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Chapter 10 Bonding and Molecular Structure: Orbital Hybridization and Molecular Orbitals

Chapter 10 Bonding and Molecular Structure: Orbital Hybridization and Molecular Orbitals. Atoms are bonded together by electrons, but what is a bond?. A bond forms when two atomic orbitals overlap to make a molecule more stable than when there was no overlap. Bonds.

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Chapter 10 Bonding and Molecular Structure: Orbital Hybridization and Molecular Orbitals

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  1. Chapter 10 Bonding and Molecular Structure: Orbital Hybridization and Molecular Orbitals Atoms are bonded together by electrons, but what is a bond? A bond forms when two atomic orbitals overlap to make a molecule more stable than when there was no overlap

  2. Bonds Wavefunction of the atoms combine to form wavefunctions for the molecule The atomic orbitals constructively interfere to form molecular orbitals 1s 1s(1) 1s(2) Molecule Atom 2 Nucleus 1 Nucleus 2 Atom 1

  3. Simple Molecular Orbitals The simplest atomic orbitals (AO’s) are the 1s orbitals, which are the ground state of hydrogen and helium H forms bonds: H—H He does not form bonds How do we explain this? The exact wavefunction of one-electron molecules such as H2+ and He23+, are known. These exact wavefunctions can be approximated using linear combinations of atomic orbitals, LCAO In LCAO, each AO is combined both in-phase and out-of-phase, corresponding to constructive and destructive interference. Constructive interference - Bonding orbital Destrstructive interference - Anti bonding orbital Has a node between atoms

  4. H2 He2     Energy Levels of LCAO-molecular orbitals MO’s orbitals energy increases with # of nodes The MO that forms when two 1s orbitals constructive interference have lower energy than those that destructively interfere.    MO energy levels are depicted using a correlation diagram which relates the energies of the MO’s relative to their constituent AO’s   • Adding e’s to H2 a bond is formed (BO = 1) • Adding e’sto He2 no bond is lost (filling both the bonding and the antibonding MO leaves the “molecule” in a higher energy state (BO = 0), than free atoms)     

  5. LCAO for the 2nd Period Elements The “dilithium” molecule can exist in very low-pressure vapours, whereas the normal state of lithium is the metallic solid Lewis theory predict Li—Li, with only two bonding electrons in its valence The net overlap of the 1s levels cancels out The net overlap of the 2s wave functions leads to a single bond, the BO = 1 The Li—Li distance in Li2 is 159 pm; at this distance the degree of overlap of the 1s orbitals of Li is negligibly small The assumption of “core” orbitals is thus valid The next molecule to consider is Be2, and like He2 it should not exist. Ignore “core” orbitals in LCAO theory

  6. LCAO from atomic p orbitals: σ-MO’s For B2, with 6 valence e-, we need additional orbitals, made from next lowest atomic orbitals 2p Here we must distinguish the orientation of the orbitals w.r.t. each other Bond axis: z-axis for simple molecules, consider pz orbital p orbitals have a node at the nucleus, In-phase combination between two pz orbitals will have two nodes, at the nuclei but not between them. - bonding out-of-phase MO will have an additional node, between the nuclei - antibonding Since antibonding orbital has more nodes it is higher in energy Both MO’s are defined as σ= cylindrical

  7. LCAO from atomic p orbitals: π-MO’s Two orbitals remain at right angles to the bond axis on each atom, the px and the py Side-on overlap which leads to a new kind of bond, the π-bond The diagram shows the case for p x It is called a π-orbital because from end-on it resembles an atomic p orbital π orbitals contain a nodal plane throughout the molecule The out-of-phase MO also has an additional node between the atoms, making it an antibonding MO The pz orbital were higher in energy than px and py. Therefore, s2pz orbitals are higher in energy (less stable) than the two p2p orbitals which are equal in energy

  8. Molecular Orbitals Atomic orbitals will combine when: 1) Geometry makes it possible Have the right shape 2) Are close in energy. The degree of mixing depends on energy difference 3) If they have the right phase Same phase – constructive interference Opposite phase – destructive interference Bond Order = [(# bonding e’s) – (# anti-bonding e’s)]/2

  9. 2pz 2pz X X Correlation Diagram for the orbitals in the second period The energy of the MO reflect that of the AO,s when atoms are aligned along the bond axis Pz is higher than Px and Py Similarly s2p is higher than p2p Bonding behavior of the second period diatomic molecules can be predicted by filling the M.O. The electron configurations of the diatomic molecules are analogous to the atom Electrons fill in the order of MO energies from lowest to highest (s1s)2(s1s*)2(s2s)2(s2s*)2(p2p)4(s2p)2(p2p*)4(s2p*)2

  10. The complete energy level diagram All the orbitals in the ground-state 2nd period elements have been considered Bonding between these elements can be predicted by adding electrons to this orbital correlation energy level diagram      Li2 – bond order 1  Be2 - fills the σ2s* orbital, BO = 0     B2 - partially fills π2p levels, BO = 1 -2 e’s parallel i.e. paramagnetic  C2 - fills π2p,- BO = 2 - diamagnetic  N2 - fills σ2p- BO = 3 - diamangetic O2- partially fills π2p* levels, BO = 2 - paramagnetic F2 -fills π2p* levels - BO = 1 Ne2 – fills σ2p*, BO = O, does not exist

