OME General Chemistry

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1 OME General Chemistry Lecture 4: VSEPR, Hybridization, MO Theory Dr. Hartwig Pohl Office: Beyer-Bau 122e Phone:

2 Molecular Structure: VSEPR What do molecules look like? The Lewis Dot Structure approach provides some insight into molecular structure in terms of bonding, but what about 3D geometry? Valence-Shell Electron-Pair Repulsion (VSEPR) The valence electron pairs surrounding an atom tend to repel each other, and will therefore adopt an arrangement that minimizes this repulsion, determining the molecule's geometry. 3D structure is determined by minimizing repulsion of electron pairs (both bonding and lone pairs of electrons) 2

3 Molecular Structure: VSEPR Electron pairs (both bonding and lone pairs) are distributed around a central atom such that electronelectron repulsions are minimized. Basic geometry determined by the number of pairs. 3

4 Molecular Structure: VSEPR linear trigonal planar tetrahedral trigonal bipyramidal octahedral 4

5 Molecular Structure: VSEPR Arranging Electron Pairs: must consider both bonding pairs and lone pairs when minimizing repulsion Example: CH 4 Lewis Dot Structure VSEPR Structure Tetrahedral (4 pairs) 5

6 Molecular Structure: VSEPR Example: NH 3 (both bonding and lone pairs) Electron Pair Geometry Tetrahedral (4 pairs) Molecular Shape Lewis Dot Structure VSEPR Structure 6

7 VSEPR Structure Guidelines The previous examples illustrate the strategy for applying VSEPR to predict molecular structure 1. Construct the Lewis Dot Structure 2. Arrange bonding and lone electron pairs in space such that repulsions are minimized (electron pair geometry) 3. Name the molecular shape from the position of the atoms. VSEPR Shorthand: Refer to central atoms as A Attached atoms are referred to as X Lone pairs are referred to as E Examples: CH 4 : AX 4 NH 3 : AX 3 E H 2 O: AX 2 E 2 BF 3 : AX 3 7

8 VSEPR: Linear (2 e Pairs) Linear (AX 2 ): angle between bonds is 180º F Be F Example: BeF 2 180º Experiments show that molecules with multiple bonds can also be linear Multiple bonds are treated as a single effective electron group More than 1 central atom? Determine the shape around each 8

9 VSEPR: Trigonal Planar (3 e Pairs) Trigonal Planar (AX 3 ): angle between bonds is 120º Example: BF 3 F B F 120º F **multiple bond is treated as a single effective electron group 9

10 VSEPR: Tetrahedral (4 e Pairs) Tetrahedral (AX 4 ): angle between bonds is 109.5º Example: CH 4 Tetrahedral electron pair geometry AND tetrahedral molecular shape! 10

11 Bonding Pairs vs. Lone Pairs The bond angle in a tetrahedral arrangement of electron pairs may vary from 109.5º due to size differences between bonding and lone pair electron densises. Bonding pair: constrained by two nuclear potensals; more localized in space Lone pair: constrained by only one nuclear potensal; less localized (needs more room) 11

12 VSEPR: Trigonal Pyramidal (4 e Pairs) Trigonal Pyramidal (AX 3 E): bond angles are <109.5º and the structure is nonplanar due to repulsion of the lone pair Example: NH 3 Electron Pair Geometry Tetrahedral (4 e pairs) Molecular Shape Trigonal Pyramidal (3 N H, 1 lone pair) 107º 12

13 VSEPR: Bent (4 e Pairs) Bent (AX 2 E 2 ): bond angles are <109.5º and the structure is non-planar due to repulsion of the lone pair Example: H 2 O 104.5º Electron Pair Geometry Tetrahedral (4 e pairs) Molecular Shape Bent (2 O H, 2 lone pairs) 13

14 VSEPR: 4 e Pairs Summary Structure Name Methane, CH 4 Ammonia, NH 3 Water, H 2 O VSEPR Shorthand Electron Pair Geometry Molecular Shape AX 4 AX 3 E AX 2 E 2 Tetrahedral Tetrahedral Tetrahedral Tetrahedral Trigonal Pyramidal Bent 14

15 AX 2 E AX 3 E AX 2 E 2 1. Refer to central atom as A 2. Attached atoms are referred to as X 15

16 Example: VSEPR What is the electron-pair geometry and the molecular shape for HCFS? a) trigonal planar, bent b) trigonal planar, trigonal planar c) tetrahedral, trigonal planar d) tetrahedral, tetrahedral 16

