Course Outline / Tentative Schedule

Week Monday Wednesday1 06‐Sep     Labor Day (holiday) 08‐Sep     The Chemical Bond: Classical Concepts2 13‐Sep     The Chemical Bond: Classical Concepts 15‐Sep      Moecular Geometry and VSEPR Theory3 20‐Sep     Molecular Symmetry Point Groups 22‐Sep     Group Theory: Representations4 27‐Sep     Group Theory: Applications 29‐Sep     Valence Bond Theory5 04‐Oct MO Theory II 06‐Oct Crystal Field Theory5 04 Oct     MO Theory II 06 Oct     Crystal Field Theory6 11‐Oct     Columbus Day(holiday) 13‐Oct     Ligand Field Theory I7 18‐Oct     Ligand Field Theory II 20‐Oct     Revision8 25‐Oct     Exam I 27‐Oct     UV‐Vis and Emission Spectroscopy9 01‐Nov    Time‐Resolved UV‐Vis Spectroscopy 03‐Nov    Time‐Resolved FTIR and Matrix Isolation Spectroscopies10 08‐Nov    Inorganic Electrochemistry 10‐Nov    Inorganic Electrochemistry11 15‐Nov    EPR Spectroscopy 17‐Nov    EPR Spectroscopy12 22‐Nov    Electron Transfer Theory 24‐Nov    Electron Transfer Theory13 29‐Nov    Revision 01‐Dec    Exam II14 06‐Dec Student presentation 08‐Dec Student presentation14 06 Dec    Student presentation 08 Dec    Student presentation15 13‐Dec    Student presentation 22‐Dec    Final Exam Deadline

What is a Chemical Bond ?• Whenever two or more atoms are held strongly together to form an aggregate that weWhenever two or more atoms are held strongly together to form an aggregate that we

describe as a molecule, we say that there are chemical bonds between them.

What is a chemical bond?

What forces hold atoms together? What forces hold atoms together?

Why do atoms combine in certain fixed ratios?

What determines the three dimensional arrangement of the atoms in a molecule?

• Experimental data, supplemented by advanced quantum mechanical methods, has providedanswers to theses fundamental questions….albeit with some bias.

• A selection of common physical techniques used

Single crystal X‐ray diffraction Neutron diffraction EXAFS

ENDOR NMR IR UV‐Vis Raman PES Calorimetry

Electrochemistry Electron Microscopy EPR MS

The Chemical Bond…Still Evolving !• When novel molecules are discovered or synthesized sometimes established ideas need toWhen novel molecules are discovered or synthesized sometimes established ideas need to

be modified.

• As researchers we must have a thorough knowledge and understanding of the fundamentaltheory in preparation to expect the unexpected, to think outside of the box, andacknowledge new data which defies traditional theory.

• Not to forget, it is sometimes the theoretician (whether they be a chemist, physicist ormathematician) who will push our accepted theories beyond their traditional boundaries,thus inspiring experimentalists to search for physical evidencethus inspiring experimentalists to search for physical evidence.

• In this course we will study classical concepts of the chemical bond and moleculargeometries. We will learn how these classical concepts were incorporated into quantummechanics (briefly ) to develop the modern descriptive/investigative methods which are( y ) p p / gstill evolving today.

Discoveries which helped define the Chemical Bond• The law of conservation of mass, also known as the principle of mass/matter conservation,The law of conservation of mass, also known as the principle of mass/matter conservation,

states that the mass of a closed system will remain constant over time, i.e. that mass cannotbe created/destroyed. This implies that for any chemical process in a closed system, themass of the reactants must equal the mass of the products.

‐ Antoine Lavoisier, 1789

• The law of definite proportions states that a chemical compound always contains exactlythe same proportion of elements by mass.

‐ Joseph Louis Proust, 1799

(An equivalent statement is the law of constant composition, which states that all samplesof a given chemical compound have the same elemental composition)

• The law of multiple proportions states that when chemical elements combine, they do so ina ratio of small whole numbers (e.g., carbon and oxygen react to form carbon monoxide (CO)or carbon dioxide (CO2), but not CO1.3). Further, it states that if two elements form morethan one compound between them the ratios of the masses of the second element to athan one compound between them, the ratios of the masses of the second element to afixed mass of the first element will also be in small whole numbers.

