Matrix isolated infrared spectroscopy of carbon clusters

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Matrix isolated infrared spectroscopy of carbon clusters
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Chandrasekhar, T. M., 1961-
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Thesis (Ph. D.)--University of Florida, 1990.
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Includes bibliographical references (leaves 116-126).
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by T.M. Chandrasekhar.
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Typescript.
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Vita.

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MATRIX ISOLATED INFRARED SPECTROSCOPY
OF CARBON CLUSTERS
















BY

T. M. CHANDRASEKHAR


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1990








































To my parents.















ACKNOWLEDGEMENTS


I would like to thank my advisor, Professor Martin

Vala, for his support, encouragement and guidance through my

five years of study in his group.

I also wish to express my gratitude to Dr. Jan

Szczepanski for his invaluable help with the experiments and

Prof. Weltner for generously lending us the Nd-YAG laser

that made this work possible. Thanks are also due to Dr.

Cliff Johnston for making available the Microvax computer

and other resources in his laboratory.

The friendship and assistance of my colleagues, Dennis,

Bill and Bob, will always be valued by the author. I also

want to express my appreciation for the craftsmanship and

expertise of the staff of the mechanical, glass and

electronics workshops.

Finally, my parents also deserve a great deal of credit

for allowing me to pursue my interest in chemistry. Their

guidance and support over the years has enabled me to reach

this point.


iii















TABLE OF CONTENTS


Page

ACKNOWLEDGEMENTS.................................. iii

LIST OF TABLES...................................... vi

LIST OF FIGURES..................................... vii

ABSTRACT............................................. ix

CHAPTERS

I INTRODUCTION........... .. ................... 1

Small Clusters: C2-C4......................... 2

Small Clusters: C5-C9.......................... 8

Large Clusters................................. 10
Ionic Clusters.................................. 19
Carbon Clusters and Soot Formation............ 21

II EXPERIMENTAL.................................. 23

Experimental Approach ............... .......... 24
Matrix Isolation Apparatus............... .... 31
Carbon Cluster Preparation..... ............... 36
Instrumentation................................ 42

III THE C5 CLUSTER ................................. 44

Introduction ................................... 44
Results............... .......... ............... 46
Normal Coordinate Analysis............... ... 52
Discussion ...................... ......... ... 55
Conclusion..................................... 59

IV THE C6 AND C8 CLUSTERS........................ 60

Introduction.................... ............... 60
Results..................... .. ........ ........ 62
Normal Coordinate Analysis.................... 76
Discussion ...................... ................ 80
Conclusion..................................... 83

iv









V THE IONIC C5+ CLUSTER......................... 84

Introduction.................................. 84
Experimental Procedure........................ 88
Results ............................ .......... 89
Discussion .................. .................. 102
Conclusion...................................... 105

VI CONCLUSIONS AND FUTURE WORK..................... 112
Future Work.................................... 112
Concluding Remarks............... ............. 115

REFERENCES................................... ........ 116

BIOGRAPHICAL SKETCH.................................. 127















LIST OF TABLES


Table Page

1 Isotopomer Stretching Frequencies for
linear C ......... ....... ................. .56

2 Observed and Calculated Isotopomer Stretching
Frequencies for linear C5................... 57

3 Expected Number of Isotopomers for Linear
Carbon Clusters............................ 66

4 Observed and Calculated Isotopomer
Stretching Frequencies for Chain-like
C6 in an Argon Matrix....................... 77

5 Observed and Calculated Isotopomer
Stretching Frequencies for Linear
C6 in an Argon Matrix....................... 78

6 Expected Number of Isotopomers for Linear
and Cyclic Carbon Clusters................... 96

7 Calculated Frequencies for Tetrahedral
C4 for 8 = 25 ............................... 98

8 Calculated Fits for Pyramidal C4............... 99

9 Observed and Calculated Isotopomer
Stretching Frequencies for Cyclic
C5 in an Argon Matrix...................... 101















LIST OF FIGURES


Figure Page

2.1 Isotopomers of C3............................... 27
(a) Linear structure....................... 27
(b) Cyclic structure......................... 27

2.2 Infrared spectrum in the 2070-1930 cm-1 region
of laser-ablated 2C products (lower spectrum)
and 12C:13C isotopically-mixed products
(upper spectrum) in unannealed argon matrices
at 12 K showing the six isotopomeric bands.... 30

2.3 Cryostat and furnace assembly................... 33

2.4 Sample degassing setup
(a) Furnace assembly.......................... 35
(b) Knudsen cell.............. ...... ... ....... 35

2.5 Experimental setup for the matrix isolation of
laser-ablated carbon in argon................ 39

2.6 Experimental setup for distinguishing between
ions and neutrals in the argon matrix......... 41

3.1 Infrared spectrum of the products of
laser-ablated 1C in an unannealed
argon matrix.................................... 48

3.2 Infrared spectra of the 2180-2070 cm-1 region
of laser vaporized graphite in an argon
matr x (12 K). Top panel: 1:1 mixture of
C: C; black dots indicate bands due to
isotopomers of linear C (cf. Table 1);
indicated 2164 cm-1 ban is from C5 and
2079.5 cm-1 from 13C5. Bottom panel: pure
12C graphite; 2128 cm-1 band has been
ascribed to 2C9......................... ...... 51

4.1 Difference spectrum [annealed (35 K) -
unannealed] of C laser-ablation
products in an argon matrix................... 65


vii









4.2 Infrared spectra over the 2070-1930 cm-1 range
of 12C products (lower spectrum) and 12C:13C
isotopically mixed products (upper spectrum)
isolated in unannealed argon matrices at 12 K
showing the six C3 isotopomeric bands......... 68

4.3 Infrared spectra over the 1980-1870 cm-1 range
of 12C products (lower spectrum) and 12C:13C
isotopically-mixed products (upper spectrum)
isolated in unannealed argon matrices at 12 K
showing the more prominent C6 isotopomer
bands (cf Table 5)........................... 71

4.4 Infrared spectra over the 2000-1920 cm-1 range
of 12C products (lower) in an unannealed
argo nmatrix. Upper spectrum shows the IR of
the 'C: 'C mixed productsin argon at 12 K
after annealing to 35 K for 15 min. Note the
increased density of bands compared to Figs.
4.2 and 4.3................ ........ ...... ...... 73

5.1 Bottom spectrum: Infrared spectrum of 12C
products in an unannealed argon matrix at
12 K showing prominent 1998 cm- C peak.
Top spectrum: Infrared spectrum of products
from a laser-vaporized 1:1 'C:'3C isotopic
mixture in an annealed argon matrix at 12 K
showing C3 isotopomer peaks ( ) and cyclic
C5+ isotopomeric peaks ( )................... 92

5.2 Left panel: Portion of infrared spectrum with
+48.0 V. on the ring eleptrode during
deposition showing the 'C + peak at 2052 cm-1
and neutral 12C3 peak at 2839 cm-'
Right panel: Portion of infrared spectrum
with -48.0 V. on the fJng electrode of an
unannealed matrix of 'C in argon at 12 K..... 94

5.3 Proposed mechanism for the formation of
cyclic C5 ..................................... 104

5.4 Proposed mechanism for the formation of the
corannulene decaradical using cyclic C5+,
C2 and C3 as precursors....................... 107

5.5 Proposed structure of C( Buckminsterfullerene). 110


viii








Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


MATRIX ISOLATED INFRARED SPECTROSCOPY
OF CARBON CLUSTERS

By

T. M. Chandrasekhar

May, 1990

Chairman: Martin T. Vala
Major Department: Chemistry

Infrared Spectroscopy is a powerful technique that can

be used to determine the size and structure of matrix

isolated clusters. It allows one to characterize the ground

state geometry of the entrapped species by measuring the

vibrational frequencies associated with the species. The

approach used to identify the sizes and ground state

geometries of the clusters identified is a variant of the

well-known isotopic substitution method in infrared

spectroscopy.

The method involves, first, the infrared spectral

recording of the products of vaporized 12C graphite,

followed by the recording of products of a vaporized sample

from a 1:1 mixture of 12C:13C powder. For a particular

cluster size and geometry, all the isotopomeric structures

possible can be expected if, during the laser vaporization

process, the graphitic carbon is atomized and the atoms

react to form clusters before deposition in the matrix. The

number of isotopomers formed for any given cluster size is

ix









dependent on the geometry of the cluster. Thus, the number

of different isotopomeric infrared frequencies observed in

the 1:1 mixed run is direct information on the geometry and

size of the cluster. Generally, the number of isotopomeric

bands does not lead to a unique choice of cluster size and

geometry, but the choices are considerably narrowed. In

order to collapse these choices to a final one, a normal

coordinate analysis is performed. A good fit is effected

when the deviation of the observed and predicted bands is

small and the force constants used to obtain the fit are

reasonable.

This method has been used to identify the infrared

bands and determine the geometries of the C5, C6, C8 and C5

clusters. The 2164 cm-, 1998 cm-1, 1952 cm- and 2052 cm

bands were assigned to the linear C5, chain-like C6, chain-

like C8 and cyclic C5+ clusters respectively.














CHAPTER I

INTRODUCTION





The chemistry and physics of clusters have long been

recognized as being of importance in such diverse areas as

catalysis and combustion.1 Carbon clusters are also of

astrophysical2 interest since small clusters have been

identified in comet tails and the atmospheres of stars.3 A

comprehensive review of the spectroscopy of carbon clusters

has recently been submitted by Weltner and Van Zee.

The study of carbon clusters has been greatly aided by

the development of new technology and experimental

techniques. Older studies which used thermal vaporization of
5-8
graphite yield C, C2 and C3 as the dominant species.8

Laser vaporization of graphite can produce a wide range of

neutral and ionic clusters'10 from C2 to C30 Larger

clusters, up to C100, have been produced using laser

vaporization and pulsed helium expansion sources.11 Some of

the background on carbon clusters will be reviewed in this

chapter.










Small Clusters: C -C
2---4


Both C2 and C3 have been extensively studied and are

well characterized.12-19 They are ubiquitous molecules and
20
have been detected in comets,20 the atmospheres of cool

carbon stars21,22 and giant circumstellar shells.23 They
24
have also been detected in electrical discharges, flames

and explosions.25

The first spectroscopic observation of a cluster of

carbon atoms was reported over a century ago by Huggins

while investigating the spectra of comets.26 The 405 nm band

group that Huggins observed was subsequently reproduced in

the laboratory by Herzberg in 1942 by an electrodeless

discharge through methane2 but was not correctly assigned

to the linear C3 molecule until Douglas reinvestigated the

spectrum in 1951.13 The absorption spectrum of C3 was also

observed by the flash photolysis of diacetylene,27

diazomethane,15a and diazopropyne.28 In addition to the

difficulties in identifying the carrier of the band system,

problems also arose in assigning the upper and lower

electronic states. Douglas determined that the 405 nm band

group arises from the C3 molecule, which he determined to be

linear in both the upper and lower electronic states. He was

however unable to determine whether the transition was of
l u- E+ or E +- nl symmetry. Finally, in two papers
published in 1963 and 1965, Gausset, Herzberg, agervst
published in 1963 and 1965, Gausset, Herzberg, Lagerqvist











and Rosen15 analyzed several bands of the 405 nm band group,

assigning the transition as A I u- X1E They also

determined the ground- and excited-state bending

frequencies, observed a large -type doubling in the XE +

state, and analyzed the A Iu state in terms of the Renner-

Teller effect.
19
Lemire et al.9 have recently reported a new band

system in the 266-302 nm region by resonant two-photon

ionization of jet-cooled C3. They determined that these

bands had E + E + vibronic symmetry, with all transitions
u g
originating from the lowest vibronic level of X1E + C3. They

also concluded that the new band systems) is(are) electric-

dipole forbidden and tentatively assigned the upper states)
1 1 29
as either a 1n or Au. Rohlfing and Goldsmith29 have

recently reported preliminary results on the stimulated

emission pumping spectroscopy of jet-cooled C3. They

obtained dispersed fluorescence spectra for excitation of 13

vibronic bands of the u+ g+ type. Kawaguchi, Matsumura,
30
Kanamori and Hirota30 have recently reported the observation

of the v3 hot bands (011)-(010), (021)-(020) and the

combination band (021)-(000) of C3 by diode laser

spectroscopy. The C3 was produced by photolysis of allene or

by an ac discharge in cyclopropane or furan.