  11. Electron Configurations of diatomic molecules You should be able to: • Write the MO electron configurations of each of these molecules • Write their Lewis Diagrams • Compare the predictions of Bond Order from the Lewis and the LCAO-MO descriptions • Compare the predictions of diamagnetism or paramagnetism from the LCAO-MO descriptions

  12. Method of hybrid orbitals For molecules with more than 2 atoms, the LCAO method is computationally complex - done on a computer The method of hybrid orbitals or sometimes valence bond theory Simplified molecular orbital method that retains the notion of a “chemical bond” rather than just a “net bond order” . It is derived from molecular shape and used to define common bonding situations. Ex) BeH2 with a central Be atom BeH2 is linear by the VSEPR method, having two equal bonds There are not two identical atomic orbitals on Be that allow us to define two equivalent bonds These are obtained by combining the atomic 2s and 2p orbitals and hybridize them into two new hybrid atomic orbitals Overlap of these new hybrid orbitals and the H 1s orbitals leads to the desired bonding orbitals

  13. BeH2 and sp hybridization       Two hybrid atomic orbitals are made to fit the shape of the molecule, in this case linear, using atomic orbitals of an excited state Be atom! Unused AO are left behind as unhybridized atomic orbitals The energy of the hybrid atomic orbitals are intermediate between those of the original constituent AO’s The hybrid orbitals combine with other orbitals, atomic or hybrid, creating both bonding and anti-bonding molecular orbitals, which are localized molecular orbitals

  14. BH3 and sp2 hybridization          BH3 is trigonal planar with three equal B—H bonds To get this shape the 2s with two 2p AO’s to generate three equivalent hybrid atomic orbitals Combination with the H 1s leads to bonding and anti-bonding molecular orbitals, which are localized molecular orbitalspointing to the corners of a triangle

  15. CH4 and sp3 hybridization             CH4 is tetrahedral with 4 equal C-H bonds To get this shape, we need to combine all the n=2 AO’s to generate four equivalent hybrid atomic orbitals In combination with the H 1s leads to bonding and anti-bonding molecular orbitals, which are localized molecular orbitalspointing to the corners of a tetrahedron

  16. Hybrid AO’s and VSEPR A hybridization scheme exists for each member VSEPR shape families Hybrid AO’s can be used both for bond pairs and for lone pairs • The hybridizations are: • Shape Family Hybridization No. of equivalent bonds • Linear sp 2 • Trigonal planar sp2 3 • Tetrahedral sp3 4 • Trigonal bipyramidal sp3d 5 • Octahedral sp3d2 6 The hybrid atomic orbitals for the Trigonal bipyramidal and octahedral shapes will not be discussed further For the first three shape families, the localized hybrid atomic orbitals description and a fully delocalized molecular orbital description are essentially equivalent This method is used throughout most organic chemistry courses

  17. H2O and sp3 hybridization O 2 H 2 LP’s       sp hybrids 3   s s 1 1   2 C-H H2O is bent and belongs to the tetrahedral family with 2 BP and 2 LP The s and p orbitals combine sp3 hybrids The 2 sp3 orbitals combine with 2 1s orbital to form 2 C-H bonds The 6 e’s from O, singly occupy 2 sp3 orbitals and doubly occupy the remaining 2 as LP’s

  18. Two central atoms: ethane VSEPR theory requires both carbon atoms to be tetrahedral The shape of the molecule, its conformation, requires that contacts be minimized between the atoms – this is known as the staggered conformation Bonding in ethane can be explained by using sp3 hybrid orbitals on each carbon atoms The H atoms bond using their 1s atomic orbitals In all there are 14 electrons or 7 electron pair bonds in the molecule 1 s C-C sp3-sp3 single bond and 6 s C-H sp3-s single bonds are formed       

  19.      Change perspective to show the π bond! Double bonds: ethene If we treat ethane by the VSEPR theory, we find that both carbon atoms are trigonal planar The molecule is planar. Why ? sp2 hybrid orbitals on each carbon atom, which leaves one atomic p orbital unused on each C atom, while H atoms use their 1s atomic orbitals There are 6 e’ pair bonds in the molecule, 5 in σ orbitals, 1 in the π orbital 1 s sp2-sp2 C-C bond, 1 p px-px C-C bond , and 4 s sp2-s C-H bonds The sigma skeleton of ethene The pi manifold of ethene  2px 2px

  20. Planarity in double bonds: ethene again planar structure of ethene can now be explained When the two CH2 fragments are co-planar can there sufficient overlap between the unhybridized p orbitals leading to the π bond If ethene is rotated by 90 along the C—C bond, the atomic p orbitals have zero net overlap Double bonds impose coplanar conformations on the joining atoms This is true for all double-bonded molecules, and is a powerful support for the bonding theories discussed Note that a double bond is always the sum of a sigma + a pi bond Single bonds are always sigma bonds, so that in ethane, all the bonds are sigma

