1. Excited Atoms & Atomic Structure

2. The Quantum Mechanical Picture of the Atom
Basic Postulates of Quantum Theory
Atoms and molecules can exist only in certain energy states. In each energy state, the atom or molecule has a definite energy. When an atom or molecule changes its energy state, it must emit or absorb just enough energy to bring it to the new energy state (the quantum condition).
Atoms or molecules emit or absorb radiation (light) as they change their energies. The frequency of the light emitted or absorbed is related to the energy change by a simple equation.

3. The Quantum Mechanical Picture of the Atom
The allowed energy states of atoms and molecules can be described by sets of numbers called quantum numbers.
Quantum numbers are the solutions of the Schrodinger, Heisenberg & Dirac equations.
Four quantum numbers are necessary to describe
energy states of electrons in atoms
– n, , m, ms
Schroedinger 3-dimensional
time independent equation
Heisenberg’s uncertainty
Equation
Dirac’s quantum
mechanical model
E. Schrodinger
W. Heisenberg

4. Quantum Numbers – n n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7
The Principal quantum number has the symbol – n.
n = 1, 2, 3, 4, “shells”
n = K, L, M, N,
The electron’s energy depends principally on n and tells the average relative distance of the electron from the nucleus.
– As n increases for a given atom, so does the average distance of the electrons from the nucleus.
– Electrons with higher values of n are easier to remove from an atom.
n = 1
n = 2
n = 3
n = 4
n = 5
n = 6
n = 7

5. Quantum Numbers –  2. The azimuthal quantum number has the symbol .
 describes the shape of the region of space occupied by the electron
When linked with n defines the energy of the electron, All wave functions that have the same value of both n and l form a subshell
 = 0, 1, 2, 3, 4, 5, (n-1)
 = s, p, d, f, g, h, (n-1)
= 0
= s
= 1
= p
= 2
= d
= 3
= f
n = 1
n = 2
n = 3
n = 4
n = 5
n = 6
n = 7

6. Quantum Numbers – m The symbol for the magnetic quantum number is m.
If  = 0 (or an s orbital), then m = 0.
There is only 1 value of m. Thus there is one s orbital per n value. n  1
If  = 1 (or a p orbital), then m = -1,0,+1.
There are 3 values of m. Thus there are three p orbitals per n value. n  2
If  = 2 (or a d orbital), then m = -2,-1,0,+1,+2.
There are 5 values of m. Thus there are five d orbitals per n value. n  3
If  = 3 (or an f orbital), then m = -3,-2,-1,0,+1,+2, +3.
There are 7 values of m. Thus there are seven f orbitals per n value, n
Theoretically, this series continues on to g,h,i, etc. orbitals.
Practically speaking atoms that have been discovered or made up to this point in time only have electrons in s, p, d, or f orbitals in their ground state configurations.
Each wave function with an allowed combination of n, l, and ml values describes an atomic orbital, a particular spatial distribution for an electron
For a given set of quantum numbers, each principal shell contains a fixed number of subshells, and each subshell contains a fixed number of orbitals

7. Atomic Orbitals n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7
Atomic orbitals are regions of space where the probability of finding an electron about an atom is highest.
s orbital properties:
There is one s orbital per n level.
 = 0
1 value of m
= 0
= s
n = 1
n = 2
n = 3
n = 4
n = 5
n = 6
n = 7

8. Atomic Orbitals The three orbitals are named px, py, pz.
p orbitals are peanut or dumbbell shaped.
They are directed along the axes of a Cartesian coordinate system.
The first p orbitals appear in the n = 2 shell.
There are 3 p orbitals per n level.
The three orbitals are named px, py, pz.
They have an  = 1.
m = -1,0, values of m

9. Atomic Orbitals
d orbital shapes

10. Atomic Orbitals
f orbital shapes

11. Quantum Numbers

12. Quantum Numbers – ms
The last quantum number is the spin quantum number which has the symbol ms.
The spin quantum number only has two possible values.
ms = +1/2 or -1/2

13. The Periodic Table and Electron Configurations
Note that the 3d subshell is higher in energy than the
4s subshell so appears in the 4th period
Day 1

