1

Chemistry 112 – Midterm Examination

Name:__________________________________

Due Thursday, November 5, 2015 Before Class (9:00 am, 147 Noyes) Rules: Closed Book, Closed Notes. Time limit: 4 hours (one sitting) Only six out of the seven problems will count toward your grade. Select the problem you would like to drop by crossing out the problem number (1-6) below. If no problem is crossed, problem 7 will not be counted.

Periodic and character tables are provided at the end of the exam.

The use of molecular model kits is allowed.

Question Points Available Points Earned Problem 1 120 Problem 2 120 Problem 3 120 Problem 4 120 Problem 5 120 Problem 6 120 Problem 7 120

Total

2

Problem 1 (120 points) 1. For each of the following molecules, assign the point group. For compounds d-f, provide metal oxidation state, d electron count and valence electron count. a.

Cl

Cl

b.

OCr

OCr

OO

O OO

Cr O Cr OOO

O

O

O

top-down view:

c.

Pt ClPt

Cl

Cl

Cl

CO

OC

d.

PP P

PP

FeMe Me

Me

Me

Me

e.

Re

S SS

Me

S SS

Me

top-down view:S

S S

S

ReS S

f.

V

2. Write out the 3x3 matrices for the following transformations operating upon the vector (x, y, z) shown below. Also, determine the trace of each matrix.

x

y

z xyz

a. identity b. C2 (z) c. σ(xy) d. inversion

Cs

C2v

C2h

C5v Fe2+, d6, 18e-

D3h Re6+, d1, 13e- Cs

V0, d5, 17e-

1 0 0 0 1 0 0 0 1

Trace: 3

-1 0 0 0 -1 0 0 0 1 Trace: -1

1 0 0 0 1 0 0 0 -1 Trace: 1

-1 0 0 0 -1 0 0 0 -1 Trace: -3

30 points

40 points

3

Fill in the character table below, corresponding to the point group containing only the above operations. Determine the point group, and assign Mulliken symbols to irreducible representations. C2h E C2 (z) σh i Ag 1 1 1 1 x2-y2, z2, xy Bg 1 -1 -1 1 xz,yz Au 1 1 -1 -1 z Bu 1 -1 1 -1 x, y 3. Tetrahedral Ni(CO)4 is shown below, with carbons labelled “a”, “b”, “c”, and “d”. Draw representation of Ni(CO)4 with atom labels under the following symmetry operations and products of operations. Proper rotation axes of order 3 are labeled with the coincident carbon label (e.g. C3 (a) passes through carbon “a”). Proper rotation axes of order 2, and improper rotation axes, are labeled according to the carbon-carbon vector they bisect. Mirror planes are labeled according to the carbon atoms they contain. Perform rotations clockwise. Note: The symmetry element labels do not change when successive operations are performed.

Ca

Ni

O

Cb

Cc

CdO

O

O

C3 (a)

a. C32 (c)

Cb

Ni

O

Cd

Cc

CaO

O

O c. C2 (ac)

Cc

Ni

O

Cd

Ca

CbO

O

O e. C3 (a) • C2 (ac)

b. S4 (bd)

Cb

Ni

O

Cc

Cd

CaO

O

O d. σd (ad)

Ca

Ni

O

Cc

Cb

CdO

O

O f. C2 (bc) • σd (ad)

Cc

Ni

O

Cb

Cd

CaO

O

O

Cd

Ni

O

Cb

Cc

CaO

O

O

32 points

4

4. a. Ferrocene (FeCp2) can perform one-electron reductions. What d-based orbital does the electron come out of upon oxidation of ferrocene? b. How do you expect the Fe-C bond distances to change upon the oxidation of ferrocene? (select one answer) Increase significantly Not change much Decrease significantly c. What is the nature of the HOMO of ferrocene? (select one answer) Anti-bonding Non-bonding Bonding 5. a. Cobaltocene (CoCp2) is also a reductant. Is cobaltocene a stronger or weaker reductant compared to ferrocene? b. Along the C5 rotation axis, what is the axial symmetry of the HOMO in cobaltocene? (select one answer) σ π δ c. What is the nature of the HOMO of cobaltocene? (select one answer) Anti-bonding Non-bonding Bonding 6. a. What is the point group resulting from adding the inversion operation to C2v? b. What is the lowest symmetry point group that has the operations of both C2v and D3d point groups? c. What is the point group resulting from removing the C3 operation from D6h?

dz2

stronger

D2h

D6h

D2h

6 points

6 points

6 points

5

Problem 2 (120 points) 1. Nonacarbonyl diiron, shown below in the D3h point group, was one of the first metal carbonyl complexes to be discovered. a. Which CO groups (bridging vs terminal) do you expect to have a stronger CO bond?