‐ John Dalton, 1803

www.jimal-khalili.com/ …a physicists (!) and presenter of documentary series “Chemistry – A Volatile History”www.imdb.com/title/tt1588194/

Concept of the Chemical Bond• Proust’s law of definite proportions (1799) and Dalton’s development of atomic theoryProust s law of definite proportions (1799) and Dalton s development of atomic theory

(1803) lead to the recognition that atoms of an element have a characteristic combiningability with other atoms, which came to be called valence.

• Existence of atoms suggested that compounds were composed of collections of atomsbound together by chemical bonds.

• In 1858 Couper began representing chemical bonds as a line between the symbols of atomsin compounds.

H H

C C

C

C C

CH H

• The idea of fixed atomic valences lead to the postulate of multiple bonds in compounds suchas C2H4 and C2H2.

H H

• These were represented by double and triple lines between the element symbols.

• Using only the ideas of valence and multiple bonding, Butlerov (1864) and Kekulé (1865)were able to deduce one of the first structural formulas, that of benzene.

• These representations had no association with electrons, whose existence was yet to berealized!

Valence• The valency of an element is often defined as the number of H atoms, or other univalentThe valency of an element is often defined as the number of H atoms, or other univalent

atom, that will combine with it.

(note: do not confuse H atoms with protons!

e g compare N valency in NH and NH +e.g. compare N valency in NH3 and NH4+

• Some atoms show multiple valence states

e.g. SnCl2 vs. SnCl4 (inert‐pair effect)

• A more accurate description of valence is the number of electrons that an atom uses inbonding.

In addition, to clarify that they are distinct phenomena:

• Formal charge is defined as the charge remaining on an atom when all bonds are removed• Formal charge is defined as the charge remaining on an atom when all bonds are removedhomolytically.

• Oxidation state is defined as the charge remaining on an atom when all bonds are removedheterolytically.y y

Stereochemistry• Before 1874 chemists had not seriously considered the possibility that atoms in a moleculeBefore 1874 chemists had not seriously considered the possibility that atoms in a molecule

might have a definite arrangement in space.

• By the second half of the nineteenth century about 10 carbon compounds were known thatexisted in two forms each of which rotated plane polarized light in opposite directions.p p g pp

• All these compounds had formulas of the type CRR’R’’R’’’.

• In 1874 van’t Hoff and le Bel independently deduced that this arose from left‐ and right‐h d d i f h l l h i bl i i f hhanded versions of the same molecule that are non‐superimposable mirror images of eachother.

• This lead to the postulate of tetrahedral geometry for the four valence positions aroundcarboncarbon.

C

H

C

H

CH C H

• Double and triple bonds were represented by bent bonds to maintain tetrahedral geometryabout carbon. Valence bond theory (hybridization) was not conceived yet.

H H

about carbon. Valence bond theory (hybridi ation) was not conceived yet.

• The existence of cis‐ and trans‐ isomers was subsequently discovered.

The Electron and Bonding

• Before the atomic structure of the elements was elucidated the nature of the chemical bond was poorly understood.

• Key developments leading to recognition of the importance of electrons in bonding:

1897 J. J. Thomson characterizes the electron(cathode ray tube experiments).

1906 Robert Mulliken determines electron charge(oil drop experiments).

1910 E t R th f d d t i l t t f th t1910 Ernest Rutherford determines nuclear structure of the atom(gold foil experiments).

1913 Henry G. J. Moseley determines atomic numbers1913 Henry G. J. Moseley determines atomic numbers(x‐ray frequency experiments)

1913 Niels Bohr’s quantum model of hydrogen atom, consistent with observed line spectra(Lymann, Balmer, Paschen, Brackett, Pfund, etc.).

Shell Model• In 1916 W. Kossel and G. N. Lewis independently recognized the stability of closed‐shellIn 1916 W. Kossel and G. N. Lewis independently recognized the stability of closed shell

configurations of inert gases (now called noble gases).

