s AO, come close to each other,the two AO's overlap and delocalize and lose their identity as AO's. The new orbitals are delocalized over both hydrogen atoms (they are attracted to both nuclei), i.e., over the whole molecule, are therefore called MO's. Instead of having two atomic orbitals, we now have two molecular orbitals. One of the MO's is lower and one higher in energy than the original AO's. The one which is lower in energy is called the BMO, while the higher energy MO is called the ABMO. All of the rules we learned about AO's also apply to MO's, they are still wave functions or orbitals. Since the BMO can accomodate two electrons, the ground state of the hydrogen molecule corresponds to the state where the BMO is doubly occupied. Of course, the electrons must have their spins paired. So we are using the Aufbau and Pauli Exclusion Principles. Since both electrons are in an orbital which is much lower in energy than when they are in the 1s AO of a hydrogen atom, they molecule is much lower in energy ( we say, more stable) than the two separate atoms. The results shown in the diagram above come from a quantum mechanical calculation using the Schrodinger equation, but of course the exact energies are obtained, as well as the mathematical expressions for the BMO and the ABMO.

An Orbital Picture of MO Formation


Requirements for Strong Covalent Bonding

1.Strong, net overlap of orbitals. 2. Two paired electrons.




Example 1: Helium atoms , atomic number 2, have 2 electrons in a 1s AO. When two of these try to combine, the bond has to have 4 electrons. Two can go into the BMO, but two must go into the ABMO. The ABMO is just as antibonding as the BMO is bonding, so no net bonding results. Helium atoms do not form stable helium molecules.

Example 2: This represents the combination of a proton with a hydrogen atom. The proton has zero electrons, the hydrogen atom has 1 e in a 1s AO. The resulting ionized hydrogen molecule can accomodate the electron in a low energy BMO, resulting in net bonding, but since there are not two electrons in the BMO, the binding is less than for the hydrogen molecule (approximately half).

Example 3: This represents an ionized Helium molecule, with three electrons. Since two can go into the BMO, only one has to enter the ABMO. The net result is weak bonding.

Example 4:This represents the attempted combination of two hydrogen atoms having electrons of the same spin (unpaired). The overlap of orbitals occurs when the atoms approach each other, and MO's are formed, but the two electrons cannot enter the BMO. The result is no net bonding.

Hybridization States of Carbon

HYBRIDIZATION: The mixing of atomic orbitals, such as s and p orbitals, to form a new, hybrid orbital for use in bonding.

Tetrahedral Hybridization

The way in which the sp3 hybrid AO's are arrived at can be viewed conceptually as follows. Start with the ground state(GS) of atomic carbon written in either the linear or energy level diagram format. Consider the formation of an excited state (ES) of carbon by the promotion of an electron from the 2s to the 2pz (the z should be a subscript) AO. With respect to bonding to hydrogen atoms or other atoms, the GS is only divalent because it has only two half-filled AO's which could be used to form covalent bonds to hydrogen atoms.In contrast, ES is tetravalent, i.e., it can bond four H atoms using the four half-filled AO's. Each C-H bond lowers the energy by about 100 kcal/mol, so the two additional bonds lower the energy by 200 kcal/mole relative to the two bonds formed by the GS. The excitation energy, i.e., the energy required to promote an electron from the 2s to the 2p AO is 96 kcal/mol. So that the extra 200 kcal/mol provided by the two additional bonds is more than enough to make the overall transaction favorable. Note that the promotion itself is unfavorable, but once the atom has bonded to form CH4, the overall result is more favorable using the ES than the GS.

However, carbon does not exactly bond via this ES, either. The ES has two different kinds of AO's available for bonding, and if these were used, they would give rise to two different bonds in methane. In fact all four bonds are exactly equivalent, and all four H's are equivalent. The second and final step in arriving at the Valence State (VS) is hybridization of all four of the valence shell orbitals to form four equivalent AO's, called tetrahedral or sp3 AO's.

Tetrahedral bonding: a specific type of tetravalent bonding in which the valence are directed to the four corners of a tetrahedron. The bond angles are approximately 109.5 degrees.

