Transcript No Slide Title

Structure and hybridization
- The Fock-equation yields the electronic structure of a molecule
for a given geometry. The canonical MOs do not reflect the
molecule’s geometry.
- Hybridization is an alternative way to obtain the electronic
structure of a molecule, which does show a clear relation with
the geometry of the molecule.
Hybridization is the mixing of atomic
orbitals with different l-quantum
numbers on the same atom.
Structure and hybridization (continued)
- Normal atomic orbitals (s, p, d, …) have a well-defined center;
i.e., an atomic nucleus.
- Normal atomic orbitals may have a well-defined orientation;
e.g., p orbitals are oriented along an axis of the reference
frame.
- Normal atomic orbitals do not have a direction; pz points
as much in the +z as in the -z direction.
- Normal atomic orbitals are not well suited to form MOs
that correspond to bonds between two atoms.
- Combining atomic orbitals with different l-quantum numbers
produces hybrids that do have a specific direction.
Structure and hybridization (continued)
s orbital

p orbital

sp hybrid
Structure and hybridization (continued)
CH4 revisited:
sp  2s  2 p x  2 p y  2 p z
(1,1,1)
sp  2s  2 p x  2 p y  2 p z
(1,1,1)
(1,1,1)
3
A
3
B
sp  2s  2 p x  2 p y  2 p z
3
C
sp  2s  2 p x  2 p y  2 p z
3
D
(1,1,1)
These hydrids point in these directions.
They are sp3-hybrids.
X   sp   1sX
2 2 2 2
Slater-determinant:  A B C D
MOs:
3
X
Structure and hybridization (continued)
Molecules with tetrahedral angles: C2H6
3
X,i
sp
sp3-hybrid on C
indication of C atom
direction of bonds involving C
X,i   sp   1sX.i , X  A, B, C
3
X,i
bonding orbitals for C-H bond
DD  sp  sp
3
D,1
Slater-det.:
3
D, 2
bonding orbital for C-C bond
      
2
2
2
2
A,1 B,1 C,1 A, 2
2
B, 2
2
C, 2
2
DD
Structure and hybridization (continued)
Molecules with tetrahedral angles: NH3
sp X3
sp3-hybrid on N
direction of bonds involving N
X   sp   1sX , X  A, B, C
3
X
bonding orbitals for N-H bonds
Slater-det.:
   sp
2
A
2
B
2
C

3 2
D
lone-pair orbital
Structure and hybridization (continued)
Molecules with 120o angles: BH3
spA2  2s  2  2 p x
1
1
sp  2s 
2  2 px 
2  2 py
2
2
1
1
2
spC  2s 
2  2 px 
2  2 py
2
2
2
B
MOs:
X   sp   1sX
Slater-determinant:
2
X
 
2
A
2
B
2
C
These are sp2-hybrids.
Structure and hybridization (continued)
Molecules with 120o angles: C2H4
2
X,i
sp
sp2-hybrid on C
indication of C atom
direction of bonds involving C
X,i   sp   1sX.i , X  A, B C-H bond
2
2
bonding orbital for C-C bond
CC  spC,1  spC,2
s bond
DD  2 pz ,1  2 pz,2 bonding orbital for C-C bond
2
X,i
p bond
Slater-det.:
     
2
2
2
A,1 B,1 A, 2
2
B, 2
2
CC
2
DD
Structure and hybridization (continued)
Molecules with 180o angles: BeH2
spA  2s  2 pz
spB  2s  2 pz
These are sp-hybrids.
MOs:
 X   spX   1sX
Slater-determinant:
 
2
A
2
B
Structure and hybridization (continued)
Molecules with 180o angles: C2H2
spX,i
sp-hybrid on C
indication of C atom
direction of bonds involving C
A,i   spA,i   1si C-H bond
C-C bond (s bond)
BB  spB,1  spB,2
CC  2 px,1  2 px,2 C-C bond (p bond)
DD  2 py,1  2 py,2 C-C bond (p bond)
2
2
2
2
2
Slater-det.: A,1A, 2BBCCDD