14. Building up the Periodic Table
The Nucleus:
The Aufbau Process
– Used to construct the periodic table
– First, Build by adding the required number of protons (the atomic number) and neutrons (the mass of the atom)
– Second, Determine the number of electrons in the atoms then add electrons one at a time to the lowest-energy orbitals available without violating the Pauli principle
Electrons:
Hund’s Rule states that each orbital will be filled singly before pairing begins. The singly filled orbitals will have a parallel spin.
– Each of the orbitals can hold two electrons, one with spin up , which is written first, and one with spin down 
– A filled orbital is indicated by , in which the electron spins are paired
– The electron configuration is written in an abbreviated form, in which the occupied orbitals are identified by their principal quantum n and their value of l (s, p, d, or f), with the number of electrons in the subshell indicated by a superscript
Pauli’s Exclusion Principle states that paired electrons in an orbital will have opposite spins.
Neon - 2p   
2s 
1s 

15. Building up the Periodic Table
Valence electrons
– It is tedious to keep copying the configurations of the filled inner subshells
– The notation can be simplified by using a bracketed noble gas symbol to represent the configuration of the noble gas from the preceding row
– Electrons in filled inner orbitals are closer and are more tightly bound to the nucleus and are rarely involved in chemical reactions Now we can write a complete set of quantum numbers for all of the electrons in these three elements as examples. Na
First for 11Na.
When completed there must be one set of 4 quantum numbers for each of the 11 electrons in Na (remember Ne has 10 electrons)
[Ne] = 1s22s22p6

16. Building up the Periodic Table
11Na
1s22s22p63s1

17. Electron Configuration of the Elements

18. Periodic Trends in Atomic Radii
In the periodic table, atomic radii decrease from left to right across a row because of the increase in effective nuclear charge due to poor electron screening by other electrons in the same principal shell. Atomic radii increase from top to bottom down a column because the effective nuclear charge remains constant as the principal quantum number increases.

19. Ionization Energies
• There are two reasons for It takes more energy to remove the second electron from an atom than the first, and so on. :
1. The second electron is being removed from a positively charged species rather than a neutral one, so more energy is required.
2. Removing the first electron reduces the repulsive forces among the remaining electrons, so the attraction of the remaining electrons to the nucleus is stronger.

20. Electron Affinities
Electron affinity (EA) of an element E is defined as the energy change that occurs when an electron is added to a gaseous atom:
E (g) + e--  E—(g)
energy change = EA.
• Electron affinities can be negative (in which case energy is released when an electron is added) or positive (in which case energy must be added to the system to produce an anion) or zero (the process is energetically neutral).
• Halogens have the most negative electron affinities.

21. Ionic Radii and Isoelectronic Series
When one or more electrons is removed from a neutral atom, two things happen:
1. Repulsions between electrons in the same principal shell decrease because fewer electrons are present.
2. The effective nuclear charge felt by the remaining electrons increases because there are fewer electrons to shield one another from the nucleus.

22. Electronegativity
Increases
Increases
Increases
The tendency of an element to gain or lose electrons is is called electronegativity (), defined as the relative ability of an atom to attract electrons to itself in a chemical compound.

23. An Overview of Chemical Bonding
Chemical bond — the force that holds atoms together in a chemical compound
Covalent bonding — electrons are shared between atoms in a molecule or polyatomic ion
Ionic bonding — positively and negatively charged ions are held together by electrostatic forces
Ionic compounds — dissolve in water to form aqueous solutions that conduct electricity
Covalent compounds — dissolve to form solutions that do not conduct electricity
Chemical bonding
1. Ionic — one or more electrons are transferred completely from one atom to another, and the resulting ions are held together by purely electrostatic forces
2. Covalent — electrons are shared equally between two atoms
3. Polar covalent — electrons are shared unequally between the bonded atoms
4. Polar bond — bond between two atoms that possess a partial positive charge (õ+) and a partial negative charge (õ-)