  21.      = C sp Double bonds: ethyne If we treat ethane by the VSEPR theory, we find that both carbon atoms are linear planar The molecule is linear. Why ? sp hybrid orbitals on each carbon atom, which leaves two atomic p orbitals unused on each C atom, while H atoms use their 1s atomic orbitals There are 5 e’ pair bonds in the molecule, 3 in σ orbitals, 2 in the π orbital 1 s sp-sp C-C bond, 2 p p-p C-C bonds , and 2 s sp-s C-H bonds The sigma skeleton of ethyne The pi manifold of ethyne 2px &2py

  22. H C O : .. H H C O H Bonding in Formaldehyde VSEPR geometry Lewis structure Flat sp2 sp2 Triangular s bonding LP   1 s sp2-sp2 C-C bond  2 s sp2-s C-H bonds   LP 2 sp2 LP’s 2py 2py p bonding  1 p py-py C-C bond

  23. .. .. +1 +1 +1 : O O : O O O .. .. -1/2 -1/2 O O -1 -1 : O : : O : .. ..       : : : : : : : : : : : : Bonding in Ozone Lewis structure VSEPR geometry Bent Resonance s sp3-sp2 bond sp2 sp2 sp2 sp2 s sp2-sp2 bond sp3 sp3 3 sp2 LP’s 3 sp3 LP’s p p-p bond Localized electrons !

  24. sp2 sp2    sp2   : : : : : :  : : : : : : Bonding in Ozone Revisited All Oxygen atoms can be considered to be sp2 hybridized instead sp2 sp2 2 s sp2-sp2 bonds sp2 5 sp2 LP’s 1 p LP p p-p bond There are 4 p electrons All 3 p orbitals combine to form 3 MO’s, therefore the LP in a p orbital and a BP in a two centre p bonding orbital is not strictly speaking correct.

  25. panti-bonding orbital pnon-bonding orbital 3p pbonding orbital O-O-O MO’ s of Ozone Three centre bonding orbital     LP’s 

  26. C C C C C C C C C C C C E Resonance, Delocalization & Conjugation A chain of alternating single and double bonds resonance allows the bonds to to be interchanged. The real situation is an average between them All the carbons are considered to be sp2 hybridized. The chain does not have to contain only carbon any atom that can involve at least 3 electrons in bonding will work as long as it can be sp2 hybridized, ex) N sp2 sp2 sp2 sp2 # nodes For a chain of N carbons that are conjugated, there are N p orbitals that form N M.O.’s, where the first N/2 are occupied. The MO will increase in energy with incresing nodes. Ex N = 4 Linear molecule A. B’ing 3 A. B’ing 2     B’ing 1  P orbitals 0 B’ing 

  27. H H H C C C C H H C C H H H H C C H H H       Bonding in trans-1,3-butadiene VSEPR geometry Lewis structure sp2 s bonding sp2 sp2 sp2 4 MO’s with 0, 1, 2 and 3 nodes: + - + - a-bonding + - - + a-bonding + + - - bonding + + + + bonding p bonding Electrons are delocalized

  28. H H H H C H H C C C C H H C H H H H             H H H Bonding in benzene VSEPR geometry Lewis structure s bonding p orbitals overlap 6 s sp2-s C-H bonds Bond order for C-C bonds is 1.5 6 s sp2-sp2 C-C bonds Electrons are delocalized 3 p p-p C-C bonds

  29. MO’s of Benzene # nodes panti-bonding orbitals 3 2 6 p 1 pbonding orbitals 0 The 6 p orbital form 6 MO with 0,1,2 and 3 nodes The MO’s with 0 and 1 node are bonding orbitals and are occupied         These represent 6 centered bonding orbitals 

  30. Lewis structure VSEPR geometry H H C C C H H C C C H H H H Bonding in Allene s bonding 4 s sp2-s C-H bonds sp2 sp2 sp 2 s sp2-sp C-C bonds 2 p p-p C-C bonds p orbitals are perpendicular do not overlap p bonding e’s not delocalized C-C B.O. = 2

  31. Bonding in large molecules sp2 sp3 sp2 sp3 sp3 sp3 sp3 s s-sp3 H -S bond 2 sp3 LP’s 2 s s-sp3 N-H bonds s sp3-sp3 S-C bond 2 s s-sp3 H-C bonds s sp2-sp2 O-C bond 1 sp3 LP p p-p O-C bond s sp3-sp2 C-C bond s sp3-sp3 C-C bond s sp2-sp3 C-O bond s s-sp3 H-C bonds 2 sp2 LP’s s sp3-sp3 C-N bond s s-sp3 H-O bond

  32. Concepts from Chapter 10 MOLECULAR ORBITALS • LCAO theory • Correlation diagrams • Bonding, nonbonding and antibonding interactions Calculating bond order using MO theory hybridization (sp, sp2 and sp3 orbitals) Sigma (σ) vs. pi (π) bonds Composition of single, double and triple bonds Resonance according to MO theory

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