Upload
sydnee-bennett
View
26
Download
0
Embed Size (px)
DESCRIPTION
Lecture 13 February 2, 2011 Reactions O2, Woodward-Hoffmann. Nature of the Chemical Bond with applications to catalysis, materials science, nanotechnology, surface science, bioinorganic chemistry, and energy. William A. Goddard, III, [email protected] 316 Beckman Institute, x3093 - PowerPoint PPT Presentation
Citation preview
1© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Nature of the Chemical Bond with applications to catalysis, materials
science, nanotechnology, surface science, bioinorganic chemistry, and energy
Lecture 13 February 2, 2011
Reactions O2, Woodward-Hoffmann
William A. Goddard, III, [email protected] Beckman Institute, x3093
Charles and Mary Ferkel Professor of Chemistry, Materials Science, and Applied Physics,
California Institute of Technology
Teaching Assistants: Wei-Guang Liu <[email protected]>Caitlin Scott <[email protected]>
2© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Last time
3© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
The homonuclear diatomic correlation diagram
Mulliken knew the ordering of the atomic orbitals and considered how combinations of the atomic orbitals would change as the nuclei were pushed together to eventually form a united atom.
4© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Separated atom limitSeparated atoms notationMO notation
5© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Separated atoms limit
Note that in each case we
get one bonding combination (no
new nodal plane) and one
antibonding combination (new nodal
plane, red lines)
6© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
At large R 2p better bonding than 2p
In earlier lectures we considered the strength of one-electron bonds where we found that
Since the overlap of p orbitals is obviously higher than pWe expect that
bonding
antibonding
7© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Summarizing united atom limit
Note for 3d, the splitting is
3d < 3d < 3d
Same argument as for 2p
8© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Correlation diagram for Carbon row homonuclear diatomics
United atom limit
separated atom limit
F2
O2
O2+
N2C2
N2+
9© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Homonuclear Diatomics Molecules – the valence bond view
Consider bonding two Ne atoms together
Clearly there will be repulsive interactions as the doubly occupied orbitals on the left and right overlap, leading to repulsive interactions and no bonding. In fact as we will consider later, there is a weak attractive interaction scaling as -C/R6, that leads to a bond of 0.05 kcal/mol, but we ignore such weak interactions here
The symmetry of this state is 1g+
10© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Halogen dimers
Next consider bonding of two F atoms. Each F has 3 possible configurations (It is a 2P state) leading to 9 possible configurations for F2. Of these only one leads to strong chemical binding
This also leads to a 1g+ state.
Spectroscopic properties are listed below .
Note that the bond energy decreases for Cl2 to Br2 to I2, but increases from F2 to Cl2. we will get back to this later.
11© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Di-oxygen or O2 molecule
Next consider bonding of two O atoms. Each O has 3 possible configurations (It is a 3P state) leading to 9 possible configurations for O2. Of these one leads to directly to a double bond
This suggests that the ground state of O2 is a singlet state.
At first this seemed plausible, but by the late 1920’s Mulliken established experimentally that the ground state of O2 is actually a triplet state, which he had predicted on the basis of molecular orbitial (MO) theory.
This was a fatal blow to VB theory, bringing MO theory to the fore, so we will consider next how Mulliken was able to figure this out in the 1920’s without the aid of computers.
12© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
O2 MO configuration
2
4
2
2
2
2
For O2 the ordering of the MOs
Is unambiguous
2
(1g)2
Next consider states of (1g)2
13© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
States arising from ()2
Adding spin we get
()2
Ground state 0.0
0.982
1.636
O2
Energy (eV)
MO theory explains the triplet ground state and low lying singlets
14© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
States based on ()2
Have 4 spatial combinations
Which we combine aswhere x and y denote
x and y
φ1, φ2 denote the angle about the axis
and F is independent of φ1, φ2 Rotating about the axis by an angle , these states transform as
skip
15© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Using the correleation diagram
In order to use the correlation diagram to predict the states of diatomic molecules, we need to have some idea of what effective R to use (actually it is the effective overlap with large R small S and small R large S).
Mulliken’s original analysis [Rev. Mod. Phys. 4, 48 (1932)] was roughly as follows.
1. N2 was known to be nondegenerate and very strongly bound with no low-lying excited states 2
4
22
2
2
4
2
4
2
2
Choices for N2
16© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
N2 MO configurations
2
4
22
2
2
4
2
4
2
2This is compatible with several orderings of the MOs
Largest R
Smallest R
17© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
N2+
But the 13 electron molecules BeF, BO, CO+, CN, N2+
Have a ground state with 2S symmetry and a low lying 2S sate.
