1. Chapter 17Many-Electron Atoms and Chemical Bonding 17.1Many-Electron Atoms and the Periodic Table 17.2Experimental Measures of Orbital Energies 17.3Sizes of Atoms and Ions 17.4Properties of the Chemical Bond 17.5Ionic and Covalent Bonds 17.6Oxidation States and Chemical Bonding

2. 17.1Many-Electron Atoms Many electron atoms and the periodic table Building up electron configurations Building up from H to Ar Building from K to Kr: Transition elements and d orbitals Electron shells and the periodic table Hund’s rule, paramagnetism and diamagnetism.

3. 1a 2a 3a4a5a6a7a8881b2b 3a4a5a6a7a 8a Building up the table from electron configurations

4. Electronic structure of atoms of the elements: (1)Atoms of the various elements differ from each other in their values of Z and electrons. (2)Electrons in atoms are arranged in orbitals and shells. (3)Orbitals are characterized by the quantum numbers n, l and m l. (4)Orbitals having the same value of n are said to be in the same shell. Orbitals having the same values of n and l are said to be in the same subshell.

5. Many electron atoms and the periodic table Comparison of the electron densities of the H atom orbitals and many electron atoms. The quantum numbers n, l and m l still have an approximate validity Every electron in an atom has a set of four quantum numbers that describe its spatial distribution and spin state. This means that every electron in a multielectron atom occupies an atomic orbital with a characteristic size, shape, energy and spin direction.

6. Building up electron configurations An electron configuration is a list of the occupied orbitals and the number of electrons in each. The electron configuration of lowest energy is termed the ground state electronic configuration. Aufbau Principle: The ground state electron configuration is built by filling the lowest energy orbitals first obeying the Pauli principle and Hund’s rule

7. The orbital approximation: The electron density of an isolated many-electron atom is approximately the sum of the electron densities of each of the individual electrons taken separately. For atoms with more than one electron, approximations are required in order to make quantitative quantum mechanical approximations. The approximation amounts to treat each electron as if it were moving in a field o charge that is the net result of the nuclear attraction and the average repulsions of all the other electrons.

8. Determining a ground state electronic configuration (1)Use the n + l rule to determine the relative energies of the atomic orbitals from 1s to ….. (2)Imagine a bare nucleus of charge +Z surrounded by empty atomic orbitals. (3)Add Z electrons to the empty orbitals starting with the lowest energy orbital first, obeying the Pauli principle at all times. (4)Electrons are placed in orbitals of lowest ener

9. Effective nuclear charge (Z eff ) on the outer electrons Maintain hydrogen atom like orbitals as an approximation, but subshell energies are not equal: E ns < E np < E nd < E nf A s electron penetrates to the nucleus more than a p electron: a p electron penetrates to the nucleus more than a d electron: more penetration, more stable, lower energy. Subshell energies: E 3s < E 3p < E 3d

11. Electron shielding of the nuclear charge by other electrons Why is the energy of a 3s orbital lower than than of a 3p orbital? Why is the energy of a 3p orbital lower than the energy of a 3d orbital?

12. Effective charge, Z eff, see by valence electrons* *Note x-axis is incorrect. What should it be?

13. Are the following two states allowed for N by the Pauli principle? 1s 2 2s 2 2p x 1 2p y 1 2p z 1 or 1s 2 2s 2 2p x 2 2p y 1 2p z 0 Hund’s rule refers to the lowest energy of electron configurations allowed by the Pauli exclusions principle. It does not forbid the existence of any of the Pauli allowed configurations. If there are more than electron configurations one allowed Pauli configuration, the lower energy on will be predicted by Hund’s rule and the others will be excited states. Which is more stable? 1s 2 2s 2 2p x (  )2p y (  )2p z (  ) is more stable than 1s 2 2s 2 2p x (  )2p y (  )2p z ()

14. The presence of two orbitally and spin unpaired electrons in the ground state of carbon makes the atom paramagnetic. A paramagnetic substance is attracted to a magnetic field. A diamagnetic substance is repelled from a magnetic field. All substances which possess one or more orbitally unpaired electrons are paramagnetic. All substances which possess only spin paired electrons are diamagnetic. Paramagnetic and diamagnetic substances

15. Examples of diamagnetic and paramagnetic atoms Which of the following atoms are paramagnetic? 1 H, 2 He, 3 Li, 4 Be, 5 B, 6 C, 7 N, 8 O, 9 F, 10 Ne 1 H, 3 L, 5 B, 7 N, 9 F must be paramagnetic since they possess an odd number of electrons. 6 C and 8 O are paramagnetic because of Hund’s rule: 6 C:1s 2 2s 2 p x 1 p y 1 8 O:1s 2 2s 2 p x 2 p y 1 p z 1 2 He, 4 Be and 10 Ne are diamagnetic.