Barger and Broida,31 Bondybey and English,32 and

Weltner and coworkers6,17 have obtained absorption spectra

of C3 in rare gas matrices. These low-temperature studies










resulted in the determination of the symmetric (vl) and

antisymmetric (v3) stretching frequencies of C3 in the 1 +

ground state and the symmetric (vl) vibration in both the

A u and X1 + electronic states. It also extended the

treatment of the Renner-Teller effect in the A Iu state.

Weltner and McLeodl7 recorded the absorption spectrum of C3

trapped in low-temperature neon, argon, and xenon matrices

and reported the v3 antisymmetric stretching frequency to be

2038 cm-1 in the ground electronic state. Vaporization of
13
60% 13C enriched samples of graphite produced six isotopomer

bands in the infrared in the 2038-1959 cm1 region. These

bands were fit to a linear C3 molecule and force constants

obtained by them.

A linear structure for C3 was also obtained by Goldring

et al.33 and Plesser, Vager and Naaman34 by the Coulomb

Explosion technique.3536 The experiment is highly sensitive

to the bond angle and the data fitted well with an ensemble

of linear C3 molecules with the above vibrational

frequencies in thermal equilibrium at 500 K. Recent
37
theoretical work by Jones37 confirmed the linear structure

for C3 and concluded that the C-C-C bond angle can be

changed by a large amount from its equilibrium value, with a

very small change in its energy or bond length.

The very low ground-state bending frequency of C3 (-63
-1
cm ) leads to large amplitude vibrational motion with

bending angles up to 60* and therefore to deviations from








5

harmonic small-amplitude models. Quasilinear and quasiplanar

molecules38 involve large nuclear motions. This prompted

Gausset et al.15 to suggest that C3 might not be linear in

the ground state but that, if a slight potential maximum
39
exists, it should be less than v2 Hoffmann, using

extended Huckel theory, predicted that C3 would be nonlinear

with an equilibrium CCC angle of -160" and a very small

barrier of -65 cm- at the linear state. However, later

calculations by Peric-Radic et al.40 using MRD-CI and by

Jones37 utilizing the parameter-free local spin density

approximation predicted a linear structure for C3. Jones

predicted the ground state bending frequency to be 75 cm-.

C2 is a well studied molecule: about 17 electronic

states of the molecule have been identified so far. Huber

and Herzberg41 have tabulated the electronic, structural,

and vibrational properties of C2 known as of about 1977.

Every year since then, there have been numerous papers

identifying C2 in some gaseous source and often adding to

the detailed knowledge of its spectroscopy.

Some of the better studied electronic band systems

studied to date are the Swan system42-47 (d3 a nu), the

Phillips system475355 (A 1i X E ), the Ballik-Ramsey
52 54, 5 q 3 54-57
system52,5455 (b3E a3n ), the Fox-Herzberg system54-57

(e3nH a3n ), the Mulliken system45'51'54,57

(D1 u X E +), the Deslandres-d'Azambuja system51'54'57

(CIg Alnu) and the Freymark system54'57 (El + Alnu).











Ab initio calculations of equilibrium geometries have
58
been done by DeFrees et al.,58 of excitation and

dissociation energies by Raghavachari59 and of geometries

and spectroscopic constants by Rohlfing and Martin.60

Franck-Condon factors have been calculated by several

authors including Walvekar and Rama,61 Brown,62 and Kuzmenko

and Chumak.63 Partition functions and thermodynamic

functions in the range of 1000 to 9000 K have been compiled

by Sauval and Tatum64 and Rossi, Maciel and Benevides-

Soares65 from the available molecular data.

Clementi and Clementi66 has carried out ab initio SCF-

LCAO calculation on C4 and predicted a linear structure with

a 3E- ground state. This corresponds to a cumulenic

structure, as Pitzer and Clementi67 had previously reported.
39
Hoffmann3, using extended Huckel theory also predicted a

linear structure for C4. A number of ab initio calculations
68-71
have been performed by several groups68-71 on C4 with the

chief contenders for ground state geometry being the triplet

linear and singlet rhombic, bicyclic structures. Most of the

calculations predicted the singlet rhombic form as slightly

more stable with the difference between the two energies

being about 5 kcal/mole.

However, a recent calculation by Bernholdt, Magers and

Bartlett,71 using various levels of coupled-cluster and many

body perturbation theory predicted that both the linear and

rhombic forms of C4 are essentially isoenergetic.











Calculations on equilibrium vaporization indicated that

entropy favors the linear form over the rhombic structure by

a factor of seven to one. The vibrational frequencies, ESR

hyperfine splitting parameters, ionization potentials and

electron affinities of both molecules were also calculated.

The IR-active frequencies of the linear form were calculated

to be 1586 cm-1 ( +) and 187 cm-1 (nu) respectively.

Sanborn72 has calculated the E + stretching frequency of

linear C4 to be 1700 cm-1. Calculations by Martin, Francois

and Gijbels73 also assigned the experimentally observed 1544
-i
cm1 band to linear C4.

Graham, Dismuke and Weltner74 have generated C4 by the

photolytic dissociation of C4H2 and the evaporation of

graphite, and trapped it at 4K in solid neon and argon. The

C4 was identified on the basis of optical and ESR studies.

Two absorption bands at 520.1 nm and 469.9 nm were assigned

to linear C4 on the basis of annealing studies. These bands

were observed to grow in a parallel fashion with the C4 ESR

signals upon repeated annealing up to 25 K. Warming above

30 K caused a loss of band intensity. More recent results on

the ESR of C4 by Cheung and Graham75 suggested that C4 had a

chain-like, albeit slightly bent structure.











Small Clusters: C5-C9


8Q76
The thermal vaporization of graphite876 yields

predominantly carbon atoms plus C2 and C3 atoms. Small

amounts of larger clusters are also produced. Early

theoretical work39,66'67'77 predicted that all clusters

containing up to ten carbon atoms should be linear. More

refined recent calculations68-71,78-80 have indicated that

some ground state clusters with four or more atoms may not

be linear. Raghavachari and Binkley79 have calculated that

odd carbon clusters have lowest energy linear structures

while even carbon clusters should be cyclic.

Other recent theoretical work by Bernholc and

Phillips81 predicted that all clusters containing between 3

and about 9 atoms should be linear. Calculations on C5 done

by Ewing and Pfeiffer,82-84 and Ott and Ray85 predicted a

ground state linear structure. Sanborn72 has calculated the

vibrational frequencies of linear C5 and C6. The IR-active

S+ vibrations were calculated to be 2210 cm-' and 1430 cm-1

for C5, and 2040 cm-1 and 1230 cm-1 for C6. Recent

theoretical studies, which include electron correlation

effects, are now sufficiently powerful to predict with high

accuracy the ground state vibrational frequencies of unknown

molecules such as carbon clusters. These calculations

generally predict frequencies that are 10% too high. For the

infrared active ungerade modes, Raghavachari and Binkley79











calculate 2344 cm-l(ou), 1632 cm-l(au), 648 cm- (Ru) and

112 cm- ( ) for linear C5 and 2184 cm-1(a ) and 1289 cm-1

(a ) for linear C6. Infrared studies on matrix isolated

carbon clusters done by Thompson, DeKock and Weltner86

assigned the 1952 cm-1 and 1544 cm-1 band to linear 12C

C6 and C8 were first detected by Drowart et al.

using mass spectrometry. Early calculations by Pitzer and

Clementi7 and Ewing and Pfeiffer82 predicted linear

structures for both molecules. MNDO calculations by Bernholc

and Phillips81 also predicted a linear structure. Ab initio

studies by Raghavachari, Whiteside and Pople80 found the

cyclic singlet structure with six pi electrons (planar D3h,

IA) to be the ground state structure with the linear 3 E

structure lying about 10 kcal/mole higher in energy. Other

calculations by Ott and Ray85 and Parasuk and Almlof87

predicted a linear ground state structure for C6.
88
Kratschmer, Sorg and Huffman88 have recorded UV-VIS

absorption spectra of carbon clusters in an argon matrix and

assigned a series of bands in the 240 to 600 nm region to

linear C4 to C9 clusters. Their assignments were as follows:

C4 (247 nm), C5 (311 nm), C6 (394 nm), C7 (447 nm), C8 (529

nm) and C9 (586 nm). These bands were assigned to E u- g

transitions in linear molecules.

Thompson, DeKock and Weltner86 have assigned the 1997
-1 -1 12
cm and 1197 cm1 bands to 12C A recent ESR study of

graphite vapour in argon and neon matrices by Van Zee et











89
al.89 concluded that C6, C8, and C10 were linear and present

in the matrices in their lowest 3E states. They also found

evidence for two forms of C10, possibly two slightly bent

isomers.

A new crystalline allotrope of carbon, "C ", which is

denser than diamond, has recently been claimed, following
9O
research on the plasma deposition of thin carbon films.9

The reported structure consists of a body-centered cubic

array of C8 cubes, forming a lattice previously postulated

by Burdett and Lee91 and termed "supercubane". Johnson and

Hoffmann92 however believe that the new form of C8 probably

has the BC-8 structure, adopted by the high-pressure y-Si

allotrope. This conclusion was reached from extended Huckel

band calculations and from discrepancies in the

crystallographic analysis and unusual bond length

distribution of the reported structure.90



Large Clusters



The mass spectrometric study of carbon clusters dates

from the first work done by Hahn et al.93,94 in 1942 in

which species containing as many as 15 carbon atoms were

observed. Prior to 1984, several workers5,6,8,9,10

successfully produced and detected carbon cluster ions

ranging in size up to 33 atoms.









11

Large Cn clusters (n 10) were produced by the pulsed

supersonic expansion of laser vaporized carbon in high

pressure helium gas by Rohlfing, Cox and Kaldor.1 The

clusters were photoionized using a 193 nm or 248 nm ArF

excimer laser and detected by a time-of-flight mass

spectrometer (TOF-MS). The cluster distribution was found to

be bimodal with both even and odd clusters being observed

for Cn, 1sns30 and only even clusters C2n for 205ns90. The

observation of only C2n clusters for large n was explained

as being due to the laser induced transformation of graphite

into "chunks" of a new, high temperature phase of carbon,

the carbyne phase, composed of cross-linked acetylene-like

linear chains (-C=C-)n

When the graphite rod was pretreated with KOH, and the

experiment repeated, clusters of the type K2C2n were

observed with n = 3-12. This was presented as evidence that

the clusters Cn for lsns24 have linear chain structures. Ab

initio calculations on linear carbon chains95 predict that

odd numbered clusters have singlet ground states while the

even numbered clusters have triplet ground states in which

most of the unpaired electron density resides on the

terminal carbon atoms. These even numbered diradical species

were thought to add a potassium atom to each end to form the

K2C2n clusters with the structure K-(C=C) -K. The formation

of a whole series of K2C2n clusters was presented as proof

that the potassium addition occurs after the formation of











the carbon clusters since addition during cluster growth

would presumably terminate carbon chain formation.

Heath et al.96 have studied the reactions of Cn carbon

clusters up to n = 40 with small molecules like H2, H20, NH3

and CH3CN and found that the initially formed even n species

for n<24 are reactive radicals with linear carbon chain

structures that can readily add H, N, or CN at the ends to

form relatively stable polyynes or cyanopolyynes. The

curious prominence of the C11, C15, C19, and, to some

extent, C23 (the An = 4 effect) was observed but could not

be interpreted satisfactorily, although others81b97 have

considered this as possible proof for the existence of ring

structures.