In between these two 2 states is a 2 state with spin orbital splitting that implies a 3 configuration
This implies that
Is the ground configuration for N2 and that the low lying states of N2
+ are
This agrees with the observed spectra
18© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Correlation diagram for Carbon row homonuclear diatomics
United atom limit
separated atom limit
F2
O2
O2+
N2C2
N2+
19© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
1s and 2s cases
BA
BA
20© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
AntiBond
BO1
2
2.5
3
2.5
0
1
2
21© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
More about O2
22© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
First excited configuration
(1g)2 Ground configuration
(1g)3(1u)3 excited configuration
(1g)3(1u)3
u
u-
u+
u
u+
u-
Strong transitions (dipole allowed) S=0 (spin)g u or u but - -
Only dipole allowed transition from 3g
-
skip
23© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
The states of O2 molecule
Moss and Goddard JCP 63, 3623 (1975)
(u)4(g)2
(u)3(g)3
24© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Role of O2 in atmosphere
Moss and Goddard JCP 63, 3623 (1975)
StrongGet 3P + 1D O atom
WeakGet 3P + 3P O atom
25© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Implications
UV light > 6 eV (< 1240/6 = 207 nm) can dissociate O2 by excitation of 3u
+ which dissociates to two O atom in 3P state
UV light > ~7.2 eV can dissociate O2 by excitation of 3u-
which dissociates to one O atom in 3P state and one in 1D (maximum is at ~8.6 eV, Schumann-Runge bands)
Net result is dissociation of O2 into O atoms
26© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Regions of the atmosphere
Temperature (K)
altit
ude
(km
)
tropopause
stratopause
102030
100
50
troposphere
stratosphere
mesosphere
O2 + h O + O
O + h O+ + e-
O + O2 O3
O3 + h O + O2
300200
Heated from earth
Heats from light
Heats from light
27© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
ionosphere
night
D layer day
Heaviside-Kennelly layerReflects radio waves to allow long distance communications
28© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
nightglow
At night the O atoms created during the day can recombine to form O2
The fastest rates are into the Herzberg states, u
u-u
+
Get emission at ~2.4 eV, 500 nm
Called the nightglow (~ 90 km)
29© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Problem with MO description: dissociation3g
- state: [(gx)(gy)+ (gy) (gx)]
As R∞ (gx) (xL – xR) and (gy) (yL – yR)
Get equal amounts of {xL yL and xR yR} and {xLyR and xR yL}
Ionic: [(O-)(O+)+ (O+)(O-)] covalent: (O)(O)
But actually it should dissociate to neutral atoms
30© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Back to valence bond (and GVB)
Four ways to combine two 3P states of O to form a bond
Open shell Closed shell
Looks good because make p bond as in ethene, BUT have overlapping doubly occupied orbitals antibonding
bad
Each doubly occupied orbital overlaps a singly occupied orbital, not so repulsive
31© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Analysis of open shell configurations
Each can be used to form a singlet state or a triplet state, e.g.
Singlet: A{(xL)2(yR)2[(yL)(xR) + (xR)(yL)]()}
Triplet: A{(xL)2(yR)2[(yL)(xR) - (xR)(yL)]()} and
Since (yL) and (xR) are orthogonal, high spin is best (no chance of two electrons at same point) as usual
32© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
VB description of O2
+
+
+
-
Must have resonance of two VB configurations
33© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Back to valence bond (and GVB)
Four ways to combine two 3P states of O to form a bond
Open shell Closed shell
Looks good because make p bond as in ethene, BUT have overlapping doubly occupied orbitals antibonding
bad
Each doubly occupied orbital overlaps a singly occupied orbital, not so repulsive
34© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
New material
35© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Bond energies
5.2 eV
36© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Bond H to O2
Bring H toward px on Left O
Overlap doubly occupied (xL)2
thus repulsive
Overlap singly occupied (xL)2
thus bonding
2A” state
Get HOO bond angle ~ 90º
S=1/2 (doublet)
Antisymmetric with respect to plane: A” irreducible representation (Cs group)
Bond weakened by ~ 51 kcal/mol due to loss in O2 resonance
37© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Bond 2nd H to HO2 to form hydrogen peroxide
Bring H toward py on right O
Expect new HOO bond angle ~ 90ºExpect HOOH dihedral ~90ºIndeed H-S-S-H:HSS = 91.3º and HSSH= 90.6º
But H-H overlap leads to steric effects for HOOH, net result:
HOO opens up to ~94.8º
HOOH angle 111.5º
trans structure, 180º only 1.2 kcal/mol higher
38© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Rotational barriers
HOOH
1.19 kcal/mol Trans barrier
7.6 kcal/mol Cis barrier
HSSH:
5.02 kcal/mol trans barrier
7.54 kcal/mol cis barrier
39© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Compare bond energies (kcal/mol)
O2 3g- 119.0
HO-O
HO-OH 51.1
68.2 H-O2 51.5
HOO-H 85.217.1
67.9 50.8
Interpretation: OO bond = 51.1 kcal/molOO bond = 119.0-51.1=67.9 kcal/mol (resonance)Bonding H to O2 loses 50.8 kcal/mol of resonanceBonding H to HO2 loses the other 17.1 kcal/mol of resonanceIntrinsic H-O bond is 85.2 + 17.1 =102.3 compare CH3O-H: HO bond is 105.1
40© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Add material for O2 + C2H4 (sing and trip)
41© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Bond O2 to O to form ozone
Goddard et al Acc. Chem. Res. 6, 368 (1973)
Require two OO bonds get
States with 4, 5, and 6 pelectrons
Ground state is 4 case
Get S=0,1 but 0 better
42© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
sigma GVB orbitals ozone
43© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Pi GVB orbitals ozone
Some delocalization of central Op pair
Increased overlap between L and R Op due to central pair
44© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Bond O2 to O to form ozone
New O-O bond, 51 kcal/mol
lose O-O resonance, 51 kcal/mol
Gain O-O resonance,<17 kcal/mol,assume 2/3
New singlet coupling of L and R orbitalsTotal splitting ~ 1 eV = 23 kcal/mol, assume ½ stabilizes singlet and ½ destabilizes triplet
Expect bond for singlet of 11 + 12 = 23 kcal/mol, exper = 25
Expect triplet state to be bound by 11-12 = -1 kcal/mol, probably between +2 and -2
45© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Alternative view of bonding in ozoneStart here with 1-3 diradical
Transfer electron from central doubly occupied ppair to the R singly occupied p.