• This led to the shell model, in which electrons are arranged in successive spherical shellswith fixed capacities:

• According to Mendeleev’s periodic table, it was understood that elements in the same grouphad the same outer shell filling, so similarities in bonding must be related to electronicconfiguration.

• In 1916 Kossel recognized that common cations (e.g. Na+, Ca2+) and anions (e.g. Cl, O2)

Ionic ModelIn 1916 Kossel recognized that common cations (e.g. Na , Ca ) and anions (e.g. Cl , O )have the same number of electrons as a preceding or following noble gas in the periodictable.

• Kossel reasoned that these cations and anions form because their electronic configurationsare stable like noble gases.

• Kossel assumed ionic compounds were held together solely by electrostatic interactions,resulting in a regular three dimensional structure forming a limitless molecule.

• The “ionic bond” is a hypothetical extreme, assuming no inter‐ionic electron sharing.

• Evidence that solids such as NaCl do consist of ions was provided by the observation thatthese materials are conducting in the molten state and in solution in solvents of highdi l i hdielectric constant, such as water.

e.g. the conductivity of sea water is six orders of magnitude greater than that of deionizedwater, the latter being a very poor conductor (critical knowledge for electrochemistry!)

• Positive alkali metal ions are easily formed because their single valence electron is held inthe atom only rather weakly by the attraction of a small core charge of +1, i.e. alkali metalshave a low ionization energy.

• Negative halogen ions are easily formed as they have a relatively high core charge of +7• Negative halogen ions are easily formed as they have a relatively high core charge of +7,strongly attracting an additional electron, i.e. halogens have a high electron affinity.

Ionization Potentials and Electron Affinities

• The first ionization energy of an atom is the minimal energy needed to remove the highestenergy, outermost electron from the neutral atom.

l l k l 1 f• It is always a positive value, e.g. +531 kJmol‐1 for Li

• Trends in ionization potentials:

increases with atomic number within a given period

follows the trend in size, as it is more difficult to remove an electron that is closer to thenucleus.

decreases down the group (for the same reason) decreases down the group (for the same reason)

• The electron affinity is the energy required to add an electron to a neutral atom in thegaseous state to form a negative ion.

• The electron affinity for various elements varies in value but in general it follows the same• The electron affinity for various elements varies in value, but in general, it follows the sametrend as the ionization potential.

• Ionization energies decrease down a group and increase across a period• Ionization energies decrease down a group and increase across a period

(metals have higher ionization energies than non‐metals)

The variation in first ionization energies across the first period

Lattice Energy• The structures of ionic crystals are determined mainly by the ways in which oppositelyThe structures of ionic crystals are determined mainly by the ways in which oppositely

charged ions of different sizes and different charges can pack together to minimize the totalelectrostatic energy.

• Assuming only electrostatic interactions, the lattice energy U is seen as the result of aninfinite series of attractive and repulsive terms.

• For a mole of NaCl(s)we define

NaCl(s)→ Na+(g) + Cl‐(g) H = UNaCl(s)→ Na (g) Cl (g) H U

• For an ion pair, the energy of attraction is

E = -kq1q2 / r

• For the NaCl lattice interactions of a single ion with its nearest neighbors gives• For the NaCl lattice, interactions of a single ion with its nearest neighbors gives

Born‐Haber Cycle for NaCl(s)

H of = H o

(sub) + I + 1/2 D + A U = - 410.9 kJ

U = H o(sub) I 1/2 D A H o

f + 410.9 kJU H (sub) I 1/2 D A H f 410.9 kJ

U = 107.7 kJ + 496 kJ + 121.17 kJ kJ + 410.9 kJ

U = 787.7 kJ

Lattice Energy• Large values of lattice energy, U, are favored byLarge values of lattice energy, U, are favored by

1. Higher ionic charges

2. Smaller ions

3. Shorter distances between ions

Selected Lattice Energies Uo (kJ mol‐1; Born‐Haber Cycle Data)Selected Lattice Energies, U (kJ mol ; Born Haber Cycle Data)

F Cl Br I O2

Li+ 1049.0 862.0 818.6 762.7 2830

Na+ 927.7 786.8 751.8 703 2650

K+ 825.9 716.8 688.6 646.9 2250

Rb+ 788 9 687 9 612 625 2170Rb 788.9 687.9 612 625 2170

Cs+ 758.5 668.2 635 602 2090

Mg2+ 2522 3795

Ca2+ 2253 3414

Sr2+ 2127 3217

Covalent Bonds and Lewis Structures

• In 1916 G. N. Lewis proposed a model of bonding to account for non‐ionic cases (e.g. Cl2,CCl4).

