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Valence bond theory Molecular orbital theorysfcheng/inchem94/Chapter 3 bonding (Continued).… · Slide 3 of 60 Atomic Orbital Overlap • Valence Bond (VB) Theory states that a covalent

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Text of Valence bond theory Molecular orbital theorysfcheng/inchem94/Chapter 3 bonding (Continued).… ·...

  • Slide 1 of 60

    Chapter 3 (continued)

    Covalent Bonding: Orbitals

    Valence bond theory

    Molecular orbital theory

  • Slide 2 of 60

    Bonding In H2

    21

    2

    21

    2

    21

    221 zyx

    +

    +

    =

    E=

    abbaba RrrrrrU

    111111

    221112

    +=

    ( )222111212122

    ,,,,,)(8

    zyxzyxUm

    h++=

  • Slide 3 of 60

    Atomic Orbital Overlap

    Valence Bond (VB) Theory states that a covalent bond is formed by the pairing of two electrons with opposing spins in the region of overlap of atomic orbitals between two atoms. This overlap region has a high electron charge density.

    The valence bond theory attempts to find the best approximation of optimal orbital overlap for all the bonds in a molecule.

  • Slide 4 of 60

    0.7433.78+ effective nuclear charge

    0.744.747Empirical

    0.7494.02

    0.8693.14

    0.90.25

    R (? )E (eV)wavefunction

    )2()1( ba =

    )1()2()2()1( baba +=

    )1()2()2()1( baba +=

    )]1()2()2()1([

    )1()2()2()1(

    bbaa

    baba

    +++=

    Theoretical treatment

    ionic

    covalent

  • Slide 5 of 60

    Bonding In H2S

  • Slide 6 of 60

    Several Important Points

    Most of the electrons in a molecule remain in the same orbital locations that they occupied in the separated atoms.

    Bonding electrons are localized in the region of atomic orbital overlap.

    For orbitals with directional lobes, maximum overlap occurs when atomic orbitals overlap end to end.

    The molecular geometry depends on the geometric relationships among the atomic orbitals of the central atom that participate in bonding.

  • Slide 7 of 60

    sp3 Hybridization Scheme

    Hybridization

    109.50

  • Slide 8 of 60

    Bonding in Methane

  • Slide 9 of 60

    Bonding in Ammonia

  • Slide 10 of 60

    The sp2 Hybridization Scheme

  • Slide 11 of 60

    The sp Hybridization Scheme

  • Slide 12 of 60

    Hybrid Orbitals Involvingd Subshells

    This hybridization allows for expanded valence shellcompounds.

    A 3s electron can be promoted to a 3d subshell which gives rise to a set of five sp3d hybrid orbitals. These molecules have a trigonal bipyramidal molecular geometry.

    One 3s electron and one 3p electron can be promoted to two 3d subshells which gives rise to a set of six sp3d2hybrid orbitals. These molecules have an octahedralmolecular geometry.

  • Slide 13 of 60

    The sp3d and sp3d2 Hybrid Orbitals

    sp3d

  • Slide 14 of 60

    Hybrid Orbitals and TheirGeometric Orientations

  • Slide 15 of 60

    Hybrid Orbitals andMultiple Covalent Bonds

    Covalent bonds formed by the end-to-end overlap of orbitals, regardless of orbital type, are called sigma () bonds. All single bonds are sigma bonds.No nodal plane along inter-nuclear axis

    A bond formed by parallel, or side-by-side, orbital overlap is called a pi () bond.One nodal plane along inter-nuclear axis

    sp2-hybrid

  • Slide 16 of 60

    Descriptions of Ethylene

    Rotational barrier for double bond

  • Slide 17 of 60

    Valence Bond Theory of the Bonding in Acetylene

    sp-hybrid

  • Slide 18 of 60

    Characteristics ofMolecular Orbitals

    Molecular orbitals (MOs) are mathematical equations that describe the regions in a molecule where there is a high probability of finding electrons.

    Bonding molecular orbitals (, ) are at a lower energy level than the separate atomic orbitals and have a high electron probability, or electron charge density.

    Antibonding molecular orbitals (*, *) are at a higher energy level than the separate atomic orbitalsand places a high electron probability away from the region between the bonded atoms.

  • Slide 19 of 60

    The 1s Orbital

    (r,,) = R(r) 0,0(,)

    0,0(,) = 1/21/2

  • Slide 20 of 60

    + +

    Constructive Interference

    ba +=

    2

  • Slide 21 of 60

    +

    -

    Destructive Interference

    ba =

    2

  • Slide 22 of 60

    Molecular Orbitals and Bondingin the H2 Molecule

    ++

    + -

    )2()1()2()1()2()1()2()1(

    )]2()2()][1()1([

    )2()1(

    baabbbaa

    baba

    total

    +++=++=

    =

    ionic covalent

  • Slide 23 of 60

    Bond order = ( # of bonding electrons - # of anti-bonding electrons )

    Electron configuration of H2 : (1s)2

    B.O. of H2 = (2 - 0) = 1

    Bond energy = 435 kJ/mol

    Bond length = 74 pm

    ab

    ab

    SH

    E

    =1

    ab

    ab

    SH

    E+

    =1

  • Slide 24 of 60

    H2-H2+

    He2

  • Slide 25 of 60

    --0(1s)2(1s*)2He2

    108238(1s)2(1s*)1H2-

    106269(1s)1H2+

    744351(1s)2H2

    Bond length (pm)

    Bond energy (kJ/mol)

