Download Bonding Conceptually easier to view bonding if one considers

Bonding
Conceptually easier to view bonding if one considers electrons as waves
Consider a two dimensional standing wave
If we constrain another point in the middle of the string we obtain the first harmonic
The signs used (+ and -) are arbitrary
Important point is the change in sign
(called a node)
Wave function of s atomic orbital
The region of space where electrons are held are called orbitals
The property and shape of orbitals is dependent on what shell the electrons are held
With 2nd row atoms, the atomic orbitals can be either s or p
(s orbitals are lower in energy than p orbitals)
A wave function is simply a mathematical formula that describes the region of space the
electron may reside in a given atomic orbital
Atomic s orbital:
In two-dimensions in three-dimensions
• No node – therefore same sign throughout sphere
Electron density dimishes further from the nucleus
Wave function of atomic p orbital
Atomic p orbital:
In two-dimensions in three-dimensions
electron
density
+
-
distance
nucleus
Important points:
Density is zero at nucleus
Lobes on opposite sides of the nucleus are out of phase
(different sign)
Combination of Two Waves
When a bond forms it is a result of combination of two atomic wave functions
Combination of Atomic Orbitals
Forms Molecular Orbitals
Energy Gain in a Covalent Bond
As atomic orbitals combine they form a new molecular orbitals that allow electrons to be
shared between the two nuclei
Bond Formation
Bonds are formed by a combination of orbitals
Orbitals – location of electrons (on time average)
(described by the wave function)
phase – describes the sign of an orbital
Only orbitals of like phase can combine in a constructive manner to form a bonding region
where the electrons can reside
This bond lowers the energy of the structure as the electrons shield the two positively charged nuclei Always get the same number of molecular orbitals as atomic orbitals used
Organic compounds are described in terms of the type of bonds
(σ sigma and π pi bonds)
σ Bonds
Electron density is symmetric along the internuclear axis
When combine two atomic orbitals we need to obtain two molecular orbitals
In addition to bonding molecular orbital shown, also obtain an antibonding orbital
Antibonding orbital is obtained by subtracting the two wave functions
In addition to combining s atomic orbitals, bonds can be formed by combining p atomic orbitals
There are 3 atomic p orbitals
- Each atomic p orbital is perpendicular (orthogonal) to the other two
This geometry allows the p orbital to form a different type of bond
P orbitals can also form σ bonds
Can add and substract two atomic p orbitals to obtain a bonding and antibonding σ bond
Bonding molecular orbital (σ bond)
Antibonding molecular orbital
If add a different p orbital a different type of bond can form
Consider adding two atomic 2py orbitals
p bond
Electron density is not symmetric about the internuclear axis
s orbitals can only form σ bonds
p orbitals can form either σ or π bonds
Three Views of Bonding for Organic Compounds
1) Total electron density
(nature)
2) Molecular Orbitals (MOs)
(computer)
3) Bonds from hybrid atomic orbitals (AOs)
(students)
Conceptually very useful concept to explain structure and reactivity
Hybrid Orbitals
If bonds formed only from atomic s or p orbitals then the bond angles would always be 90˚
Also could not fill atoms’ valence shell with covalent bonds
Consider carbon
In a covalent bond electrons are shared between two atoms
(each atom donates one to the sharing)
In carbon there are only two unpaired valence electrons
therefore only two covalent bonds are possible
An atom can combine its atomic orbitals to form hybridized orbitals
Same rules apply for combining atomic orbitals to form hybrid orbitals
1) Get same number of hybridized orbitals as starting atomic orbitals used to form hybrid
2) Shape of hybridized orbitals is obtained by the mathematical addition of the wave
functions for the atomic orbitals
The name (designation) of hybridized orbitals merely refers to the number and type of atomic orbitals used in the formation
sp Orbital
Combine one s orbital with one p orbital
If the orbitals are substracted then an indentical hybridized orbital is obtained directed 180˚ from the first
Realize that if one s orbital and one p orbital are hybridized then two p orbitals remain
Consider acetylene (also called ethyne)
- When looking at a Lewis dot multiple bond structure, only one σ bond can be between two atoms