• Noting that most molecules have an even number of electrons, Lewis proposed the shared‐electron‐pair bond, later renamed the covalent bond by Irving Langmuir (1919).

• Lewis saw achieving a noble‐gas configuration (rule of eight) as the impetus for formingcovalent bonds.

• Lewis regarded the rule of two, implying pairs of electrons in bonded atoms, as moreimportant than the rule of eight.

• More exceptions to the rule of eight were known (e.g. PCl5) than to the rule of two (e.g.,NO)NO).

i.e., not many examples of stable radical species.

• The association between a shared electron pair and a chemical bond became a definingconcept of chemistry, and the previous line notation (—) came to symbolize a shared pair.

Lewis Models Based upon the Tetrahedron

• The prevalence of octets, seen as four electron pairs, suggested a tetrahedral geometry,even for double and triple bond cases.

• These structures are similar to the bent bonds postulated from directed valenceconsiderationsconsiderations.

C

H

C

H

H

H

CH C H

H H

real bonds

purecovalent

hypotheticalpure ionic• The ionic model of Kossel and the

covalent model of Lewis suggesteda continuum of bond types, based

equal esharing

covalent

no esharing

a continuum of bond types, basedon the degree of electron sharing.

covalentionic

increasing bond polarity

Electronegativity

“Electronegativity () is a chemical property that describes the ability of an atom to attract 

electron density towards itself in a covalent bond” (Pauling 1932)

• The electronegativity is dependent on the hybridization of the atom

(Valence bond theory…later).

s orbitals experience stronger nuclear charge than p orbitals of same principal quantum 

number, therefore (C)  increases with higher s character of hybrid orbital:

(C 3) 2 5 (C 2) 2 9 (C ) 3 95(Csp3) = 2.5; (Csp2) = 2.9; (Csp)= 3.95[note: values may vary dependent on method of calculation]

of an element increases with increasing oxidation number of that element

e.g., (FeIII) > (FeII)

http://goldbook.iupac.org/Graphs/E01990.3.map.html

Electronegativity (Mulliken)

• Robert S. Mulliken calculated as the average of ionization energy and electron affinity (1934).

• Problems:• Problems:

Electron affinity data are not reliably known for many elements.

Both A and I refer to gaseous atoms, not atoms in a chemical bond.

Electronegativity (Pauling)

• Pauling's scale is based on the increase in bond energy, D, for a heteronuclear bond comparedto the average of the homonuclear bond energies of two bonded atoms.

H2(g) 2H(g) H o = + 435 kJ mol-1 = D(H2)

F2(g) 2F(g) H o = + 155 kJ mol-1 = D(F2)

HF(g) H(g) + F(g) H o = + 565 kJ mol-1 = D(HF)

1 1D(H2) + D(F2)

2

= (435 + 155) kJ mol-1

2

= 295 kJ mol-1

• Pauling attributed the extra bond strength to Coulombic attraction between the partial ioniccharges on the atoms created by unequal sharing; i.e., partial ionic character.

Th P li l 4 0 h i l i i i fl i• The Pauling scale sets = 4.0 as the maximum electronegativity, given to fluorine.

• The electronegativity of the elements increases substantially in progressing from left to right (early to late transition metals) across the periodic table– increased penetration effect (stronger effective nuclear charge)

• The electronegativity of main group elements increases in progressing up a column– decreased shielding effect (stronger effective nuclear charge)

• The electronegativity of transition metal elements increases in progressing down a columnpoor shielding from diffuse d orbitals‐ poor shielding from diffuse d orbitals

Allred‐Rochow Electronegativities

• In 1958, A. L. Allred and E. G. Rochow1 defined electronegativity as the electrostatic forceexerted by the nucleus on the valence electrons.