Now can form a bond the L singly occupied p.
Hard to estimate strength of bond
46© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Ring ozone
Form 3 OO sigma bonds, but p pairs overlap Analog: cis HOOH bond is 51.1-7.6=43.5 kcal/mol. Get total bond of 3*43.5=130.5 which is 11.5 more stable than O2.Correct for strain due to 60º bond angles = 26 kcal/mol from cyclopropane. Expect ring O3 to be unstable with respect to O2 + O by ~14 kcal/mol, But if formed it might be rather stable with respect various chemical reactions.
Ab Initio Theoretical Results on the Stability of Cyclic Ozone L. B. Harding and W. A. Goddard III J. Chem. Phys. 67, 2377 (1977) CN 5599
47© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Photochemical smog
High temperature combustion: N2 + O2 2NO
Thus Auto exhaust NO
2 NO + O2 2 NO2
NO2 + h NO + O
O + O2 + M O3 + M
O3 + NO NO2 + O2
Get equilibrium
Add in hydrocarbons
NO2 + O2 + HC + h Me(C=O)-OO-NO2
peroxyacetylnitrate
48© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
More on N2
The elements N, P, As, Sb, and Bi all have an (ns)2(np)3 configuration, leading to a triple bond
Adding in the (ns) pairs, we show the wavefunction as
This is the VB description of N2, P2, etc. The optimum orbitals of N2 are shown on the next slide.
The MO description of N2 is
Which we can draw as
49© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
GVB orbitals of N2
Re=1.10A
R=1.50A
R=2.10A
50© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Hartree Fock Orbitals N2
51© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
52© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
2
2
2
2
2
2
4
4
2
The configuration for C2
4
1
1
3
1
53© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
2
2
2
2
2
2
4
4
2
The configuration for C2
4
1
1
3
1
From 1930-1962 the 3u was thought to be the ground state
Now 1g+ is ground state
Si2 has this configuration
54© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Ground state of C2
MO configuration
Have two strong bonds,
but sigma system looks just like Be2 which leads to a bond of ~ 1 kcal/mol
The lobe pair on each Be is activated to form the sigma bond. The net result is no net contribution to bond from sigma electrons. It is as if we started with HCCH and cut off the Hs
55© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
C2, Si2,
56© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
57© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Low-lying states of C2
58© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
59© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
60© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Include B2, Be2, Li2, Li2+
61© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
Re-examine the energy for H2+
For H2+ the VB wavefunctions were
Φg = (хL + хR) and
Φu = (хL - хR) (ignoring normalization)
where H = h + 1/R. This leads to the energy for the bonding state
eg = <L+R|H|L+R>/ <L+R|L+R> = 2 <L|H|L+R>/ 2<L|L+R>
= (hLL + hLR)/(1+S) + 1/R
And for the antibonding state
eu = (hLL - hLR)/(1-S) + 1/R
We find it convenient to rewrite aseg = (hLL + 1/R) + /(1+S)
eu = (hLL + 1/R) - /(1-S)
where = (hLR - ShLL) includes the terms that dominate the bonding and antibonding character of these 2 states
62© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
The VB interference or resonance energy for H2+
The VB wavefunctions for H2+
Φg = (хL + хR) and Φu = (хL - хR) lead tog = (hLL + 1/R) + /(1+S) ≡ ecl + Eg
x
u = (hLL + 1/R) - /(1-S) ≡ ecl + Eux
where = (hLR - ShLL) is the VB interference or resonance energy and
cl = (hLL + 1/R) is the classical energy
As shown here the dominates the bonding and antibonding of these states
63© copyright 2011 William A. Goddard III, all rights reserved Ch120a-Goddard-L13
stop