George Mason University General Chemistry 211 Chapter 11 Theories of Covalent Bonding Acknowledgements Course Text: Che

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2. Molecular Structure - Summary Atomic theory Molecular Weight (MW) � Neutrons + Protons Mass, Atomic Mass units, Law of Definite Proportions Moles, Chemical Equations, Stoichiometry Gas Laws, Thermodynamics (reaction energy) Quantum Theory � waves vs particles, electronic structure of atoms energy absorption, emission electronic energy levels quantum numbers, electron shells Periodicity � orbital diagrams Pauli exclusion principle Aufbau Principle for populating subshells 2 6/26/2012

3. Molecular Structure - Summary Bonding � Valence electrons Periodic table Ionic Bonds Covalent Bonds Electronic Configuration Lattice Energy, Born-Haber cycle, Bond energy Geometry � Lewis diagrams Resonance, Octet Rule Formal Charge (valence electrons � unbonded electrons � � bonded electrons) Valence-Shell Electron Pair Repulsion Model (VSEPR) Molecular Notation � AXaEb Xa � Bonding pairs Eb � Nonbonding pairs sum(a + b) determines geometry (linear, tetrahedral) if �b� > 0 molecule may form dipole (polar) 3 6/26/2012

4. Valence Bond Theory Valence bond theory is an attempt to explain the covalent bond from a quantum mechanical view According to this theory, a bond forms when two atomic orbitals �overlap� The space formed by the overlapping orbitals has a capacity for two electrons that have opposite spins, +1/2 & -1/2 (exclusion principle) Note: Each orbital forming the bond has at least one unfilled slot to accommodate the electron being shared from the other orbital The bond strength depends on the attraction of the nuclei for the shared electrons 4 6/26/2012

5. Valence Bond Theory Valence bond theory (con�t) The greater the orbital overlap, the stronger (more stable) the bond The extent of the overlap depends on the shapes and directions of the orbitals An s orbital is spherical, but p and d orbitals have more electron density in one direction than in another Whenever possible, a bond involving p or d electrons will be oriented in the direction that maximizes overlap 5 6/26/2012

6. Valence Bond Theory 6 6/26/2012

7. Hybrid Orbitals One might expect the number of bonds formed by an atom would equal its unpaired electrons Chlorine, for example, generally forms one bond and has one unpaired electron - 1s22s22p5 Oxygen, with two unpaired electrons, usually forms two bonds - 1s22s22p4 However, carbon, with only two unpaired electrons, generally forms four (4) bonds C (1s22s22p2) [He] 2s22p2 The four bonds come from the 2 (2s) paired electrons and the 2 (2p) unpaired electrons For example, methane, CH4, is well known The uniqueness of these bonds is described next 7 6/26/2012

8. Hybrid Orbitals Linus Pauling proposed that the valence atomic orbitals in the molecule are different from those of the isolated atoms forming the molecule Quantum mechanical computations show that if specific combinations of orbitals are mixed mathematically, �new� atomic orbitals are obtained The spatial orientation of these new orbitals lead to more �stable� bonds and are consistent with observed molecular shapes These new orbitals are called: �Hybrid Orbitals� 8 6/26/2012

9. Hybrid Orbitals Types of Hybrid Orbitals 5 common types 9 6/26/2012

10. SP Hybrid Orbitals SP Hybridization 2 electron groups surround central atom Linear shape, 180o apart VB theory proposes the mixing of two nonequivalent orbitals, one �s� and one �p�, to form two equivalent �sp� hybrid orbitals Orientation of hybrid orbitals extend electron density in the bonding direction Minimizes repulsions between electrons Both shape and orientation maximize overlap between the atoms 6/26/2012 10

11. �sp� Hybrid Orbitals 6/26/2012 11

12. �sp2� Hybridization sp2 - trigonal planar geometry (Central atom bonded to three ligands)  The three bonds have equivalent hybridized shapes The sp2 hybridized orbitals are formed from: 1 �s� orbital and 2 �p� orbitals Note: Of the 4 orbitals available (1 s & 3 p) only the s orbital and 2 of the p orbitals are used to form hybrid orbitals Note: Unlike electron configuration notation, hybrid orbital notation uses superscripts for the number of atomic orbitals of a given type that are mixed, NOT for the number of electrons in the orbital, thus, sp2 (3 orbitals), sp3 (4 orbitals), sp3d (5 orbitals) 6/26/2012 12

