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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
Sec. 3 - Orbitals Forsey
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.
Sec. 3 - Orbitals Forsey
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
Sec. 3 - Orbitals Forsey
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
Sec. 3 - Orbitals Forsey
5
Molecular Orbital Diagram
* energy 1s 1s atomic H – H atomic orbital molecular orbital H orbital H
Sec. 3 - Orbitals Forsey
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
Sec. 3 - Orbitals Forsey
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)
Sec. 3 - Orbitals Forsey
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?
+
Sec. 3 - Orbitals Forsey
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
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tial
en
erg
y
Sec. 3 - Orbitals Forsey
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
Sec. 3 - Orbitals Forsey
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
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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?
Sec. 3 - Orbitals Forsey
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
Sec. 3 - Orbitals Forsey
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)
Sec. 3 - Orbitals Forsey
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
Sec. 3 - Orbitals Forsey
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
Sec. 3 - Orbitals Forsey
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
Sec. 3 - Orbitals Forsey
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.
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Sec. 3 - Orbitals Forsey
18
1s2
2s2
2p2
2sp3
1s2
forms 4 bonds
C C
po
ten
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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
Sec. 3 - Orbitals Forsey
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
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en
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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)
Sec. 3 - Orbitals Forsey
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)
Sec. 3 - Orbitals Forsey
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
Sec. 3 - Orbitals Forsey
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
Sec. 3 - Orbitals Forsey
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