Chemistry 1B, Fall 2012 Lectures 15-16

Transcription

1 Chemistry 1B Fall 2012 Quantum Mechanics of the Covalent Bond for chapter 14 animations and links see: 1 LISTEN UP!!! WE WILL BE COVERING SECOND PART OF CHAPTER 14 (pp ) FIRST You will go CRAZY unless you concentrate on the material presented in lecture and homework 2 1

2 quantum mechanics of covalent bonding diatomic molecules: what is the quantum mechanical glue which produces a stable molecule? (pp ) On Midterm polyatomic molecules: quantum mechanical description of bonding and GEOMETRY (pp and ) not on Midterm but ON FINAL 3 why do atoms form bonds to become molecules? lonely separated H atoms 432 kj/mol bond energy 74 pm bondlength happy, covalently bonded H atoms 4 2

3 full quantum mechanical treatment solving the Schrödinger equation experiment theory bond length: bond energy: 74 pm 432 kj/mol 74 pm kj/mol QM rules!!! 5 molecular orbital (approximation) the orbitals for electrons in molecules are described by combinations of atomic orbitals (a.o.s) on the atoms involved in the bond these orbitals (wavefunctions) are called molecular orbitals (m.o.s) our MISSION will be to: understand the nature of the m.o. s, their energies and their electron densities (Y 2 ) fill the m.o. s with covalent bonding electrons to give ground and excited configurations (states) understand the properties of diatomic molecules (bond strength, bond length, and magnetic properties) in terms of these electron configurations and orbital properties 6 3

4 interaction of atomic orbitals to form molecular orbitals atomic orbitals [waves] on the atoms involved in a bond can interact [wave interference] in two ways: add (constructive interference) subtract (destructive interference) 7 constructive and destructive interference of ao s constructive interference of 1s aos (contours) constructive interference of 1s aos (elevation) destructive interference of 1s aos (contours) destructive interference of 1s aos (elevation) originally from: 8 4

5 constructive interference to form bonding molecular orbital The atomic orbitals can add (constructive interference) to form a bonding molecular orbital. Properties of bonding orbital (from constructive interference of a.o.s) the bonding molecular orbital has a lower energy than the two contributing atomic orbitals the electron probability cloud ( 2 ) has a greater electron density between the nuclei than would noninteracting atoms 9 destructive interference to form antibonding molecular orbital The atomic orbitals can subtract (destructive interference) to form an antibonding molecular orbital. Properties of antibonding orbital (from destructive interference of a.o.s) the antibonding molecular orbital has a higher energy than the two contributing atomic orbitals the electron probability cloud ( 2 ) has a lower electron density between the nuclei than would noninteracting atoms (notice node) 10 5

6 constructive and destructive interference of 1s orbital waves Figure destructive interference constructive interference 11 1s molecular orbitals in hydrogen molecule higher energy lower electron density lower energy higher electron density 12 6

7 from handouts for chapter 13 (Dickerson, Gray, Haight) 1s * 1s : cylindrically symmetric around internuclear axis (x) *: antibonding (destructive interference) 1s: from 1s a.o. s 13 molecular orbital energy diagram (figure 14.28) 2 e s configuration: 1s 2 H 2 bond order= ½ (20)=1 (single bond) 14 7

8 mo diagrams for He 2 and He2 (fig , 14.29) He 2 (3e s) He 2 (4e s) configuration: ( 1s ) 2 ( * 1s ) 1 configuration: ( 1s ) 2 ( * 1s ) 2 bond order =(21)/2 = 0.5 bond order =(22)/2 =0 no covalent He 2 molecule observed 15 when will two a.o. s interact to form an m.o.?? two a.o. s must have similar energy (for homonuclear diatomics 1s 1s, 2s 2s, 2p 2p, etc, also 2s 2p to some extent) the two a.o. s must have nonzero overlap (be able to have net constructive and destructive interference; see in a moment) the degree of stabilization of the bonding m.o. and the degree of destabilization of antibonding m.o. depend on the extent of the interaction (overlap) between a.o. s 16 8

9 homonuclear diatomic molecules of the second period the 1s atomic orbitals on the two atoms interact to give 1s and * 1s molecular orbitals the 2s atomic orbitals on the two atoms interact to give 2s and * 2s molecular orbitals although the 2s has a lower energy than an 2s atomic orbital, the energy of the 2s is higher than the * 1s 17 resulting energy level diagrams for Li 2 and Be 2 (fig 14.34, extra) 2s and * 2s differ in energy 2 nd row atoms 1s and * 1s have nearly same energy Li 2 6e s ( 1s ) 2 ( * 1s ) 2 ( 2s ) 2 b.o. = (42)/2=1 Be 2 8e s ( 1s ) 2 ( * 1s ) 2 ( 2s ) 2 ( * 2s ) 2 b.o. = (44)/2=0 no covalent Be 2 molecule observed 18 9

10 how p x p x, p y p y and and p z p z interact text uses xdirection for interatomic direction x A B all 2p atomic orbitals have the same energy 19 Zumdahl figure (interaction among 2p a.o.s on different atoms sideon interactions endon interaction 20 10

11 molecular orbitals from atomic porbitals (simple story) from interactions of the six porbitals (3 each from two atoms), six mo s will be formed these 2p mo s will have higher energy than the 2s and * 2s (2p ao s have higher energy than 2s) only the interactions (p x p x, p y p y, and p z p z ) occur (in the simple story) endon porbitals (p x p x ) have greater interactions than sidebyside porbitals (p y p y, and p z p z ) 21 how p x p x interact ( endon ) A x B 2p x ao on A A ADD B 2p x ao on B constructive interference no node A 2p mo B A B 2p x ao 2p x ao on A on B SUBTRACT destructive interference yo node A B * 2p mo 22 11