Heath et al. and Rohlfing, Cox and Kaldor's conclusions

are in marked contrast to the conclusions reached by

McElvany and coworkers. They detected an abrupt change in
98
the reactivity of Cn clusters (n = 3-30) with D2 and 0298

HCN99 and small hydrocarbons like CH4, C2H2 and C2H00

between n = 9 and 10. They interpreted this as the result of

a structural change from linear to monocyclic rings in the

cluster ions between n = 9 and 10. Similar conclusions were

reached by Yang et al.101 in UPS studies of negative carbon

clusters in the 2-30-atom range. They found that in the 2-9-

atom range, the even numbered chains had open shell

electronic structures with high electron affinities while

the odd chains had closed shell singlet ground states (for











the neutral) and substantially lower electron affinities.

Clusters in the 10-29-atom range gave UPS patterns

consistent with monocyclic ring structures. Calculations by

Bernholc and Phillips81 and Ott and Ray85 support these

conclusions and predict cyclic ground states for n>9.

Among the larger clusters, the C60 cluster has received
102
much attention recently. Smalley and coworkers02 repeated

the experiment of Rohlfing et al and observed that the size

distribution of the large even-numbered carbon clusters was

extremely sensitive to vaporization conditions. When the

helium carrier gas pressure and residence time in the nozzle

were increased, C60 was found to account for more than 50%

of all clusters observed. They also discovered that the C60

cluster was extremely inert and proposed that the extreme

stability of the cluster could be accounted for by the

formation of a closed spherical shell structure that had no

reactive edges. The proposed structure for C60, dubbed

Buckminsterfullerene was that of a soccerball: 12 pentagons

and 20 hexagons arrayed on the surface of a sphere with

icosahedral symmetry.

A study on the reactivity of carbon clusters with small

molecules such as NO, CO, H2, 02, SO2 and NH3 by Zhang et

al.103 found that C60 was particularly inert. Small carbon

clusters (C with n<40) were found to be very reactive,

while the larger even n clusters (40
inert. The relative inertness of the even clusters in the











40-80 range suggested that these clusters (but not the odd

ones) too can form closed shells by using a combination of

pentagons and hexagons. Kroto04 has presented a set of

simple, empirical chemical and geodesic rules that relate

the stability of carbon cages mainly to the disposition of

pentagonal rings, or various directly fused pentagonal ring

configurations. He predicted that the fullerenes Cn for

which n = 24, 28, 32, 36, 50, 60 and 70 should have enhanced

stability relative to near neighbors.

Thompson105 has used Euler's relations to deduce that

in such a structure, there will always be 12 pentagons

together with n/2 10 hexagons, where n is the number of

carbon atoms. The most stable clusters are those with only

moderately strained rings and a large number of resonance

forms. C60 for instance has been calculated to have 12500

Kekule structures.1

Cox, Reichmann and Kaldor107 have suggested that the

enhanced C60+ signal observed by Smalley and coworkers could

be due to an increased cross section for the formation of

C60 at the frequency of the ionizing laser and not due to
103,108 107
its added stability. Both Smalley0308 and Cox07 observed

an intense peak for C60 using F2(7.9 eV) and ArF(6.4 eV)

ionizing lasers. However, Cox and coworkers observed a

greatly diminished C60 peak using a KrF(4.99 eV) ionizing

laser.











A remarkable feature of these cage structures is that

they are hollow and present the possibility of trapping a

wide variety of atoms inside the sphere. The concept of

hollow molecules made from two-dimensional carbon sheets was

first suggested by Jones109 in 1966. He showed that Euler's

closure requirement,



12 = 3n3 + 2n4 + in5 + On6 In7 2n8 -...



where nk is the number of k-sided faces, applies to such

cages. For carbon only cages, k = 5 or 6 are likely

(although k = 7 should not be overlooked) so 12 pentagonal

faces are necessary although the number of hexagonal ones is

arbitrary.

Heath et al.0 and Weiss at al. have produced

stable complexes of the formula C60M where M = La, K and Cs

by treating the graphite disks with the corresponding alkali
107
metal halides. Cox, Reichmann and Kaldor07 have reported

attaching more than one metal atom to C60 and producing ions

with the formulae C K+, C K2 and CnK3 for 40
O'Brien, Heath, Curl and Smalley108 have generated

large jet-cooled cluster ions as large as C80 by the direct

vaporization of graphite, without the use of an ionization

laser, and studied the laser-induced fragmentation behavior

of these ions by tandem TOF-MS. They found that two distinct

photophysical regimes could be identified. The first applied











to clusters with 34 atoms or more, all of which dissociate

to produce even numbered fragments. Large even clusters

fragmented by the loss of high energy C2, while odd ones

lost a single C atom. The second regime applied to clusters

composed of 31 atoms or less, all of which fragment by the

loss of C3. These two regimes were separated by C32 which

fragments to produce smaller cluster ions in the 10 and 19

atom size ranges. These results were interpreted as

consequences of the large even clusters having edgeless,

spheroidal cage structures with the small ones having linear

or ring structures.

UPS studies of mass-selected negative ion clusters by

Yang et al.112 in the 48 to 84 atom range revealed three

closed shell clusters with appreciable HOMO LUMO gaps:

C50(0.3-0.6 eV), C60(1.5-2.0 eV) and C70(0.7-1.2 eV). C60

was also found to have the lowest electron affinity (2.6-2.8

eV) of any cluster. Heath, Curl and Smalley113 have observed

a narrow band at 386 nm in the UV absorption spectrum of

C60, and assigned it to the 0-0 band of the first allowed

Tlu A electronic transition. The measurement was made

using "laser depletion spectroscopy" based on the absorption

and depletion of the C60-adduct signals, the adduct being

either a C6H6 or CH2Cl2 molecule. This was in agreement with

the calculations of Larsson, Volosov and Rosen114 for the

energy of the lowest electric dipole allowed transition of

icosahedral C60. The UPS results along with the observation











of a single narrow absorption in the UV suggested a rigid,

highly symmetrical structure for C60.

Very high mass even carbon clusters have been prepared

by Lineman, Somayajula, Sharkey and Hercules115 by the

ionization of chrysene, pyrene and anthracene by a fourth

harmonic (265 nm) Q-switched Nd-YAG laser. Positive C +
n
cluster ions for n = 50 to 584 and negative cluster ions Cn

up to n = 200 were observed by this method. The laser energy

and focus conditions were found to play a key role in the

type of carbon cluster formed. In contrast to previous

studies, no dominant C60 or C60 peak was observed in the

mass spectra. This was in agreement with Cox, Reichmann, and
107
Kaldor's 07 earlier work, where they showed that the

magnitude of the C60+ signal could be influenced by the

frequency of the ionizing laser and suggested that the

intense C60 signals of earlier experiments could be due to

a favourable ionization cross-section at the laser frequency

used, and not due to any inherent stability of the cluster.

The 265 nm Nd-YAG (4.69 eV) used by Lineman et al. was very

close in energy to the KrF(4.99 eV) ionizing laser used by

Cox and coworkers.

O'Keefe, Ross and Baronavski116 have also reported

preparing very high mass positive carbon cluster ions Cn+ up

to n = 110 by the direct vaporization of graphite using a

Nd-YAG laser. They found that this required high laser

energy (>10 mJ) and long irradiation times. In contrast,











Lineman et al.115 have produced the same clusters from

chrysene using a single laser shot at relatively low laser

energy (2.0 pJ; power densities less than x10l6 W/cm2).

The possible existence of such highly stable and

symmetric clusters as C60 has provoked a great deal of

interest among theoreticians.117-130 Most of these,

consisted of semi-empirical calculations extending the

planar Huckel theory and including the three dimensional

character of the cluster. It involved placing the pi

orbitals at an angle of 23 degrees with respect to each

other, and required a rehybridization of the carbon atom.

These calculations generally agreed on the stability of

the truncated icosahedral structure of C60. The HOMO-LUMO

energy gap was found to be somewhere between 2.2 and 4.2 eV

and the qualitative ordering of energy levels and bond

character were in general agreement. Two ab initio

calculations, the first by Disch and Schulman131 at the STO-

3G level and the second by Luthi and Almlof132 at the large-

scale restricted Hartree-Fock level have been performed

yielding bond distances, the ionization potential and the

electron affinity. Vibrational frequencies have been

calculated by Newton and Stanton,128 Disch and Schulman,131

Coulombeau and Rassat,133 Wu, Jelski and George,134 and
135
Weeks and Harter.135 Due to its high symmetry, the C60

molecule has only four Infrared active (tlu) and ten Raman

active (eight h and two a ) fundamentals.
g9 g











Ionic Clusters



The laser vaporization of graphite is known to produce

ions in addition to the dominant neutral species. Honig6

discovered as early as 1954 that graphite filaments heated

to 2600 K emitted negative carbon clusters Cn containing

between one and eight atoms with the dominant species being

C C2 and C3 Drowart et al.8 measured the ionization

potential of C2 and found it to be 12.0 0.6 eV. Furstnau,

Hillenkamp and Nitsche and Bloomfield et al.136 generated

positive and negative ions by the direct laser vaporization
137
of graphite. Geusic et al. conducted detailed studies on

the photofragmentation of carbon cluster cations containing

between 3 and 20 atoms. For most of the cations, the loss of

C3 was observed to be the dominant reaction channel,

possibly due to the special stability of C3. C5+ was

observed to fragment to C2 and C3+, probably due to the

lower ionization energy of C3. C1 + was another exception

with the dominant channel being C1 loss to produce C10 .

Reactions of carbon cluster cations with small molecules

like D2 and 02,98 HCN,99 CH4, C2H2 and C2H4100 by McElvany

and coworkers revealed that C7 C8 and C9+ react at two

different rates. This was attributed to the existence to two

isomers, with the more reactive isomer assumed to be linear,

while the slower reacting ions were assumed to be cyclic. An

abrupt change in reactivity was also observed as the cluster











ion size increased from n = 9 to n = 10. This too was

interpreted as due to a change in structure from linear to

cyclic, with all clusters greater than or equal to ten atoms

being cyclic.

On the theoretical front, Bernholc and Phillips81

carried out self-consistent MNDO calculations on neutral,

positive and negative chains and rings in the C2-C26 range

and predicted that the most stable positive ions should be

C11 C15, C19 and C23 and the most stable negative ions

C14, C18 and C22-

Very little is known about the electronic and

vibrational structure of carbon cluster ions. C2 was first
138
identified by O'Keefe, Derai and Bowers, and later in a
139
neon matrix by Forney, Althaus and Maier. They formed

12C2 and 13C by the photolysis of acetylene and

halogenated acetylenes with the best results obtained with

chloroacetylene. Three bands corresponding to the
4 4
B E X transition were observed. The same transition
u g
was later studied by laser excitation spectroscopy by
140 141
Rosslein, Wyttenbach and Maier40 and Maier and Rosslein.141

The first observation of electronic transitions in C2

was by Herzberg and Lagerqvist,24 who saw both absorption

and emission between the ground X2 + and excited B2 u

states in a flash discharge of methane. The carrier of those
142
bands was identified by Lineberger and Patterson42 by the

two-photon photo-detachment spectroscopy of C2 in a mass-











selected negative ion beam. Subsequent work143-146 by

Lineberger's group established the electron affinity of C2

and determined rotational and vibrational constants for the

B and X electronic states. Oka and coworkers147 have

observed the infrared spectrum of the A2 I X 2 +

transition of C2 by using difference laser frequency

spectroscopy. The ion was also prepared in argon matrices by

Milligan and Jacox148 using VUV photolysis of acetylene and

using X-irradiation of acetylene in Ar, Kr and Xe matrices

by Frosch.149 The B2 + 2 + transition was observed in

both emission and absorption in all three matrices.



