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.