Fe

OCOC CO

OCCO

CO

Fe

COCO

OC

FeCOOC

OC

CO

COOC

bridging CO

terminal CO

Top-down view:

b. Using the labeled version of nonacarbonyl diiron shown below, write out transformation matrices for the following operations. For each completed matrix, draw a box around the elements corresponding to the carbons that are related by the symmetry in this point group.

i. C2 (containing carbon C8)

0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 0 0 1

0 0 0 0 0 0 0 0 0 1 0

x

C1 C2 C3 C4 C5 C6 C7 C8

C9

Fe1

Fe2

=

C6 C5 C4 C3 C2 C1 C9 C8

C7

Fe2

Fe1

terminal

4 points

34 points

Fe1

C8C9 C7

C3 C1

C2

Fe2

C4

C5C6

6

ii. S32

(clockwise)

0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 1

x

C1 C2 C3 C4 C5 C6 C7 C8

C9

Fe1

Fe2

=

C2 C3 C1 C5 C6 C4 C9 C7

C8

Fe1

Fe2

c. In a paper discussing the X-ray crystal structure of this compound, authors F. A. Cotton and Jan M. Troup make the following statement:

J. Chem. Soc. Dalton Trans. 1974, pg. 800. List the symmetry operations that are lost upon distorting from D3h to C3h symmetry. d. Describe in a short sentence what kind of conformational or structural change would cause nonacarbonyl diiron to exist in C3h symmetry, as the paper describes. e. Draw a new picture of nonacarbonyl diiron in the C3h point group. Use whichever projection shows the structure most clearly.

FeCOOC

CO

bridging CO

terminal CO

CO

CO

OC

three C2's (perpendicular to C3) and 3 σv's (parallel to C3)

e.g. a rotation of the central 3 carbonyls (C7-C9) about the C3 axis by an angle ≠ 60°, 120°.

4 points

6 points

6 points

Fe1

C8C9 C7

C3 C1

C2

Fe2

C4

C5C6

7

f. Consider the hypothetical case in which you have a pure sample of nonacarbonyl diiron that is isotopically enriched in 13C on just one of the bridging carbonyl ligands, that you have misplaced among natural abundance nonacarbonyl diiron. Provide two analytical techniques that you could use to determine which of your ampules contains this precious 13C labeled compound? Explain.

Fe

OCOC 13CO

OCCO

CO

Fe

COCO

OC

h. The structure of Fe2(CO)9 was not always known. In 1934, Sidgwick and Bailey propose the following structures on the basis of the crystallographic symmetry and unit cell parameters of Fe2(CO)9. What are the point groups of the two structures shown? Give a detailed explanation for why you would not expect these structural isomers to be likely, considering what you know about the molecular orbital picture of CO. Proc. R. Soc. A, 1934, 144 pg. 521–537.

e.g. 1. IR spectroscopy could distinguish between 12CO and 13CO based on the C-O stretching frequency (lower for 13CO). 2. Mass Spectrometry will tell you the exact mass of the compound, distinguishing between labelled/unlabeled compound by exactly 1 atomic mass unit. 3. 13C NMR will exhibit a strong er resonance for the isotopically enriched compound.

C3v Cs

The HOMO and LUMO of CO are both primarily carbon-based, therefore the σ-acid and π-basic nature orbitals of Fe0 will primarily want to bind CO at carbon, not at oxygen.

8 points

12 points

8

2. Shown below is the structure of IF5, an interhalogen compound.

z

x yI

F4

F2

F3

F5

F1

a. Assign the point group of IF5 and list all symmetry operations.

b. Group the symmetry operations that belong to the same class and complete the character table for the point group of IF5 using the information provided by the Mulliken symbols and the functions listed in the table.

__C4v__ E 2_C4___ _C2____ 2σv 2_ σd ___

A1 1 1 1 1 1 z, z2

A2 1 1 1 -1 -1 Rz

B1 1 -1 1 1 -1 x2−y2

B2 1 -1 1 -1 1 xy

E 2 0 -2 0 0 (x, y), (xz, yz)

c. Using a similarity transformation, show that the σv operations are conjugates.