Carbon Clusters and Soot Formation



The kinetics of soot particle growth1,150 has been a

topic of much interest and research because of its

importance in understanding combustion processes. Zhang et

al.103 have proposed a scheme for the formation of C60 as a

byproduct of soot formation. Significant support for their

proposal was provided by Gerhardt, Loffler and Homann1 who

reported observing C60 as a dominant ion in a sooting

flame.

Kroto and McKay152 have proposed a carbon nucleation

scheme involving a corannulene framework which results in

quasi-single crystal particles of concentric, spiral-shell

internal structure and overall quasi-icosahedral shape. They











have also proposed that due to the ample quantities of

hydrogen present in soot, there may be no need for pentagons

to form stable, more or less closed structures since

stability could be acheived simply with hexagonal nets and

internal C-H bonds with the hydrogens located at pentagonal

vertices with respect to each other. An intriguing way to

look at this surface, is as a single sheet of hexagonal

graphite with 12 pentagonal defects (only 12, whatever the

size) systematically inserted during growth to form an

essentially continuous icosahedral monosurface. The growing

onion-like particle would have a distorted icosahedral

shape. This proposal received substantial support when
153
Iijima53 observed polyhedral concentric shell structures in

electron micrographs of carbon particles.

It is clear that the chemistry of carbon clusters is

rich and varied, and many questions about the structures,

and the electronic and vibrational properties of even the

smaller clusters remain to be answered. The practical

implications of a thorough knowledge of carbon cluster

chemistry could be profound in areas ranging from combustion

and catalysis to the mechanism of thin film growth and

interstellar chemistry. This thesis deals with the

characterization of some small carbon clusters by infrared

spectroscopy. Specifically, it presents evidence for the

vibrational frequency assignments and ground state

geometries of C5, C6, C8 and C5.















CHAPTER II

EXPERIMENTAL







A detailed description of the experimental setup used

to generate and study the carbon clusters is presented here.

Matrix isolation involves mixing the vapour of the sample of

interest with a large excess of the matrix gas (typically an

inert gas) and freezing the mixture on a cold window to form

a matrix. The sample molecules are trapped in the solid

inert gas and isolated from each other. This minimizes or

eliminates interactions between the sample molecules and

greatly simplifies spectra. Also the molecules are

vibrationally cold at the temperatures used. Matrix

isolation spectrosopy offers an ideal technique to study

highly reactive species such as radicals and ions. The

matrix allows one to stabilize and accumulate these species

in sufficiently high concentrations to allow study by

absorption spectroscopy.











Experimental Approach



The approach used in this study to identify the sizes

and ground state geometries of the clusters identified is a

variant of the well-known isotopic substitution method in

infrared spectroscopy. The method involves, first, the

infrared spectral recording of the products of vaporized 12C

graphite, followed by the recording of the products of a

vaporized sample from a 1:1 mixture of 12C:13C graphite

powder. For a particular cluster size and geometry, all the

isotopomeric structures possible can be expected if, during

the laser vaporization process, the graphitic carbon is

atomized and the atoms react to form clusters before

deposition in the matrix.

The number of isotopomers formed for any given cluster

is dependent on the geometry of the cluster. Thus, the

number of different isotopomeric infrared frequencies

observed in the 1:1 mixture run, is direct information on

the geometry and size of the cluster. Generally, the number

of isotopomeric bands does not lead to a unique choice of

cluster size and geometry, but the choices are considerably

narrowed. In order to collapse these choices to a final one,

a normal coordinate analysis is performed. A good fit is

effected when the deviation of the observed and predicted

bands is small and the force constants used to obtain the

fit are reasonable.











To illustrate the method, the C3 cluster will be

discussed. Three structures are possible: linear, bent and

cyclic (equilateral triangle). Figure 2.1 shows the number

and types of isotopomeric structures expected for the linear

and cyclic cases. The shaded circles represent 13C atoms.

The bent case is similar to the linear structure and will

have an identical number of isotopomers as the linear case,

the only difference being the angle subtended by the two

external carbons on the central carbon atom. It can be seen

that the linear and bent structures possess six isotopomers

while the cyclic structure has only four isotopomers.

C3 has one infrared active stretching vibration with

a+ symmetry. The value of this vibrational frequency for

the 13C substituted isotopomers will be red shifted relative
12 13
to the 12C3 frequency by varying amounts, with the all- C3

isotopic frequency being red shifted the most. For linear

carbon clusters, it can be shown from the Teller-Redlich

rule154 that the frequencies for the two completely

substituted isotopomers will obey the relation



13vi / 12vi = 0.9606.



This relation dictates that for 1C cluster frequencies in

the 2000 cm-1 (C-C stretch) range, its 13C partner will

absorb -80 cm-1 to lower energy. The mixed isotopomers will,

of course, fall within these limits.


































Figure 2.1

Isotopomers of C3.

(a) linear structure.
(b) cyclic structure.





0--~--0-----0
*-----0 0





(a)









(b)









28

Figure 2.2 shows the infrared spectrum of the products

of laser vaporized graphite in an argon matrix (200 scans,
-1
0.25 cm-1 resolution). The bottom panel shows the spectrum

of 12C in argon while the top one shows the spectrum for the

1:1 mixture of 1C and 13C isotopes. Both spectra are for

unannealed matrices. It can be seen that six bands are built

on the 2039 cm-1 band with the lowest energy band appearing
-1 o1 12
at 1961 cm- or 78 cm-1 away from the all- C isotopomer

band at 2039 cm-1. The appearance of six bands conclusively

excludes the equilateral cyclic structure but does not allow

a distinction between the bent or linear structures.

However, the spread of the six bands fulfills the Teller-

Redlich criterion for linear molecules.

To confirm this conclusion, a normal coordinate

calculation can be carried out and the predicted bands fit

to the experimentally observed ones. A good fit with

reasonable force constants would constitute conclusive proof
17a
for the above assignment. Weltner and McLeod17a have

obtained such a fit and determined the force constants to be

10.34 mdyn/A (for the C-C stretch) and +0.542 mdyn/A for the

interaction between the adjacent C-C stretches.

An similar approach has been used to assign the

vibrational frequencies and determine the structures of the

C5, C, C8 and C5+ clusters, the subjects of this study.
C5, c6 c8 adC lses h ujcso hssuy




























Figure 2.2

Infrared spectrum in the 2070-1930 cm-' region

of laser-ablated 1C products (lower spectrum)

and 12C:13C isotopically-mixed products

(upper spectrum) in unannealed argon matrices

at 12 K showing the six C3 isotopomeric bands.
Resolution 0.25 cm-1
Resolution = 0.25 cm.




























V












2039cm-1
(C3)



I lf il i i l i i l i


2000
./cm-1


LUC'3


1975


1950


l m


A AAAm


2UOU


2025











Matrix Isolation Apparatus



The apparatus used to achieve the temperatures

necessary for the formation of inert gas matrices consisted

of a two stage helium refrigerator (Air Products, Displex

Model DE202), shown in Figure 2.3. A Knudsen cell furnace

assembly is shown attached to the shroud. Cooling is

achieved by the expansion of compressed helium gas.

Temperatures as low as 10K can be reached. The cold window

assembly was mounted on a cold finger at the bottom of the

second stage and was surrounded by a copper radiation shield

attached to the first stage of the Displex. The radiation

shield, maintained at 40-60 K, acted as a thermal barrier to

heat transfer from the outer vacuum shroud to the lower

stage and the window assembly. The cryostat could rotate

ninety degrees in either direction inside its fixed outer

vacuum shroud. Figure 2.4 shows the the details of the

Knudsen cell furnace assembly and the Knudsen cell. The

setup shown was used to degas the sample of 13C before use

in the experiment.

The temperature of the sample window was set by an Air

Products APD-B temperature controller and measured by a

gold-chromel, 0.07% Fe thermocouple with the thermocouple

junction mounted near the middle of the oxygen free copper

window holder. The thermocouple was calibrated against the

temperature of liquid nitrogen. The cold finger was equipped



































Figure 2.3

Cryostat and furnace assembly.













ELECTRICAL ---


He GAS

C
THERMOCOUPLE
ond
HEATING WIRES

EXPANDER
Ist STAGE
2nd STAGE



COPPER COLD TIP

TARGET WINDOW

RADIATION SHIELD


ROTATABLE JOINT


GAS


ASSEMBLY

































Figure 2.4

Sample Degassing Setup.

(a) Furnace assembly.
(b) Knudsen Cell.


















PYROMETER
VIEWPORT


FURNACE O-RING MOUNTIf
COOLING GROOVE FLANGE
WATER


(b)


D
t--Ta


To CELL

0.215"
I-- 1.00" --
END CAP


0.250"


T
0.75"
J_


I- 0.70" ---


To STRAP











with a 10 watt variable duty cycle heater used to control

the temperature of the window. The window assembly was

screwed on to the cold-finger of the cryostat and an indium

gasket was used to ensure good thermal contact with the

cold-finger.

The interior of the shroud was evacuated to pressures

less than 1 X 10-6 Torr. by a two inch air-cooled oil

diffusion pump (Alcatel PDR 250, pumping speed = 200 L/sec.)

and a 450 L/minute mechanical roughing pump (Alcatel 2020).

The low pressures are necessary to achieve the low

temperatures and to prevent the condensation of contaminants

including atmospheric gases on the window. The pressure was

monitored by an ion gauge (Model 4336P, Kurt J. Lesker Co.)

and read off a Granville-Phillips 270 Gauge Controller.



Carbon Cluster Preparation



The carbon clusters were generated by focussing the

second harmonic output (532 nm, ~0.1 mJ/pulse, 10 Hz)

of a pulsed Q-switched Nd-YAG laser (Spectra Physics, DCR-11

Nd-YAG) on the graphite rod. The rod was rotated at a rate

of approximately 6 rev./hr. to expose a fresh surface for

every pulse. The graphite vapour that resulted was mixed

with argon gas and deposited on the cryostat's cesium iodide

window which was maintained at 12 K. The high purity argon

gas (Research purity, 99.9995% pure, Matheson Gas Products)











was bled into the cryostat through a micro-metering needle

valve (Whitey Co.) in a continuous flow. Factors that

influence the production of a good matrix include laser

power, laser focus, the distance between the carbon source

and the sample deposition window, and the flow rate of the

matrix gas. These factors had to be varied and optimized to

get the spectra described in this work.

For the mixed isotope experiments, a 1:1 mixture of 12C
13
and 1C powders was pressed into a pellet and mounted on the

side of the Displex shroud as shown in Figure 2.5. The 12C

powder was prepared by scraping a rod of the afore-mentioned

graphite. The 13C powder ( 98.4 atom%, Isotec Inc.) was

degassed in a tantalum Knudsen cell at 1500 K for one hour

before mixing with the 12C powder. The laser was focused on

a different spot on the pellet every 5 minutes during

deposition.

In order to distinguish between ions and neutrals, a

modification to the experimental setup described above was

necessary. A small copper wire ring was mounted "0.5 cm in

front of the sample window and electrically insulated from

it and its copper mount. This was done by tying the copper

ring to two parallel glass capillary tubes and gluing the

glass tubes to the copper window mount as shown in Figure

2.6. By applying a potential to the ring ions could either

be attracted to or repelled from the deposition window

depending on the polarity of the ring with respect to the


































Figure 2.5

Experimental setup for the matrix isolation
of laser-ablated carbon in argon.


















TO PUMPS


KBr WINDOW


Nd-YAG LASER BEAM

































Figure 2.6

Experimental setup for distinguishing between
ions and neutrals in the argon matrix.




































COPPER RING


COLD FINGER


INDIUM GASKET





GLASS ROD


Csl WINDOW









LOW TEMPERATURE EPOXY


COPPER WINDOW HOLDER











window holder which was held at ground. In a second

approach, a small tungsten filament acting as an electron

gun was mounted in close proximity to the sample window

("2.0 cm), and used to neutralize any positive ions present

in the matrix. Simultaneously, a band at 904 cm-1, ascribed

to the ArH+ ion55 was also monitored for changes in its

intensity.