16. The energy of an orbital of a hydrogen atom or any one electron atom only depends on the value of n shell = all orbitals with the same value of n subshell = all orbitals with the same value of n and l an orbital is fully defined by three quantum numbers, n, l, and m l

17. The energy of subshells increase with l for a given value of n

18. The (n + l) rule of orbital energies in a multielectron atom. Electrons fill orbitals of different energies by filling the lowest energy first. The energies of orbitals of multielectron atoms follow the (n + l) rule: the lowest value of (n + l) has the lowest energy. Examples with (n + l) 1s (1 + 0) < 2s (2 + 0) < 3s (3 + 0) < 3p (3+1),< 4s (4 + 0) < 3d (3 + 2) < 4p (4 + 1) When n + l is the same for two orbitals, the orbital with the higher value of n has the higher energy.

19. Shell and Subshell Structure Atomic Energy Levels according to the (n + l) rule Buildup (aufbau) Principle

20. Relative orbital energies for the multielectron atom. The energy of an orbital of a multielectron atom depends on n and l (but not m l ) 2s < 2p 3s < 3p < 3d ~ 4s (may switch with Z) Note energy levels are getting closer together for n = 3 as expected from the Bohr atom. This means that factors ignored may have to be considered

21. Classification of orbitals of a many electron atom according to their energies. A group of orbitals with exactly equal energies comprise a subshell. Example: 2p x, 2p y and 2p z Orbitals with same value of n and different value of l comprise a shell. Example: 2s and 2p comprise a shell. The orbital approximation ignores electron-electron repulsion, but takes into account Hund’s rule: electrons with parallel spins (  ) tend to stay apart compared to electrons with antiparallel spins (  ).

22. Orbital shells and the building up of the periodic table A shell is a set of orbitals with the same value of n and l for a H atom. The Ar atom has shells as shown (left) in the profile of electron density as a function of distance from the nucleus The last shell are the valence electrons of our Lewis structures!

23. Electronic structure and the periodic table Electrons in the outermost shell of an atom are the most important in determining chemical properties. Chemical reactions involve only the outer (valence) electrons. The inner (core) electrons are not involved in chemical reactions. Elements in a given vertical column (families) of the periodic table have similar outer-shell electron configurations and similar properties. They are isoelectronic with respect to the number of valence electrons. Elements in a row show regular trends in their properties due to the continuing increase in the number of valence electrons until a shell is filled.

24. The Pauli exclusion principle and magic number of electrons. Two equivalent statements of the exclusion principle: (1)No two electrons may have the same set of four quantum numbers; (2)No more than two electrons may occupy the same orbital. Because of the Pauli exclusion principle, outer electrons do not “fall” into the inner shell. Thus, the atom is stable.

25. The Pauli principle imposes structure on the many electron atom. Without it, all the electrons might be expected to crowd into the low energy orbitals. With it the electrons are organized, filled orbitals with no more than two electrons. The ground state is the lowest energy organization of electrons around the nucleus. The electron organization is described by electron configurations. The ground state of an atom corresponds to the lowest energy electron configuration.

26. Ground state electron configuration of a many electron atom : Governs reactivity of atoms under normal condition Imagine a bare nucleus of charge +Z Imagine empty orbitals surrounding the nucleus Fill the orbitals with Z electrons for the neutral atom following two principles: Aufbau principle: fill lowest energy orbitals first Pauli exclusion principle: each electron must have four different quantum numbers (maximum of 2 electrons in an orbital).

27. Constructing the periodic table by filling orbitals with electrons (electron configurations). Aufbau: Fill 1s orbital first Pauli: no more than two electrons in the 1s orbital The basis of the duet rule: filling a shell 1s subshell filled with 2 He = stable electron core given symbol [He]. Construction of the first row of the periodic table. Electron configurations: 1 H and 2 He.

