5.03 Exam 1

Christopher C. Cummins

February 18, 2011

Instructions

Clearly write your name at the top of this front page. Check your exam document tomake sure you have all 8 pages. This examination is closed-book and no calculators orelectronic devices may be employed. There are four multi-part questions; each part of eachquestion will be given equal weight for scoring purposes. Read all questions carefully beforewriting down any answers. Enjoy the material!

1

Inorganic Chemistry 2

1. Write down the corresponding Schoenflies symbol (point group label) next to the pic-ture of each molecule shown below. The point group flowchart is provided on the nextpage.

(a) Square planar XeF4.

(b) Planar B(OH)3 in the conformation shown.

(c) C60, also known as Buckminsterfullerene.

(d) Ferrocene, Fe(η5-C5H5)2, in the depicted staggered conformation.

Inorganic Chemistry 3

(e) Hydrogen peroxide, H2O2, in the depicted conformation.

Structure

Linear orlow symmetry

highly symmetric(octahedral,tetrahedral,icosahedral)

Normalsymmetry

Sure? More than oneCn axis of C3

or higher?

linear i

i

D

C

C

C

C

8h

8v

s

i

1

6C5

3C4

3S4

i

I

I

h

i

O

O

h

i

T

T

h

Td

C C2 nDnh

Dnd

Dn

S

v

2n

Cnh

Cnv

S2n

Cn

Yes

Yes

Yes

Yes

Yes

YesYes Yes

Yes

YesYes

Yes

Yes

Yes Yes Yes

Yes

Yes

Yes

Yes

No

No

No

No

No

No

No

No

No

No

No

No

NoNo

No

No

Spe

cial

G

roup

Ele

men

ts

Hig

h S

ymm

etry

Ele

men

ts

Nor

mal

Sym

met

ryE

lem

ents

(m

ost

com

mon

)

linea

rsi

ngle

ele

men

t

icos

ahed

ral

octa

hedr

alT

etra

hedr

alD

ihed

ral

S i

n g

l e

A

x i

s

Inorganic Chemistry 4

2. This question pertains to the normal mode vibrations for the ammonia molecule, NH3.The C3v character table is provided.

(a) Give a list of the set of characters that would be required as input to RE-DUCE.EXE in order to obtain the Mulliken symbols for the irreducible repre-sentations of the C3v point group corresponding to the normal mode vibrationsof NH3.

(b) The normal modes for ammonia are found to transform as follows: 2A1 + 2E.How many bands are expected in the infrared spectrum of NH3?

(c) How many bands are expected in the Raman spectrum of NH3?

(d) How many degrees of freedom does ammonia possess, altogether?

Inorganic Chemistry 5

(e) Write down the Mulliken symbols that correspond to translations and rotationsfor NH3.

(f) The infrared spectrum of ammonia is shown below. What is the approximateenergy range for the N–H stretching vibrations?

(g) Sketch the ammonia molecule and use vectors to represent atom motions for astretching vibration having A1 symmetry.

Inorganic Chemistry 6

3. This question pertains to the Berry Pseudorotation (BPR).

(a) What is the point group for the structure of SF4 at the transition state for BPR?

(b) How many of the atoms in SF4 are moving in the course of a single BPR event?

(c) By how many degrees does the SF4 molecule appear to have rotated after a singleBPR event?

(d) Is a single BPR event sufficient to exchange all the 19F environments for the SF4

molecule?

(e) If the 19F NMR spectrum of SF4 were recorded at a very low temperature suchthat the BPR process was essentially stopped (frozen, static structure), then howmany lines would be expected in the 19F NMR spectrum, and what should be theratio of their intensities?

Inorganic Chemistry 7

4. Above are pictured in ascending order according to energy a grouping of the molecularorbitals of B2H6. The grouping includes only the chemically significant valence orbitals;core orbitals are not included. The choice of Cartesian axes is such that the terminalhydrogens reside in the yz plane.

Inorganic Chemistry 8

(a) Using the character table for D2h (provided above), assign each of the picturedmolecular orbitals to its correct irreducible representation, and write the corre-sponding Mulliken symbol above, next to each orbital’s picture.

(b) Next to the picture of the highest energy occupied molecular orbital for B2H6,write “HOMO”.

(c) Next to the picture of the lowest energy unoccupied molecular orbital for B2H6,write “LUMO”.

(d) Draw a circle around the MO that both has lots of boron 2s character and belongsto the totally symmetric representation of the D2h point group.

(e) Draw a square around the pictured MO that involves overlap of boron px atomicorbitals with s orbitals from the bridging hydrogens.