Instrumentation



A Nicolet 7199 Fourier Transform Infrared spectrometer

was used to record the infrared data. It was equipped with a

water cooled globar source and MCT and TGS detectors. All

the spectra used in this work were recorded by the MCT

detector due to its greater sensitivity and better signal-

to-noise ratio. The spectrometer was purged with dry

nitrogen to exclude any water in the optical path and to

protect the beam splitter.

The heart of the spectrometer consists of a Michelson

interferometer. One arm of the interferometer has a

stationary plane mirror while the other arm has a movable

mirror assembly mounted on dual air bearings and driven by a

linear induction motor. Light from the source is split by

the KBr beamsplitter and travels down the two arms of the

interferometer to be reflected back to the beam splitter and

through the sample on to the detector. The recombined beam











leaving the beamsplitter shows constructive or destructive

interference, depending on the relative path lengths from

the beamsplitter to the fixed mirror and the beamsplitter to

the moving mirror assembly. If the path lengths are

identical or differ by an integral number of wavelengths,

constructive interference occurs, whereas if the difference

is a half-integral number of wavelengths, the beams cancel

at the beamsplitter. By moving the moving-mirror assembly,

the flux at the detector is varied and one obtains an

interferogram. Each data point on the interferogram is the

sum of individual frequencies. The frequency domain data of

interest is then recovered by performing the Fourier

Transform on the interferogram. This operation is performed

by the Nicolet 1180 computer.

Fourier Transform spectroscopy allows one to detect

very weak signals with relatively high signal-to-noise ratio

by just increasing the number of scans collected. This is of

importance in the experiments of interest, since many of the

clusters (especially in the mixed isotope experiments) are

present in very small concentrations.















CHAPTER III

THE C5 CLUSTER





Introduction



The first calculation on C5 was conducted Pitzer and
67
Clementi67 and predicted a linear structure for the

molecule. Ewing and Pfeiffer82 have calculated the total

energies, bond lengths, charge distribution and electronic

configurations for linear C clusters for n = 2-6. Later

calculations83,84 by them took a number of non-linear

geometries into account as well and found the linear singlet

form to be the most stable by more than 60 kcal/mole.

Similar conclusions were reached by Ott and Ray85 in a

recent study on equilibrium geometries of Cn clusters. A

MINDO/2 study by Slanina and Zharadnik56 predicted the most

stable structure of C5 to be a trigonal bipyramid.

An infrared study of matrix isolated carbon clusters

has been performed by Thompson, DeKock and Weltner. In

this work carbon was vaporized from a tantalum furnace

(yielding C, C2 and C3) and the larger clusters were

produced by annealing the matrix. Infrared bands were









45

correlated by their intensity behaviour upon annealing and

structures assigned from partial isotopic studies using
13
95%-enriched 1C in conjunction with normal coordinate

calculations. The 1952 cm-1 and 1544 cm- bands were
12
assigned to the a stretches of 12C.
u 5
In the present investigation a similar approach was

adopted. First, those bands that correlated with each other

in terms of change in intensity upon annealing were

identified. Second, the mixed isotope effect (1:1 mixtures

of 12C:13C) was used to assign a particular IR band to a

specific carbon cluster and to determine the cluster

geometry. This was done by comparing the number of

isotopomeric structures expected for a certain geometry with

the number of isotopomeric peaks observed. The assignment

was then confirmed by performing a normal coordinate

analysis on the molecule and fitting the calculated

frequencies to the observed ones. The resulting force

constants were found to be reasonable, and provided
-1
evidence for the assignment of the 2164 cm- band to linear

C5'



Results



The infrared spectrum of the 12C products obtained via

laser ablation of graphite is similar to that obtained by

thermal vaporization followed by strong annealing. Figure











3.1 shows the prominent bands observed here, (2164 cm ,
-1 199 cm'l-1
2039 cm1, 1998 cm1 and 1952 cm ) which have been seen

previously by Thompson, DeKock and Weltner.86

Isotopic substitution is a powerful method for

elucidating the structures of small carbon clusters. Using a

1:1 mixture of 12C:13C powder, all the isotopomeric

structures possible for a particular cluster geometry can be

expected if, during the laser vaporization process, the

carbon is atomized and the atoms react to form clusters in

the vapour before deposition. Each isotopomer will give rise

to an IR band whose frequency is shifted from its parent

(containing only 12C).

For a 1:1 sample mixture of 12C:13C graphite, the

number of isotopomers for a particular cluster size can be

easily determined. For linear clusters with even (2n) or odd

(2n + 1) atoms, the number of isotopomeric species is given

by

I2n = 2(212n-2 2n-2
and

2n+1 = 212n


where obviously I1 = 2 and 12 = 3. The possible number of
156
isotopomers is 6 for C3, 10 for C4, 20 for C5 and 36 for

C6. Other possible structures for C5 are trigonal

bipyramidal, square pyramidal and cyclic, for which the
































Figure 3.1

Infrared spectrum of the products of

laser-ablated 12C in an unannealed

argon matrix. Resolution = 1 cm-.














2039


-1
2164 cm
IA


2100


-1
cm

1998 cm1


1952cm1
1952 cm
I


L


2000
V/cmr


1900


2200


1800


~cs~Lh


E A R











number of isotopomers are reduced to 12, 12 and 8,

respectively.

Figure 3.2 shows the infrared spectrum of the products

of laser-vaporized graphite in an argon matrix (200 scans,

1 cm- resolution). The bottom panel shows the spectrum of
12C in argon. It clearly shows a prominent band at 2164 cm-1

and a less intense band at 2128 cm-1. The 2128 cm-1 band had
86
previously been assigned to C9 by Thompson et al. The top

panel shows the mixed isotope spectrum and clearly shows 20

bands (marked by dots) built on the 2164 cm-1 band. These

isotopomer bands are also seen to fulfill the Teller-Redlich

criterion: the separation between the bands at the

extremities is 84.5 cm-1. The presence of 20 isotopomer

bands coupled with the fulfilment of the Teller-Redlich

criterion strongly suggests that the 2164 cm-1 band is due

to linear C5.

Linear C5 has two au IR-active stretching vibrations,

of which the the larger one is expected in the 2000 cm1

region. The second band is expected to lie at lower energy.

A band at 1544 cm-1, about 50 times less intense than the

2164 cm-1 band, was observed to decrease in intensity

markedly and in parallel with the 2164 cm-1 band upon

annealing at 35 K. A search for 20 isotopomer bands

associated with the 1544 cm-1 band was made in the mixed

isotope spectrum, but none were found.



























Figure 3.2

Infrared spectra of the 2180-2070 cm-1 region of

laser vaporized graphite in an argon matrix (12 K).

Top panel: 1:1 mixture of 12C:13C; black dots indicate

bands due to isotopomers of linear C5 (cf. Table 1);
-1 12 -1
indicated 2164 cm band is from 12C5 and 2079.5 cm-
13 12
band from 1C5. Bottom panel: pure 1C graphite;
-1 12
2128 cm band has been ascribed to 12C.

Resolution = 1 cm-1
Resolution = 1 cm.











2164cm-1


2079.5cm-1



.il
lI


I I I I I I I I 1 I


2128 cm-1
I


I I I I I I I I I I I


2140


2100


v /cm1


2180











Normal Coordinate Analysis



The linear C5 molecule possesses D h symmetry. The au

asymmetric stretch is expected to be the most intense IR

active band. The internal coordinates used in the

calculations were 'R', the outer C-C stretch, and 'r', the

inner C-C stretch. The symmetry coordinates were constructed

by taking symmetry adapted linear combinations of the

internal coordinates.

The symmetry coordinates158 were defined as follows:



S1 = R1 + R2 ------ a symmetric stretch.

S2 = R1 R2 ------ u asymmetric stretch.

S3 = rl + r2 ------ a symmetric stretch.

S4 = r r2 ------ au asymmetric stretch.



Only the C-C stretching vibrations were considered in the

analysis since the bending modes were outside the range of

our spectrometer. The normal coordinates obtained consisted

of two ou IR active stretches and two a IR inactive

stretches. The force constants used in the analysis were

designated as "fR" for the outer bond; "fr frr" for the

inner bond; "fRR" for the interaction between the outer

bonds and "frR" for the interaction between the outer and
rR
inner bonds. fRR was assumed to be negligible and set equal
to zero. In the valence force field treatment31 of this
to zero. In the valence force field treatment of this









53

molecule, the terms frr and fr always appear together in the

form fr frr and therefore no attempt was made to separate

the two variables. The general expression for E +vibrations
159
as given by Smith and Leroi for C302, was used to

calculate the values of the force constants fR and fr-frr as

a function of frR. For a symmetric carbon chain it reduces

to


22
2 X[2fR + 3fr 2fRr] + 5pC2[fRfr fRr2] = 0



where X = (2ncv)2 and pC = 1/12. Solving for X, one gets


( + 2 )/C = 2fR + 3r 2fRr






X12 = 5pC fRfr fRr2]


(1)


(2)






(3)


from which one obtains


f -frr
r rr


= 1/6(A + 2frR) + 1/2[(2frR/3 + A/3)2 -

8/3(B + frR2)1/2


(4)


and


= (B + fR2) / (f frr)


and


(5)











A and B are constants, which are defined as

A = (1 + 2) / PC and B = K 2 / 5pC2

The values of the force constants obtained were in

millidynes per Angstrom. The previously mentioned IR bands

at 2164 and 1544 cm-1 (1 and v2), which were observed to

behave in a parallel manner upon annealing, were used in the

fit. The force constants, fR and fr frr vary as a function

of fRr' and their values were calculated for a series of

values of fRr* Sets of these three force constants for any

given value of fRr were used in the normal coordinate

analysis and this procedure repeated with several sets until

a suitable fit was obtained. The force constants obtained by

this procedure were fr = 11.357 mdyn/A; fr frr = 9.989

mdyn/A; frR = 1.350 mdyn/A and fRR = 0. Table 1 gives the

list of frequencies obtained for all twenty isotopomers of

C5'

The vibrational frequencies of the linear C5 molecule

were later calculated using a different program60 which

allowed all three force constants to be varied independently

and used a least squares fitting subroutine to fit the

calculated frequencies with the experimental ones. The force

constants obtained by this fit were comparable to the ones

obtained by the earlier method. The frequencies obtained are

listed in Table 2. The fit can be seen to be excellent with

the rms difference between calculated and experimental

frequencies equal to 1.043 cm-1. The force constants











obtained were fR = 11.109 mdyn/A, fr = 10.253 mdyn/A and

fRr = 1.499 mdyn/A.


Discussion



The results of the normal coordinate analysis are

presented in Table 1. The force constants obtained: f =

11.357 mdyn/A fr frr = 9.989 mdyn/A and fRr = 1.350

mdyn/A, compare favourably with the force constants obtained

by Smith and Leroi159 for C302. The values of the above

three force constants for C302 are 15.41, 9.34 and 1.27

mdyn/A respectively. The excellent fit, and the reasonable

values of the force constants obtained, constitute
-1
conclusive proof for the assignment of the 2164 cm- band to
125

The absence of 20 isotopomeric bands associated with

the 1544 cm-1 band in the mixed isotope spectrum, is not
-1
surprising, given the very low intensity of the 1544 cm1

band in the 1C spectrum. The intensity of the isotopomeric

bands, if observed, would on an average be 1/20 of the

parent peak's intensity in the 12C spectrum. The 1544 cm-'

band lacks the isotopomeric data to support its assignment

with the same degree of certainty as the 2164 cm- band.

This makes its assignment to linear C5 less certain.

Recent calculations by Martin, Francois and Gibels73

assigned the 1544 cm1 band to the 3 vibration of C4 but
g











TABLE 1


Isotopomer Stretching Frequencies for Linear C5.


Obs. Freq. Calc. Freq.a Difference Structure of Stat.

v/cm-1 v/cm-1 Av/cm-1 Isotopomer Wts.


