The Chemical Bond I Bonds as Orbital Overlap Molecular Orbital Diagrams Hybridization Additional Bonding Schemes

CHEM 3722 Chapter 12 2 Atomic Orbitals and Orientation We’ve solved hydrogen-like atoms and found the orbital shapes  Let’s get the orientation of each down  Our orbitals had no specific orientation, except with respect to each other  We’ll use some alternate pictures that have a specific orientation For example: y zz yx Rotate by 45°

CHEM 3722 Chapter 12 3 Orbitals Pictures We’ll picture the orbitals in this way In terms of energy, we write these as an energy level diagram Two different phases E

CHEM 3722 Chapter 12 4 The Energetics of Bonding I Can imagine the bonding process in terms of bringing two hydrogen atoms together from far away  As they approach, the E lowers as the atomic orbitals begin to interact  The interaction is composed of (1) nuclear-nuclear repulsion, (2) electron-electron repulsion, and (3) electron-nuclear attraction  The most stable distance (minimum energy on this potential energy curve) is where the attractions outweigh the repulsions Increased electron density between the nuclei stabilizes the molecule!

CHEM 3722 Chapter 12 5 The Energetics of Bonding II But, need to know why an atom would bond?  All bonds result in the lowering of energy of the electrons in the system  Not all electrons are lowered in energy, but the net result is a more stable arrangement of the electrons Consider the H 2 molecule  Each has one occupied orbital: 1s  Let’s ‘watch’ the energy change But what about He 2 ? Atomic orbital Region of energy where two electrons can reside Result of bonding Called molecular orbitals. Formed from the two atomic orbitals interacting. Note that the net effect is two lower energy e - ’s. There is no net E-loss in this alteration of electron energies. That is, the energy released in lowering 2 e - is used to promote the other 2. Thus, this bond doesn’t happen: nonbonding!

CHEM 3722 Chapter 12 6 Molecular Orbitals I To picture the MO’s, consider them as the “overlap” of the AO’s.  Phase of overlap matters  Since made from s-orbitals, we’ll denote this MO in similar terms But, we’ll use Greek letters for bonds  Call the overlap a  molecular orbital If overlap is out of phase, then we’ll denote it as an antibonding orbital (  *)  Other orbital can overlap similarly Look at p and s Overlap of s-orbitals Internuclear axis If overlap is along this axis, then the MO formed is .  

CHEM 3722 Chapter 12 7 Molecular Orbitals II bonding In terms of probability, we can see that bonding regions show an enhanced electron density between the two nuclei. The probability is high that the electron- nucleus attraction will keep nuclei together. Antibonding Antibonding regions show a reduced electron density between the nuclei, and thus the electron-nucleus attraction is away from the stable bond length.

CHEM 3722 Chapter 12 8 Molecular Orbitals III Any set of orbitals that overlap along the internuclear axis are considered to be  bonds.  And the antibonding MO is a  * bond Here are a few other examples Can also make a  -bond with d-orbitals x y =   p y  p y

CHEM 3722 Chapter 12 9 Molecular Orbitals IV Any set of orbitals that overlap perpendicular to the internuclear axis are said to  -bond  The antibonding orbital is  * Any set of orbitals that overlap at any other angle to the internuclear axis are said to  -bond  The antibonding orbital is  *  Best example is two d yz orbitals

CHEM 3722 Chapter Putting It All Together Carbon Monoxide  First draw Lewis Dot Structure This shows 3 bonding pairs (between nuclei) and 2 nonbonding pairs Expect a , a  and another  bond  Now consider orientation and orbitals involved (we’ll draw 2 of 3 dimensions) This should match Lewis Structure  We see p y -p y overlap forming  bond  We see p bonds in p x -p x and p z -p z overlap C O C O  -bond pzpz pxpx  -bond In the other  * In the other 

