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Lecture 2

Lecture 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

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Lecture 2

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  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): • Write electronic structure in groups as follows: (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc. • Electrons in higher groups (to the right) do not shield those in lower groups • 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 • 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 4s electrons are the first ones removed when a 1st row transition metal forms a cation

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

  7. Ionization Energy (IE): Energy required to remove an electron from a gaseous atom or ion. Tendency 1: IE1 decreases on going down a group ( n, r increase and Zeff is constant). Tendency 2: IE1 increases along a period (Zeff increases, r decreases) Exception: Half-filled or filled shell are particularly stable 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) Similar for: Al, S

  8. Tendency 1: IE1 decreases on going down a group ( n, r increase and Zeff is constant). Tendency 2: IE1 increases along a period (Zeff increases, r decreases) Maximum for noble gases Minimum for H and alkali metals

  9. 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)

  10. 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

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

  12. Effective atomic radius (covalent radius) covalent radius =1/2(dAA in the A2 molecule) Example: H2: d = 0.74 Å ; so rH= 0.37 Å To estimate covalent bond distances e.g.: R----C-H: d C-H = rC + rH = 0.77 + 0.37 =1.14 Å

  13. 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(Zeff ~ constant as n increases because of shielding). Tendency 2: Atomic radii decrease along a period (Zeff increases and n is constant)

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

  15. Simple Bonding Theories Lewis electron-dot diagrams are very simplified but very useful models for analyzing bonding in molecules 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

  16. He Li Be B C N O F Ne Generally, atoms with the same outer orbital structure appear in the same column

  17. 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

  18. 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.

  19. 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.

  20. Number of Bonds 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

  21. 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)

  22. Bonding Patterns

  23. 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.

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

  25. 10e around P Expanded shells When it is impossible to write a structure consistent with the octet rule increase the number of electrons around the central atom 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.

  26. 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

  27. Favored structure • provides minimum formal charges • places negative formal charges on more electronegative atoms • implies smaller separation of charges 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

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

  29. 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.

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

  31. 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

  32. Basic molecular shapes

  33. Basic molecular shapes ABn

  34. Removing atoms from one basic geometry generates other shapes

  35. The geometries of electron domains

  36. Molecular geometries

  37. Molecular geometries Note that lone pairs adopt equatorial positions

  38. Molecular geometries

  39. Similar for higher steric numbers

  40. Lone pairs are larger than bonding pairs

  41. Effect of lone pairs on molecular geometry

  42. 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.

  43. Boiling Points and Hydrogen bonding

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

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

  46. Symmetry and group theory

  47. Natural symmetry in plants

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