2164 2164.4 0.4 12-12-12-12-12 1
2161 2161.5 0.5 13-12-12-12-12 2
2158 2158.3 0.3 13-12-12-12-13 1
2146 2144.5 1.5 12-13-12-12-12 2
2144 2142.5 1.5 12-12 12-13-13 2
2142 2140.7 1.3 13-12-12-13-12 2
2140 2138.5 1.5 13-13-12-12-13 2
2129 2132.0 3.0 12-12-13-12-12 1
2128 2128.5 0.5 13-12-13-12-12 2
2126 2124.7 1.3 13-12-13-12-13 1
2122 2120.7 1.3 12-13-12-13-12 1
2120 2117.9 2.1 13-13-12-13-12 2
2117.5 2115.0 2.5 13-13-12-13-13 1
2111 2111.6 0.6 12-13-13-12-12 2
2109 2109.3 0.3 13-13-13-12-12 2
2106.5 2106.9 0.4 13-12-13-13-12 2
2104.5 2104.4 0.1 13-13-13-12-13 2
2086 2086.5 0.5 12-13-13-13-12 1
2083 2083.1 0.1 13-13-13-13-12 2
2079.5 2079.5 0.0 13-13-13-13-13 1




aForce constants used: fR = 11.357 mdyn/A, fr-frr = 9.989

mdyn/A, fRr = 1.350 mdyn/A and fRR = 0. The frequencies

2164 cm-1 and 1544 cm-1 were used to determine fR and


fr-frr while varying fRr.













TABLE 2

Observed and Calculated Isotopomer
Stretching Frequencies for Linear C,.


Obs. Freq. Calc. Freq.a Difference Structure of Stat.

(v/cm- ) (v/cm-1) (Av/cm-1) Isotopomer Wts.


2164 2164.59 -0.59 12-12-12-12-12 1
2161 2162.19 -1.19 13-12-12-12-12 2
2158 2159.69 -1.69 13-12-12-12-13 1
2146 2145.18 0.82 12-13-12-12-12 2
2144 2143.54 0.46 12-12 12-13-13 2
2142 2142.13 -0.13 13-12-12-13-12 2
2140 2140.41 -0.41 13-13-12-12-13 2
2129 2129.46 -0.46 12-12-13-12-12 1
2128 2126.55 1.45 13-12-13-12-12 2
2126 2123.48 2.52 13-12-13-12-13 1
2122 2122.30 -0.30 12-13-12-13-12 1
2120 2120.12 -0.12 13-13-12-13-12 2
2117.5 2117.86 -0.36 13-13-12-13-13 1
2111 2109.46 1.54 12-13-13-12-12 2
2109 2107.50 1.50 13-13-13-12-12 2
2106.5 2105.65 0.85 13-12-13-13-12 2
2104.5 2103.55 0.95 13-13-13-12-13 2
2086 2085.23 0.77 12-13-13-13-12 1
2083 2082.52 0.48 13-13-13-13-12 2
2079.5 2079.67 -0.17 13-13-13-13-13 1



aForce constants obtained: fR = 11.109 mdyn/A, fRr = 1.499

mdyn/A, fr = 10.253 mdyn/A and fRR = frr = 0.











the 2164 cm- band was attributed to linear C5. Shen and

Graham61 have recently assigned the 1544 cm- band to

linear cumulenic C4. They generated the C4 by the photolysis

of C4H2, diacetylene, C4H6, 1,3-butadiene C4D2, and various
13
3C-substituted and deuterated isotopomers of C4H6.
-1
The assignment of the 2164 cm- band to linear C5 by

this work,162 enabled the detection of C5 in the

circumstellar shell163 of the carbon star IRC+10216.
164
Moazzen-Ahmadi, McKellar and Amano64 have observed the

rovibrational spectrum of gas-phase C5 produced by a hollow

cathode discharge in C2H2 + He and C2H4 + He mixtures by

tunable diode laser spectroscopy. They obtained a gas-phase

value of 2169.4 cm-1 for the band origin, a value of 5.4 cm

higher than the matrix-isolated value. Similar results

were obtained by Heath et al.165 on supersonically cooled

carbon clusters produced by the laser vaporization of

graphite.

It is worth noting that C5 preserves its linear

structure in the argon matrix. The argon lattice does not

seem to distort the molecule to any detectable extent. Solid

argon is known to have a face-centered cubic structure. If

the Van der Waal radius of argon is assumed to be 1.91 A,1

then the removal of two adjacent argon atoms from the

lattice would result in a cavity whose longest dimension

would be 7.64 A. If the covalent radius of a doubly bonded

carbon atom is taken to be 0.67 A,166 then the length of the









59

C5 molecule will be 6.7 A and would allow it to fit in this

cavity.

The relative intensities of the isotopomer bands as

seen in Figure 3.2 appear to be anomalous since on

statistical grounds one expects the variation of band

intensities to be as given in column 5 of Table 1. Although

the spectrum is symmetric about its midpoint, 2124 cm-1, as
12 13
expected, the intensities of, e.g., pure 1C5 and 1C5

molecules are clearly exaggerated. This is attributable to

the fact that vaporization does not take place from an

isotopic mixture at the atomic level but from a mixture of
12 13
grains of essentially pure 1C and 1C graphite.



Conclusion



The 2164 cm- IR band has been conclusively shown to

belong to the linear C5 species. The assignment of the 1544
-i
cm1 band is less certain however. The utility of infrared

spectroscopy and mixed-isotope studies in establishing the

structure of small clusters has also been demonstrated.















CHAPTER IV

THE C6 AND C8 CLUSTERS





Introduction



Clusters such as C6 and C8 are present in very small

quantities in graphite vapour when compared to species like

C2 and C3. C6 and C8 were first detected by Drowart et al.

in graphite vapour by mass spectroscopy.

The earliest theoretical calculations on Cn molecules

were carried out by Pitzer and Clementi.67 They concluded

that these molecules are linear and suggested that at about

n = 10, cyclic structures might become more stable. They

also predicted that linear molecules with odd n would have
E ground states and would be more stable than those with n

even which have 3E ground states. Similar conclusions were

reached by Ewing and Pfeiffer8183 from single-determinant

Hartree-Fock calculations on linear C molecules. A MINDO/2

study conducted by Slanina and Zahradnik156 on Cn (n = 4-7)

clusters with different geometries predicted that the most

the most stable structure is non-linear. For C6, for

example, they considered the linear (D.h), cyclic planar









61

(D6h), square bipyramid (C2v) and trigonal bipyramidal (D3h)

structures and found the square bipyramidal structure to be

the most stable. An MNDO study by Bernholc and Phillips81

considered neutral, positive and negatively charged chains

and rings in the C1 C26 range. They concluded that the

chain-like structure was most stable through C9 while the

monocyclic ring was the most stable structure in the C10 -

C25 range for neutrals. The maximum stabilities were found

to be at 10, 14, 18 and 23 atoms for neutrals.

Recent ab-initio calculations on C6 by Raghavachari,

Whiteside and Pople80 concluded that the cyclic singlet

structure with six n electrons (planar D3h, A ) was the

most stable structure with the linear 3E structure lying
g
about 10 kcal/mole higher. The vibrational frequencies

calculated for the IR active ou stretches of the linear

molecule were 2184 cm-1 and 1289 cm-1. Other calculations by

Ewing and Pfeiffer83 at the Hartree-Fock level concluded

that the linear C6 structure was most stable. Recent

calculations by Parasuk and Almlof,87 using

multiconfiguration self-consistent field (MCSCF) and

multireference configuration interaction (MRCI) methods with

large basis sets, predicted that the ground state structure

of C6 is linear with a cumulene-like electronic structure
3-_
having E symmetry. Similar results were obtained by Ott
85
and Ray.85 They too concluded that cyclic rings are

preferred over linear chains for n>9.











Thompson et al.86 have reported IR spectra of carbon

vapour trapped in an argon matrix. Studies on highly

enriched 95% 13C together with annealing studies led them to

assign the 1997 cm-1 and 1197 cm- bands to 12C6 and the

1920 band to 13C. However, Kratschmer and Nachtigall167 in

a similar study did not observe a correlation between the

1997 cm-1 and 1197 cm-1 bands with annealing. They also
88
recorded UV/VIS absorption spectra88 and observed a series

of bands in the 247-600 nm region which they assigned to C4

C9 clusters on the basis of growth and decay during

annealing. The 394 nm and 529 nm bands were assigned to C6

and C8 respectively. A recent ESR study of graphite vapour
89
in argon and neon matrices by Van Zee et al.8 concluded

that linear C6, C8 and C10 molecules were present in the

matrices in their lowest 3E states which are presumably

their ground states. They also found evidence for two forms

of C10, possibly two slightly bent isomers.



Results



The infrared spectrum of the products of laser

vaporized graphite was shown in the previous chapter in

Figure 3.2. Figure 4.1 shows the difference spectrum

(annealed minus unannealed) over the 2200-1800 cm-1 region

after strong annealing. The negative peaks decrease in

intensity upon annealing while the positive ones increase.











Upon annealing the matrix, it was observed that the 2164

cm- and 2039 cm- bands decreased in intensity, while the

1998 cm-1 band increased sharply. The 1952 cm-1 band grows

slightly with annealing and then decreases.

The isotopic substitution method outlined in the

previous chapter is then used to assign these bands. As

mentioned earlier, for linear clusters, the various

isotopomer bands are expected to lie in an ~80 cm-1 interval
12
lower in energy from the 1C cluster band. The number of

isotopomers expected for linear Cn carbon clusters in the

n=3 to 8 range are 6 for C3, 10 for C4, 20 for C5, 36 for

C6, 72 for C7 and 136 for C8. This implies that as the

cluster size increases, the isotopomer bands must become

increasingly crowded in the -80 cm-1 interval specified by

the Teller-Redlich criterion. Table 3 gives the expected

average densities for linear clusters from C3 to C8. For

linear C6, a band is predicted about every 2 cm-1, whereas
-1
for linear C8 a band is expected about every 0.5 cm .

Figure 4.2 gives the unannealed spectra for 12C

products and 12C:13C mixed products in the 2070-1930 cm-1

range. The three major 1C product peaks appear at 2039

cm 1998 cm-1 and 1952 cm-1. In the mixed isotope spectrum

the six isotopomer bands built on the 2039 cm-1 band are

readily seen. Strikingly, in the mixed isotope spectrum the

1998 cm-1 and 1952 cm-1 12C parent peaks and their

isotopomer partners appear to have disappeared. In fact they
































Figure 4.1

Difference spectrum [annealed (35 K) -
12
unannealed] of 1C laser-ablation

products in an argon matrix.
























+0.3


w
1 0.0
z
m
cr-Q3-


S-0.6



2200


2052cm-1


12164cm1 :C5


1998cm-1::c
I 8


12C/Ar: Annealed
-Unannealed


:C3


I I I I I I I I I I I1


2100


2000
.9/cr-1


1900











TABLE 3


Expected Number of Isotopomers for
Linear Carbon Clusters.



Cluster Number of Band Density

Bands (Bands/cm-)


C3 6 0.075

C4 10 0.125

C5 20 0.25

C6 36 0.45

C7 72 0.90

C8 136 1.725




























Figure 4.2

Infrared spectra over the 2070-1930 cm-1 range of
1C products (lower spectrum) and 12C:13C isotopically

mixed products (upper spectrum) isolated in unannealed

argon matrices at 12 K showing the six C3 isotopomeric

bands. Resolution = 0.25 cm-1
bands. Resolution = 0.25 cm.







68









V






u 12C


0
n'
4-4
O

< 1c 2039cm-1 i cm 1952cm1
209m19L ml5c~


i9/cm-1











have just diminished greatly in intensity. The 1952 cm-1 is

just barely visible in the mixed isotope run, but becomes

easily discernable upon absorbance scale expansion (cf. Fig.

4.3). Its isotopomer partners stretch down to 1877 cm-1, 75

cm- away. However, the isotopomeric peaks based on the 1998
-1
cm band are lost in the baseline in an unannealed matrix.