17 VSEPR: Beyond the Octet Valence Shell Expansion (Lecture 3) systems with expanded valence shells can have five or six electron pairs around a central atom P 120º Ex: PCl 5 trigonal bipyramidal 90º Ex: SF 6 octahedral S 90º 90º 17

18 VSEPR: VSEPR: 5 electron 5 electron pairs pairs VSEPR: 5 e Pairs Consider Consider the structure the structure of SFof SF 4 (34 e -, 4 (34 e -, AX 4 E) AX 4 E) What is the optimum arrangement What is the arrangement of the e of pairs electron of in electron SF 4 (34 VE, AX pairs pairs around 4 E)? around S? S F F F F F F F F S?? S S?? S F F F F F F F Compare Compare e pair e angles pair angles Compare angles between the lone pair and other electron pairs lone-pair lone-pair / lone-pair bond-pair: / bond-pair: vs. bond two pairat two 90 o at 2(90º),, two o, at 2(120º) two at o 120 o three 3(90º) three at 90 o at 90 o bond-pair bond-pair / bond-pair: / bond-pair: vs. four pairat four 90 o 4(90º), at, one o 1(120º), at one 120at o 120 three o 3(90º), three at 902(120º) o at, three o, three at 120at o 12 Repulsive Repulsive forces forces (strongest (strongest to weakest): to weakest): F F S F Repulsive forces: lone-pair/lone-pair > lone-pair/bond-pair > bond-pair/bond-pair lone-pair/lone-pair lone-pair/lone-pair > lone-pair/bond-pair > lone-pair/bond-pair > bond-pair/bond-pair > bond-pair/bond-pair OR F F F SF e pair geometry: trigonal bipyramidal molecular shape: seesaw F 18

19 VSEPR: 5 e Pairs What is the optimum arrangement of the e pairs in I 3 (22 VE, AX 2 E 3 )? Driving force for structure (c) is to maximize the angular separation of the lone pairs! e pair geometry: trigonal bipyramidal molecular shape: linear 19

20 VSEPR: 5 e Pair Geometries 20

21 VSEPR: 6 e Pairs Which of these is the most likely structure for XeF 4 (AX 4 E 2 )? e pair geometry: octahedral molecular shape: square planar 21

22 VSEPR: 6 e Pair Geometries 22

23 Example: VSEPR What is the expected shape of ICl 2+? (a) linear (b) bent (c) tetrahedral (d) square planar VE = 20 AX 2 E 2 electron pair geometry = tetrahedral (4 e pairs) molecular shape = BENT 23

24 Molecular Dipole Moments The VSEPR molecular shape can be used to determine the polarity of a molecule 1. Draw the Lewis Dot Structure to determine the bonding pacers and position of lone-pairs in the molecule 2. IdenSfy the electron pair geometry of the molecule 3. Determine the molecular shape by placing lone-pairs in the most likely positions around the central atom 4. Inspect the structure! If one side of the molecule has more electronegative atoms than the other, then the molecule has a net dipole no net dipole 24

25 Molecular Dipole Moments Carbon Dioxide CO 2 (16 VE, AX 2 ) linear, linear Water H 2 O (8 VE, AX 2 E 2 ) tetrahedral, bent The C=O bonds have dipoles of equal magnitude but opposite direction, so there is no net dipole moment! The O H bonds have dipoles of equal magnitude that DO NOT cancel each other, so water has a net dipole moment 25

26 Molecular Dipoles (cont.) Symmetric molecules do not have a net molecular dipole! symmetric asymmetric symmetric 26

27 Example: Molecular Dipoles Write the Lewis Dot Structure and VSEPR structures for CF 2 Cl 2. Does it have a dipole moment? 27

28 Valence Bond Theory Valence Bond Theory: how the atomic orbitals of the dissociated atoms combine to give individual chemical bonds when a molecule is formed. Overlapping of atomic orbitals of the participating atoms forms the chemical bond. There can be 2 types of overlapping orbitals: sigma bonds occur when the orbitals of two shared electrons overlap head-to-head pi bonds occur when two orbitals overlap when they are parallel. Note: single bonds have one sigma bond, double bonds consist of one sigma bond and one pi bond, and triple bonds contain one sigma bond and two pi bonds. 28