C4v: E, C4, C43, C2, σv(x), σv(y), σd(1), σd(2) 6 points

28 points

12 points

z

x yI

F4

F2

F3

F5

F1

IF1

F3

F4

F5

F2

IF3

F1

F4

F5

F2

IF4

F2

F1

F5

F3

C4

C43

σv(x)

σv(y)

σv(y) = C43 *σv(x) * C4

9

Problem 3 (120 points) 1. Consider bicyclo[2.2.2]octane, which is drawn in the D3h point group.

HH

HH

H

H

H

H

H H

H H

H

H You are attempting to obtain fluorinated versions of bicyclo[2.2.2]octane. Mass spectral data indicates that you have isolated a product formulated as C8H10F4 and you suspect that you have one of the isomers labeled below as A-D. Fill in the table below with the predicted total number of 19F-NMR signals, 13C-NMR signals (assume no overlapping NMR resonances), and polarimetric behavior for each isomer. Note: An achiral molecule will not affect polarized light (“0”), while enantiopure chiral molecules will; enantiomers rotate polarized light by the same angle, in opposite directions (“x”, “-x”).

Point Group? Cs C2v Cs C3

Number of 13C NMR Signals 6 3 6 4

Number of 19F NMR Signals 3 1 2 2

Polarimetry (0, x, -x) 0 0 0 x, -x

Symmetry element

responsible for lack of chirality

σ σ σ --

2. Based on your analysis in part 1, will you be able to definitively assign which of the above isomers you have if you have collected the 13C NMR, 19F NMR, and polarimetry data? yes

32 points

4 points

10

3. Upon considering additional data related to the synthetic protocol, you realize that in fact you have to consider all possible isomers that have NMR and polarimetry data consistent with structure “C” shown in part 1 (same number of peaks in spectra, same result by polarimetry). Draw these isomers.

F F

F F

F F

F F

F F

F F F F

F

FF

F

F F

4. An application of your compounds requires only chiral versions for interactions with substrates. You are also limited to compounds that display a single peak by 19F NMR. Draw all isomers (including enantiomers) of formula C8H12F2 that are chiral and have this NMR characteristic. Label them with E, F…

F

F F

F F

F

F

F

E F G HF

F

F

F

I J

5. Fill in the table below:

Isomer Point group

Number of

13C-NMR signals

E F G H I J

C2 C2 C2 C2 C2 C2

4 4 4 4 4 4

36 points

36 points

12 points

11

Problem 4 (120 points) The eight molecular orbitals of the π−system of the cyclooctatetranene dianion (COT2−) are shown below, in two different perspectives.

Ψ1 Ψ2 Ψ3 Ψ4 Ψ5 Ψ6 Ψ7 Ψ8

1. Assign the point group of COT2−. (5 points)

D8h 2. Obtain the characters of the reducible representation Γ for the set of eight pz orbitals on COT2−. (15

points)

E C8 C83 C4 C2 C2’ C2’’ i S8

3 S8 S4 σh σv σd Γ = 8 0 0 0 0 −2 0 0 0 0 0 −8 2 0 3. Express Γ as a sum of irreducible representations, either by inspection or by using the formula

shown in class. Show your reasoning/work. (15 points) Γ = A2u + E1g + E1u + E3g + B2u Ψ1 is pz like A2u Ψ2 and Ψ3 are xz, yz like E1g Ψ4 and Ψ5 are xyz, z(x2−y2) like E1u Ψ6 and Ψ7 are z•x(x2−3y2), z•y(3x2−y2) like A2u•E3u = E3g Ψ7 is antisym with respect to C8 (B), antisymmetric to inversion (ungerade), symmetric to σv. B2u

12

4. Sketch the molecular orbital diagram for the π−system of COT2− and populate with electrons. Indicate the number of nodes along the C8 axis for each MO. (15 points)

0 nodes

1 nodes

2 nodes

3 nodes

4 nodes

5. A) Assign Mulliken symbols to Ψ1 - Ψ4 using the table below. (5 points)

B) By inspection, provide normalized functions Ψ4, Ψ5, and Ψ8 in terms of the eight pz atomic orbitals. (15 points) C) Functions Ψ2 and Ψ6 are expressed in the table below in terms of the variable x. Looking at the

orbital depictions and applying orthogonality between Ψ2 and Ψ3 and between Ψ6 and Ψ7,to express Ψ3 and Ψ7 in terms of x. (20 points)