• Used effective nuclear charges, Z*, calculated by Slater’s rules2, using the formulag , , y , g

AR = (3590 Z*/r2) + 0.744

where r is the covalent radius in pm, and the constants fit the values to the Pauling scaling.

• Allred‐Rochow values typically add a second decimal place and suggest subtle differencesAllred Rochow values typically add a second decimal place and suggest subtle differencesbetween elements with similar values on the Pauling scale.

Scale  Cl  N

Pauling3 3.1  3.0

Allred‐Rochow  2.83  3.07

1 A. L. Allred and E. G. Rochow, J. Inorg. Nucl. Chem., 5, 264-268 (1958)2 J. C. Slater, Phys. Rev., 36, 57 (1930).3 Recalculated by A. L. Allred, J. Inorg. Nucl. Chem., 17, 215 (1961).

Group Electronegativity

• (M) only useful for purely M‐L σ‐bonding complexes.

• Characteristic bonding in transition metal complexes has exceptionally strong effect on (LnM).( n )

• Thus reactivity determined by influence of  and  interaction on (M) orbitals.

• Group electronegativity e.g. (L5M) will vary depending on the ligand set 

(L5M) increases with  acceptor (and decreasing  donor) strength of L.

• Must consider (LnM) as trends deviate from that predicted by (M) alone.

Drawing Lewis Structures1. Arrange the atoms of the compound or complex ion so as to show how they are linked1. Arrange the atoms of the compound or complex ion so as to show how they are linked

together by chemical bonds. When in doubt, assume that the least electronegative atom iscentral.

2. Count the valence electrons for each atom. For non‐transition elements, the number ofvalence electrons is the same as the group number of the element. For a complex anion, addelectrons equal to the negative charge. For a complex cation, subtract electrons equal to thepositive charge. The total is the number of electrons to be used in generating the model.

3 Draw in single bonds ( ) between all atoms that are linked together keeping in mind that3. Draw in single bonds (–) between all atoms that are linked together, keeping in mind thateach bond represents the use of two electrons from the total established in step 2.

4. With the remaining electrons, first add pairs (:) to all of the outer atoms to make octets(except H), then add any leftover electrons to the central atom. The octet for each atom( p ), yincludes pairs used to make bonds in step 3.

5. Leave no electrons unpaired unless the total number of electrons is odd.

6 Count the number of electrons about the central atom to see if an octet has been made6. Count the number of electrons about the central atom to see if an octet has been madethere. If not, try moving non‐bonding pairs (:) from outer atoms to make double or triplebonds to the central atom. However, note that

(a) hydrogen and the halogens do not form multiple bonds

(b) elements in the third and higher periods usually do not form effective multiple bonds.

Drawing Lewis Structures (contd.)7. If there are too few electrons to give octets to all atoms (except hydrogen), the central atom7. If there are too few electrons to give octets to all atoms (except hydrogen), the central atom

might be electron deficient, particularly if it is Be, B, or Al. Examples: BeH2, BCl3, AlCl3.

However,

a) outer atoms are never electron deficienta) outer atoms are never electron deficient

b) C, N, O, and F almost always have an octet.

8. Sometimes central atoms from the third and higher periods have more than an octet(h l ) b l h l l(hypervalence), but only when necessary. Examples: PCl5, XeF2, XeF4.

However,

a) outer atoms are never hypervalent

b) C, N, O, and F are never hypervalent.

8. The representation of any anion or cation should be surrounded by square brackets ([ ]) withthe charge indicated on the outside as a superscript.the charge indicated on the outside as a superscript.

9. Count up the number of electrons in the completed model to be sure it is the same as thetotal established in step 2.

Formal Charge

• In terms of "electron book‐keeping" of Lewis models, some bonds are formed by each atomcontributing electrons.

• In other cases one atom seems to be donating a pair of electrons to the other.g p

• Formal charges are the hypothetical charges atoms would have if all elements had the sameelectronegativity.

