Post on 23-Jan-2016
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Chapter 14
Covalent Bonding: Orbitals
SP3 Hybridization of methane
The 2s orbital and the three 2p orbitals are
combined to form four equivalent orbitals,
called sp3 hybrids.
)(2
1
)(2
1
)(2
1
)(2
1
4
3
2
1
zyx
zyx
zyx
zyx
ppps
ppps
ppps
ppps
SP2 Hybridization of ethylene
One 2s and two 2p orbitals are used to form these hybrid orbitals.
Use px and py to hybridize.
SP Hybridization of CO2
SP Hybridization of CO2
SP Hybridization of CO2
SP Hybridization of CO2
SP Hybridization of CO2
dsp3 Hybridization
dsp3 Hybridization
d2sp3 Hybridization
The combination of hydrogen 1s atomic orbitals to form MOs
sg1
eu: ungerad
s σ*u1
The rules of molecular orbital theory
1. The electron probability of both MOs is centered along the line passing through the two nuclei.2. The MOs are available for occupation by
electrons. The 1s atomic orbital of the hydrogen atoms no longer exist.
3. If the two electrons occupy the lower energy MO, this situation favors molecule formation. (Bonding)
The rules of molecular orbital theory
4. If the two electrons were forced to occupy the higher energy MO, the separated state would be favored. (Antibonding)
5. The electrons have the greatest probability of being between the nuclei on bonding MO.
6. Bonding MO:σ1s Antibonding MO:σ1s*
7. Electrons configuration 1σ1s2
12 1s)(σon for Honfiguratielectron c g
2*22 )1(1s)( son for Heonfiguratielectron c
1*2
2 )1(1s)( son for Heonfiguratielectron c
Molecular Orbitals of Li2 (1s22s1)
22*21212
2
)2s()1(1s)( 2121 sssss
on for Lionfiguratielectron c
Bond Order
Larger bond order indicates the
greater bond strength.
2
electrons gantibondin ofnumber -electrons bonding ofnumber order bond
Molecular Orbitals of B2 (1s22s22p1)
Molecular Orbitals of B2
22*22*2
122122
2
)2p()2()2s()1(1s)(
221221
ss
psspss
on for Bonfiguratielectron c
Paramagnetism and Diamagnetism
Paramagnetism causes the substance to be attracted toward the including magnetic.
Diamagnetism causes the substance to be repelled from the including magnetic.
Paramagnetism is associated with unpaired electrons, and diamagnetism is associated with paired electrons.
When liquid oxygen is poured into the space between the poles of a strong magnet, it remains there until it boils away.
Bond order
=?
The Correctly Molecular Orbitals of B2
The σ2p orbital is changed by p-s mixing, the energies of π2p and σ2p orbitals are reverse.
The p-s mixing also changes the energies σ2p and σ2p
* such that they are no longer equally spaced relative to the energy of the free 2s orbital.
The Order in MOs Filling
pPP
PσPπPπ
ssss
222
)222(
2211
*1
*1
*
11
**
Electron Characterization in MO
Degenerate orbitals: electrons in an atomic subshell are orbitals at identical energy levels.
Multiplicity: M=2S+1
M=1 singlet M=2 doublet M=3 triplet
NO
NO+ and CN-
Molecular Orbital of HF
The resonance structures for O3 and NO3
-
The benzene molecule consists of a ring of six carbon atoms with one hydrogen atom bound to ach carbon; all atoms are in the same plane.
The s bonding system in the benzene molecule
The MO system in benzene is formed by combining the six p orbitals
The p orbitals used to form the bonding system in the NO3
- ion
The MO Diagram for System
highest energy bonding pi-orbital (HOMO)
lowest energy antibonding pi-orbital (LUMO)
Molecular Spectroscopy
Etotal=Etrans+Eelec+Evib+Erot+Enucl
Eelec: electronic transitions (UV, X-ray)
Evib: vibrational transitions (Infrared)
Erot: rotational transitions (Microwave)
Enucl: nucleus spin (nuclear magnetic
resonance) or (MRI: magnetic resonance
imaging)
UV/VIS
Vacuum UV or Far UV (λ<190 nm )
The molecular orbital diagram for the ground state of NO+
Selection Rule: does not change M=2S+1 during electron transition
The molecular structure of beta-carotene
Vibrational Spectroscopy
...), , , (vn
v
) (nhvE
kmm
mm μ
μ
kv
)Rk(RF
l energy vvibrationa
ator.nic oscillas a harmo
ed n be treat (bond) cafrom Rlacements Small disp
v
vvv
e
e
3210number quantum al vibrationthe
vibration theoffrequency sticcharacteri the
1Δn2
1
constant) force ,mass (reduced2
1
0
0
21
21
The potential curve for a diatomic molecule
Morse energy curve for a diatomic molecule.
Selection Rule of Infrared Spectrum
Molecule must have change in dipole moment due to vibration or rotation to absorb IR radiation.
Homonuclear diatomic molecules will have no IR spectrum.
Molecule dipole moment interacts with IR photon electric field.
