COMPARISON WITH ESR RESULTS

D. S. TINTI

10. COMPARISON WITH ESR RESULTS

.···

..

.

·

{·

1'{9

conforrners. In this way the statistical weight of a conformer can be related to its relative energy. In C₆H₅D, for example, the statistically favored conformation is the one at higher energy. In all Gases it is found

· .· ·that the conforn1a tion with the most deuterium atoms on the double primed

p~1itions (see the third paragraph of Section 7) lies at highest f:nergy. The lowest energy conformation is the one with the most deuteriums at the single· primed positions. The observed statistical weights and energy O:i..~dering of the conformers are in exact agreement with those expected for a distorted benzene, as shown in Fig. 2. In the high concentration limit the intensity ratio should approach the Boltzmann ratio, which can be deter_mined frorn the statis- tical weights and the measured energy differences between the multiplet

·components. The calculated Boltzmann ratio for the multiplet components of

C6^H5^~ is 0. 2 at 4. 2° K and 0. 005 at 1. 7° K. As. shown in Fig. 3, the agreement with the experimental data is very good.

180

the DJ.Yl. = ±1 absorption lines for each crystal orientation remained s1'1arp, but they shifted such. that L'le zero-field splittirig parameter Z ren1ained nea:rly constant while ^J X - Y ^J, with increasing temperature, decreased from

-1 . -1 . .

about 0. 050 em to 0. 038 em . This result shows the approach at high temperature to trigonal symmetry where

I

^{X - Y}

I =

0. The obsel~vation of only two sharp absorptions for e2.ch crystalline direction establishes a

10 - l

>

10 ·sec conformer conversion rat-a.

The fast tunneling rate implied by the ESR experiments is at . first sight inconsistent with the results of the optical eJo...rperiments, which give an interconversion rate slow compared with the rate of triplet decay.

l l

The two results seem to differ by a facto:r of 10 or more! Differences in the experimental conditions of the two experiments of course exist.

The optical experiments haye been carried out at 4. 2°I~ or below,· whereas·.

the ESR experiments were at 20°K, or above; theoptical experim8nts used.

· crystalline benzene while tlle ESR experiments used mesitylene in B-tri-

methylborazole.

First, let's see

. if

the assumption of weak interactions between the molecule and its environment is reasonable in the light of the ESR and optical experiments. The most probable mechanism for interconversion in this case would be intramolecular tunneling among the triad of nearly degenerate states of a nontrigonally symmetric isotopic modification of benzene. Theoretically,' one would expect a fast tunneling rate.¹·5, 36 For example, taking a ring distortion corresponding to a carbon atom displace- . . ment of 0. 04-0.1

A,

tunneling of carbons between conformers would occur

12 -1 . - l

at a rate -10 sec for a barrier height of 500 em . In order to bring the theoretical tunneling rate into line with the optical experiments, a

... -~

, .. ···--:::·-.

. 0

distortion of at least 1 A or an nnreasonably high barrier would be required.

While such a large distortion may be possible, there is no independent experimental evidence for it. We therefore conclude~ in agreement with the discussion in Sec. 8, that the interaction between the· molecule and the crystal field is not negligible.

If the distortion were purely intrinsic the effect of the crystal

·field is to present an energetically fa vo1·ed environment for one orientation

of the distorted molecule. This is the picture given by van der Waals and

·de Groot. On the other hand, if the distortion were purely extrinsic, the·

potential surface with a triad of minima does not really exist. Any attempt

. .

to rotate the molecule results in distortion and the two things cannot be separately treated. In either case, only a single emitting state exists in each molecule. The observed splitting is therefore associated with

zero-point energy differences among different molecules in the crystal with different orientations of the deuterium atoms in the fi site symmetry

of the crystal field.

If the distortion were intrinsic, emission or absorption studies at higher temperatures should reveal states resulting from the higner energy conformers. Failure, thus far, to photograph any emission from the higher energy conformers allows an estimate to be·~made of the minimum · energy depression from Boltzmann considerations. For C₆H₆ in C₆D₆ a weak

. -1

single line has been seen 8 em to higher energy of the 0, 0 line of the C₆H₆ phosphorescence when the latter was heavily exposed on the phot<?graphic plate.

This has been tentatively assigned to ¹³ C¹² C₅H₆ whose 0, 0 line i.s calculatect37

"

- l

to be blue shifted some 15 em from· C₆H_{6 •} A complete spectral analysis · of the system built in this origin is prevented at this time by the heavy background of C₆H₆ lines. Since its position is roughly where predicted and emission fron1 it is expected, we will assume the assignment to

...

. '

' .