CHEM 3722 Chapter More Diatomic MO-Diagrams Homonuclear diatomics show a slight change as Z increases   mo’s appear before  mo’s until Z = 7 (Nitrogen)

CHEM 3722 Chapter Polyatomic Molecules MO’s are easy to create for diatomics  Things get tougher if we add atoms  Take AlCl 3 as an example Doesn’t obey octet rule Lewis dot structure shows three single bonds  Thus, three  bonds Structure looks like this:  How do p-orbitals arrange themselves this way and stay orthogonal? Don’t appear to be perpendicular Make a basis set of the H-like atomic orbitals & make new orbitals  Requires us to make linear combinations of atomic orbitals to make NEW atomic orbitals  Call this hybridization But why? Can we justify this?

CHEM 3722 Chapter Hybridization Cl has it’s p-orbitals ready to bond to the Al, but Al has two types of valence orbitals available: s and p (p x, p y, p z )  This means that the lowest energy orbital available for overlap is the s.  But, only one Cl can bond with this orbital  To make three equal energy orbitals available to the Cl’s, Al “hybridizes” So we use the H-like orbitals to generate three different but energetically equivalent atomic orbitals  In math terms, the linear combinations are… Energy s ppp sp 2 p

CHEM 3722 Chapter sp 2 hybrids and AlCl 3 We can picture the hybrid orbitals as spreading out perpendicular to the remaining p-orbital  They are in the xy-plane  Three lobes must get as far apart as possible  This is a trigonal planar arrangement of hybrid orbitals Can see how the orbitals ‘do’ this pictorially, too

CHEM 3722 Chapter sp hybrids If need two identical bonding orbitals, use an s and a p orbital in an sp hybrid  For example, LiH 2 Pictorially, the linear combination goes like

CHEM 3722 Chapter Multiple Bonds In sp and sp 2 hybridization, there remains a p-orbital (or two)  Can this orbital involve itself in some sort of bonding?  Sure, but not along the internuclear axis, so must be  -bonding! This is the basis for double and triple bonds  For example, consider ethane

CHEM 3722 Chapter sp 3 hybrids If need four identical bonding orbitals, use an s and all three p orbitals in an sp 3 hybrid  For example, H 2 O H H O

CHEM 3722 Chapter Other Bonding Types So far, only showed covalent bonding Other bonds  Metallic  Ionic  Coordinate Covalent  Three center, two electron bonds Ionic Bonds  Purely Coulombic interactions  Electrons are not “shared” they are transferred (in a sense)  NaCl is perfect example NaCl = Na + --Cl - or Na - --Cl +  We know first ionic species is best, but both are probably present in any sample NaCl has character of both, but has mainly the character of Na + -- Cl -

CHEM 3722 Chapter Coordinate Covalent Often the e’s shared in a covalent type bond don’t come from both atoms, but instead from one atom, molecule, or ion  For Example: W(CO) 6 Usually occurs with a transition metal as central atom (d-orbitals are the key) Species that donates both electrons is called a ligand  CO and O 2 are both ligands for Hemoglobin, and this is why CO can suffocate you when inhaled in great amounts Not only is it a substitute ligand, it also bonds better because the O can pull electron density from the C. This makes the Carbon antibonding MO a better electron donar AND it makes the ‘backbonding’ more stabilizing  Backbonding is the donation of electron density of the metal back to the ligand In regular O 2, the nonpolar nature of the molecule limits these effects

CHEM 3722 Chapter Center, 2 Electron Bonds Most bonds are between two atoms  They are 2 center, 2 electron bonds (2c-2e bonds) A center is a nucleus 3c-2e bonds occur when two electrons hold together 3 nuclei Most common examples: Al 2 H 6 and B 2 H 6  The second is called diborane  BH 3 is hard to make because diborane is so stable in comparison  Orbital overlap looks like sp 3 hybrid orbital of boron 2sp 3 hybrid orbital of boron 1 s-orbital of H 2 1