Mulliken

symbol

Normalization

constant Pz1 Pz2 Pz3 Pz4 Pz5 Pz6 Pz7 Pz8

Ψ1 = A2u (1/8)1/2 1 1 1 1 1 1 1 1

Ψ2 = E1g 1/(2x2+4)1/2 −x −1 0 1 x 1 0 −1

Ψ3 = E1g 1/(2x2+4)1/2 0 1 x 1 0 −1 −x −1

Ψ4 = E1u 1/2 −1 0 1 0 −1 0 1 0

Ψ5 = E1u 1/2 0 1 0 −1 0 1 0 −1

Ψ6 = E3g 1/(2x2+4)1/2 x −1 0 1 −x 1 0 −1

Ψ7 = E3g 1/(2x2+4)1/2 0 1 −x 1 0 −1 x −1

Ψ8 = B2u (1/8)1/2 1 −1 1 −1 1 −1 1 −1

13

D) Use the principle of atomic orbital conservation (an atomic orbital is used 100% over all molecular orbitals it participates in) to find the value of x. (15 points)

Apply on pz1

𝟏𝟏𝟖𝟖

+𝟐𝟐𝒙𝒙𝟐𝟐

𝟐𝟐𝒙𝒙𝟐𝟐 + 𝟒𝟒+𝟏𝟏𝟒𝟒

+𝟏𝟏𝟖𝟖

= 𝟏𝟏

𝟐𝟐𝒙𝒙𝟐𝟐

𝟐𝟐𝒙𝒙𝟐𝟐 + 𝟒𝟒=𝟏𝟏𝟐𝟐

𝒙𝒙𝟐𝟐 = 𝟐𝟐

𝐱𝐱 = √𝟐𝟐

E) Show that atomic orbital Pz5 and Pz6 have equal contributions in the degenerate set consisting of Ψ6 and Ψ7. (15 points)

Total contribution of Pz5 in Ψ6 and Ψ7 = 2/8

Sum of contributions of Pz6 in Ψ6 and Ψ7 = 1/8 + 1/8 = 2/8

14

Problem 5 (120 points) Consider uranocene, U(COT)2.

1. Assign the point group of U(COT)2. (5 points)

D8h 2. By inspection, express the 5f and the 6d orbitals of uranium as a sum of irreducible representations.

(10 points) Γ5f = A2u + E1u + E2u + E3u Γ6d = A1g + E1g + E2g 3. Given the expression below of the lowest energy molecular orbital of the π system of (COT)2-,

provide normalized expressions of the two lowest energy SALCs of the bis-cyclooctatetranyl framework in U(COT)2, using Pz1 to Pz16. (10 points)

Ψ1 = (1/8)1/2 (Pz1 + Pz2 + Pz3 + Pz4 + Pz5 + Pz6 + Pz7 + Pz8)

SALC1 = 14

([𝑝𝑝𝑧𝑧1 + 𝑝𝑝𝑧𝑧2 + 𝑝𝑝𝑧𝑧3 + 𝑝𝑝𝑧𝑧4 + 𝑝𝑝𝑧𝑧5 + 𝑝𝑝𝑧𝑧6 + 𝑝𝑝𝑧𝑧7 + 𝑝𝑝𝑧𝑧8]+ [𝑝𝑝𝑧𝑧9 + 𝑝𝑝𝑧𝑧10 + 𝑝𝑝𝑧𝑧11 + 𝑝𝑝𝑧𝑧12 + 𝑝𝑝𝑧𝑧13 + 𝑝𝑝𝑧𝑧14 + 𝑝𝑝𝑧𝑧15 + 𝑝𝑝𝑧𝑧16])

SALC2 = 14

([𝑝𝑝𝑧𝑧1 + 𝑝𝑝𝑧𝑧2 + 𝑝𝑝𝑧𝑧3 + 𝑝𝑝𝑧𝑧4 + 𝑝𝑝𝑧𝑧5 + 𝑝𝑝𝑧𝑧6 + 𝑝𝑝𝑧𝑧7 + 𝑝𝑝𝑧𝑧8][𝑝𝑝𝑧𝑧9 + 𝑝𝑝𝑧𝑧10 + 𝑝𝑝𝑧𝑧11 + 𝑝𝑝𝑧𝑧12 + 𝑝𝑝𝑧𝑧13+ 𝑝𝑝𝑧𝑧14 + 𝑝𝑝𝑧𝑧15 + 𝑝𝑝𝑧𝑧16])

15

4. Use the template provided below to sketch the first ten lowest energy SALCs of the bis-cyclooctatetranyl framework in U(COT)2. When a node passes through an atom, mark the p orbital with an X. Provide Mulliken symbols for these SALCs. (40 points)