With strong annealing, they emerge from the baseline and are
86
readily recognized (cf. Fig. 4.4). Thompson et al. have

shown that the 13C partner to the species responsible for

the 1998 cm-1 band absorbs at 1920 cm-1, a spread of 78

cm-1. By tracking the behaviour of the bands in the overlap

region (1952-1920 cm- ) with progressive annealing, it was
-l1
possible to decide which bands belong to the 1998 cm- set

and which to the 1952 cm- set. The 1952 cm1 set could be

readily identified in the unannealed spectrum and their

intensities changed little upon annealing. In contrast, the

1988 cm-1 set was barely discernable in comparison to the

1952 cm-1 set in the unannealed matrix, and grew

substantially in the annealing process until their
-l.
intensities were comparable to the 1952 cm- set. The two

band systems overlap in the 1952-1920 cm-1 region as seen in

Figure 4.4. Thus the annealing study allowed one to

distinguish between the two sets of bands. The band density

for the 1998 cm-1 set is markedly higher (-1.4 bands/cm-1)

than for the 1952 cm-1 set (-0.47 bands/cm- ). It can be

seen in Table 3, that from the band density criterion alone,




























Figure 4.3

Infrared spectra over the 1980-1870 cm1 range

of 12C products (lower spectrum) and 12C:13C

isotopically-mixed products (upper spectrum)

isolated in unannealed argon matrices at 12 K

showing the more prominent C6 isotopomer

bands (cf Table 5). Resolution = 0.25 cm-.


















1952cm-1 1877cm-











1894cm-1
I


1950


1925


l9/cm-1


12





























Figure 4.4

Infrared spectra over the 2000- 1920 cm1 range of

1C products (lower) in an unannealed argon matrix.

Upper spectrum shows the IR of the 12C:13C mixed

products in argon at 12 K after annealing to 35 K for
11
15 min. Resolution = 0.25 cm-1. Note the increased

density of bands compared to Figs. 4.2 and 4.3.









73














V
V

z12c 13C





c




12C



an
--.----C8 *- -------------





< 1998 cm- 1952cm"1





I I I I 1 I I I I I I I I I I I I I
2000 1975 1950 1925
7/cm41











the 1998 cm-1 band cannot be ascribed to a linear cluster

smaller than C8. The observation of 35 bands in the 1952
-i
cm- set (linear C6 has 36 isotopomers) spread over a 75
-i -1
cm- (1952-1877 cm ) interval strongly suggests that this

band could be due to linear C6.

This attribution nicely explains the apparent

disappearance of the 1998 cm-1 band and the great diminution

of the 1952 cm-1 band upon isotopic substitution. For linear

C8 the intensity originally concentrated in the 12C8 band

must be spread among 136 isotopomer peaks, while for linear

C6 it must be spread among only 36 isotopomer peaks. So,
12
even though the 1C run shows similar intensities for the

2039 cm-1, 1998 cm- and 1952 cm- peaks, complete isotopic

substitution would reduce the individual isotopomeric peak

intensities to "1/6 (C3), 1/136 (C8) and 1/36 (C6) the
12
intensity of the respective 1C parent.

It is possible to use the isotopic intensity diminution

in a semi-quantitative way to determine the number of

carbons (n) in a linear cluster.1 The following relation

with C3 is used as the internal standard:



I(12C3)/I(12Cn) = (N3/Nn) (Ii(C3)/I (Cn)) (1)



where I(12C3) and I(12C ) are the intensities of the 12C


SThis approach was conceived by a colleague, Dr. Jan
Szczepanski.











parents for the major IR bands due to C3 (i.e., 2039 cm-)

and the unknown C n; N3 and N are the number of possible

isotopomers for C3 and C respectively; and I (C3) and
i 12
I (Cn) are the intensities of the 12C parent peaks in the

mixed isotope spectrum. Expressions giving the possible

number of isotopomers for an even numbered linear cluster

containing n atoms are68


Nn = 2(2Nn_2 2n/22) (2)


and Nn, = 2Nn where n' is odd and equal to n + 1. Obviously,

N1 = 2 and N2 = 3. Thus N3 = 6 possible isotopomers. By

solving (1) for N and substituting it into (2), it is

possible to determine n. To test this approach the data for

C5 (cf. Fig. 4.4) were used: I(12C5)/12C3) = 0.49,

I (C3)/1i(C5) = 6.2 from which N = 18.2 = 20. From (2) this

gives n = 5. For the 1952 cm-1 band intensity data we find

I(12 C)/I( 12C3) = 0.51, I (C3)/Ii(Cn) = 11.3, so that

Nn = 34.6 = 36. Thus n = 6. This is in agreement with the

conclusion drawn above from the band density data.



Normal Coordinate Analysis


Thirty-five isotopomeric peaks lying between 1952 cm-1

and 1877 cm-1 are observed (36 are expected for chainlike










C6) and are listed in Table 4. The normal coordinate

analysis was done by fitting five force constants to sixteen

of the bands (marked with asterisks in Table 4), 10 from the
12C end and 6 from the 13C end of the isotopomer list. The

force constants varied to effect the fit were: fR, outer

bond stretching force constant, fr, next inner bond stretch,

fm, middle bond stretch, frm interaction between r and m

bond stretches and fRr' interaction between R and r bond

stretches. The program6 used to obtain the fit allowed all

five force constants to be varied independently until the

best fit with the experimental data was obtained. The fit

described here is for a slightly bent C6 (hence the use of

the term "chainlike" instead of linear). The best fit to a

linear C6 geometry was considerably worse, with a RMS

deviation of 2.2 cm-1 and as shown in Table 5. In

comparison, the best fit for the bent structure (Table 4)
-1
had a RMS deviation of 1.79 cm .

A number of different bent structures were tried and

the best fit obtained for the structure described below. Let

us consider the C atoms of the molecule numbered in

sequence: C1-C2C-C-C4-C5-C6. Keeping the C1-C2, C3-C4 and

C5-C6 bonds parallel, the C2-C3 and C4-C5 bonds are bent 15

degrees away from linear in opposite directions (i.e. trans-

like) and further twisted 7 degrees out-of-plane in an

opposite sense. Although a number of bending angles were

tried, the final choice of angles may not be unique, and it












TABLE 4


Observed and Calculated Isotopomer Stretching


Chain-like C,


Frequencies for


in an Araon Matrix.


Observedb Calc'd Diff. Observed Calc'd Diff.

v/cm-1 v/cm-1 A/c1 vm/cm- v/cm-1 Av/cm-1


*1952.5 1950.4 2.1 1908.0 1907.3 0.7
*1947.5 1945.1 2.4 1906.5 1906.5 0
*1942.5 1941.5 1.0 1905.2 1905.6 -0.4
*1938.5 1942.4 -3.9 1904.7 1905.3 -0.6
*1937.0 1938.5 -1.5 1901.9 1901.8 0.1
*1936.4 1934.9 1.5 1901.6 0.3
*1932.4 1932.8 -0.4 1899.7 1900.5 -0.8
*1931.5 1934.3 -2.8 1894.3 1895.9 -1.6
*1929.2 1928.5 0.7 1892.0 1895.3 -3.3
*1926.5 1924.6 1.9 1891.0 1895.1 -4.1
1923.3 1923.3 0 1890.2 1892.4 -2.2
1922.5 1922.0 0.5 1889.5 1891.5 -2.0
1918.2 1915.7 2.5 *1888.2 1888.3 -0.1
1917.5 1915.2 2.3 *1886.3 1885.1 1.2
1916.5 1914.4 2.1 *1883.7 1882.7 1.0
1913.5 1913.2 0.3 *1883.0 1883.8 -0.8
1912.3 1912.1 0.2 *1878.3 1877.9 0.4
1910.3 1911.7 -1.4 *1877.2 1873.9 3.3


aForce constants found: fR=10.9367 mdyn/A;


fr=9.4468 mdyn/A;


fm=9.7160 mdyn/A; fRr=1.1401 mdyn/A; frm=0.9306 mdyn/A

(R = outer bond, r=inner bond, m=middle bond).

bBands marked were used in the initial fitting to


determine force constant parameters.


m


-- --uc-- f


a


Y












TABLE 5


Observed and Calculated Isotopomer Stretching


Frequencies for Linear CA


in an Argon Matrix.


Observedb Calc'd Diff. Observed Calc'd Diff.

v/cm-1 v/cm-1 Av/cm-1 v/cm- v/cm- Av/cm-


*1952.5 1951.4 1.1 1908.0 1908.5 -0.5
*1947.5 1947.4 0.1 1906.5 1907.6 -1.1
*1942.5 1944.6 -2.1 1905.2 1905.6 -0.4
*1938.5 1942.2 -3.7 1904.7 1904.6 0.1
*1937.0 1939.6 -2.6 1901.9 1902.9 -1.0
*1936.4 1936.1 0.3 1902.9 -1.0
*1932.4 1934.6 -2.2 1899.7 1901.8 -2.1
*1931.5 1932.8 -1.3 1894.3 1897.8 -3.5
*1929.2 1928.4 0.8 1892.0 1896.3 -4.3
*1926.5 1925.3 1.2 1891.0 1895.9 -4.9
1923.3 1924.0 -0.7 1890.2 1894.9 -4.7
1922.5 1923.4 -0.9 1889.5 1892.4 -2.9
1918.2 1915.6 2.6 *1888.2 1889.7 -1.5
1917.5 1914.9 2.6 *1886.3 1886.4 -0.1
1916.5 1914.7 1.8 *1883.7 1884.8 -1.1
1913.5 1914.4 -0.9 *1883.0 1882.4 0.6
1912.3 1914.2 -1.9 *1878.3 1878.1 0.2
1910.3 1913.8 -3.5 *1877.2 1874.9 2.3


aForce constants found:


fR=11.3064 mdyn/A;


fr=8.7636 mdyn/A;


fm=9.0604 mdyn/A; fRr=1.1636 mdyn/A; frm=0.6225 mdyn/A

(R = outer bond, r=inner bond, m=middle bond).
Bands marked were used in the initial fitting to


determine force constant parameters.











is possible that other choices might give a comparable fit.

This distortion from linear geometry is possibly the result

of packing stresses induced by the argon matrix. The bond

lengths of the C-C bonds used in this calculation were

obtained from Raghavachari's80 estimation of the bond

lengths of a cumulenic structure. The outer bonds C1-C2 and

C5-C6 were assumed to be 1.3 Angstroms while the remaining

three inner bonds were assumed to be 1.266 Angstroms. It is

interesting to note in this regard that C5, which is known

to be linear fits easily into a vacancy created by the

removal of two adjacent argon atoms, but linear C6 will not

fit into this cavity.

No normal coordinate analysis was attempted for C8

since the large number of very closely spaced bands

precludes any meaningful fit.



Discussion



The assignments of the 1952 cm-1 and 1998 cm-1 bands to

C6 and C8, respectively, differ from the the assignments

proposed by Thompson et al.86 Using intensity changes upon

thermal annealing and partial isotopic substitution (5% 12C

and 95% 13C) these authors had attributed the 1998 cm-1 band
d-1 -1
to C6 and the 1952 cm-1 band to C5. Because the 1998 cm

band increases with annealing while the 2039 cm-1 (C3) band

decreases, these authors suggested that two C3 clusters










react in the matrix to form C6. Given the assignments of

this work, it seems likely that C3 reacts with C5 (both of

whose bands decrease upon annealing) to form C8. Whether two

C31s react to form C6 is more problematic, since the 1952

cm-1 (C6) band increases slightly upon annealing and then

decreases upon stronger annealing. Perhaps two C3's react to

form C6, which if the matrix becomes soft enough at higher

annealing temperatures, can react further to form larger

clusters (C7, C8, C9, etc.). This possibility needs to be

pursued further. At any rate, it is clearly evident from the

change in the C6 peak intensity upon annealing that the

majority of the C6 observed is formed in the gas phase and

not in the matrix as a consequence of some chemical

reaction.