28. Filling the orbitals of 3 Li, 4 Be and 5 B Aufbau: Fill 1s orbital first, then 2s, then 2p. Pauli: no more than two electrons in the 1s orbital. 2s subshell filled with 4 Be.

29. For carbon, how do the two 2p electrons distribute themselves in the three 2p orbitals? For nitrogen, how do the three 2 p electrons distribute themselves in the three 2p orbitals? Filling the orbitals of 6 C and 7 N. The need for a third rule (Hund’s rule):

30. Hund’s rule: Applies when filling the orbitals of a subshell with electrons (np or nd or nf subshells). Or more generally when filling orbitals of identical energy When adding electrons to a subshell, the ground state electronic configuration is formed by maximizing the number of electrons with parallel spins (  )(  ) before pairing two electrons in one orbital (  )(). Example: 6 C = [He]2s 2 2p x (  )2p y (  )2p z () = ground state Example: 6 C = [He]2s 2 2p x (  )2p y ()2p z () = excited state

32. Filling the orbitals of 6 C and 7 N. The need for a third rule (Hund’s rule): Hund’s Rule: When electrons occupy orbitals of the same energy, the lowest energy state corresponds to the configuration with the greatest number of orbitally and spin unpaired electrons. When the configuration is written as 1s 2 2s 2 2p 2 it is understood that two different p orbitals are occupied.

33. Filling the orbitals of 8 O, 9 F and 10 Ne Filling the 2p subshell produces another stable configuration of electrons which serves as the core shell of the third row: symbol [Ne]

34. Summary: Electron configurations from 1 H to 10 Ne. No new features for the electron configurations from 11 Na to 18 Ar.

35. The third full row of the periodic table: 19 K- 36 Kr The 4s orbital is slightly more stable than the 3d orbital at the beginning of the third full period of the periodic table: 19 K = [Ar]4s 1 3d 0 20 Ca = [Ar]4s 2 3d 0 The reason is that the 4s orbital has a higher probability of being closer to the nucleus and see a greater effective Z eff than a 3d orbital. The 4s and 3d orbitals are close in energy in the one electron atom. Difficult to predict stability for multielectron atom.

36. Electron configuration of the transition elements: 21 Sc through 30 Zn 21 Sc, 22 Ti, 23 V, 24 Cr, 25 Mn, 26 Fe, 27 Co, 28 Ni, 29 Cu, 30 Zn 19 K = [Ar]4s3d 0 20 Ca = [Ar]4s 2 3d 0 What would you expect for 21 Sc? 21 Sc = [Ar]4s 2 3d 1. Not quite correct…. The 3d electron is lower in energy than the 4s electron in 21 Sc from experiment: 21 Sc = [Ar] 3d 1 4s 2 d orbitals raise their ugly heads!

38. Ground State Electron Configurations ORBITALS and Hund ’ s Rule

39. “Expected” and found electron configurations of the d block elements from Z = 21 to Z = 30

41. Atomic Electronic Configurations 1 H to 36 Kr Group I:ns 1 Group II:ns 2 Group III:ns 2 p 1 Group IV: ns 2 p 2 Group V: ns 2 p 3 Group VI:ns 2 p 4 Group VII: ns 2 p 5 Group VIII: ns 2 p 6

44. 17.2Experimental Measures of Orbital Energies Photoelectron spectroscopy Periodic trends in ionization energies Periodic trends in electron affinities

45. Ionization Energy Measure of the effort needed to remove electron(s) from a ground state atom: –Values are positive –Obtained by photoelectron spectroscopy X + h X + + e -  E = IE 1 –Second ionization energy always exceeds first X X + + e -  E = IE 1 X + X 2+ + e -  E = IE 2

46. Reactivity increases with the number of shells shielding the electrons in the outer (valence) shell. DEMONSTRATION lA FamilyVoltsValence Shell Li5.392s 1 Na5.143s 1 K4.344s 1 Rb4.185s 1 Cs3.896s 1 Ionization Energy The Alkali Metal (IA) Family of Elements

47. Reactivity increases with the number of shells shielding the electrons in the outer (valence) shell. DEMONSTRATION lA FamilyVoltsValence Shell Li5.392s 1 Na5.143s 1 K4.344s 1 Rb4.185s 1 Cs3.896s 1 Ionization Energy: The Alkali Metal (IA) Family of Elements