13. �sp2� Hybridization 6/26/2012 13

14. sp3 Hybrid Orbitals sp3 (4 bonds, thus, Tetrahedral geometry) The sp3 hybridized orbitals are formed from: 1 �s� orbital and 3 �p� orbitals Example� Carbon is the basis for �Organic Chemistry� Carbon is in group 4 of the Periodic Chart and has 4 valence electrons � 2s22p2 The hybridization of these 4 electrons is critical in the formation of the many millions of organic compounds and as the basis of life as we know it The following slides show 3 different forms of the electronic structure and explains why the hybridized form reflects the observed structure of organic compounds 6/26/2012 14

15. SP3 Hybrid Orbitals 6/26/2012 15

16. SP3 Hybrid Orbitals One bond on carbon would form using the 2s orbital while the other three bonds would use 3 2p orbitals This does not explain the fact that the four bonds in CH4 appear to be identical Valence bond theory assumes that the four available atomic orbitals (2s22p2) in carbon combine to make four equivalent �hybrid� orbitals 6/26/2012 16

17. Hybrid Orbitals Hybrid orbitals are orbitals used to describe bonding that is obtained by taking combinations of atomic orbitals of an isolated atom In the case of Carbon, one �s� orbital and three �p� orbitals, are combined to form 4 sp3 hybrid orbitals The carbon atom in a typical sp3 hybrid structure has 4 bonded pairs and zero unshared electrons, therefore, tetrahedral structure AXaEb (a + b) 4 + 0 = AX4 The four sp3 hybrid orbitals take the shape of a tetrahedron 6/26/2012 17

18. Hybridization of Carbon in CH4 6/26/2012 18

19. Spatial Arrangement ofsp3 Hybrid Orbitals 6/26/2012 19

20. sp3d Hybrid Orbitals sp3d (5 molecules, thus, Trigonal Bypyramidal geometry) Molecules with central atoms from Period 3 or higher, can utilize �d� orbitals in the formation of hybrid orbitals The sp3d hybridized orbitals are formed from: 1 �s� orbital, 3 �p� orbitals, 1 �d� orbital PCl5 AXaEb AX5E0 hybrid orbitals � 5 (sp3d) 20 6/26/2012

21. SP3d Hybrid Orbitals 6/26/2012 21

22. Diagrams of Hybrid Orbitals Showing their Spatial Arrangements 6/26/2012 22

23. Hybrid Orbitals To obtain the bonding description of any atom in a molecule, you proceed as follows: Write the Lewis electron-dot formula for the molecule From the Lewis formula, use the VSEPR theory to determine the arrangement of electron pairs around the central atom, i.e., the geometry From the geometric arrangement of the electron pairs, obtain the hybridization type Assign valence electrons to the hybrid orbitals of this atom one at a time, pairing only when necessary Form bonds to the central atom by overlapping singly occupied orbitals of other atoms with the singly occupied hybrid orbitals of the central atom 6/26/2012 23

24. Oxygen Atom Bonding in H2O 6/26/2012 24

25. Practice Problem What hybrid orbitals of sulfur are involved in the bonding in sulfur trioxide (SO3)? a. sp b. sp2 c. sp3 d. sp2d e. sp3d2 Ans: b 6/26/2012 25

26. Sulfur Trioxide � Hybrid Orbitals 6/26/2012 26

27. Nitrogen Atom Bonding in NH3 6/26/2012 27

28. Multiple Bonds Types of Covalent Bond & Orbital Overlap Orbitals can overlap two ways Side to Side or End to End Two types of Covalent Bonds: Sigma Bonds (C-C) pi (?) Bonds (C=C) Multiple Bonds 6/26/2012 28

29. Multiple Bonds End-to-End overlap & Sigma Bonds The C � C bond in Ethane (C2H6) involves overlap of 1 sp3 orbitals from each carbon Each of the six (6) C � H bonds involves the overlap of a Carbon sp3 and a Hydrogen 1 s orbital All bonds involve overlap of one end of orbital with the end of the other orbital The bond formed from end-to-end overlap is called a �sigma bond� (symbol - ?) 6/26/2012 29

30. Multiple Bonding According to valence bond theory, one hybrid orbital is needed for each bond (whether a single or multiple) and for each lone pair For example, consider the molecule: ethene (or ethylene) 6/26/2012 30

31. Multiple Bonding Each carbon atom is bonded to three other atoms and no lone pairs, which indicates the need for three hybrid orbitals This implies AX3E0 (trigonal) sp2 hybridization 1 2s & 2 2p orbitals The third 2p orbital is left unhybridized and lies perpendicular to the plane of the trigonal sp2 hybrids The following slide represents the sp2 hybridization of the carbon atoms 6/26/2012 31