182

13 12

C C₅H₆ is correct. No other emission was detected to the high energy side of the C₆H₆

9,

0 line. Thus, it is probable that emission from the higher potential minima of the distorted molecule in the fi cage was not observed at 4. 2° K. Higher temperature experiments are planned in an attempt to observe these features. Estimating that emission 10 -2 as

intense as the C₆H₆ 0, 0 line would have been detected, a minimum energy difference of roughly 15. em -1 between the potential minima in th~ crystal is necessary. This is the correct order of magnitude fo:r rapic;l conversion

. -1

above 20° K where kT ~ 14 em ~

-~ Thus, at the present time, the optical experiments can be made · consistent with the interpretation of the ESR experiments where an intrinsically

3 .

distorted B₁u benzene molecule is preferentially oriented in the crystal site

- l

such that other orientations are energetically less stable by at least 15 em

· However, the detection of the relatively large splittings caused by the

.fi site, the lack of vibronic evidence for distortions, the failure to find any optical evidence for the higher confo.rmers, the likelihood of a nonquinoidal

distortion (even in the C

_{.,... 2}

h site approximation), and the smallness of the zero ..

point energy effects would seem to be more consistent with a purely extrinsic distortion. On the other han¢1, the fact that the distortion appears larger

3 1

for the B₁u state than for the B₂u state, and the agreement between the ESR experimental results and their quantitative interpretation on the basis

3 . .

of a quinoidal B₁u state give weight to the argument in favor of au, __ intrinsic

distortion •. ·· ^..

. ~ . ' ... '·

. . .• ·

·· .. ^·· .·

.·. · .. ·

·:----- .

. ·.'· :

We would like to thank Professor G. W. Robinson for his valuable . discussions concerning the interpretation presented in this paper and for

his help in the writing style. One of us (DST) would also hke to acknowledge Drs. R. Kopelman and C. H. Ting and Messrs. E. R. Bernstein and S.D.

Colson for many valuable discussions throughout the preparation of this paper. V.fe are also grateful for the predoctoral fellowships from the

National Science Foundation ( GCN) and the National Aeronautics aild Space · Administration (DST). In addition, GCN thanks the Petroleum Research Fund for support of a portion of this work carried out at the University of Rochester. The 1. 8 m Jarrell-Ash Spectrometer used in part of this work· was made available by a grant to the California Institute of Technology from the Alfred P. Sloan Foundation. · · ·

.. . ^·. _{! :}

·.: .. ' . '

. ,·· .. . ,

: ..

.

.

^.

. . . ^.

... .. ^{.· ;>}

· .. · .. ^·

.·'

~ ..

----

^~

'·.

... ·

.. ^{: ..}

' ... ·· ^..

·: :

. .

' .

. . ^. . ·-·.,· '

. , ..

·. ··=·:.

. . ~ -.. .

•.,

.·

•.:.

.. ^{: ..}

· .

..

184

REFERENCES

1. G. N. Lewis and M. Kasha, ·J. Am. Chern. Soc. ~' 2100 (1944).

2. 0. Redlich and E. K. Holt, J. Am. Chern. Soc. 67, 1228 (1945).

""""' ^.

~: S. H. Sponer and E.· Teller, .Revs. Modern Phys. ..., 13, 75 (1941) • 4. H. Shull, J. Chern. Phys. 17, _,...,.... 295 (1949).

5. G. W. Robinson, J. Mol. Spectry. 6, _{. ...,} 58 (1961). _.

6. R. S. Mulliken, Revs. Modern Phys.

1.1.,

204 (1942); A. D. Walsh, J. Chern. Soc. pp 2260-2331 (1953); D. A. Ramsay in "Determination· of Organic StruCture by Physical Methods, "edited by F. C. Nachod

·and W. D. Phillips (Ac~demic Press, Inc., New York, 1962), vol. 2, · chap. 4. See also the elegant paper on the rotational analysis of the . 2600

A

absorption system of benzene by J. H. Callomon, T. M. Dunn,

and I. M. Mills (Phil. Trans. Roy. Soc.

lli'

499 (1966)], where the geometry and symmetry of the lowest excited singlet state of gaseous benzene is discussed and proven to be exactlY. point group Q₆h.

7, W. Moffitt, J. Chern. Phys. ~' 320(1954).

8. A. D. Liehr, Z. Naturf. Ai6, 641 (1961).

. ~

9. M. Goeppe1·t-Mayer and A. L. Sklar, J. Chern. Phys. _..., 6, 645 (1938) .

10. W. C. Price and A. D. Walsh, Proc. Roy. Soc. (London) A191, 22 (1947).

~

11. S. D. Colson and E. R. Bernstein, J. Chern. Phys. _. 43, 2661 (1965).

. ,...,....