48. Ionization energies (ionization potentials): The ionization energy (IE) of an atom is the minimun energy required to remove an electron from a gaseous atom. X(g) X + (g) + e - The first ionization energy IE 1 is the energy required to remove the first electron from the atom, the second ionization energy IE 2, is the energy required to remove the second electron from the +1 positive ion of the atom and so on. Conclusions from experimental IE values: An abrupt change in IE in going along a row or column of the periodic table indicates a change in the valence electron shell or subshell. Let’s take a look:

49. Experimental data and theoretical ideas Explain the “two slopes” for the ionization energies of carbon.

50. 6 C 1s 2 2s 2 2p 2 6 C +5 1s 1 2s 0 2p 0 6 C +4 1s 2 2s 0 2p 0 6 C +3 1s 2 2s 1 2p 0 6 C +2 1s 2 2s 2 2p 0 6 C +1 1s 2 2s 2 2p 1 It gets more and more energy to remove an electron from an increasingly positively charged atom. The first smaller slope is due to removal of n = 2 electrons, the second larger slope is due to removal of n = 1 electrons.

51. Ionization energies in tabular form

52. Ionization energies in graphical form

55. Periodic trends of the first ionization energies of the representative elements: What are the correlations across and down?

56. The electron affinity (EA) of an atom is the energy change which occurs when an atom gains an electron. X(g) + e - Xe - (g) Electron affinities of the representative elements: What are the correlations across and down?

58. Ionization energies in tabular form

59. Ionization energies in graphical form

60. Periodic trends of the first ionization energies of the representative elements: What are the correlations across and down?

61. The electron affinity (EA) of an atom is the energy change which occurs when an atom gains an electron. X(g) + e - Xe - (g) Electron affinities of the representative elements: What are the correlations across and down?

62. 17.3Sizes of Atoms and Ions The radii of atoms and ions Covalent radius, atomic radius and ionic radius Periodic trends in the radius of atoms and ions Radii generally increase down a group (n of outer shell increases) and decrease (Z eff decreases for same shell) from left to right across a period. Cations are generally smaller than their parent atoms and anions are larger.

63. Atomic Volume

65. Covalent Radii from Experiment The covalent radius is defined as half the distance between two atoms bound by a single bond in a molecule.

66. Periodic properties of atomic radius: What are the correlations? General Rule: The size of an atom decreases in a row as the nuclear charge increases and the size of an atom increases in a column as the nuclear charge increases

69. 17.4Properties of the Chemical Bond Bond length: Bond enthalpy: Bond order: The distance between the nuclei of two bonded atoms. The energy required to break a bond between two atoms. The number of shared electron pairs (not electrons) in a covalent bond.

70. Bond Lengths H 2 = 0.74 Å F 2 1.42 Cl 2 1.99 Br 2 2.28 I 2 2.67 ClF1.09 BrCl2.14 BrF1.76 ICl2.32 HF0.92 HCl1.27 HBr1.41 HI1.61 N 2 1.09 O 2 1.21 NO1.15 CO1.13

71. The Nature of the Chemical Bond Pose the question: “ Why do atoms sometimes form stable molecules and compounds …. and sometimes not? ” Or perhaps reducing the general question to more limited questions for which there is a higher probability of getting answers: –“ What is the energy in bonds? ” –“ What is the distance between atoms? ” –“ What is the shape and geometry that results? ”

72. Li 2 105 Na 2 71 K 2 50 Rb 2 46 Cs 2 44 F 2 154 Cl 2 247 Br 2 192 I 2 151 N 2 946 O 2 498 Bond Energies H 2 = 400 kJ/mol

73. Bond Energy (Enthalpy)

74. 17.5Ionic and Covalent Bonds Ionic bonds: Electron density is mainly transferred from one atom to another atom to create a bond between two atoms. Covalent bonds: Electron density is shared by two bonded atoms. Electronegativity: A measure of the ability of an atom in a bond to attract electrons from other atoms. Percent covalent (ionic) character: A measure of the polarity of a bond between two atoms.

76. Electronegativity (EN): a measure of the ability of an atom to attract electrons to itself in competition with other atoms