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

+

-

nucleus

distance

electrondensity

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 HH

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