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Lecture 2

Lecture 2. Placing electrons in orbitals. 5p. E. Approximate order of filling orbitals with electrons. 4d. 5s. 3d. 4s. 4p. 3p. 3s. 2p. 2s. 1s. 5p. E. 4d. 5s. 3d. 4s. 4p. 3p. 3s. 2p. 2s. 1s. Shielding and effective nuclear charge Z*

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Lecture 2

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  1. Lecture 2

  2. Placing electrons in orbitals

  3. 5p E Approximate order of filling orbitals with electrons 4d 5s 3d 4s 4p 3p 3s 2p 2s 1s

  4. 5p E 4d 5s 3d 4s 4p 3p 3s 2p 2s 1s

  5. Shielding and effective nuclear charge Z* In polyelectronic atoms, each electron is attracted to the nucleus and repelled by the other electrons (both n and l must be taken into account) Electrons 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: Zeff = Z* = Z – s (Z is the nuclear charge and s is the shielding constant) **

  6. 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. • Note the order does not correspond to filling order. The shielding constant for each group is formed as the sum of the following contributions: • 2. Electrons in higher groups (to the right) do not shield those in lower groups • 3. An amount of 0.35 from each other electron within the same group except for the [1s] group where the other electron contributes only 0.30. • 4. If the group is of the [s p] type, an amount of 0.85 from each electron with principal quantum number one less and an amount of 1.00 for each electron with an even smaller principal quantum number • If the group is of the [d] or [f], type, an amount of 1.00 for each electron in a lower group (to the left). • Note that (1) as Z increases so does Z* leading to smaller orbitals as we move to right in a period s is the sum of all contributions

  7. Vanadium, Z = 23 (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc. For V: 4s (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) 2 x 1 8 x 1 8 x .85 3 x .85 .35 s = 19.7 Z* = 23 -19.7 = 3.3

  8. Vanadium, Z = 23 (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc. For V: 3d (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) 2 x 1 8 x 1 8 x 1 2 x .35 0  s = 18.7 Z* = 23 – 18.7 = 4.3

  9. Vanadium, Z = 23 (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc. For V+ (4s23d2): 3d (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) 2 8 x 1 8 x 1 .35 0 18.35

  10. Vanadium, Z = 23 (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc. For V+: 3d (1s) (2s, 2p) (3s, 3p) (3d) 2 8 x 1 8 x 1 3 x .35 s = 19.05 Z* = 23 – 19.05 = 3.95

  11. 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

  12. Spin Multiplicity Frequently there are several ways of putting electrons into a partially filled subshell. For example, a p2 configuration. or Both electrons in same orbital. Larger electron-electron repulsion. Pc, higher energy a positive quantity. or Two electrons of same spin. Energy reduced by exchange energy, Pe, a negative quantity.

  13. Further Example, p4. Pc + 3Pe (1-3, 1-4, 3-4) or Pc + 2Pe or 2 Pc + 2Pe

  14. Holds maximum of 5 4s electrons are the first ones removed when a 1st row transition metal forms a cation

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

  16. 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

  17. 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

  18. B ([He]2s22p1 [He]2s2) lower IE than Be ([He]2s2 [He]2s1) Due to 2p being further away from nucleus. Special “dips” Ga: ([Ar]4s2 3d104p1 ([Ar]4s2 3d10 ) lower IE than Zn: ([Ar]4s2 3d10 ([Ar]4s2 3d9 ) Due to relative instability of the 4p electron in Ga O: ([He]2s22p4 [He]2s22p3) lower IE than N: ([He]2s22p3 [He]2s22p2) Due to instability of the 4th 2p electron in O

  19. 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 (have maximum of Z*) • Minimum for noble gases (minimum for Z* for elec in next shell) • Much smaller than corresponding IE (working against smaller Z*)

  20. 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

  21. The size of corresponding orbitals tends to grow with increasing n.As Z increases, orbitals tend to contract, but with increasing number of electrons shielding 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 .)

  22. Pictorially, here are the trends in radii…..

  23. Anion formation increases e-e repulsions (usually increased shielding) so they spread out more SIZE INCREASES Cation formation vacates outermost orbital and decreases e-e repulsions (usually decreased shielding) SIZE DECREASES Ionic radii

  24. 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

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

  26. 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

  27. 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.

  28. 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.

  29. 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

  30. 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)

  31. Bonding Patterns

  32. 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.

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

  34. 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.

  35. 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

  36. 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

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

  38. 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.

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

  40. 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

  41. Basic molecular shapes

  42. Basic molecular shapes ABn

  43. Removing atoms from one basic geometry generates other shapes

  44. The geometries of electron domains

  45. Molecular geometries

  46. Molecular geometries Note that lone pairs adopt equatorial positions

  47. Molecular geometries

  48. Similar for higher steric numbers

  49. Lone pairs are larger than bonding pairs

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