Absorption causes increase in vibration amplitude/rotation frequency.
Molecules with permanent dipole moments (µ) are IR active
Types of Molecular VibrationsStretch- change in bond length
symmetric stretching
asymmetric stretching
Types of Molecular Vibrations Bend- change in bond angle
scissoring
wagging
rocking
twisting/torsion
Normal Modes of Vibration
Linear molecule of N atoms: normal modes = 3N - 5
Nonlinear molecule of N atoms: normal modes = 3N - 6
IR spectrum
The three fundamental vibrations for sulfur dioxide
Rotational Spectroscopy
nd lengthaverage boR
mm
mmssreduced maμ
μRI
e molaculertia of thent of ineI: the mom
....), , , number (Jal quantumJ:rotation
J)J(JI
E
e
e
J
21
21
2
2
3210
1 12
Selection Rule: A molecule must have a permanent dipole moment
Rotational Spectroscopy
http://en.wikipedia.org/wiki/Rovibrational_coupling
(cm-1)
Abs
e
R BranchP Branch
l=-5
l=-4
l=-3
l=-2
l=-1 l=1
l=2
l=3
l=4
l=5
2B 4B 6B 8B
Vibrational-Rotational Spectrum
Calculate Bond Length of Heteronuclear Diatomic Molecule
21
21
2
2
2
8
1 )1(12
mm
mmI
hB
μRI
JJhBJ)J(JI
E
e
J
轉動慣量
縮減質量
Nuclear Magnetic Resonance Spectroscopy
The rules for determining the net spin of a nucleus1. If the number of neutrons and the number of protons
are both even, then the nucleus has NO spin.
2. If the number of neutrons plus the number of protons is odd, then the nucleus has a half-integer spin (i.e. 1/2, 3/2, 5/2)
3. If the number of neutrons and the number of protons are both odd, then the nucleus has an integer spin (i.e. 1, 2, 3)
Nuclei Unpaired Protons
Unpaired Neutrons
Net Spin
1H 1 0 1/2 2H 1 1 1 31P 1 0 1/2
23Na 1 2 3/2 14N 1 1 1 13C 0 1 1/2 19F 1 0 1/2
A nucleus of spin I will have 2I + 1 possible orientations.
分裂能階數目
Larmor Precession
In the absence of an external magnetic field, these orientations are of equal energy.
If a magnetic field is applied, then the energy levels split. Each level is given a magnetic quantum number, m.
Nucleus in a Magnetic Field
The lower energy level will contain slightly more nuclei than the higher level.
It is possible to excite these nuclei into the higher level with electromagnetic radiation.
The frequency of radiation needed is determined by the difference in energy between the energy levels.
Calculating transition energy
2
hBE
: magnetogyric ratio and is a fundamental nuclear constant which has a different value for every nucleus.B: the strength of the magnetic field at the nucleus ∆E↑B↑
分裂能階大小與磁場強弱成正比
The Absorption of Radiation by a Nucleus in a Magnetic Field
If energy is absorbed by the nucleus, then the angle of precession, q, will change.
For a nucleus of spin 1/2
, absorption of radiation "flips" the magnetic moment so that it opposes the applied field.
Chemical Shift
The magnetic field at the nucleus is not equal to the applied magnetic field; electrons around the nucleus shield it from the applied field.
The difference between the applied magnetic field and the field at the nucleus is termed the nuclear shielding.
Electrons in s-orbitals Spherical symmetry and circ
ulate in the applied field A magnetic field which oppo
ses the applied field. Applied field strength must b
e increased for the nucleus to absorb at its transition frequency.
This upfield shift is also termed diamagnetic shift.
Electrons in p-orbitals
No spherical symmetry. They produce comparatively large magnetic
fields at the nucleus, which give a low field shift.
This "deshielding" is termed paramagnetic shift.
Proton Chemical Shift Ranges
= ( - ref) ×106 / ref
tetramethylsilane, Si(CH3)4, (TMS)
Spin - Spin coupling
The protons on neighboring carbons will generate magnetic fields whose magnetic moments will interact with the magnetic moment of the external magnetic field.
This results in the splitting of the NMR signal.
NMR of Ethanol
-CH2-
-CH3
Methyl peak splitting into a triplet
the ratio of areas 1:2:1
Methylene peak splitting into a quartet
the ratio of areas 1:3:3:1
Configuration Peak Ratios
A 1
AB 1:1
AB2 1:2:1
AB3 1:3:3:1
AB4 1:4:6:4:1
AB5 1:5:10:10:5:1
AB6 1:6:15:20:15:6:1
Pascal's triangle
The molecular structure of bromoethane
The NMR spectrum of CH3CH2Br (bromoethane) with TMS reference
tetramethylsilane, Si(CH3)4
The molecule (2-butanone)
(B) (C)
(D)
(A)
(B)
(A)
(C)
A technician speaks to a patient before heis moved intot eh cavity of a magnetic resonance imaging (MRI).
A colored Magnetic Resonance Imaging (MRI) scan through a human head, showing a healthy brain in side view.