24. The Continuous Range of Bonding Types
Covalent and ionic bonding represent two extremes.
In pure covalent bonds electrons are equally shared by the atoms.
In pure ionic bonds electrons are completely lost or gained by one of the atoms.
Most compounds fall somewhere between these two extremes.
All bonds have some ionic and some covalent character.
For example, HI is about 17% ionic
The greater the electronegativity differences the more polar the bond.
Day 2

25. OXIDATION NUMBERS Guidelines for assigning oxidation numbers.
The oxidation number of any free, uncombined element is zero.
The oxidation number of an element in a simple (monatomic) ion is the charge on the ion.
In the formula for any compound, the sum of the oxidation numbers of all elements in the compound is zero.
In a polyatomic ion, the sum of the oxidation numbers of the constituent elements is equal to the charge on the ion.
Fluorine has an oxidation number of –1 in its compounds.
Hydrogen, H, has an oxidation number of +1 unless it is combined with metals, where it has the oxidation number -1.
Examples – LiH, BaH2
Oxygen usually has the oxidation number -2.
Exceptions:
In peroxides O has oxidation number of –1.
Examples - H2O2, CaO2, Na2O2
In OF2, O has oxidation number of +2. Use the periodic table to help with assigning oxidation numbers of other elements.
IA metals have oxidation numbers of +1.
IIA metals have oxidation numbers of +2.
IIIA metals have oxidation numbers of +3.
VA elements have oxidation numbers of –3 in binary compounds with H, metals or NH4+.
VIA elements below O have oxidation numbers of –2 in binary compounds with H, metals or NH4+.

26. OXIDATION NUMBERS
NH3
ClO-
H3PO4
MnO4-
Cr2O72-
C3H8

27. Formal Charges Cl=N-O O=N-Cl
The most likely formula for a molecule or ion is usually the one in which the formal charge on each atom is zero or as near zero as possible
Negative formal charges are more likely to occur on the more electronegative elements
Lewis dot formulas in which adjacent atoms have formula charges of the same sign are usually not accurate
Cl=N-O
O=N-Cl

28. Formal Charges - + H N H B Cl Al + H ∙∙ O H ∙∙ N H ∙∙ S

29. Covalent Bonding Covalent bonds are formed when atoms share electrons.
If the atoms share 2 electrons a single covalent bond is formed.
If the atoms share 4 electrons a double covalent bond is formed.
If the atoms share 6 electrons a triple covalent bond is formed.
The attraction between the electrons is electrostatic in nature
The atoms have a lower potential energy when bound.
Covalent bonds in which the electrons are shared equally are designated as nonpolar covalent bonds.
Nonpolar covalent bonds have a symmetrical charge distribution.
To be nonpolar the two atoms involved in the bond must be the same element to share equally.

30. Polar and Nonpolar Covalent Bonds
Covalent bonds in which the electrons are not shared equally are designated as polar covalent bonds
Polar covalent bonds have an asymmetrical charge distribution
To be a polar covalent bond the two atoms involved in the bond must have different electronegativities.
Some examples of polar covalent bonds. HF

31. Polar and Nonpolar Covalent Bonds
Compare HF to HI.

32. Polar and Nonpolar Covalent Bonds
Polar molecules can be attracted by magnetic and electric fields.

33. Dipole Moments
Molecules whose centers of positive and negative charge do not coincide, have an asymmetric charge distribution, and are polar.
These molecules have a dipole moment.
The dipole moment has the symbol .
 is the product of the distance,d, separating charges of equal magnitude and opposite sign, and the magnitude of the charge, q.
There are some nonpolar molecules that have polar bonds.
There are two conditions that must be true for a molecule to be polar.
There must be at least one polar bond present or one lone pair of electrons.
The polar bonds, if there are more than one, and lone pairs must be arranged so that their dipole moments do not cancel one another.