12. J.

.

^. ' E. Lennard-Jones, Proc. Roy. Soc. . . (London)~' 280 (1937) ·. .

13. W. D. Robey and A. D. McLachlan, J. Chern. Phys. 33, 1695 (1960).

. . ~ -

14. H. C. Longuet-Higgins and L. Salem,. Pro c. Roy. Soc. (London)

-illi'

172 (1959).

· 15. M. S. de Groot and J. H. van der Waals, Mol. Phys •

.§_,

545 (1963).

,. : . . .

. . , : ...

. '• . .. ....

.... ^{··.' .} _{·.: .}

. ^{. ,}.

\ •. ·._.·: ^:';.

...

. ·:

.. ·,

185

16. H. Sternlicht, G. C. Nieman, and G. W. Robinson, J. Chern. Phys. ,..,.,... 38, 1326 (1963).

17. E. R. Bernstein, S. D. Colson, D. S. Tinti, and G. W. Robinson, to·

be published. See following section of this thesis •.

18. A. C. Albrecht, J. Chern. Phys. ~' ·354 (1963).

19. The only ground-state vibration of C₆H₆ which has shown a site group

- l

splitting in the phosphorescence spectrum is the 606 em (e₂₀.) mode .

20.

- l

The measured splitting is 3 em .

0

This vibration (v_{5 ,} b₂g) is assigned from combination bands a frequency of 995 em ^{- l} by Mair and Hornig. 21

. However, on the basis of the re- quired symmetry18

· for vibronic interactions in a B₁u state and by

. comparison of the various isotopic benzenes, we feel that zi₅ should be

- l

correctly assigned a value of 1004 em for crystalline benzene .

. Very recent Raman spectral studies22 of solid benzene agree with

this new assignment.

21. . R. D . . Mair and D . . F. Hornig, J. Chern. Phys.

]1,

1236 (1949) .

. 22. M. Ito and T. Shigeoka, Spectrochim. Acta~ 1029 (1966); A. R. Gee

and G. W. Robinson, private communication.

23. E. G. Cox, Revs. Modern Phys.

1Q,p

159 (1958); E. G .. Cox,

D. W. J. Cruickshank, and J. A. S~ Smith, Proc. Roy. Soc. (London) A247, 1 (1958)~

~

24. See Sec. 8 where certain splittings observed in the infrared spectrum of isotopic inl.xed crystals· are briefly discussed.

2.5. R. Kopelman, to be submitted to J. Chern. Phys.

26. G. Herzberg, Atomic Spectra and Atomic Structure (Dover Publica- tions, New York, 1944).

·,.

.,

186

· 27. This model assumes all off-diagonal matrix elements of both the F - and G matrices28 to be zero· and ignores translational and rotational- -degrees of freedom. While this may not be a good approximation,

especially with regard to the G~-matrix, it is hoped that these errors cancel when the differences in zero -point energies are taken.

· 28. E. B. Wilson, Jr., J. C. Decius, and D. C. Cross, Molecular Vibrations (M_cGraw-Hill Book Co., Inc., New Yor~ 1955).

29. F. M. Garforth, C. K._ Ingold, and H. G. Poole, J. Chern. Soc. 1948, 508 .

~

30. · V. L. Broude, Usp. Fiz. Nauk

H_,

577 (1961) [English translation Soviet Phys. -Usp .

.1_,

584 (1962)) ..

31. S. Leach and R. Lopez-Delga~o, J. chim. P'hys .

.§.1,

1636 (1964). · 32. E. R. Bernstein and G. W. Robinson, private communication ..

33. _ M. S. de Groot, I. A.M. Hesselmann, and J. H~ van der Waals,

-Mol. Phys.

1.£,

91 (1965).

34. · This is easily shown from ^th~ data g,iven by E. R. Andrew and . R. G. Eades, Proc. Roy. Soc.· (London)~' 537 (1953).

35 •. Approximately 75% of the total phosphorescence intensity i.n these

m~xed crystals arises from progressions built on vibrations that cor~

. . - l. - l

. :~-<~:-.~relate with: the e₂g 1178 em and 1595 em vibrations of C₆H_{6 •}

-36. · C. H. Townes and A. L. Schawlow,'.Microwave Spectroscopy,_ .

(McGraw-Hill Book Co.; Inc., New York~ 1955) p. 304.

-37. C. H •. Ting, private c~:n);lmunication.· _: _--

·.··•.

• ' ' . I

.···

.-. _{• . .}

.· ':

... . .... .

^~

'' .

\ ^.

' ' ...

. · ...

. -- · .. ^{: ~ : :~: . .' ...}

' '

·-

; .