    B.O.Electron configuration

    Species

  • Slide 26 of 60

    Lewis Structure

    Hetero-nuclear Diatomic Molecule

  • Slide 27 of 60

  • Slide 28 of 60

    Electron configuration of Li2 : KK(1s)2B.O. of Li2 = (2 - 0) = 1

    Bond length = 267 pm

    2nd Period Homo-nuclear Diatomic Molecules

  • Slide 29 of 60

    Molecular Orbitals Formed byCombining 2p Atomic Orbitals

    ++ +

    ____

    _ + +__

    1 node inter-nuclear axis

    + +_ _

    +_

    1 node along inter-nuclear axis

    _ +

    +__

  • Slide 30 of 60

    Diamagnetic Paramagnetic

  • Slide 31 of 60

    Molecular Spectroscopy

    UV-Vis

    IRMicrowave

  • Slide 32 of 60

    KE = h? - BE

    The Photoelectric Effect

  • Slide 33 of 60

    X-ray Photoelectron Spectroscopy (XPS) - using soft x-ray (200-2000 eV) radiation to

    examine core-levels.

    Ultraviolet Photoelectron Spectroscopy (UPS) - using vacuum UV (10-45 eV) radiation to examine

    valence levels.

    Photoelectron spectroscopy- a single photon in/ electron out process

  • Slide 34 of 60

    Light sources: a Helium lamp emitting at 21.2 eV (He I radiation)or 40.8 eV (He II radiation)

    Ultraviolet Photoelectron Spectroscopy(UPS)

    KoopmansTheorem

    For a closed-shell molecule, the ionization energy of an electron in a particular orbital is approximately equal to the orbital energy.

    I.E. = Eorbital = B.E.

    such as H2 ? H2+ + e-

    .... ,....

    EKhvEIorEIhvEK=

    =

  • Slide 35 of 60

    Vibrational Fine Structure in PES

  • Slide 36 of 60

    Vibrational energy states

    )v'(....

    )21

    v()21

    v()v( 2

    ++=

    ++=

    vib

    eee

    EEIEKhv

    xhvhvE

    where Evib+(v) = E+(v = v) - E+(v = 0) is the extra (i.e., energy above v = 0) vibrational energy of the ion.

    Lines corresponding to different vibrational energy levels of H2+ , v = 0, 1, 2, 3, . . .,

  • Slide 37 of 60

    Figure 4.4: He(I) UPS spectrum of HCl gas.

    1. Loss of a bonding electron decreases the bond order, increasing the bond length in the resulting cation compared to the parent molecule.

    2. Loss of a nonbonding electron has no effect on bond order or bond length.

    3. Loss of an antibonding electron increases the bond order, decreasing the bond length of the cation compared to the parent molecule.

  • Slide 38 of 60

  • Slide 39 of 60

    N = N+ Jwhere N+ and Jrepresent the rotational quantum numbers of the ion and the neutral, respectively.

  • Slide 40 of 60

    Vibrational frequencies from UPS spectra of CO and N2

    1706CO+ (B)

    1549CO+ (A)

    2200 ? weakly antibondingCO+ (X)2157CO (cm-1)molecule

    1936N2+ (A)

    2331N2

  • Slide 41 of 60

    Paramagnetic

  • Slide 42 of 60

    Paramagnetism of Oxygen

  • Slide 43 of 60

    Molecular Orbitals of Homo-nuclear Diatomic Molecules of 2nd Period

  • Slide 44 of 60

    Bonding in Benzene

    The -Bonding Framework

    sp2

  • Slide 45 of 60

    The -Molecular Orbitals of Benzene

    E

    +

    ++ _

    _

    node

    node

    -M.O. of benzene

  • Slide 46 of 60

    3 nodes

    2 nodes

  • Slide 47 of 60

  • Slide 48 of 60

    Conjugated Double Bonds

    E

    -M.O.

    Bonding

    Anti-bonding

  • Slide 49 of 60

    Band Theory

    This is a quantum-mechanical treatment of bonding in metals.

    The spacing between energy levels is so minute in metals that the levels essentially merge into a band.

    When the band is occupied by valence electrons, it is called a valence band.

    A partially filled or low lying empty band of energy levels, which is required for electrical conductivity, is a conduction band.

    Band theory provides a good explanation of metallic luster and metallic colors.

  • Slide 50 of 60

    bonding

    Anti-bonding

  • Slide 51 of 60

    The 2s Band in Lithium Metal

    Bonding

    Anti-bonding

    e- e-Valence band

    Conduction band

  • Slide 52 of 60

    Band Overlap in Magnesium

    Valence band

    Conduction band

  • Slide 53 of 60

    Band Structure of Insulatorsand Semiconductors

  • Slide 54 of 60

    Density of states in (a) metal, (b) semimetal (e.g. graphite).

    (a) (b)

    Density of state= dn/dE

    n = number of states

  • Slide 55 of 60

    Conductivity of Graphite

    insulator

    e- -conductor

  • Slide 56 of 60

    Fermi distribution (a) at T= 0, and (b) at T> 0. The population decays exponentially at energies well above the Fermi level.

    Population,1

    1/)( +

    = kTEeP

    Fermi level - the highest occupied orbital at T= 0

    (a) (b)

    where, = chemical potential

    When E= , P= 1/2

  • Slide 57 of 60

    Fermi distribution at T> 0 for (a) Intrinsic semiconductor, (b)Fermi distribution and the band gap

    (a) (b)population

  • Slide 58 of 60

    Extrinsic semiconductor: (a) n-type, e.g. P doped Si(b) p-type, e.g. Ga doped Si.

  • Slide 59 of 60

    Conductivity () & Energy Gap (Eg)

    kT

    Ee

    g

    kTE g

    2ln ln 0

    2/0

    =

    =

  • Slide 60 of 60