34. Molecular Dipole Moments
• In complex molecules that contain polar covalent bonds, the three-dimensional geometry and the compound’s symmetry determine if there is a net dipole moment
• Mathematically, dipole moments are vectors; they possess both a magnitude and a direction
• Dipole moment of a molecule is the vector sum of the dipole moments of the individual bonds in the molecule
• If the individual bond dipole moments cancel one another, there is no net dipole moment
• Molecular structures that are highly symmetrical (tetrahedral and square planar AB4, trigonal bipyramidal AB5, and octahedral AB6) have no net dipole moment; individual bond dipole moments completely cancel out
• In molecules and ions that have V-shaped, trigonal pyramidal, seesaw, T-shaped, and square pyramidal geometries, the bond dipole moments cannot cancel one another and they have a nonzero dipole moment
Polar Molecules must meet two requirements:
One polar bond or one lone pair of electrons on central atom.
Neither bonds nor lone pairs can be symmetrically arranged that their polarities cancel.

35. Polar Covalent Bonds

36. Polar Covalent Bonds Ionic Polar Covalent Covalent
Determine Inductive effect
Count the number of electrons the element should have
Determine how equally electrons are shared (DEN) >1.7 consider it ionic
Oxidation number Formal charge
Day 3

37. Writing Lewis Formulas: The Octet Rule
The octet rule states that representative elements usually attain stable noble gas electron configurations in most of their compounds.
Lewis dot formulas are based on the octet rule.
We need to distinguish between bonding (or shared) electrons and nonbonding (or unshared or lone pairs) of electrons.
N - A = S rule
Simple mathematical relationship to help us write Lewis dot formulas.
N = number of electrons needed to achieve a noble gas configuration.
N usually has a value of 8 for representative elements.
N has a value of 2 for H atoms.
A = number of electrons available in valence shells of the atoms.
A is equal to the periodic group number for each element.
A is equal to 8 for the noble gases.
S = number of electrons shared in bonds.
A-S = number of electrons in unshared, lone, pairs.

38. Writing Lewis Formulas: The Octet Rule
For ions we must adjust the number of electrons available, A.
Add one e- to A for each negative charge.
Subtract one e- from A for each positive charge.
The central atom in a molecule or polyatomic ion is determined by:
The atom that requires the largest number of electrons to complete its octet goes in the center.
For two atoms in the same periodic group, the less electronegative element goes in the center.
Select a reasonable skeleton
The least electronegative is the central atom
Carbon makes 2,3, or 4 bonds
Nitrogen makes 1(rarely), 2,3, or 4 bonds
Oxygen makes 1, 2(usually), or 3 bonds
Oxygen bonds to itself only as O2 or O3, peroxides, or superoxides
Ternary acids (those containing 3 elements) hydrogen bonds to the oxygen, not the central atom, except phosphates
For ions or molecules with more than one central atom the most symmetrical skeleton is used
Calculate N, S, and A

39. Writing Lewis Dot Formulas
N ever Have a Full Octet
Always Have a Full Octet
Sometimes Have a Full Octet
Sometimes Exceed a Full Octet

40. Writing Lewis Dot Formulas
Count the number of electrons brought to the party (element’s group number)
For ions we must adjust the number of electrons available.
Add one e- for each negative charge.
Subtract one e- for each positive charge.
Select a reasonable skeleton
The least electronegative is the central atom
See prior periodic table for number of electrons involved in bonding
Group I 2 electrons or 1 bond
Group II 4 electrons or up to 2 bonds
Group III Al and B, 6 or 8 electrons up to 3 or 4 bonds
C,N,O,F must have 8 electrons (up to 4 bonds for C, 3 for N, 2 for O, and 1 bond for F).
All others must have at least 8 electrons (up to 4 bonds), but may have more.
When a choice for the central atom in a molecule or polyatomic ion is unclear:
For ions or molecules with more than one central atom the most symmetrical skeleton is used
The atom that requires the largest number of electrons to complete its octet goes in the center.
For two atoms in the same periodic group, the less electronegative element goes in the center.
Calculate Formal charges, adjust bonds for lowest numbers (zero preferred) and allow for resonance structures

41. Writing Lewis Formulas:
Write Lewis dot and dash formulas for hydrogen cyanide, HCN.
Write Lewis dot and dash formulas for sulfur trioxide, SO3.
Write Lewis dot and dash formulas for the sulfite ion, SO32-.
There are three possible structures for SO32-.
The double bond can be placed in one of three places.
When two or more Lewis formulas are necessary to show the bonding in a molecule, we must use equivalent resonance structures to show the molecule’s structure. Double-headed arrows are used to indicate resonance formulas.
Write dot and dash formulas for BBr3.
Write dot and dash formulas for AsF5.

