1. Lecture 2

2. Shielding and effective nuclear charge Z* In polyelectronic atoms, each electron feels the attraction of the nucleus and the repulsion of the other electrons (both n and l must be taken into account) Each electron acts as a shield for electrons electrons farther away from the nucleus, reducing the attraction between the nucleus and the distant electrons Effective nuclear charge: Z* = Z – S (Z is the nuclear charge and S is the shielding constant) **

3. Shielding and effective nuclear charge Z*: Z* = Z – S (a measure of the nuclear attraction for an electron) To determine S (Slater’s rules): 1.Write electronic structure in groups as follows: (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc. 2.Electrons in higher groups (to the right) do not shield those in lower groups 3.For ns or np valence electrons: other electrons in the same n group: 0.35; except for 1s where 0.30 is used. electrons in the n-1 group: 0.85 electrons in the n-2, n-3,… groups: 1.00 4.For nd and nf valence electrons: other electrons in the same nd or nf group: 0.35 electrons in groups to the left: 1.00 S is the sum of all contributions

4. Shielding and effective nuclear charge Z*: There is a particular stability associated with filled and half-filled shells 4s electrons are the first ones removed when a 1st row transition metal forms a cation

5. Holds maximum of 5

6. Vanadium, Z = 23 (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc. VV+V+ ConfigZ*Z* Z*Z* 3d 3 4.34s 0 3d 2 4.65 4s 2 3.33d 4 3.954s 2 4.15 For V: 3d (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) 2 8 x 1 8 x 1 2 x.35 0 18.7 For V: 4s (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) 2 8 x 1 8 x.85 3 x.85.35 18.7 For V + : 3d (1s) (2s, 2p) (3s, 3p) (3d) 2 8 x 1 8 x 1 3 x.35 18.7 For V+ (4s 2 3d 2 ): 3d (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) 2 8 x 1 8 x 1.35 0 18.7 For V+ (4s 2 3d 2 ): 4s (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) 2 8 x 1 8 x.85 2 x.85.35 18.7

7. Periodic trends Generally, atoms with the same outer orbital structure appear in the same column

8. Ionization Energy (IE): Energy required to remove an electron from a gaseous atom or ion. Tendency 1: IE 1 decreases on going down a group ( n, r increase and Z eff is constant). Tendency 2: IE 1 increases along a period (Z eff increases, r decreases) Exception: Half-filled or filled shell are particularly stable B ([He]2s 2 2p 1  [He]2s 2 ) lower IE than Be ([He]2s 2  [He]2s 1 ), O ([He]2s 2 2p 4  [He]2s 2 2p 3 ) lower IE than N ([He]2s 2 2p 3  [He]2s 2 2p 2 ) Similar for: Al, S

9. Tendency 1: IE 1 decreases on going down a group ( n, r increase and Z eff is constant).Tendency 2: IE 1 increases along a period (Z eff increases, r decreases) Maximum for noble gases Minimum for H and alkali metals

10. Special “dips” B ([He]2s22p1  [He]2s2) lower IE than Be ([He]2s2  [He]2s1), O ([He]2s22p4  [He]2s22p3) lower IE than N ([He]2s22p3  [He]2s22p2)

11. Electron affinity (EA) = energy required to remove an electron from a gaseous negatively charged ion (ionization energy of the anion) to yield neutral atom. Maximum for halogens Minimum for noble gases Much smaller than corresponding IE

13. The size of atoms Atoms are not spheres with defined limits !! How can we measure them? How much can we “squeeze” them?

14. Effective atomic radius (covalent radius) covalent radius =1/2(d AA in the A 2 molecule) Example: H 2 : d = 0.74 Å ; so r H = 0.37 Å To estimate covalent bond distances e.g.: R----C-H: d C-H = r C + r H = 0.77 + 0.37 =1.14 Å

15. The size of orbitals tends to grow with increasing n. As Z increases, orbitals tend to contract, but with increasing number of electrons mutual repulsions keep outer orbitals larger Tendency 1. Atomic radii increase on going down a group (Z eff ~ constant as n increases because of shielding). Tendency 2: Atomic radii decrease along a period (Z eff increases and n is constant)