29 Valence Bond Theory Sigma bonds occur when the orbitals of two shared electrons overlap head-to-head Hydrogen, H 2 Hydrogen Fluoride, HF H A (1s) H B (1s) H (1s) F (2p) σ-bond H A H B σ-bond H F 29

30 Getting an Orbital Picture Methane: The VSPER structure tells us to expect a tetrahedral molecular shape with bond angles of 109.5º What do the molecular bonding orbitals look like between the C H atoms?? Problem: Our current definition of orbitals doesn t quite work valence electrons describe outer shell of electrons s and p orbitals 90º 30

31 Orbital Hybridization New orbitals are constructed from the pre-existing s, p, and d-orbitals of atoms to give us a better molecular picture hybrid orbitals A few guidelines 1. Hybridize the central atom ONLY (others as needed) 2. Only use the valence shell electrons 3. The number of hybrid orbitals formed = number of atomic orbitals used 31

32 Methane: sp 3 Hybridization Methane, CH 4 4 hybrid orbitals are needed to form 4 C H bonds 4 atomic orbitals are required: s + p + p + p = sp 3 2p 2p 2p 2s valence shell of an isolated C atom Orbital Hybridization sp 3 sp 3 sp 3 sp 3 needed in order to form 4 sigma bonds to H 32

33 Formation of sp 3 Hybrid Orbitals Fig s 2p x 2p y 2p z 33

34 Formation of Covalent Bonds Fig x sigma bonds formed between 1s orbitals from the 4 H atoms and each of the sp 3 orbitals from the central C atom. 1s sp 3 1s sp 3 sp 3 sp 3 1s 1s 34

35 Water: sp 3 Hybridization Water, H 2 O 4 hybrid orbitals are needed to form 2 O H bonds and 2 lone pairs 4 atomic orbitals are required: s + p + p + p = sp 3 2p 2p 2p 2s valence shell of an isolated O atom Orbital Hybridization sp 3 sp 3 sp 3 sp 3 2 lone pairs, 2 available for sigma bonds with H 35

36 BF 3 : sp 2 Hybridization BF 3 - trigonal planar according to VSEPR Theory (incomplete octet exception) Lewis Dot Structure Electron Pair Geometry (trigonal planar) Molecular Shape (trigonal planar) What kind of orbital form the B F sigma bonds? 36

37 BF 3 : sp 2 Hybridization Boron Trifluoride, BF 3 3 hybrid orbitals are needed to form 3 B F bonds 3 atomic orbitals are required: s + p + p = sp 2 2p 2p 2p 2s valence shell of an isolated B atom Orbital Hybridization sp 2 sp 2 sp 2 2p 3 sp 2 electrons available for sigma bonds to F one empty p-orbital still left over 37

38 BeCl 2 : sp Hybridization BeCl 2 - linear according to VSEPR Theory Beryllium Dichloride, BeCl 2 2 hybrid orbitals are needed to form 2 B Cl bonds 2 atomic orbitals are required: s + p = sp 2p 2p 2p 2s valence shell of an isolated Be atom Orbital Hybridization sp sp 2p 2p 2 sp electrons available for sigma bonds to Cl 2 empty p-orbitals still left over 38

39 PCl 5 Bringing in the d-orbitals Lewis Dot Structure 90º VSEPR trigonal bipyramidal P 120º 5 hybrid orbitals are needed to form 5 P Cl bonds 5 atomic orbitals are required: s + p + p + p + d= sp 3 d 3d 3d 3d 3d 3d 3p 3p 3p 3s 3d 3d 3d 3d sp 3 d sp 3 d sp 3 d sp 3 d sp 3 d 5 sp 3 d electrons available for 5 sigma bonds to Cl atoms 39

40 PCl 5 : Summary of Structural Models Lewis Dot Structure VSEPR Getting the full picture P Hybrid Orbitals 40

41 SF 6 : sp 3 d 2 Hybrid Orbitals Lewis Dot Structure VSEPR S 90º 6 hybrid orbitals are needed to form 6 S F bonds 6 atomic orbitals are required: s + p + p + p + d + d= sp 3 d 2 90º 3d 3d 3d 3d 3d 3p 3p 3p 3s 3d 3d 3d 3d sp 3 d 2 sp 3 d 2 sp 3 d 2 sp 3 d 2 sp 3 d 2 sp 3 d 2 6 sp 3 d 2 electrons available for 6 sigma bonds to F atoms 41

