Lecture 9/29/2014 amazonaws com
Lecture 9/29/2014 Monday, September 29, 2014 9:25 AM
Quiz 2 Wed -focused on point groups and group theory (character tables)
Valence bond theory (VB) -stop @ electrons --> make bonds, work it out w/ electrons -localized orbital approach -start w/ electron Molecular orbital theory (MO) -electrons come last -put together -delocalied orbital approach -add electrons in the end (set up orbitals first, then put in electrons) VB doesn't explain molecules in their excited states, but MO does Starting w/ H2 (actually complicated if want to get it correct) --> VB theory for diatomic molecules each H has 1 electron (labeled 1 and 2)
the electrons are indistinguishable....each H needs 1 electron, but can swap them electron #1 of HA can be both with HA and with HB.....same for electron # 2 when you bring them together, they form a bond (bond length = 0.74 Angstroms apart) new wave function = phi +
above = linear combination of wavefunctions started w/ 2 wave functions (1 per H atom), but now ended with just 1 But need to have same # wave functions at beginning and end --> that's why we also have phi -
Inorganic Chemistry Page 1
must have the same # of atomic orbitals at the beginning as molecular orbitals @ end start w/ 2 wavefunctions --> end w/ 2 wavefunctions ALWAYS end up w/ the same # of wavefunctions that you started with the + wavefunction is the lowest in energy --> = bonding wavefunction ; stabilized the - wavefunction = higher in energy --> = antibonding wavefunction; destabilized when form a bond, that bonding wavefunction should be lower in energy than the original wavefunctions of the atom...or else there isn't a thermodynamic reason to make a bond
problem....this isn't really accurate missing 3 things electrons now feel nuclear charge from 2 nuclei
e- #1
e- #2
electron feels charge from both nuclei 1) Consider the effect of effective nuclear charge (Z eff); doesn't feel Zeff of 1, but rather
Inorganic Chemistry Page 2
above = fudge factor 1 but still not accurate -also have possibility that one H has both electrons and other has none --> have electrostatic attractions fudge factor 2) Both electrons can be on same nuclei (b/c 1s can technically have 2 electrons) ==> ionic contribution to the bonding
ionic contribution lambda tells to what extent you have ionic contribution
experimentally, we know that for H2, we have 6% ionic contribution
but still not accurate because 1s is spherical, have just as much chance as having electron density on side of bond as you do on opposite side of bond... how to get electron density to come just between the 2 atoms? z direction is the direction of the bond --> use the pz orbital because it points toward the bond 3) Pauling: if only the 1s orbitals are used, no increase in electron density between the 2 nuclei --> must incorporate the 2pz orbitals (just a tiny bit of those orbitals)
normalization factor
calulated: you have 99% 1s character and 1% p z character these above 3 are the biggest factors, but there still are a lot more other factors needed to account for in order to get accurate calculation
Inorganic Chemistry Page 3
Consider: HF The F atom uses its 2pz (has electron # 1) and H uses 1s (has electron #2) 1st approximation: --> going to end up w/ 2 wave functions (bonding and antibonding)
Add electron density between 2 nuclei for H, adding 2pz.....for F, using 2s (not 1s because = core electron) and 2p z
25% 2s character 75% 2pz character
There's some ionic contribution (have to have some or else HF wouldn't be an acid) But not that much contribution --> only little bit ionic contribution (50%)
new example: O2: lewis structure shows no unpaired electrons according to VB theory, O 2 = diamagnetic but in reality, O2 = paramagnetic... even the VB fudge factors don't explain it Hybridization (when mix orbitals or wavefunctions, they have to be close in energy) -generate hybrid orbitals by mixing atomic orbitals that = close in energy to obtain spatially oriented orbitals want this, for example methane, b/c want tetrahedral shape and p orbitals don't have tetrahedral shape by themselves VB provides a bonding picture which remains localized (looking at individual C-H bonds without looking at other bonds) coordination
hybrid
linear
sp
HC=CH
trigonal planar
sp2
BH3
tetrahedral
sp3
CH4 Inorganic Chemistry Page 4
tetrahedral
sp3
trigonal bipyramidal dsp3
CH4 PCl5
octahedral
d2sp3
SF6
Square planar
dsp2
PtCl4
Know this table: exam queston --> what is the hybridization of a given molecule sp hybridization s + p orbital --> linear geometry (not because you want a triple bond)
no matter what type of orbitals you have, 2 orbitals are always orthogonal
one sp bond goes one direction, other one goes in opposite direction
--> normaliation factor
must end up with phi 2 = 1 so that's why you need 1/sqrt[2]
Inorganic Chemistry Page 5
normalized and orthogonal wavefunctions 3 atomic orbitals --> 3 hybrids for sp2 --> all orthogonal and all normalized
sp3 ....not equal bonds, nor are they localized --> molecular orbital theory (more accurate than VB)
Valence bond theory: localized bonding scheme -start w/ electron and make bonds wherever possible Molecular orbital theory: delocalized bonding scheme -start w/ atomic orbital -add electrons last, always -still doing linear combination like we did for wavefunctions, but now doing linear combinations of atomic orbitals (LCAO) # molecular orbitals = # atomic orbitals used for derivation start w/ simplest molecule H2
--> same energy for the 2 1s' of the 2 H atoms
--> combine 2 atomic orbitals to form 2 molecular orbitals
bonding
Inorganic Chemistry Page 6
antibonding N = normalization factor
N-based on overlap integral: S
