bonding - Bryn Mawr College

This is so
WRONG!
-13.6 eV
-18.6 eV
-40 eV
How is amount of mixing determined:
l = - ∫ Y2HY1 dt
E2 - E1
energy of perturbation
energy separation
How is DE determined:
(DE is change in E after mixing)
DE =
S
( ∫ Y2HY1 dt)2
E2 - E1
(energy of perturbation)2
energy separation
3s
Na
I
Br (-12.5 eV)
Cl (-13.7 eV)
F-
F (-18.6 eV)
-10.6 eV
-15.8 eV
-19 eV
-32 eV
s (anti- bonding)
p (anti- bonding)
s (non-bonding)
p (bonding)
s (bonding)
s (non-bonding)
What’s better and worse here?
SPARTAN STUDENT MECHANICS PROGRAM: PC/x86
Run type: Geometry optimization
(Analytical Gradient)
(MM/Amide correction used)
Model: RHF/PM3
Number of shells: 4
3 S shells
1 P shells
Number of basis functions: 6
Number of electrons: 8
Use of molecular symmetry enabled
Molecular charge: 0
Spin multiplicity: 1
Point Group = CNV Order = 2 Nsymop = 4
This system has 2 degrees of freedom
Initial Hessian option
Hessian from MMFF94 calculation used.
Max. Max.
Neg.
Cycle
Energy Grad. Dist.
Eigen
1 -221.3325 0.06046 0.00229
2 -223.5289 0.00133 0.00002
3 -223.5364 0.00072 0.00000
4 -223.5370 0.00003 0.00000
Heat of Formation:
-223.537 kJ/mol
Energy Due to Solvation
Solvation Energy -34.383
Semi-Empirical Program CPU Time :
Semi-Empirical Program Wall Time:
Use of molecular symmetry enabled
1.53
2.10
5.0.0
Cartesian Coordinates (Angstroms)
Atom
X
Y
Z
--------- ------------- ------------------------1 O O1
0.0000000 0.0000000 0.3740089
2 H H1
0.0000000 0.7678384 -0.1870045
3 H H2
0.0000000 -0.7678384 -0.1870045
Point Group = CNV Order = 2 Nsymop = 4
Closed-Shell Molecular Orbital Coefficients
MO #
1
2
3
4
5
Eigenvalues: -1.35331 -0.64607 -0.53372 -0.45262 0.14921
(ev):
-36.82537 -17.5805 -14.5237 -12.3165 4.06018
1 O1
2 O1
3 O1
4 O1
5 H1
6 H2
S1
PX
PY
PZ
S
S
A1
-0.87791
0.00000
0.00000
0.10489
-0.33035
-0.33035
B1
0.00000
0.00000
-0.76801
0.00000
-0.45286
0.45286
A1
-0.33309
0.00000
0.00000
-0.83472
0.31008
0.31008
MO #
6
Eigenvalues: 0.19592
(ev):
5.33138
1 O1
2 O1
3 O1
4 O1
5 H1
6 H2
S1
PX
PY
PZ
S
S
B1
0.00000
0.00000
-0.64044
0.00000
0.54306
-0.54306
Atomic Charges:
Electrostatic Mulliken Natural
1 O1
: -0.709 -0.359 -0.358
2 H1
: +0.354 +0.179 +0.179
3 H2
: +0.354 +0.179 +0.179
Bond Orders
1 O1
H1
2 O1
H2
Mulliken
: 0.968
: 0.968
B2
0.00000
-1.00000
0.00000
0.00000
0.00000
0.00000
A1
-0.34397
0.00000
0.00000
0.54060
0.54288
0.54288
anti-bonding
anti-bonding
non-bonding
non-bonding
Two
“lone pairs”
but not equivalent!
bonding
Two
“O-H bonds”
bonding
but not equivalent!
BH3
Closed-Shell Molecular Orbital Coefficients
MO #
1
2
3
4
5
Eigenvalues: -0.83413 -0.44511 -0.44511 0.0563 0.08456
(ev):
-22.69773 -12.1121 -12.112 1.53242 2.30087
1 B1
2 B1
3 B1
4 B1
5 H1
6 H2
7 H3
S1
PX
PY
PZ
S
S
S
MO #
Eigenvalues:
(ev):
1 B1
2 B1
3 B1
4 B1
5 H1
6 H2
7 H3
S1
PX
PY
PZ
S
S
S
A1'
-0.76782
0.00000
0.00000
0.00000
-0.36989
-0.36989
-0.36989
E'
0.00000
-0.58025
0.19790
0.00000
-0.61052
0.48559
0.12493
E'
0.00000
0.19790
0.58025
0.00000
0.20822
0.42462
-0.63284
6
7
0.18581 0.18581
5.05614 5.05614
E'
0.00000
-0.13038
0.77919
0.00000
0.08261
-0.46887
0.38626
E'
0.00000
0.77919
0.13038
0.00000
-0.49371
0.17531
0.31840
A2"
0.00000
0.00000
0.00000
-1.00000
0.00000
0.00000
0.00000
A1'
0.64066
0.00000
0.00000
0.00000
-0.44330
-0.44330
-0.44330
Mainly
B 2p
lcao’s
Note p bonds!