42 Summary of Hybrid Orbitals 42

43 Summary of Hybrid Orbitals (cont.) 43

44 Multiple Bonds sigma bonds occur when the orbitals of two shared electrons overlap head- to- head s + p p + p pi bonds occur when two orbitals overlap when they are parallel p + p single bonds one sigma bond, double bonds one sigma bond and one pi bond, and triple bonds one sigma bond and two pi bonds 44

45 Double Bonds: Ethylene Draw the Lewis Dot Structure of Ethylene (C 2 H 4 ). VE = 12 C H C H H H Apply VSEPR Theory and determine hybridization. H H C C H H sp 2 Both C atoms are trigonal planar in electron pair geometry AND molecular shape (3 e pairs around each carbon) Note: multiple bonds count as 1 e pair in VSEPR Theory models. 45

46 Ethylene: sp 2 Hybridized Orbitals 2p 2p 2p 2s sp 2 -Orbital valence shell of an isolated C atom p-orbital sp 2 -Orbital Orbital Hybridization sp 2 sp 2 sp 2 2p 3 sp 2 electrons available for sigma bonds to C and H atoms fourth electron moves to 2p orbital because no electron pairs are present on the C atom sp 2 -Orbital one singly occupied p-orbital available for pi-bonding 46

47 Ethylene: Sigma & Pi Bonding SIGMA BONDS end-to-end overlap of the sp 2 hybridized orbitals of C with the neighboring C atom and s-orbitals from respective H atoms PI BONDS side-by-side overlap of the unhybridized p-orbitals from each neighboring C atom p-orbital p-orbital -bond -bond 47

48 Ethylene: The Full Picture 48

49 Triple Bonds: Acetylene C 2 H 2 1. Lewis Dot Structure VE = 10 C C 2. VSEPR Structure linear (AX 2 ) H H H C C H 3. Hybridization sp hybridized C-atoms 2p 2p 2p 2s valence shell of an isolated C atom 2p sp 2p sp 2 sp electrons for sigma bonding to C and H atoms two unhybridized p-orbitals available for pi-bonding 49

50 Acetylene: The Full Picture -bond -bond + = -bond sigma bonds pi bonds 50

51 Carbon Dioxide (CO 2 ) 1. Lewis Dot Structure VE = VSEPR Structure linear (AX 2 ) 3. Hybridization sp hybridized C-atom 2p 2p 2p 2s valence shell of an isolated C atom 2p sp 2p sp 51

52 CO 2 : The Full Picture 52

53 Nitrogen (N 2 ) 1. Lewis Dot Structure VE = 10 N N 2. VSEPR Structure linear (AX 2 ) 3. Hybridization sp hybridized N-atom 2p 2p 2p 2s valence shell of an isolated N atom 2p sp 2p sp 53

54 N 2 : The Full Picture 54

55 What s Next? So far Atomic Orbitals (AOs) & Bonding Models We have discussed the electronic structure of atoms and how they can form bonds with other atoms. Next Molecular Orbital Theory Positions and energies of electrons in molecules can be described in terms of molecular orbitals (MOs): a spatial distribution of electrons in a molecule that is associated with a particular orbital energy While VSEPR and valence bond theory are applied to predict the structures of molecules, MO theory is used to determine orbital interaction and valence electron configuration within the molecular orbitals of a molecule. 55

56 Molecular Orbital Theory A method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule (delocalized). Overlapping atomic orbitals are described by mathematical equations called wave functions (Lecture 2) Molecular orbitals are constructed using a linear combination of atomic orbitals (LCAOs): the mathematical sums and differences of wave functions that describe overlapping atomic orbitals Types of MOs: bonding, anti-bonding, and non-bonding orbitals 56

57 Molecular Orbital Theory Bonding MOs: mathematical sums of wave functions Adding two atomic orbitals corresponds to constructive interference between two waves, which reinforces their intensity and increases the internuclear electron probability density Ex: the molecular orbital corresponding to the sum of two 1s orbitals is called a 1s combination: 1s 1s(A) + 1s (B) Antibonding MOs: mathematical difference of wave functions Subtracting two atomic orbitals corresponds to destructive interference between two waves, which reduces their intensity, causes a decrease in the internuclear electron probability density, and contains a node where the electron density is zero Ex: the molecular orbital corresponding to the difference of two 1s orbitals is called a * 1s combination: * 1s 1s(A) 1s (B) 57