32. Multiple Bonding 6/26/2012 32

33. Multiple Bonding Each carbon atom is sp2 hybridized Each of the carbon atom�s 4 valence electrons fill � its 3 sp2 orbitals and its unhybridized 2p orbital, which lies perpendicular to sp2 plane Two sp2 orbitals of each carbon form C � H sigma (?) bonds by overlapping the 1 s orbitals of the two H atoms The 3rd sp2 orbital of one carbon forms a C � C (?) bond with the sp2 orbital of the other carbon with end-to-end overlap A pi (?) bond is formed when the two unhybridized 2p orbitals (one from each carbon) overlap side-to-side, forming two regions of electron density, one above and one below the ?-bond axis A double bond always consists of: one ?-bond and one ? bond 6/26/2012 33

34. Multiple Bonding Two of the sp2 hybrid orbitals of each carbon overlap end-to-end with the 1s orbitals of the 2 hydrogen atoms forming a sigma bond The remaining sp2 hybrid orbital, one on each carbon, overlap end-to-end to form a sigma bond 6/26/2012 34

35. Multiple Bonding The remaining �unhybridized� 2p orbitals, one on each of the carbon atoms, overlap side-to-side, one on top of the sigma bond and one on the bottom of the sigma bond, forming a p bond 6/26/2012 35

36. Practice Problem Use valence bond theory to describe the bonding in CO2 Ans: 1. Draw Lewis structure 2. Determine hybridization 3. Draw diagram of hybrid atomic orbitals 4. Pair electrons (O) with hybrid C orbitals  forming sigma bonds 5. Pair electrons (O) with unpaired p electrons  in C atom to form pi (?) bonds 6/26/2012 36

37. Practice Problem (Con�t) 6/26/2012 37

38. Molecular Orbital (MO) Theory Molecular Orbital (MO) theory is a theory of the electronic structure of molecules in terms of molecular orbitals, which may spread over several atoms or the entire molecule MO theory explains the observed and computed energy differences among orbitals, which Valence Bond theory does not As atoms approach each other and their atomic orbitals overlap, molecular orbitals (MO) are formed Note: Only outer (valence) Atomic orbitals (AO) interact enough to form Molecular Orbitals (MO) Electron motions are complex making solutions to the Schroedinger equation approximations Mathematically, the combination of atomic orbitals to form molecular orbitals involves adding or subtracting atomic wave functions 6/26/2012 38

39. Molecular Orbital (MO) Theory Adding Wave Functions Forms a �Bonding� (?) molecular orbital (MO) Region of high electron density between nuclei Electron charge between nuclei is dispersed over a larger area than in atomic orbitals (AO) MO orbital energy is lower than in the AO because of the reduction in electron repulsion Bonding MO is more stable than AO 6/26/2012 39

40. Molecular Orbital (MO) Theory Subtracting Wave Functions Forms a �Nonbonding� (?*) molecular orbital The node between the nuclei has most of the electron density outside the node with very little density (zero) between the nuclei Thus, the electrons do not shield one nuclei from the other resulting in increased nucleus-nucleus repulsion Therefore, the antibonding MO has a higher energy than the corresponding atom orbitals (AO) When the antibonding orbital is occupied, the molecule is less stable than when the orbital is not occupied 6/26/2012 40

41. Molecular Orbital Theory Example: The bonding of two hydrogen atoms s1s (bonding) molecular orbital is formed s1s * (antibonding) molecular orbital is formed The following slide illustrates the relative energies of the molecular orbitals compared to the original atomic orbitals Because the energy of the two electrons in the bonding orbital is lower than the energy of the individual atoms, the molecule is stable 6/26/2012 41

42. Molecular Orbital Theory 6/26/2012 42

43. Bonding and Antibonding Orbitals from 1s Hydrogen Atom Orbitals 6/26/2012 43

44. Bond Order The term bond order refers to the number of electron pairs shared between two atoms The bond order of a diatomic molecule is defined as one-half the difference between the number of electrons in bonding orbitals, nb, and the number of electrons in antibonding orbitals, na 6/26/2012 44

45. Bond OrderH2 6/26/2012 45

46. Bond OrderHe2 6/26/2012 46

47. Diatomic HomonuclearSubstances in 2p period 6/26/2012 47 The 2p orbitals can overlap in two ways End-to-End gives ?2p and ?*2p molecular orbitals (MO) Side-to-Side gives a pair of ?2p and ?*2p MOs The order of MO energy levels, whether bonding or nonbonding, is based on the AO (atomic orbital) energy levels and on the mode of the p orbital combination MO formed from 2s orbitals are lower in energy than 2p orbitals because 2s AOs are lower in energy than 2p AOs Bonding MOs are lower in energy than antibonding MOs ?2p is lower in energy than ?*2p ?2p is lower in energy than ?*2p