42. Stereochemistry
Stereochemistry is the study of the three dimensional shapes of molecules.
Valence Shell Electron Pair Repulsion Theory
Commonly designated as VSEPR
Principal originator
R. J. Gillespie in the 1950’s
Valence Bond Theory
Involves the use of hybridized atomic orbitals
L. Pauling in the 1930’s & 40’s

43. VSEPR Theory
Regions of high electron density around the central atom are arranged as far apart as possible to minimize repulsions.
There are five basic molecular shapes based on the number of regions of high electron density around the central atom.
Lone pairs of electrons (unshared pairs) require more volume than shared pairs.
Consequently, there is an ordering of repulsions of electrons around central atom.
Criteria for the ordering of the repulsions:
Lone pair to lone pair is the strongest repulsion.
Lone pair to bonding pair is intermediate repulsion.
Bonding pair to bonding pair is weakest repulsion.
Mnemonic for repulsion strengths
lp/lp > lp/bp > bp/bp
Lone pair to lone pair repulsion is why bond angles in water are less than 109.5o.
Valence-shell electron-pair repulsion (VSEPR) model predicts the shapes of many molecules and polyatomic ions but provides no information about bond lengths or the presence of multiple bonds

44. VSEPR Theory
Frequently, we will describe two geometries for each molecule.
Electronic geometry is determined by the locations of regions of high electron density around the central atom(s).
Molecular geometry determined by the arrangement of atoms around the central atom(s).
Electron pairs are not used in the molecular geometry determination just the positions of the atoms in the molecule are used.

45. VSEPR Theory
Two regions of high electron density around the central atom.
Three regions of high electron density around the central atom.
Four regions of high electron density around the central atom.

46. VSEPR Theory
Five regions of high electron density around the central atom.
Six regions of high electron density around the central atom.

47. VSEPR Theory
An example of a molecule that has different electronic and molecular geometries is water - H2O.
Electronic geometry is tetrahedral.
Molecular geometry is bent or angular.
An example of a molecule that has the same electronic and molecular geometries is methane - CH4.
Electronic and molecular geometries are tetrahedral.

48. The VSEPR Model

49. The VSEPR Model
The same basic approach will be used in every example of molecular structure prediction:

50. The VSEPR Model
Day 4

51. Shorthand for organic molecules

52. Valence Bond (VB) Theory
• A more sophisticated treatment of bonding is a quantum mechanical description of bonding, in which bonding electrons are viewed as being localized between the nuclei of the bonded atoms
• The overlap of bonding orbitals is increased through a process called hybridization, which results in the formation of stronger bonds
Regions of High Electron Density
Electronic Geometry
Hybridization 2
Linear sp 3
Trigonal planar
sp2 4
Tetrahedral
sp3 5
Trigonal bipyramidal
sp3d 6
Octahedral
sp3d2

53. Valence Bond Theory: A Localized Bonding Approach

54. Hybridization of s and p Orbitals
• Localized bonding approach uses a process called hybridization, in which atomic orbitals that are similar in energy but not equivalent are combined mathematically to produce sets of equivalent orbitals that are properly oriented to form bonds.
• Spatial orientation of the hybrid atomic orbitals is consistent with the geometries predicted using the VSEPR model.
• New combinations are called hybrid atomic orbitals because they are produced by combining (hybridizing) two or more atomic orbitals from the same atom.
• Hybrid atomic orbitals are formed via promotion of an electron from a filled ns2 subshell to an empty np or (n – 1)d valence orbital, followed by hybridization.

55. Hybridization of s and p Orbitals
• The combination of an ns and an np orbital gives rise to two equivalent sp hybrids oriented at 180º.
• Combination of an ns and two or three np orbitals produces three equivalent sp2 hybrids or four equivalent sp3 hybrids.