- Therefore all additional bonds are always π bonds
Hybridized Bonding View of Acetylene
The two hybridized sp orbitals form σ bonds with the other carbon and a hydrogen,
The remaining p orbitals form two additional π bonds to form a total of three bonds between carbon
sp2 Hybridization
- Can also hybridize by combining one s orbital with two p orbitals
(would allow formation of three covalent bonds – one from each sp2 hybridized)
All three sp2 orbitals are in the same plane
(120˚ apart from one another)
The remaining p orbital is perpendicular to this plane
The hybridized sp2 orbitals can form σ bonds
The pz orbital can form a π bond
sp3 Hybridization
To form four equivalent bonds carbon can hybridize all of its valence orbitals
(three p and one s to form four sp3 hybrids)
The four sp3 hybridized orbitals have a bond angle of 109.5˚
How to View 3-Dimensional Objects
Organic chemists use a wedge and dash line system to designate stereochemistry
Wedge line – object is pointing out of the plane
Dash line – object is pointing into the plane
H
H
H
H
Bond Rotation
Bonding between two atoms is a result of the overlap of the orbitals from each atom
If only a σ bond is formed between two atoms, then the bond can be rotated a full 360˚ and maintain the same overlap of the orbitals
- Consequence of orbitals being symmetric about the internuclear axis
Causes substituents to have different relative placement depending upon bond rotation
Rigidity of π Bonds
In contrast, π bonds are not symmetric about the internuclear axis
If π bonds would rotate the bond would lose overlap and hence the bond would be broken
Cis versus Trans
The rigidity of a π bond causes different compounds to be formed that cannot rotate to
interconvert (hence they have different physical properties)
If substituents are on the same side of the double bond, it is called a cis compound
If substituents are on opposite sides of the double bond, it is called a trans compound
Isomers
The cis and trans compounds are one type of relationship that are called isomers
Isomers are any two compounds that are different but have the same molecular formula
Isomers can be further classified as being either stereoisomers (having same formula but differing in the three dimensional arrangement, thus configurational) or constitutional isomers (compounds are bonded in a different pattern)
In summary:
s orbitals can only form σ bonds
p orbitals can form either σ or π bonds
Hybridized orbitals form σ bonds
Multiple bonds are formed with one σ bond and additional π bonds
lone pair of electrons often go into hybridized orbitals
Why do atomic orbitals hybridize?
Allows some atoms to form more covalent bonds
Allows atoms to form bonds at different angles
Molecular geometry is therefore dependent upon the type of hybridization undertaken
Hybridization
Hybridization affects geometry
Likewise geometry affects hybridization
Key points – only electrons in p orbitals can resonate
(need orbital overlap)
Resonates
sp2 hybridization
Cannot resonate
sp3 hybridization
How to determine molecular structure
Determine number of σ bonds from an atom
Determine number of lone pair of electrons on an atom that are not involved in resonance
The addition of the above two numbers equals the number of hybridized orbitals required
Remaining atomic p orbitals are used to form multiple bonds
If a lone pair is involved in resonance it must reside in an atomic p orbital
to allow orbital overlap
Experimental Evidence for Resonance Affecting Hybridization and Geometry
Consider an amide group:
If the lone pair is resonating with the carbonyl then the N atom is sp2 hybridized,
If the lone pair is not resonating then the N atom is sp3 hybridized
Evidence that the N is resonating and is sp2 hybridized:
Infrared (IR) spectroscopy (chapter 12) – can measure energy required to cause a bond
vibration, energy of carbonyl stretch is low compared to other carbonyls not in resonance
Nuclear Magnetic Resonance (NMR – chapter 13) – can measure electronic environment around
a nucleus, observe two distinct environments for CH3 groups – thus cannot rotate freely
X-ray – can measure atomic positions, amide structures display nearly 120˚ bond angles for
C-N-C bond angles while this angle is close to 109.5˚ for C-N-C bond angle in amines
Acidity – can measure how easy it is to protonate a nitrogen in an amide versus a nitrogen in
a nonresonating amine, much harder to protonate amide lone pair due to resonance