Note that in the mixing process, all four valence shell orbitals (but not the inner shell orbital) are mixed together into one grand wave function which is divided into four equal parts. Again, we could ask "where does the idea for a tetrahedral orbital come?" Basically, again from quantum theory but also from experimental observation of equivalent H atoms in methane and the tetrahedral angle in methane and in analogous hydrocarbons (alkanes).

Shapes of Hybrid Orbitals. All hybrid AO's are basically very similar in shape. They are like the p orbitals in that they have two lobes and are oriented in a specific direction, i.e., they point toward a nucleus to which they are bonding. However, they are unlike p orbitals in that the "size" of the two lobes are unequal. The origin of the shape of a hybrid orbital is most easily illustrated by the mixing of a single 2p AO with the 2s AO, to give an sp hybrid AO.

Hybridization of Other Atoms

The Hybridization States of Other Atoms. It is not only carbon which bonds using hybridized AO's. Most other atoms do, too. Consider oxygen and nitrogen as familiar examples.


The Reasons for Hybridization

Why does Hybridization Occur? Two primary reasons can be given:

(1) The hybridized orbitals provide better overlap and stronger bonding because like a p orbital they are oriented toward a specific nucleus in bonding, but they are superior to a p orbital in that they do not "waste" a lobe of equal size to the one generating the bonding.

(2) Spatially, the 2p and 2s orbitals occupy very similar volumes of space. It is virtually impossible for another atom to overlap with one of them without also simultaneously overlapping with the other.

The Trigonal Hybridization State

The sp2 Hybridization State. Consider boron:


Trigonal Hybridization of Carbon. Carbon can also be trigonally hybridized under two different sets of circumstances: (1) When it is isoelectronic with boron and (2) When it is doubly bonded to another atom (any atom which can form two valencies).

Definition: Isoelectronic species--- two chemical species which have the same number of total electrons or the same number of electrons in the valence shell.

Example: Boron atoms have 5 electrons and carbon atoms have 6. Positively charged carbon cations have one less electron and thus are isoelectronic with B. Similarly, negatively charged boron is isoelectronic with neutral carbon (both have 6 e). Positively charged nitrogen is isoelectronic with neutral carbon.

The Isoelectronic Principle



Carbocations: The family of trivalent,positively charged carbon species is called the "carbocation" family. The simplest example is the methyl carbocation:

Hybridization in Alkenes


Doubly Bonded Carbon: Neutral carbon atoms can also hybridize trigonally if the carbon is bonded to only three atoms. In this case the third, unhybridized p orbital(which is now singly occupied) is used to form a second bond ( a pi bond) of a novel type to one of the three atoms. An extremely important case is that in which carbon doubly bonds to another carbon atoms, as in the molecule ethene. In this molecule, both carbon atoms are trigonally hybridized and each is bonded to to other hydrogen atoms.


This is the sigma framework of ethene. But remember that each carbon has a 2p AO left over, unhybridized, which is singly occupied and thus able to form another bond, if everything is set up for overlap. Below the VS for neutral carbon in a situation for forming a double bond is shown:

Pi Bonds

The fourth valency for each carbon atom is then filled by forming a pi bond between the two carbon atoms, using the overlap of the 2pz AO's on each carbon. Thus the carbon atoms are joined be two bonds, this being called a double bond, but one bond is a sigma bond and the other a pi bond.

Note that although the carbons are tetravalent--i.e., they have four bonds each-- they are only bonded to three atoms. This is the situation in which carbon typically uses trigonal hybridization.

DEFINITION: A Pi Bond is a bond formed by sidelong or lateral overlap of two p type orbitals (not by end-on or sigma type overlap).

The Digonal Hybridization State

DIGONAL HYBRIDIZATION. When carbon is bonded to only two other atoms it needs, to complete a tetravalency, to form a triple bond to one of these atoms (or double bonds to both of them; see later). A triple bond consists of a sigma bond plus two pi bonds. If you recall, a pi bond requires the overlap of two p type orbitals in a "lateral" or sidelong fashion. Since carbon in this situation must form two pi bonds, it must leave two 2p AO's unhybridized, so that only one is mixed in:

Note that the second pi bond is perpendicular to the first. It will use the py orbital, while the first pi bond, in our illustration, used the 2pz AO's.