48. Diatomic HomonuclearSubstances in 2p period 6/26/2012 48 Atomic p orbitals (AO) can interact more extensivelyEnd-to-End than Side-to-Side Thus, ?2p MO is lower in energy than ?2p The destabilizing effect of the ?*2p MO is greater than that of the ?*2p MO The energy order for MOs derived from 2p orbitals is: ?2p < ?2p < ?*2p < ?*2p Several factors are involved in the relative energies of the various molecular orbitals (MO) Bond length Bond energy Bond order Magnetic properties Electron valence shell configuration

49. Diatomic HomonuclearSubstances in 2p period Factors that affect the MO energy level order There are three (3) mutually perpendicular 2p orbitals in each atom of a diatomic molecule (2px 2py, 2pz) When the 6 p orbitals (3 from each element) combine, only one orbital from each element can interact end-to-end forming a ? (bond) and a ?* (antibonding) Molecular Orbital (MO) The other two pairs of orbitals interact side to side to form two ? MOs and two ?* MOs of the same energy giving the expected MO diagrams for the p-block Period 2 homonuclear diatomic molecules 6/26/2012 49

50. Diatomic HomonuclearSubstances in 2p period 6/26/2012 50

51. Diatomic HomonuclearSubstances in 2p period 6/26/2012 51 Other factors influence the MO energy level order �s" and �p� AOs can be similar in energy or differ considerably in energy, which determines whether the orbitals mix or don�t mix O, F, Ne atoms are relatively small and electron repulsions raise the energy of 2p orbitals high enough above 2s orbitals to minimize orbital mixing Atoms, such as B, C, N, are larger in size and the �s� and �p� AOs have less electron repulsion and the energy difference between 2s & 2p is less, resulting in mixing of the �s� & �p� orbitals

52. Diatomic HomonuclearSubstances in 2p period This smaller difference in energy of the 2p & 2s orbitals in the P, C, N atoms permits some mixing of the orbitals between the 2s orbital of one atom and the end�on of the 2p orbital of the other atom This orbital mixing: lowers the energy of the ?2s and ?*2s MOs and raises the energy of the ?2p and ?*2p MOs The ? MOs are not affected The effect of the mixing is the reversal of the ?2s and ?2p MOs ?2p < ?2p < ?*2p < ?*2p The next slide illustrates these differences 6/26/2012 52

53. Diatomic HomonuclearSubstances in 2p period 6/26/2012 53

54. Diatomic HomonuclearSubstances in 2p period 6/26/2012 54

55. Diatomic Homonuclearsubstances in 2p period 6/26/2012 55

56. Sample Problem 6/26/2012 56

57. Sample Problem 6/26/2012 57

58. Diatomic HeteronuclearSubstances in 2p period Heteronuclear diatomic molecules are composed of two different atoms � HF NO , etc. Heteronuclear molecules have �Asymmetric� MO diagrams Atoms with greater effective nuclear charge (Zeff) draw their electrons closer to the nucleus, thus, they have higher electronegativity 6/26/2012 58

59. Diatomic HeteronuclearSubstances in 2p period 6/26/2012 59

60. Diatomic HeteronuclearSubstances in 2p period Example Bonding in Heteronuclear Nitrogen Monoxide, NO Highly reactive compound because it has a lone electron Two possible Lewis Structures Not clear where lone electron resides (N or O) Lower Formal charge on N suggests structure I MO theory predicts electron resides closer to the Nitrogen atom Measured bond energy suggests bond order higher than 2 6/26/2012 60

61. Diatomic HeteronuclearSubstances in 2p period 6/26/2012 61

62. Molecular Orbital Template(without 2s � 2p mixing) 6/26/2012 62

63. Molecular Orbital Template(with 2s � 2p mixing) 6/26/2012 63

64. Equation Summary 6/26/2012 64

65. Equation Summary VESPR Model Molecular Notation: AXaEb A � The Central Atom (Least Electronegative atom) X � The Ligands (Bonding Pairs) a � The Number of Ligands E � Non-Bonding Electron Pairs b � The Number of Non-Bonding Electron Pairs Double & Triple Bonds count as a �single� electron pair The Geometric arrangement is determined by: sum (a + b) 6/26/2012 65