56. Hybridization of s and p Orbitals
• Both promotion and hybridization require an input of energy; the overall process of forming a compound with hybrid orbitals will be energetically favorable only if the amount of energy released by the formation of covalent bonds is greater than the amount of energy used to form the hybrid orbitals.

57. Hybridization Using d Orbitals
• Hybridization not restricted to ns and np atomic orbitals
• Bonding in compounds that have central atoms in the third period and below can be described using hybrid atomic orbitals
• Central atom uses its valence (n – 1)d orbitals and its ns and np orbitals to form hybrid atomic orbitals, which allows them to accommodate five or more bonded atoms
• Using the ns orbital, all three np orbitals, and one (n – 1)d orbital gives a set of five sp3d hybrid orbitals that point toward the vertices of a trigonal bipyramid
• Combination of the ns orbital, all three np atomic orbitals, and two (n – 1)d orbitals gives a set of six equivalent sp3d2 hybrid orbitals oriented toward the vertices of an octahedron

58. Hybridization Using d Orbitals

59. Molecular Shapes and Bonding
In the next sections we will use the following terminology:
A = central atom
B = bonding pairs around central atom
U = lone pairs around central atom
For example:
AB3U designates that there are 3 bonding pairs and 1 lone pair around the central atom.

60. Linear Electronic Geometry:AB2 Species (No Lone Pairs of Electrons on A)
1s 2s 2p
Be  
1s sp hybrid 2p
   

61. Trigonal Planar Electronic Geometry: AB3 Species (No Lone Pairs of Electrons on A)
1s 2s 2p
B 
1s sp2 hybrid
    

62. Tetrahedral Electronic Geometry: AB4 Species (No Lone Pairs of Electrons on A)
C [He]    .

63. Tetrahedral Electronic Geometry: AB4 Species
Valence Bond Theory (Hybridization)
2s p
C [He] ­¯ ­ ­ .
four sp3 hybrids
Þ ­ ­ ­ ­ .
Tetrahedral Electronic Geometry: AB3U Species
2s p
N [He] ­¯ ­ ­ ­
four sp3 hybrids
Þ ­¯ ­ ­ ­
Tetrahedral Electronic Geometry: AB2U2 Species
four sp3 hybrids
Þ ­¯ ­¯ ­ ­
2s p
O [He] ­¯ ­¯ ­ ­

64. Tetrahedral Electronic Geometry: ABU3 Species (Three Lone Pairs of Electrons on A)
Valence Bond Theory (Hybridization)
2s p
F [He] ­¯ ­¯ ­ ­
four sp3 hybrids
Þ ­¯ ­¯ ­ ­

65. Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2, and AB2U3
4s p 4d
As [Ar] 3d10   ___ ___ ___ ___ ___ ß
five sp3 d hybrids d
     ___ ___ ___ ___
Day 5

66. Compounds Containing Double Bonds
Valence Bond Theory (Hybridization)
C atom has four electrons.
Three electrons from each C atom are in sp2 hybrids.
One electron in each C atom remains in an unhybridized p orbital
2s 2p three sp2 hybrids 2p
C  Þ   
An sp2 hybridized C atom has this shape.
Remember there will be one electron in each of the three lobes.
Top view of
an sp2 hybrid

67. Compounds Containing Double Bonds
The single 2p orbital is perpendicular to the trigonal planar sp2 lobes.
The fourth electron is in the p orbital.
Side view of sp2 hybrid
with p orbital included.

68. Compounds Containing Double Bonds
Two sp2 hybridized C atoms plus p orbitals in proper orientation to form C=C double bond.
The portion of the double bond formed from the head-on overlap of the sp2 hybrids is designated as a s bond.
The other portion of the double bond, resulting from the side-on overlap of the p orbitals, is designated as a p bond.

69. Compounds Containing Triple Bonds
A  bond results from the head-on overlap of two sp hybrid orbitals.
The unhybridized p orbitals form two p bonds.
Note that a triple bond consists of one  and two p bonds.

70. Summary of Electronic & Molecular Geometries
Day 6