2b_Orbitals_post

Sec. 3 - Orbitals Forsey

1

Quantum Mechanics (non mathematical approach)

• A mathematical description of bonding that takes into account the wave nature of electrons• A wave equation is solved to yield a series of wave functions for the atom• The wave functions psi () describe a series of states with different energies for each electron. Wave Equations are used to calculate:

The energy associated with the state of the electronThe probability of finding the electron in a particular state

Phase sign: Wave equations, when solved, may be positive, negative or zero

Wave equations can reinforce each other if they have the same sign or interfere with each other if they have different signs


2

Atomic Orbitals (AOs)

The physical reality of is that when squared (2) it gives the probability of finding an electron in a particular location in spacePlots of 2 in three dimensions generate the shape of s, p, d and f orbitalsWe will only explore s and p orbitals.

Orbital: a region in space where the probability of finding an electron is large

The typical representation of orbitals are those volumes which contain the electron 90-95% of the time.

The sign of the wave function does not indicate a greater or lesser probability of finding an electron in that location. The greater the number of nodes in an orbital the higher its energy

2s and 2p orbitals each have one node and are higher in energy than the 1s orbital which has no node.


3

Molecular Orbital Theory

The combination of atomic orbitals on different atoms forms molecular orbitals (M.O.’s), so that the electron belongs to the whole or fraction of the molecule. The most important property of atomic orbitals is their ability to combine and overlap to form complex wave functions.

Atomic orbitals are described as wave functions () and have a sign () associated with it. The combination of the wave function can produce destructive or constructive interference. This is called the linear combination of atomic orbitals (LCAO). The number of new orbitals generated in this way equals the number of orbitals that we started with

+ or + or

++ + ++ +

¯ ¯

node

The positive and negative signs represent the phase of the wave

constructive interference destructive interference


4

Consider two Hydrogen Atoms

1s 1s

* 1s antibonding

1s bonding- Sigma bond puts electron density between atoms to create bonding

- Cylindrically symmetrical orbital about internuclear axis

The number of atomic orbitals combined must

equal the number of molecular

orbitals formed

Nodal plane

Constructive combination (1s + 1s)

Destructive combination (1s – 1s)

-Reduction of electron density between nuclei

- Higher energy – less stable


5

Molecular Orbital Diagram

* energy 1s 1s atomic H – H atomic orbital molecular orbital H orbital H


6

Head on linear combination of p orbitals

+ -+ -2px 2px

Nodal plane

-bonding MO (2px + 2px)

* antibonding MO (2px - 2px)

In phase combination

Out of phase combination


7

+

- +

-

++- -

+

+

-

-

or

or

Sideways linear combination of p orbitalsNodal plane

Out of phase combination

In phase combination

-bonding MO (2px + 2px)

* antibonding MO (2px - 2px)


8

Shapes of Molecules

VSEPR : Valence shell electrons pair repulsion theoryHelps predict the spatial arrangement of atoms in polyatomic molecules or ions

C

H

HH

H

Tetrahedral

N

HH

H

O

H

H

Trigonal pyramidal

Bent

109.5°

107°

105°

C CH

H

H

H

B

F

F

F

Trigonal planar120°

C NH

H

H

C OH

H

BeH H

C CH H

C NH

C OH

Linear180°

But this does not tell us anything about what is

happening to the orbitals?

+


9

Describe the bonding and the orbitals of BeCl2

Electronic configuration of Be is 1s22s2

Electronic configuration of Cl is 1s22s22p63s23p5

Filled outer shell how can this bond?

VSEPR: Each set of valence shell electrons on the central atom are arranged so that the repulsion is as small as possible.

Be

BeCl2 should be linear – this is what we observe experimentally

1s2

2s2

2p

Could promote

one electron

Filled outer shell how can this

bond?

But this would produce dissimilar orbitals with non equivalent overlap between the s orbital of Be and the p orbital of chlorine and the p of Be and p of chlorine.Experimentally it is found that the bonds are identical. For the s and p orbitals to be identical or equivalent they must have changed shape or hybridized

BeBe

Cl Can participate in a bond

po

ten

tial

en

erg

y


10

sp hybridization

1s2

2s2

2p

The combination of one atomic 2s orbital with one atomic 2p orbital will produce two hybridized molecular orbitals called sp hybridized orbital

Be

Orbital hybridization is a mathematical combination of the 2s and 2p wave functions to obtain wave functions for the new orbitals

unhybridized p orbitals

sp hybridizedcan form two

bonds

Be ClCl

only one p orbitalof chlorine’s shown Cl Be Cl

Two -bonding MO (p + sp) (antibonding not shown)

Cl Be Cl

empty p orbitals not shownpo

ten

tial

en

erg

y

2p

2sp


11

Acetylene (HCCH) linear sp hybridized

C 1s22s22p2 4 valence electrons

1s2

2s2

2p2

C

H C C H

Each carbon has two sigma bonds

po

ten

tial

en

erg

y

1s2

2sp

2p

bond is the sideways linear combination of two p orbitals

180°

can form bond

can form bond

C

combine one s and one p orbital to form twosp2 hybridizedorbitals

What type of bond can the p orbitals form?


12

Acetylene (HCCH) (only bonding orbitals shown)

H HCCC+C H HCCC+C H HCCC+C H HCCC+C H HCCC+C H HCCC+C H HCCC+C +C +C

bonds

bonds


13

H

H

So why is there hybridization. Remember hybridization is only a model to describe what is seen in nature.