Drawing MO diagram
Inorganic Chemistry Page 7
Quiz 2 Wed -focused on point groups and group theory (character tables)
Valence bond theory (VB) -stop @ electrons --> make bonds, work it out w/ electrons -localized orbital approach -start w/ electron Molecular orbital theory (MO) -electrons come last -put together -delocalied orbital approach -add electrons in the end (set up orbitals first, then put in electrons) VB doesn't explain molecules in their excited states, but MO does Starting w/ H2 (actually complicated if want to get it correct) --> VB theory for diatomic molecules each H has 1 electron (labeled 1 and 2)
the electrons are indistinguishable....each H needs 1 electron, but can swap them electron #1 of HA can be both with HA and with HB.....same for electron # 2 when you bring them together, they form a bond (bond length = 0.74 Angstroms apart) new wave function = phi +
above = linear combination of wavefunctions started w/ 2 wave functions (1 per H atom), but now ended with just 1 But need to have same # wave functions at beginning and end --> that's why we also have phi -
Inorganic Chemistry Page 1
must have the same # of atomic orbitals at the beginning as molecular orbitals @ end start w/ 2 wavefunctions --> end w/ 2 wavefunctions ALWAYS end up w/ the same # of wavefunctions that you started with the + wavefunction is the lowest in energy --> = bonding wavefunction ; stabilized the - wavefunction = higher in energy --> = antibonding wavefunction; destabilized when form a bond, that bonding wavefunction should be lower in energy than the original wavefunctions of the atom...or else there isn't a thermodynamic reason to make a bond
problem....this isn't really accurate missing 3 things electrons now feel nuclear charge from 2 nuclei
e- #1
e- #2
electron feels charge from both nuclei 1) Consider the effect of effective nuclear charge (Z eff); doesn't feel Zeff of 1, but rather
Inorganic Chemistry Page 2
above = fudge factor 1 but still not accurate -also have possibility that one H has both electrons and other has none --> have electrostatic attractions fudge factor 2) Both electrons can be on same nuclei (b/c 1s can technically have 2 electrons) ==> ionic contribution to the bonding
ionic contribution lambda tells to what extent you have ionic contribution
experimentally, we know that for H2, we have 6% ionic contribution
but still not accurate because 1s is spherical, have just as much chance as having electron density on side of bond as you do on opposite side of bond... how to get electron density to come just between the 2 atoms? z direction is the direction of the bond --> use the pz orbital because it points toward the bond 3) Pauling: if only the 1s orbitals are used, no increase in electron density between the 2 nuclei --> must incorporate the 2pz orbitals (just a tiny bit of those orbitals)
normalization factor
calulated: you have 99% 1s character and 1% p z character these above 3 are the biggest factors, but there still are a lot more other factors needed to account for in order to get accurate calculation
Inorganic Chemistry Page 3
Consider: HF The F atom uses its 2pz (has electron # 1) and H uses 1s (has electron #2) 1st approximation: --> going to end up w/ 2 wave functions (bonding and antibonding)
Add electron density between 2 nuclei for H, adding 2pz.....for F, using 2s (not 1s because = core electron) and 2p z
25% 2s character 75% 2pz character
There's some ionic contribution (have to have some or else HF wouldn't be an acid) But not that much contribution --> only little bit ionic contribution (50%)
new example: O2: lewis structure shows no unpaired electrons according to VB theory, O 2 = diamagnetic but in reality, O2 = paramagnetic... even the VB fudge factors don't explain it Hybridization (when mix orbitals or wavefunctions, they have to be close in energy) -generate hybrid orbitals by mixing atomic orbitals that = close in energy to obtain spatially oriented orbitals want this, for example methane, b/c want tetrahedral shape and p orbitals don't have tetrahedral shape by themselves VB provides a bonding picture which remains localized (looking at individual C-H bonds without looking at other bonds) coordination
hybrid
linear
sp
HC=CH
trigonal planar
sp2
BH3
tetrahedral
sp3
CH4 Inorganic Chemistry Page 4
tetrahedral
sp3
trigonal bipyramidal dsp3
CH4 PCl5
octahedral
d2sp3
SF6
Square planar
dsp2
PtCl4
Know this table: exam queston --> what is the hybridization of a given molecule sp hybridization s + p orbital --> linear geometry (not because you want a triple bond)
no matter what type of orbitals you have, 2 orbitals are always orthogonal
one sp bond goes one direction, other one goes in opposite direction
--> normaliation factor
must end up with phi 2 = 1 so that's why you need 1/sqrt[2]
Inorganic Chemistry Page 5
normalized and orthogonal wavefunctions 3 atomic orbitals --> 3 hybrids for sp2 --> all orthogonal and all normalized
sp3 ....not equal bonds, nor are they localized --> molecular orbital theory (more accurate than VB)
Valence bond theory: localized bonding scheme -start w/ electron and make bonds wherever possible Molecular orbital theory: delocalized bonding scheme -start w/ atomic orbital -add electrons last, always -still doing linear combination like we did for wavefunctions, but now doing linear combinations of atomic orbitals (LCAO) # molecular orbitals = # atomic orbitals used for derivation start w/ simplest molecule H2
--> same energy for the 2 1s' of the 2 H atoms
--> combine 2 atomic orbitals to form 2 molecular orbitals
bonding
Inorganic Chemistry Page 6
antibonding N = normalization factor
N-based on overlap integral: S
Drawing MO diagram
Inorganic Chemistry Page 7