Mainly
B 2s-F 2p
lcao’s
Mainly
F 2s lcao’s
Benzene
How does
the
bonding
concepts
we’ve
seen here
relate to
what you
might
have seen
before, in
Organic?
z
y
eg
3d t2g
x
Now, can we
tackle bigger
3p t
molecules,
like
3s a one with
six bonds?
1u
1g
eg
t1u
a1g
.F
Oh
S valence orbitals (9)
F donor (sp) orbitals (6)
Instead of;
. F
2p
Because harder to draw
z
a1
g
y
t1u
eg
3d t2g
eg
t2g
x
3p t1u
3s a1g
eg
t1u
a1g
eg
.F
Oh
S valence orbitals (9)
t1u
F donor (sp) orbitals (6)
a1g
SF6
Instead of;
. F
2p
Because harder to draw
a1
g
t1u
3d
eg
eg
t2g
t2g
3p t1u
3s a1
g
eg
t1u
a1
eg
g
Bonding MO’s
8 e- gives 4 bonds!
Oh
t1u
a1
g
SF6
. F
a1
g
t1u
Two views:
A) 4 bonds distributed over
six S-F pairs
B) 4 bonds (covalent ) +
2 “bonds” ionic (S6+-F-)
3p t1u
3s a1
g
eg
t1u
a1
eg
g
t1u
a1
g
SF6
Getting Larger:
Probably need to use a
computer….
Mo(CO)6
Molybdenum carbonyl
MO # , Energy, eV
MO 24
MO 22
MO 13
MO 1
MO 50 - LUMO
MO 49 - HOMO
MO 44
MO 35
MO 39
Sometimes MOs are
hard to interpret
LUMO
HOMO
L a.o.’s
M a.o.’s
ML4 - D4h
3s
Na
I
Br (-12.5 eV)
Cl (-13.7 eV)
F-
F (-18.6 eV)
4p t1u
4s a1
g
eg
3d
t2g
eg
t1u
a1
3rd row M,
Valence
Atomic
orbitals
g
Oh
ML6
:L
6s-donors
s ONLY,
Like H or NH3
Symmetry Adapted Group Orbitals for 6 s-donors
t1u
a1
g
eg
4p t1u
4s a1
g
eg
3d
t2g
t2g
eg
t1u
a1
3rd row M,
Valence
Atomic
orbitals
g
eg
Oh
t1u
a1
g
ML6
:L
6s-donors
s ONLY,
Like H or NH3
t1u
a1
M-L s anti-bonding MO’s
g
eg
4p t1u
4s a1
g
eg
3d
t2g
3rd row M,
Valence
Atomic
orbitals
M-L s bonding MO’s
t2g
eg
t1u
a1
eg
g
Oh
t1u
a1
g
ML6
:L
6s-donors
s ONLY,
Like H or NH3
t1u
a1
M-L s anti-bonding MO’s
g
eg
4p t1u
What is Do?
4s a1
g
eg
3d
t2g
3rd row M,
Valence
Atomic
orbitals
M-L s bonding MO’s
t2g
eg
t1u
a1
eg
g
Oh
t1u
a1
g
ML6
:L
6s-donors
s ONLY,
Like H or NH3
Symmetry Adapted Group Orbitals for 6 p-donors
t1u
a1
M-L s anti-bonding MO’s
g
eg
4p t1u
4s a1
g
eg
3d
t2g
3rd row M,
Valence
Atomic
orbitals
M-L s bonding MO’s
t2g
eg
t1u
a1
g
t2g
t2u
t1g
t1u
12 L
p orbitals
eg
t1u
a1
g
Oh
:L
6s
p-donors
Like Cl-
..
L
t1u
a1
M-L s anti-bonding MO’s
g
eg
4p t1u
4s a1
Effect on Do?
t2g
g
eg
3d
t2g
3rd row M,
Valence
Atomic
orbitals
M-L s bonding MO’s
t2g
eg
t1u
a1
g
t2g
t2u
t1g
t1u
12 L
p orbitals
eg
t1u
a1
g
Oh
:L
6s
p-donors
Like Cl-
t1u
a1
M-L s anti-bonding MO’s
g
eg
4p t1u
CO
t2g
4s a1
t2g
t2u
t1g
t1u
12 L
p orbitals
g
eg
3d
t2g
t2g
3rd row M,
Valence
Atomic
orbitals
M-L s bonding MO’s
t2g
t2u
t1g
t1u
12 L
p orbitals
eg
t1u
a1
eg
g
Oh
t1u
:L
6s
p-acceptors
Like CO, CN-
a1
g
ML6
eg
eg
eg
t2g
Do
Do
t2g
t2g
eg
eg
t2g
t2g
3d
eg
t2g
t2g
3d
t2g
t2g
Case 1.
L is p innocent
(sigma donor only)
Do
Case 2.
L is p base
(sigma donor and
p donor)
3d
t2g
12 L
p
orbitals
Case 3.
L is p acid
(sigma donor and
p acceptor)
12 L
p
orbitals
Getting Larger:
Probably need to use a
computer….
Mo(CO)6
Molybdenum carbonyl
MO # , Energy, eV
MO 24
MO 22
MO 13
MO 1
MO 50 - LUMO
MO 49 - HOMO
MO 44
MO 35
MO 39
Sometimes MOs are
hard to interpret
LUMO
HOMO
L a.o.’s
M a.o.’s
ML4 - D4h
dx2-y2
dz2
dyz
dxz
dxy
L a.o.’s
M a.o.’s
ML4 - D4h