If bonding occurred with orbitals px and py the bond angle should be 90°

90° We do not observe 90° H-C-H bond

angles

The strength of the orbital is directly related to the overlap of the orbitals. p

orbitals provide inefficient overlap because the p orbital has equal electron

density on either side of the nucleus

overlap only occurs at one lobe

50% s and 50% pwith large and small lobes

stronger bond than a p orbital – more electron density between atoms

They are aimed 180° from each other

Be

H

H

H H

-

+

Minimized electron repulsion between

orbitals.

H

electron repulsion

constructive(2p + 2s)

destructive(2p - 2s)


14

Trigonal planar sp2 hybridization

BF3 B 1s22s22p1 (3 valence electrons)

1s2

2s2

2p2

B

po

ten

tial

en

erg

y

B

F F

F

120°

No 90° bond angles therefore no

unhybridized p orbitals involved in

bonding

3 bonds

The combination of one 2s orbital with two 2 p orbitals will produce three identical sp2 orbitals oriented 120° to each other. Each with 1/3 s

character and 2/3 p character.

3 fluorines will form 3 bond

3F

2p

2sp2

1s2

B

an electron from each of the fluorine's p orbital will bond with an electron in each of the borons sp2 hybridized orbitals

BFF

F

empty p orbital


15

Ethene sp2 hybridization C C

H

H

H

H

bond angles 120°

1s2

2s2

2p2 2p

2sp2

1s2

C

both carbons form 3 bonds and one bond

H

H

C

C

1s

1s

sp2

p

(sp2-sp2)

(sp2-s)

(sp2-s)

(p-p)

po

ten

tial

en

erg

y

C


16

Remember a bond is created form the sideways overlap of two unhybridized p orbital thus there is no rotation around a carbon – carbon double bond which accounts for cis-trans isomers

No net overlap of bonding orbitals which would break the bond


17

1s2

2s2

2p2

2sp3

1s2

Methane sp3 hybridization

C C

The combination of one 2s orbital with three 2p orbitals

will produce four identical sp3

hybridized orbitals oriented 109.5° to each other. Each with

1/4 s character and 3/4 p character.

po

ten

tial

en

erg

y


18

1s2

2s2

2p2

2sp3

1s2

forms 4 bonds

C C

po

ten

tial

en

erg

y

2p

2sp2

1s2

forms 3 bonds

forms 1 bond

1s2

2sp

2p

C C

H

H

H

H

H C C H

bond angles 120°

bond angles 180°

C

H

HH

H

bond angles 109.5°

Ground state sp3 sp2 sp

forms 2 bonds

forms 2 bonds

Summary so far

C C


19

Draw the energy diagram for the nitrogen in ammonia (NH3)

1s2

2s2

2p2

2sp3

1s2

N N

N

HH

Helectronic configuration of N 1s22s22p3

What is the approximate shape of ammonia?

What is the hybridization of the nitrogen?

po

ten

tial

en

erg

y

Tetrahedral (trigonal pyramidal) because there are four “things” around the central atom. 3 hydrogens and a nonbonding lone pair

It has to be sp3 because there are no unhybridized orbitals involved in sigma bonding (otherwise it could not be tetrahedral)


20

Draw the energy diagram for the oxygen in water (H2O)

1s2

2s2

2p2

2sp3

1s2

O O

electronic configuration of O 1s22s22p4

What is the approximate shape of water?

What is the hybridization of the oxygen atom?

O

H

H

po

ten

tial

en

erg

y

Tetrahedral (Bent) because there are four “things” around the central atom, 2 hydrogens and a 2 nonbonding lone pairs

It has to be sp3 because there are no unhybridized orbitals involved in sigma bonding (otherwise it could not be tetrahedral)


21

What is the hybridization of the nitrogen in Pyridine?

N

First put lone pair on the nitrogen

How many atoms and lone pairs are around the nitrogen

What geometry does the nitrogen have?

What is the hybridization?To form a bond how many unhybridized p orbitals does the nitrogen atom have?

Draw the orbital energy level diagram of the hybridized nitrogen atom

1s2

2s2

2p2

2sp2

1s2

N N

po

ten

tial

en

erg

y

N

2p


22

What is the hybridization of the oxygen in acetone?

H3CC

O

CH3

First put lone pair on the oxygen

How many atoms and lone pairs are around the oxygen

What geometry does the nitrogen have?

What is the hybridization?To form one bond how many unhybridized p orbitals does the oxygen atom have?

Draw the orbital energy level diagram of the hybridized oxygen atom

1s2

2s2

2p2

2sp2

1s2

O O

po

ten

tial

en

erg

y

2p C OH3C

H3C

We really don’t know if the oxygen is sp2 hybridized because you can not measure the bond angles between the lone pairs or the lone pair oxygen carbon bond angle. But VSEPR would indicate that the oxygen is sp2 and it forms a pi bond to an sp2 carbon


23

Summary

C

H

HH

H

Tetrahedral

Trigonal pyramidal

Bent

109.5°

107°

105°

C CH

H

H

H

B

F

F

F

Trigonal planar120°

N

HH

H

O

H

H

C NH

H

H

C OH

H

BeH H

C CH H

C NH

C OH

Linear180°

sp3 sp2 sp

+

one s and one p atomic orbital form two sp

hybridized molecular orbitals

one s and two p atomic orbital form three sp2 hybridized

molecular orbitals one s and three p atomic orbital form four sp3 hybridized

molecular orbitals

Always think of the bond angles when determining the hybridization of an atom

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