17. Ionic radii Cation formation vacates outermost orbital and decreases e-e repulsions SIZE DECREASES Anion formation increases e-e repulsions so they spread out more SIZE INCREASES **

18. Lewis electron-dot diagrams are very simplified but very useful models for analyzing bonding in molecules Simple Bonding Theories Valence electrons are those in the outer shell of an atom and they are the electrons involved in bonding The Lewis symbol is the element’s symbol plus one dot per valence electron

19. LiBe BCNOFNe He Generally, atoms with the same outer orbital structure appear in the same column

20. The octet rule Atoms tend to gain, lose or share electrons until they are surrounded by eight valence electrons (i.e., until they resemble a noble gas) Molecules share pairs of electrons in bonds and may also have lone pairs

21. Octet Rule, Lewis Structures Electrons can be stabilized by bond formation. H atom can stabilize two electrons in the valence shell. C  F can stabilize 8 electrons in the valence shell. Two electrons around H; Eight electrons complete the octet of C  F.

22. Completing the Octet Ionic Bonding: Electrons can be transferred to an atom to produce an anion and complete the octet. Covalent Bonding: Electrons can be shared between atoms providing additional stabilization.

23. Number of Bonds H: 1 more electron H + 2 moreH - 0 more C: 4 moreC 2+ 6 moreC - 3 more N: 3 moreN + 4 moreN - 2 more O: 2 moreO + 3 moreO - 1 more F: 1 moreF + 2 moreF - 0 more Additional stabilization that can be provided by some atoms: Bonds make use of the additional stabilizing capability of the atoms. # Bonds = (Sum of unused stabilizing capability)/2

24. Formal Charge Formal charge may begiven to each atom after all valence shell electrons have been assigned to an atom. –Non-bonding electrons are assigned to the atom on which they reside. –Bonding electrons are divided equally between the atoms of the bond. Formal charge = (# valence shell electrons in neutral atom) - (# nonbonding electrons) - ½ (# bonded electrons)

25. Bonding Patterns Formal charge CNO 1 0

26. Lewis Diagrams (3 * 4 + 6 * 1) / 2 = 9 bonds How many bonds left to draw? 9 – 8 = 1 bond left Put remaining bond(s) in any place where the octet rule is not violated.

27. Resonance forms When several possible Lewis structures with multiple bonds exist, all of them should be drawn (the actual structure is an average)

28. Expanded shells When it is impossible to write a structure consistent with the octet rule increase the number of electrons around the central atom 10e around P Only for elements from 3rd row and heavier, which can make use of empty d orbitals See also: L. Suidan et al. J. Chem. Ed. 1995, 72, 583.

29. Formal charge Apparent electronic charge of each atom in a Lewis structure Formal charge = (# valence e - in free atom) - (# unshared e - on atom) -1/2 (# bonding electrons to atom) Total charge on molecule or ion = sum of all formal charges Favored structures provide minimum formal charges place negative formal charges on more electronegative atoms imply smaller separation of charges Formal charges are helpful in assessing resonance structures and assigning bonding

30. To calculate formal charges Assign All non-bonding electrons to the atom on which they are found Half of the bonding electrons to each atom in the charge Favored structure provides minimum formal charges places negative formal charges on more electronegative atoms implies smaller separation of charges

31. Problem cases - expanded shells - generating charge to satisfy octets

32. Formal charges and expanded shells Some molecules have satisfactory Lewis structures with octets but better ones with expanded shells. Expansion allows a atom having a negative charge to donate into a positive atom, reducing the charges.

33. Charges may generated so as to satisfy the octet.

34. Valence shell electron pair repulsion (VSEPR) theory (a very approximate but very useful way of predicting molecular shapes) Electrons in molecules appear in bonding pairs or lone pairs Each pair of electrons repels all other pairs Molecules adopt geometries with electron pairs as far from each other as possible Electron pairs define regions of space where they are likely to be: Between nuclei for bonding pairs Close to one nucleus for lone pairs those regions are called electron domains the steric number is the sum of electron domains

35. Basic molecular shapes

36. AB n

37. Removing atoms from one basic geometry generates other shapes

38. The geometries of electron domains

39. Molecular geometries

40. Molecular geometries Note that lone pairs adopt equatorial positions

41. Molecular geometries

42. Similar for higher steric numbers

43. Lone pairs are larger than bonding pairs

44. Effect of lone pairs on molecular geometry

45. Electronegativity Scales The ability to attract electrons within a chemical, covalent bond Pauling: polar bonds have higher bond strengths. Electronegativity assigned to each element such that the difference of electronegativities of the atoms in a bond can predict the bond strength.