12 from Zumdahl (fig ) destructive energy constructive 23 from handouts (DGH) (endon from 2p x a.o.s) node perpendicular to bond 2p x constructive 2p x destructive 2px * 2px 24 12

13 how side on, p y p y and and p z p z interact A 2p y ao on A Ḇ 2p y ao on B constructive interference A B 2py mo A 2p y ao on A B destructive interference 2p y ao on B A B * 2py mo 25 from Zumdahl (fig ) p y p y = and * destructive energy constructive 26 13

14 sideon porbitals from 2p y a.o. s (from DGH, see handout) 2py * 2py : one nodal plane (which includes internuclear axis) 27 why p x and p y orbitals DO NOT interact text uses xdirection for interatomic direction 2p x and 2p y atomic orbitals DO have the same energy (meets criterion #1) BUT constructive _ 2p x ao destructive _ 2p y ao no net overlap; no net interference; no interaction x 28 14

15 energy of mo s from porbitals (simple case), figure endon (p x p x ) interaction is stronger than sidebyside: E 2p < E 2p and E *2p > E *2p there are two pairs of sidebyside patomic orbitals (p y p y and p z p z ): the pairs ( 2py, 2pz ) have the same energy and ( * 2py, * 2pz ) have the same energy 2p A 2p A This order applies to O 2,F 2, and Ne 2 29 life is complicated: 2s A 2p xb interactions (and 2p xa 2s B ) In some atoms, the 2s and 2p orbitals are sufficiently similar in energy that constructive and destructive interactions occur between 2s and 2p x on differing atoms 2p ao s will make contributions to the 2s mo s and 2s ao s will make contributions to 2p mo s the resulting energy level scheme: applies to B 2, C 2, and N 2 figure

16 summarizing (fig and 14.40) simple O 2, F 2, Ne 2 with 2s2p mixing B 2, C 2, N 2 31 know properties of B 2,C 2, N 2, O 2, F 2, and their ions (fig ) 32 16

17 properties of B 2,C 2, N 2, O 2, F 2, and their ions (Silberberg fig ) 33 mo s and properties of homonuclear diatomic molecules (fig 14.41) mole cule Li 2 Be 2 B 2 C 2 N 2 O 2 F 2 Ne 2 configuration b.o Bond energy (kj/mol) Bond Length (pm) ( 2s ) D ( 2s ) 2 ( * 2s ) 2 0 0?? ( 2s ) 2 ( * 2s ) 2 ( 2p ) 2 ( 2s ) 2 ( * 2s ) 2 ( 2p ) 4 P or D P D ( 2s ) 2 ( * 2s ) 2 ( 2p ) 4 ( 2p ) D ( 2s ) 2 ( * 2s ) 2 ( 2p ) 2 ( 2p ) 4 ( * 2p ) P ( 2s ) 2 ( * 2s ) 2 ( 2p ) 2 ( 2p ) 4 ( * 2p ) D ( 2s ) 2 ( * 2s ) 2 ( 2p ) 2 ( 2p ) 4 ( * 2p ) 4 ( * 2p ) 2 0 0?? 34 17

18 N 2 diamagnetic O 2 paramagnetic Joanna and Steve 35 third row just like second row but using 3s and 3p orbitals Cl 2 (14 VE s) ( 3s ) 2 ( * 3s ) 2 ( 3p ) 2 ( 3p ) 4 ( * 3p )

19 heteronuclear diatomic molecules N O H F 37 heteronuclear diatomic molecules: same rules for homonuclear m.o.s apply BUT now: same a.o.s on two atoms will not have the same energy (still, a.o.s with similar energies combine to form m.o.s) the two a.o. s will NOT contribute equally to a given mo 38 19

20 heteronuclear diatomic (NO, fig ) N x O greater 2p on N observations NOT predicatble from Lewis structures NO bond stronger than double bond; b.o= 2.5 unpaired electron resides to a greater extent on N energy of O a.o. s LOWER (but ~similar) to N a.o. s greater 2p on O need to be told use light atom energy scheme 11 valence e s 39 heteronuclear diatomic (HF fig 14.45) H x F more H1s than F2p x 1s on H and 2p x on F have similar energies and interfere to form and * mos the occupied has a greater contribution from 2p x on F leading to H F dipole moment H F Z 1s on H will NOT interact with 2 py or 2 pz on F (no overlap) y,z perpendicular to HF bond more 2p x on F than 1s on H 6 valence e s 40 20

21 END OF MATERIAL FOR MIDTERM #2 41 delocalized bonding (p 685): NOT on midterm P 685 Delocalized bonding will be covered after we study hybridization and will NOT be on midterm #2 and P 690 Spectroscopy later 42 21

22 the floating frog 43 the magnet 44 22

23 the frog The Frog That Learned to Fly (Molecular Magnetism and Levitation) originally from: 45 the frog s OK!!! 46 23

24 End of 47 bond order bond order = ½ [ no. of bonding electrons no of antibonding electrons] 48 24

25 Zumdahl fig s A and 1s B have little overlap; 1s and * 1s have similar energies A 2s A and 2s B have greater overlap; 2s and * 2s have greater energy difference (splitting) B 49 resulting energy level diagrams for Li 2 and Be 2 (fig 14.34, extra) 2s and * 2s differ in energy 2 nd row atoms 1s and * 1s have nearly same energy Li 2 6e s ( 1s ) 2 ( * 1s ) 2 ( 2s ) 2 b.o. = (42)/2=1 Be 2 8e s ( 1s ) 2 ( * 1s ) 2 ( 2s ) 2 ( * 2s ) 2 b.o. = (44)/2=0 no covalent Be 2 molecule observed 50 25