The assignment proposed here for C6 is in good accord

with recent theoretical predictions. Raghavachari et al.80

calculated IR-active frequencies of 2184 cm-1 and 1289 cm-1
-1 -1
for cumulene-like linear C6 and 1173 cm and 1056 cm for

acetylene-like linear C6. The experimental frequencies of

1952 cm-1 and 1197 cm-1 are within 12% and 8%, respectively

of the predicted cumulenic C6 values. They are sufficiently

distant from the acetylenic-C6 values to conclude that the

cumulenic form is the structure favoured by linear C6. This

conclusion is further supported by the theoretical stability

calculations. They show that the cumulenic form is 33.3
kcal./mole more stable than the acetylenic structure.80
kcal./mole more stable than the acetylenic structure. It










is worth recalling that some theoretical calculations

predict cyclic C6 structures considerably more stable than

the linear forms: the D3h distorted ring lies lowest with

the symmetric D6h ring 3.5 kcal/mole higher. The cumulenic

linear structure lies at 19.3 kcal/mole. The natural

question then is: why do we observe linear C6 rather than

cyclic C6?
89
The answer has been provided by Van Zee et al., who

estimate that for equilibrium concentrations in a laser

vaporization plume at 3000 or 4000 K with a AH = +10

kcal/mole (for the conversion of the D3h ring to the

cumulinic linear form) the K ratio (= Plinear/Pring) will

be 50 at 3000 K and 200 at 4000 K. Thus the concentration of

the linear form in the vapour before deposition is expected

to be far greater than that of the cyclic form, and our

observation of the linear form is understandable. It will be

of interest to determine whether the more stable cyclic

structure may be formed from the linear upon vigorous matrix

annealing.
No comparison of the experimental C8 frequency with

recent theoretical values is possible as none has been

reported for linear C8. However, comparison to a simple

model is instructive. Halford69 has given an expression for

the stretching frequencies of a model linear chain which has

force constants (k) for all bonds. For N number of atoms of

mass m in the chain, the n stretching frequencies are given










by


vn = (k/n2m)1/2 sin(nn/2N) (3)



where n = 1, 2,...,N-1 and only the even n frequencies will

be IR active. Choosing the C3 frequency (2039 cm- ) to

calibrate this expression yields (k/n m)1/2 = 2354.5 cm-.

Then the expression gives for C5: 2239 cm- (2164 cm-) and

1384 cm-1 (1544 cm-1); experimental frequencies are given in

parentheses. For C6: 2039 cm-1 (1952 cm- ) and 1177 cm-

(1197 cm-1); for C8: 2175 cm-1 (1998 cm1), 1665 cm- and

902 cm-1. Thus even this simple expression mimics the

placement of the highest energy IR band of C8 between the C5

and C6 bands, as we find. Although further work is needed

for a firm conclusion, it appears that C8 is also present in

the cumulenic form.


Conclusion



In summary, evidence from infrared spectroscopic

studies has led to the assignment of the 1952 cm-1 and 1998

cm-1 bands to the C6 and C8 clusters, respectively. The

structures of these species were found to be probably linear

or possibly slightly bent with cumulenic-type bonding. The

bending of the molecule could be due to a matrix effect. It

is interesting to note that linear C6 will not fit in a








83

vacancy left by the removal of two adjacent argon atoms as

C5 will. The limitations of the mixed isotopomer technique

become evident for the larger Cg cluster. As the size of a

linear or chain-like cluster increases, its number of

isotopomers increases very rapidly and since these bands are

spread over ~80 cm-1, they become too closely spaced to make

any fit to calculated frequencies meaningful.














CHAPTER V

THE IONIC C5 CLUSTER





Introduction



The laser vaporization of graphite is known to produce

ions in addition to the dominant neutral species. The

earliest work was reported by Honig6 in 1954 and by

Dornenburg et al.170 in 1961. Furstenau, Hillenkamp and

Nitsche9 have observed positive and negative ions from the

laser vaporization of thin carbon foils. They found that the

distribution of laser-induced carbon cluster ions indicated

an upper limit for the electron temperature of the carbon

plasma to be between 40,000 and 60,000 K, corresponding to

3-5 eV. For Cn clusters with n < 9, they found that the

odd-even rule with An = 2 is satisfied. In the mass

spectrum, the positive ions were found to have maxima for

odd n while the negative ions for even n. This was followed

by work by Furstenau and Hillencamp0 in which the above

conclusions were confirmed.

Rohlfing et al.11 reported the generation of a

supersonic beam of ionic carbon clusters by laser











vaporization of graphite within the throat of a pulsed

nozzle. They observed clusters Cn for n = 1-190 with a

distinctly bimodal distribution: (i) Both even and odd

clusters for Cn, 15n530; and (ii) only even clusters C2n,

20sns90. The alterations in the observed Cn signals were

interpreted on the basis of cluster formation and stability

arguments. Linear carbon clusters generated by a spark
171 +
source discharge were studied by Leleyter. For Cn odd n

values were found to be more abundant, while for Cn the

even values were more abundant with negative ion intensities

dropping rapidly for n>9.

Bloomfield et al.136 have produced carbon cluster ions

both by the photoionization of neutral clusters using 193 nm

radiation and directly by the vaporization of graphite with

a high power laser. For the former, a laser power of

approximately 2x109 W/cm2 was found to be adequate, while

cluster ion production required two to three times this

intensity. The laser-generated Cn+ spectra were found to be

similar to those obtained by Furstenau and Hillencamp.10

However, the photoionized spectra were different for

clusters with greater than thirty atoms. In the direct Cn

production, there was a progressive fall off in intensity

with increasing cluster size with only a weak even-odd

alternation in abundance. However, when neutral Cn clusters

were ionized, only even clusters were seen to be formed. For

the negative clusters, an even-odd alternation was observed








86

in the abundances of the clusters. For the lighter clusters,

magic numbers were found to exist for n = 5, 10, 12, 16, 18

and 22. The negative ion data were not in agreement with

that obtained by Furstenau and Hillencamp, who observed

maxima only for even n with rapidly declining intensity

beyond n=9.

Geusic et al.137 have conducted detailed studies on the

photofragmentation of carbon cluster cations containing

between 3 and 20 atoms. They observed that for most Cn the

loss of C3 was the dominant reaction channel, due to the

special stability of C3.78172'173 C3 loss is not

necessarily the dominant loss channel from all metastable

Cn+ ions.174 For example, C11+ decomposes mainly via C1

elimination, the C3 loss being the minor pathway. The unique

loss of one carbon atom from C11 probably reflects the

special stability of the C10+ ion which has been predicted

to have a ring structure.79 C5 was found to fragment to C2

and C3 as C3 has a lower ionization energy than C2. The

structure of small carbon cluster ions has been studied by

reacting the ions with small hydrocarbons, HCN, D2 and

02.98 It was found that the reactivity of the cluster ions

undergoes an abrupt change as the cluster size increases

from C9 to C10. This has been rationalized on the basis of

the cluster changing its structure from a chain-like to a

cyclic form.











On the theoretical front, Bernholc and Phillips81 have

carried out self-consistent modified neglect of differential

overlap (MNDO) calculations on neutral, positive and

negative chains and rings in the C2-C26 range. The most

stable positive ions were found to be C11, C15 C19 and

C23 ; the most stable negative ions were C14 C18 and

C22 The observed (4n+3) periodicity of Cn+ clusters is in

conformity with Huckel's rule.

Islam and Ray75 have carried out a Hartree-Fock study

on ionized linear, three-dimensional and ring-shaped

clusters. For C + clusters, they observed that clusters with

n = 7, 11, 15 and 19 were the most stable in agreement with

the results of Rohlfing et al.11 The stability of ionized

clusters was examined by computing the fragmentation energy

of the clusters.

The technique of matrix isolation spectroscopy has been

applied sparingly to the study of ionic species until

recently, partly because of the sensitivity problem, common

to all ion spectroscopies, but probably more importantly due

to the matrix perturbation problem for charged species. The

interaction of charged species with most host matrices may

be sufficiently strong so that either no spectrum is

obtainable or the spectrum obtained tells little about the

isolated molecular ion. For these reasons, the only matrices

generally found suitable for studies of isolated ions are

inert gas matrices.










Very little work has been done on carbon cluster ions

in matrices. Milligan and Jacox148 have prepared C2 by the
149
VUV photolysis of acetylene in argon matrices. Froch4 too

has generated C2 in argon, krypton and Xe matrices by the

X-irradiation of acetylene and studied its emission

spectrum. Brus and Bondybey176 have measured the laser

excitation spectrum of C2- produced by the photolysis of

acetylene in neon, argon, krypton and xenon matrices, and

provided an explanation for the formation of the ion, using

121.6 nm radiation as the ionizing radiation. Forney,

Althaus and Maier139 have recently recorded the electronic

absorption spectrum of C2 in neon matrices produced by the

the VUV photolysis of acetylene and halogenated acetylenes

with the best results being obtained with chloroacetylene.

A considerable amount of work has been done on the

spectroscopy of benzenoid cations in matrices. Work on the

IR spectroscopy of ions in matrices was recently reviewed by

two of its leading practitioners, Andrews177 and Jacox.178

The electronic spectroscopy of ions, both in the gas phase

and in matrices, has been reviewed by Miller and Bondybey179
180
and Bondybey and Brus.80


Experimental



The experimental procedure used in studying the C5 ion

was very similar to that described earlier. A modification








89

was required to differentiate between ions and neutrals. It

is well known9,10 that positive and negative ions are

produced in the laser vaporization process.

Two approaches were used to determine whether the 2052

cm-1 band was due to a neutral or an ionic species. In the

first, a small copper wire ring ("2 cm dia.) was mounted

~0.5 cm in front of the CsI sample window and electrically

insulated from it and its copper mount. Small positive and

negative voltages (upto 48V.) were applied to the ring to

attract (or repel) carbon cluster ions formed in the laser

vaporization process. In the second approach, a small

tungsten filament acting as an electron gun, mounted in

close proximity to the sample window, was used to neutralize

any positive cluster ions present. Simultaneously, a band at

904 cm1, ascribed to the ArH+ species, was also

monitored.


Results



Laser vaporization of graphite followed by trapping of

the vaporized products in an argon matrix results in the

appearance of many infrared bands. In the 1970-2060 cm-1

region (cf. Fig 5.1, bottom spectrum) two prominent bands at

2039 cm-1 and 1998 cm-1 together with a number of less

intense bands, including one at 2052 cm-1 can be readily

observed in an unannealed matrix. The 2039 cm-1 is known8











to belong to C3 and the 1998 cm- band was assigned to

chain-like C8 in the previous chapter. Upon annealing, the

2052 cm-1 band increases in intensity.

The evidence for the assignment of this band to an

ionic species is the following. In Figure 5.2 are shown the

spectra observed in two separate runs using a positive or

negative voltage on the ring during deposition. Figure 5.2

shows the result obtained with +48 V and -48 V on the ring.

The laser focus and other conditions were similar although

the overall absorbance of the two varied substantially due

to different deposition times. To compensate for this, the

ratio of the 2052 cm-1 band intensity to the 2039 cm-1

(neutral C3) band intensity was determined. For the -48 V.

ring potential the ratio was 0.63, while for the +48 V. it

was 0.17. The ratio is expected to be larger for the

negative potential if the species producing the 2052 cm-1

band is a positive ion, as we observe. As confirmation of

this, electron flow from the tungsten-filament electron gun

caused the complete disappearance of this band, as well as

the ArH+ band155 at 904 cm-.

For a 1:1 (12C:13C) mixed isotope sample, the top

spectrum in Figure 5.1 was observed after annealing the

matrix. The five bands marked with an inverted triangle are

the isotopomers of C3 (the sixth one lies at -1960 cm- ).

The myriad of bands to lower energy of the 1998 cm-1 band

are due68 to a number of the 136 isotopomers belonging to