Lecture 6. Molecular orbitals of heteronuclear diatomic molecules.
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Transcript of Lecture 6. Molecular orbitals of heteronuclear diatomic molecules.
Lecture 6
Molecular orbitals of
heteronuclear diatomic molecules
The general principle of molecular orbital theoryInteractions of orbitals (or groups of orbitals) occur when
the interacting orbitals overlap. the energy of the orbitals must be similarthe interatomic distance must be short enough but not too short
A bonding interaction takes place when:
regions of the same sign overlapAn antibonding interaction takes place when:
regions of opposite sign overlap
Combinations of two s orbitals in a homonuclear molecule (e.g. H2)
Antibonding
Bonding
In this case, the energies of the A.O.’s are identical
More generally:ca(1sa)cb(1sb)]
n A.O.’s n M.O.’s
The same principle is applied to heteronuclear diatomic molecules
But the atomic energy levels are lower for the heavier atom
Orbital potential energies (see also Table 5-1 in p. 134 of textbook)
Average energies for all electrons in the same level, e.g., 3p(use to estimate which orbitals may interact)
The molecular orbitals of carbon monoxide
CO
cc(C)co(O)]
2s 2p
C -19.43 -10.66
O -32.38 -15.85
E(eV)
Each MO receives unequal contributions from C and O (cc ≠ co)
Group theory is used in building molecular orbitals
CO C°v (use C2v)
z
s pz
px py
A1
A1
A1
A1
B1 B2
B1 B2
“C-like MO”
“O-like MO”
Frontier orbitals
“C-like MO’s”
“O-like MO’s”
mixing
Larger homo lobe on C
Bond order 3
A related example: HF
H F C°v (use C2v)
s (A1) 2p(A1, B1, B2)
H -13.61 (1s)
F -40.17 (2s) -18.65
No s-s int.(E > 13 eV)
Non-bonding(no E match)
Non-bonding(no symmetry match)
Extreme cases: ionic compounds (LiF)
Li transfers e- to F
Forming Li+ and F-
A1
A1
Molecular orbitals for larger molecules
1. Determine point group of molecule (if linear, use D2h and C2v instead of D∞h or C∞v)
2. Assign x, y, z coordinates (z axis is higher rotation axis; if non-linear y axis in outer atoms point to central atom)
3. Find the characters of the representation for the combination of 2s orbitals on the outer atoms, then for px, py, pz. (as for vibrations, orbitals that change position = 0, orbitals that do not change =1; and orbitals that remain in the same position but change sign = -1)
4. Find the reducible representations (they correspond to the symmetry of group orbitals, also called Symmetry Adapted Linear Combinations SALC’s of the orbitals).
5. Find AO’s in central atom with the same symmetry
6. Combine AO’s from central atom with those group orbitals of same symmetry and similar E
F-H-F-
D∞h, use D2h
1st consider combinations of2s and 2p orbitals from F atoms
8 GROUP ORBITALSDEFINED
Group orbitals can now be treated as atomic orbitalsand combined with appropriate AO’s from H
1s(H) is Ag so it matches two group orbitals 1 and 3
Both interactions are symmetry allowed, how about energies?
-13.6 eV
-40.2 eV
-13.6 eV
Good E matchStrong interaction
Poor E matchweak interaction
Bonding e
Non-bonding e
Lewis structureF-H-F-
implies 4 e around H !
MO analysisdefines 3c-2e bond
(2e delocalized over 3 atoms)
CO2
D∞h, use D2h
(O O) group orbitals the same as for F F
But C has more AO’s to be considered than H !
CO2
D∞h, use D2h
No match
Carbon orbitals
Ag-Ag interactions B1u-B1u interactions
All four are symmetry allowed
Primary Ag interaction
Primary B1u interaction
Bonding
Bonding
Non-bonding
Non-bonding
4 bondsAll occupied MO’s are 3c-2e
LUMO
HOMO
The frontier orbitals of CO2
Molecular orbitals for larger molecules: H2O
1. Determine point group of molecule: C2v
2. Assign x, y, z coordinates (z axis is higher rotation axis; if non-linear y axis in outer atoms point to central atom - not necessary for H since s orbitals are non-directional)
3. Find the characters of the representation for the combination of 2s orbitals on the outer atoms, then for px, py, pz. (as for vibrations, orbitals that change position = 0, orbitals that do not change =1; and orbitals that remain in the same position but change sign = -1)
4. Find the irreducible representations (they correspond to the symmetry of group orbitals,also called Symmetry Adapted Linear Combinations SALC’s of the orbitals).
5. Find AO’s in central atom with the same symmetry
6. Combine AO’s from central atom with those group orbitals of same symmetry and similar E
For H H group orbitals
v’ two orbitals interchanged
E two orbitals unchanged
C2 two orbitals interchanged
2 20 0
v two orbitals unchanged
No match
pz
bonding
slightlybonding
antibonding
px
bonding
antibonding
py
non-bonding
3 10
Find reducible representation for 3H’s
Irreducible representations:
Molecular orbitals for NH3
pz
bonding
Slightlybonding
anti-bonding
bonding
anti-bonding
LUMO
HOMO
Projection OperatorAlgorithm of creating an object forming a basis for an irreducible rep from an arbitrary function.
^^
RRh
lP
jj
jj
Where the projection operator sums the results of using the symmetry operations multiplied by characters of the irreducible rep. j indicates the desired symmetry.
lj is the dimension of the irreducible rep. h the order order of the group.
1sA 1sB
z
y
Starting with the 1sA create a function of A1 sym
¼(E1sA + C21sA + v1sA + v’1sA) = ¼ (1sA + 1sB+ 1sB + 1sA)
Consider the bonding in NF3
N
F
F F
N
F
F F
N
F
F F
N
F
F F
A 3 0 -1
A B C D
B 3 0 1
C 3 0 1
D 3 0 1
A = A2 + E
B = C = D = A1 + E
1
23
Now construct SALC
^^
RRh
lP
jj
jj
A = A2 + E
PA2(p1) = 1/6 (p1 + p2 + p3 + (-1)(-p)1 + (-1)(-1p3) + (-1)(-p2)
N
F
FF C3N
F
FF
N
F
FF C3'
N
F
FF
N
F
FF vN
F
FF
p1-p1
N
F
FF
N
F
FFv'
p1
-p3
N
F
FF
N
F
FFv''p1 -p2
No AO on N is A2
N
F
FF
E:
PA2(p1) = 2/6 (2p1 - p2 - p3) = E1
Apply projection operator to p1
But since it is two dimensional, E, there should be another SALC
N
F
FF
PA2(p2) = 2/6 (2p2 - p3 - p1) = E’
But E1 and E’ should be orthogonal want sum of products of coefficients to be zero.
E2 = E’ + k E1.= (-1 +k*2) p1 + (2 + k(-1)) p2 + (-1 + k(-1)) = 0
Have to choose k such that they are orthogonal.
0 = (2/6)2 (2(-1 + k*2) -1 (2 + k(-1)) -1 (-1 + k(-1))
k = ½
E2 = 2/6 (3/2 p2 - 3/2 p3)N
F
FF
N
F
FF
N
F
FF
N
F
FF
N
F
FF
The geometriesof electron domains
Molecular shapes:When we discussed
VSEPR theory
Can this be describedin terms of MO’s?
Hybrid orbitals
s + p = 2 sp hybrids (linear)
s + 2p = 3 sp2 hybridstrigonal planar
s + 3p = 4 sp3 hybridstetrahedral
s + 3p + d = 5 dsp3 hybridstrigonal bipyramidal
s + 3p + 2d = 6 d2sp3 hybridsoctahedral