58 Bonding vs. Antibonding 58

59 Energy-Level Diagrams The energies of the molecular orbitals versus those of the parent atomic orbitals can be shown schematically in an energy-level diagram The electron configuration of a molecule is shown by placing the correct number of electrons in the appropriate energy-level diagram 1. The bonding combination is always lower in energy (more stable) than the AOs, and the antibonding combination is always higher in energy (less stable) 2. Obey the Pauli Principle and Hund s Rule just like with filling orbitals in atomic electron configurations 59

60 Bond Order in MO Theory In the molecular orbital approach, bond order is defined as one-half the net number of bonding electrons and can be calculated from the completed energy-level diagram bond order = (# bonding e ) (# antibonding e ) 2 Electrons in antibonding molecular orbitals cancel electrons in bonding molecular orbitals. Electrons in nonbonding orbitals have no effect and are not counted. Bond orders of 1, 2, and 3 correspond to single, double, and triple bonds, respectively. Molecules with predicted bond orders of 0 are less stable than the isolated atoms and do not normally exist. 60

61 MOs w/ np Atomic Orbitals Just as with ns orbitals, MOs can be formed from np orbitals by taking their mathematical sum and difference. Remember: p-orbitals are not spherically symmetrical each np subshell has np x, np y, np z orbitals σ Bonding: When two positive lobes with appropriate spatial orientation overlap (two np z atomic orbitals) constructive interference σ(np z ) = np z (A) np z (B) σ Antibonding: When a positive and negative lobe with appropriate spatial orientation overlap destructive interference σ*(np z ) = np z (A) + np z (B) 61

62 MOs w/ np Atomic Orbitals The remaining p-orbitals on each of the two atoms np x and np y do not point directly toward each other but are perpendicular to the internuclear axis side-to-side interactions (π) vs. head-to-head (σ) π Bonding: Constructive interference of side-by-side p-orbitals π(np x ) = np x (A) + np x (B), π(np y ) = np y (A) + np y (B) π Antibonding: Destructive interference of side-by-side p-orbitals π*(np x ) = np x (A) np x (B), π(np y ) = np y (A) np y (B) 62

63 Energy-Level Diagram: p-orbitals 63

64 Simple MO Rules Molecular orbital energy-level diagrams for diatomic molecules can be created if the electron configuration of the parent atoms is known, following the rules below: 1. Number of molecular orbitals produced is the same as the number of atomic orbitals used to create them 2. As the overlap between two atomic orbitals increases, the difference in energy between the resulting bonding and antibonding molecular orbitals increases 1. When two atomic orbitals combine to form a pair of molecular orbitals, the bonding molecular orbital is stabilized about as much as the antibonding molecular orbital is destabilized 2. The interaction between atomic orbitals is greater when they have the same energy 64

65 Examples: F 2 and O 2 Fluorine, F VE = 7 1s 2 2s 2 2p 5 Fluorine, F 2 VE = 14 Oxygen, O VE = 6 1s 2 2s 2 2p 4 Oxygen, O 2 VE = 12 65

66 Heteronuclear Diatomic Molecules A similar procedure can be applied to molecules with two dissimilar atoms, called heteronuclear diatomic molecules When two nonidentical atoms interact to form a chemical bond, the interacting atomic orbitals do not have the same energy. Use a molecular orbital energy-level diagram that is skewed or tilted toward the more electronegative element. 66

67 Nonbonding Molecular Orbitals MO theory can explain the presence of lone pairs of electrons by determining the presence of nonbonding molecular orbitals (nb). 67

68 Valence Bond Theory & MO Theory More complex molecules that contain multiple bonds: hybrid atomic orbitals are used to describe σ bonding and molecular orbitals to describe π bonding 68

69 MO Theory & Resonance Structures π bonding between 3+ atoms: Requires combining 3+ unhybridized np orbitals on adjacent atoms to generate π bonding, antibonding, and nonbonding molecular orbitals extending over all of the atoms. Note: Filling the resulting energy-level diagram with the appropriate number of electrons explains the bonding in molecules or ions that previously required the use of resonance structures in the Lewis electron-pair approach 69

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