5. Using the 5f and 6d orbitals on uranium, and the ligand-based SALCs of the bis-cyclooctatetranyl framework, provide a molecular orbital diagram of U(COT)2. (Note: Place 5f lower in energy than 6d. For the purposes of this problem, ignore the empty orbitals of (COT)2-.) (5 points)

6. Label each metal-based orbital with their f/d−parentage. (10 points) 7. Label each molecular orbital with the axial symmetry (along the C8 axis) and type of the U−COT

interaction (e.g. σ, σ*, etc.). (15 points) 8. Populate the molecular orbital diagram with electrons. (15 points)

16

9. Do you predict U(COT)2 to be paramagnetic? If so, how many unpaired electrons? (5 points)

Yes. Two unpaired electrons 10. What is the valence electron count and f-count of U(COT)2? (5 points)

f2

17

Problem 6 (120 points) 1. Construct an MO diagram for a generic compound ML4 of Td symmetry. Use the s, p, and d

orbitals on the central atom M, and the s orbitals of the four ligands L as the basis set. Assign Mulliken symbols for each molecular orbital (5 points). Label each molecular orbital with the symmetry of the M−L interaction (e.g. n.b., σ, σ*) (5 points). Draw a box around the molecular orbitals that are primarily metal d orbital-based, and label with their d-orbital parentage (10 points). Populate with electrons assuming M is a group 8 metal (5 points).

d

s

p

4L

a1(σ∗)

t2(σ∗)

t2(σ∗), dxy, dxz, dyz

e(nb), dx2-y2, dz

2

a1+t2(σ)

18

2. Looking only at the d orbitals of ML4, provide a Walsh diagram for a distortion to D4h symmetry. Keep the coordinate system the same. Label each MO in the D4h point group only with its d-orbital parentage (no Mulliken symbols required) (20 points).

3. Consider [Pt(NH3)4]2+ and Ni(PEt3)4. Predict which geometry would be preferred for each of these

compounds based on an analysis of the Walsh diagram constructed above. Clearly indicate which orbital(s) in the diagram lead to your decision for each compound.

[Pt(NH3)4]2+ is D4h: dz2 is the lower HOMO for this d8 complex. (5 points) Ni(PEt3)4 is Td: the t2 set is the lower HOMO for this d10 complex. (5 points)

dxy, dxz, dyz

dx2-y2, dz

2

dxy

dz2

dx2-y2, dyz, dxz

19

4. Consider a metal calixarene complex M(OR)4. The calixarene ligand enforces a square planar geometry at the metal center. Assume that the calixarene-derived ligand is a good π−donor. Each phenoxide moiety has two lone pairs available for π-bonding, but only consider the lone pairs on oxygen that are in the xy plane (the others have poor overlap). Draw the SALCs derived from these oxygen p-orbitals (Mulliken labels are not required) (10 points). Starting from the d-orbital splitting diagram for σ-only interactions, obtain the MO diagram taking into account M−OR π interactions where overlap is feasible by symmetry. Note that the coordinate system is slightly rotated around z compared to part 2. Sketch the molecular orbital(s) that display these π-interactions (10 points). Indicate their bonding / antibonding character (5 points). Label the relevant MOs with their d-orbital parentage (5 points).

dx2-y2

dz2

dxy, dyz, dxz

4p

nb, dxz, dyz

π

nb

(σ∗), dz2

(σ∗), dx2-y2

(π∗), dxy

20

5. Consider axial binding of one molecule of CO to each of the calixarene complexes Zr(OR)4, Mo(OR)4, and Ru(OR)4. Rank the CO stretching frequency of (RO)4Zr−CO, (RO)4Mo−CO, (RO)4Ru−CO, and free CO from smallest to largest (10 points). Support your answer by providing a molecular orbital diagram for the interaction between the M(OR)4 fragment and CO (10 points). Report the valence electron count, the oxidation state, and the d-electron count for (RO)4Zr−CO, (RO)4Mo−CO, and (RO)4Ru−CO (15 points).

(RO)4Zr−CO: Zr(IV), d0, 12e−

(RO)4Mo−CO: Mo(IV), d2, 14e−

(RO)4Ru−CO: Ru(IV), d4, 16e−

Ru(CO) < Mo(CO) < CO < Zr(CO)

dxz, dyz

dz2

dx2-y2

dxy

(π), dxz, dyz

(σ∗), dz2

(σ∗), dx2-y2

(π∗), dxy

HOMO (CO)

LUMO (CO)

21

Problem 7 (120 points) 1. Consider the Fe(PR3)3 cation labelled “A” below (R = alkyl or aryl). a. What is the oxidation state of iron? FeI

b. What is the d-count? d7

c. What is the valence electron count? 13 d. What is the point group of this ion? D3h

2. Sketch SALCs for the set of phosphine ligands, using three s-orbitals as your basis set (approximate the phosphines as σ-donors). Assign Mulliken symbols to the SALCs you have sketched and provide normalized wavefunctions.