46. Boiling Points and Hydrogen bonding

48. Hydrogen bonding in ice The density of water decreases when it freezes and that determines the geology and biology of earth

49. Hydrogen bonding is crucial in biological systems Secondary structure of proteins DNA replication

50. Symmetry and group theory

51. Natural symmetry in plants

52. Symmetry in animals

53. Symmetry in the human body

54. The platonic solids

55. Symmetry in modern art M. C. Escher

56. Symmetry in arab architecture La Alhambra, Granada (Spain)

57. Symmetry in baroque art Gianlorenzo Bernini Saint Peter’s Church Rome

58. Symmetry in Native American crafts

59. 7th grade art project Silver Star School Vernon, Canada

60. Re 2 (CO) 10

61. C2F4C2F4 C 60

62. Symmetry in chemistry Molecular structures Wave functions Description of orbitals and bonds Reaction pathways Optical activity Spectral interpretation (electronic, IR, NMR)...

63. A molecule is said to have symmetry if some parts of it may be interchanged by others without altering the identity or the orientation of the molecule Molecular structures

64. Symmetry Operation: Movement of an object into an equivalent or indistinguishable orientation Symmetry Elements: A point, line or plane about which a symmetry operation is carried out

65. 5 types of symmetry operations/elements Identity: this operation does nothing, symbol: E Element is entire object

66. Proper Rotation: Rotation about an axis by an angle of 2  /n How about: NFO 2 ? H2OH2O NH 3 C2C2 C3C3

67. 180° (2  /2) C2C2 The Operation: Proper rotation C n is the movement (2  /n) The Element: Proper rotation axis C n is the line Applying C 2 twice Returns molecule to original oreintation C 2 2 = E

68. How about: NFO 2 ? H2OH2O NH 3 C 2 180º C 3, 120º Proper rotation axes

69. Rotation angleSymmetry operation 60ºC6C6 120ºC 3 (= C 6 2 ) 180ºC 2 (= C 6 3 ) 240ºC 3 2 (= C 6 4 ) 300ºC65C65 360ºE (= C 6 6 )

70. C2C2 C2C2 C 2, C 4 Rotation 2  m/n PtCl 4 Proper Rotation: Rotation about an axis by an angle of 2  /n

71. The highest order rotation axis is the principal axis and it is chosen as the z axis 2  /2 = C 2 2  /4 = C 4 C n n = E

72.   Reflection and reflection planes (mirrors)

73.  (reflection through a mirror plane) NH 3  Only one  ?

74. H2OH2O 

75. ’’ H2OH2O

76. B FF F If the plane contains the principal axis it is called  v B FF F If the plane is perpendicular to the principal axis it is called  h  n = E (n = even)  n =  (n = odd)

77. Inversion: i Center of inversion or center of symmetry (x,y,z)  (-x,-y,-z) i n = E (n is even) i n = i (n is odd)

78. Inversion not the same as C 2 rotation !!

80. Figures with center of inversion Figures without center of inversion

81. Improper rotation (and improper rotation axis): S n rotation about an axis by an angle 2  /n followed by reflexion through perpendicular plane

82. S 4 2 = C 2 Also, S 4 4 = E; S 2 = i; S 1 = 

83. Symmetry operations and elements OperationElement proper rotationaxis (C n ) improper rotationaxis (S n ) reflexionplane (s) inversioncenter (i) IdentityMolecule (E)

84. Symmetry point groups The set of all possible symmetry operations on a molecule is called the point group (there are 28 point groups) The mathematical treatment of the properties of groups is Group Theory In chemistry, group theory allows the assignment of structures, the definition of orbitals, analysis of vibrations,... See: Chemical applications of group theory by F. A. Cotton

85. To determine the point group of a molecule

87. Groups of low symmetry