Assigning Formal Charge

1. Write the electron dot structure (Lewis dot model) for the compound or complex ion.

2. Count electrons about each atom by the following method:

b d d ( ) non‐bonded pair (:) = 2

bonded pair (–) = 1

[Note: This is not the same as the method used to determine octets in constructing Lewis dotmodels.]

3. Compare the number of electrons counted in this manner with the number of valenceelectrons the isolated neutral atom would have.

4. If the count is higher than for the neutral atom, assign a negative formal charge equal to thedifference. Write the formal charge inside a circle next to the atom (e.g.,).

5. If the count is lower than for the neutral atom, assign a positive formal charge equal to thedifference. Write the formal charge inside a circle next to the atom (e.g.,).

6. The algebraic sum of all positive and negative formal charges for a neutral molecule shouldbe zero. For a complex ion, it should equal the net charge on the ion.

Assigning Lewis Structures

• When trying to decide among possible Lewis structures, those most conforming to thefollowing criteria probably are most plausible:

All atoms have the smallest formal charges.g

Negative formal charges are assigned to electronegative elements, and positive chargesare assigned to electropositive elements.

Adjacent atoms do not have the same formal charge if a structure that avoids this can Adjacent atoms do not have the same formal charge, if a structure that avoids this canbe drawn.

The preceding guidelines do not apply if there is no other plausible model (e.g., CN–).

(OK to assign charge to carbon, even though nitrogen is more electronegative.)

Exceptions to the Octet Rule

• Sometimes central atoms from the third and higher periods have more than an octet(hypervalence) in their Lewis structures, but only when necessary.

Examples: PCl5, XeF2, XeF4.p 5, 2, 4

• However,

a) outer atoms are never hypervalent

b) C, N, O, and F are never hypervalent in their common compounds.

• If there are too few electrons to give octets to all atoms (except hydrogen), the central atomIf there are too few electrons to give octets to all atoms (except hydrogen), the central atommight be electron deficient, particularly if it is Be, B, or Al.

Examples: BeH2, BCl3, AlCl3. However,

a) outer atoms are never electron deficienta) outer atoms are never electron deficient

b) C, N, O, and F almost always have an octet.

Arbitrary Hypervalence

• Do not expand valence in an attempt to minimize formal charges if a structure that obeysthe octet rule can be drawn.

• Drawing hypervalent structures in such cases implies use of d orbitals by the central atom,g yp p y ,which are generally not available for significant participation in bonding with non‐transitionelements.

Example: The following structure (shown in many books) is not reasonable, even though thef l h h b dformal charges have been minimized.

• Lewis avoided structures like these!

• Drawing them is tantamount to taking formal charge too seriously!g g g y

Limitations of the Lewis Model

• Wedded to the notion that a bond is defined by a shared pair of electrons.

• Does not adequately handle bond polarity.

• Implies static location of electrons.

• Cannot adequately represent differences in electron distribution between atoms in differentCannot adequately represent differences in electron distribution between atoms in different

molecules.

• Cannot represent the overall distribution of electrons across molecules.

• Must resort to “resonance” to describe cases that do not have simple electron pair bonds.

• Cannot represent bonding in cases like boranes (e.g., B2H6) that have bridging hydrogens.p g g 2 6 g g y g

• Nonetheless, Lewis models are the simplest and most direct way of representing

qualitatively the linkages and relative bonding strengths in most molecules.

1 D t i th id ti t t f th t l

Assigning Metal Oxidation State1. Determine the oxidation state of the metal.

balance the ligand charges with an equal opposite charge on the metal.

This is the metal's formal oxidation state.

To determine ligand charges, create an ionic model by assigning each M‐L electron pair to the more electronegative atom (L). This should result in stable ligand species or ones known as reactive intermediates in solution.

2 D t i th d l t t2. Determine the d electron count.

Subtract the metal's oxidation state from its group #.

9 – 1 = 8

3. Determine the electron count of the complex

by adding the # of electrons donated by each ligand to the metal's d electron count.

5 x 2e = 10e

Metal : 8 eLigands: 10e

Total: 18e