PR3

PR3

FeR3P

PR3

PR3

FeR3PPR3

PR3

FeR3P

A1'

E'

Ψ = (1/6)1/2 (2S1 - S2 - S3)Ψ = (1/3)1/2

(S1 + S2 + S3) Ψ = (1/2)1/2 (-S

3. Construct a molecular orbital diagram for A using the SALCs sketched above, and only the five d-orbitals of Fe. Label each molecular orbital with Mulliken symbol and the character of the interaction (e.g. n.b., σ, σ*). Label the metal-based molecular orbital with their d-parentage.

8 points

16 points

18 points E', E'',

A1'

E', A1

'

1a1'

1e''

2e'

2a1'

1e'

dx2-y2, dxy (σ∗)

dz2 (σ∗)

dxz, dyz (nb)

22

4. Below are shown three hypothetical Fe fragments, based upon similar molecules synthesized in the Peters laboratories at Caltech. Assume that the σ-donating abilities of the phosphines do not change. Sketch qualitatively how the relative energies of the d-orbitals for A (from part 3) change upon being perturbed into each of the new structures. Clearly label the d-parentage.

1e''

2e'

2a1'

z2

x2-y2, xy

xz, yz

z2

z2

z2

x2-y2, xy

x2-y2, xy x2-y2, xy

xz, yz

xz, yz xz, yz

24 points

23

5. Assuming no additional distortions of fragments A-D, consider the N2 adducts and nitrides. Maintain the same formal oxidation state for Fe across fragments A-D, with the N2 adducts as Fe(I) and the nitrides Fe(IV). An example is depicted below for fragment A:

Fill in the table below with 8 diagrams, showing the d-orbital splitting for: I. The N2 adduct of each of A-D II. The nitride of each of A-D Clearly label the d-parentage, the character of the orbitals in terms of the M-N2 and M-N interactions (e.g. n.b., σ, σ*, π, π*, π backbonding) and add the correct number of electrons. A B C D

I

1e''

2e'

2a1'

z2

x2-y2, xy

xz, yzz2

z2

z2

x2-y2, xy

x2-y2, xy x2-y2, xyxz, yz

xz, yz xz, yz

II

1e''

2e'

2a1'

z2x2-y2, xy

xz, yzz2

z2

z2

x2-y2, xy

x2-y2, xy x2-y2, xy

xz, yz

xz, yz xz, yz

I. All dz2: σ* (M-N2) All dxz, dyz: π (M-N2) All dxy, dx2-y2: nb (M-N2)

I. All dz2: σ* (M-N) All dxz, dyz: π* (M-N) All dxy, dx2-y2: nb (M-N)

40 points

24

6. Predict which nitride will be the most stable for the A-D fragments by indicating the M-N bond

order for all of them.

A B C D

e-(bond)- e-(anti-bond) 6-4=2 6-0=6 6-4=2 6-4=2

Bond Order 1 3 1 1

Structure B will give the most stable nitride 7. Fragment C was found to be quite flexible. Propose a distortion that is expected to increase the

stability of the nitride derived from this fragment. Clearly draw it.

Fe

B

PR2

PR2

R2P

+Fe

B

PR2

PR2R2P

+

distorting to tetrahedral geometryabout Fe, and lengthening the Fe-Binteraction 40+

END OF EXAM

10 points

4 points

25

26

27

28

29

𝑓𝑓𝑧𝑧3 𝑓𝑓𝑦𝑦𝑧𝑧2

𝑓𝑓𝑥𝑥(𝑥𝑥2−3𝑦𝑦2)

𝑓𝑓𝑥𝑥𝑧𝑧2 = 𝑓𝑓𝑥𝑥(4𝑧𝑧2−𝑥𝑥2−𝑦𝑦2)

𝑓𝑓𝑥𝑥𝑦𝑦𝑧𝑧 𝑓𝑓𝑦𝑦(3𝑥𝑥2−𝑦𝑦2)

𝑓𝑓𝑧𝑧(𝑥𝑥2−𝑦𝑦2)

30