188

,•'

,.

Figure 1

Niicrophotometer tracing of tha phospho~escence of 1. O% C,)-I;:;D in

- l

C₆D₆ host crystal at 4. 2°K sho~;ing the 7 em doublet structure in the vibronic tra..."'lsitions. The 1574 em ^{·- l} and 1591. em b^{- l} ands were traced from a plate exposed a factor of three less. Intensity .is in arbitrary units •. ·

.. ·.

: ... · ... ^{· ..}

-..•.

·,_ .. .. ,·_.·.- :/_

! :-

,·

. ^, .·· :·· ...

.... :'. . . . ^~-

,.,-

'. ~. ',· ,'

. ':

..

^{:~ .•..}

. . . ~ ..

'.· . . .. _· ... '.'· · .. ···.

.. ~ ·.·_: \• .. ,.·· ~-:-.. :~ ... ·.:_~---::<

'· ... ··-..

. ·-· ^' ..

_·, . ^' . ·"·,.'·

· ...

.. -·

·.·

...

·' .. , .· _-·

.. .

•· ' l

·.- .

. ^"

.... ^_ .. '.· ...

-.. ^:

. -.. ^·.

'. ··.·--.

. ...

. . . ^~ \.

:.:.. .

.. ·.

. , -~

; ..

: ,. : _.-.

-._ ..

,:·

. ^~ .--. .. ^'. ·._ :

. . ··.·

,:. __ .

.•

.,·

,• : .

· ^{.. _} ·:·

-·-· .

'' o I

~A · Jv~.

0,0 704 em1 . "4 {b2) 858 em1 vrab<b,)

980 ern1 995 e

m

1 "1 (a,) "5 (b2)

A

1075 ern1 "15 (bl) 1158 em1 1175 em1 "9b(bl) "9o(a,) 1574 ern1 1591 em1 "sb(b,) v8o(a,)

..

.,

. /:

. \

. '

· .

190

...

Figure 2

Conforn.J.ations of an exaggerated _... D₂h.benzene for various isotopic modifications. The number in parenthesis is the statistical weight of the conformation. The numbers at the bottom of the figure ^gi-~e the number of deuteriums in the apical or single primed positi<?n

(see teA-t) for the conformers in the column dire_ctly above. · The

: prefixes

^.m.,~.§,

and,.& denote meta, para, symmetric a...J.d asymmetric

• , . I . -.~ . . ,

respectively~_{. . .} >_{' .} ·>-_. ., _. ^-_. ^~_{. ::} ^- · _.

. ^{· ..• --.. ..-. .'·.}

' ·.··

.. · ..

. ^{' . ~} . .. .

·.· .··, ·. :·-.·· ^{,• •'} .. ·: .

. ~~ . ' . : ', .. f: .

. .

·

. .

. .

·.

. . .-:. : .·.·.

. .

.. ...

... . . '

.. . . .. ^{· ..} _.

. .. ^-.... , ·-\

. ^{· .·}

:-: · . .

-~--:

.. .. · ' . ~-

. ^. · ::-. , .. . '

. . .

^·.· .. :.·:. ,. _: .... ;

~' . ^.

•, .. . .

. .. . ^'

.. ^{; ' .•}

.. .. .

' . . ^-

.,.

•• 0 • : , ' • • ~-'.

.... ... . ·.

·•·· ..

.

^{· .}

...

; .· ... '·. _·-:··

~· .. --: ^:. . .

·· .

. -. ·-/ '

: ^~ .....

··.·:·. ·, . ,;·.·:

.. ^' ,···._ .

. . ^: . . ^{.. -}·.~-.-.

-·· .. · ^:-

:.:··

' ..

. .

:-·. '• .

.. ·-..

,,· . ^_.·

.. ...

. . . . ^,.

: ...

. ^·' .. ..

..

^.

0

D

C

₆

H

₅

D OD 0

(2) ( l)

D

m-C

₆

H

₄

D

₂

DOD Oo

(() (2)

D

p-C6H4D2 Do~ CJ

D

(2) (I)

D

. s-C

₆

H

₃

D

₃

DCJo

D D

a-C ₆H₃ 0₃

oO~ DOD DCJ

D

(l) (I) ₍

''

^.)

D

m-C₆H₂ D₄

oo~ oCJ o

D D

(2) ( l)

0 2

:. 191

,.,

·.

:·· .· ,.

Figure 3

The integrated phosphorescence intensity ratio for the high energy to low ·energy conformer of C₆H₅D in C₆D₆ host crystal as a ~unction

of guest concentration~

·.· ....

~ .. ^·.

· .. ·

·.:-· ... ^~ .;

...

_{', :, .}

:I •' ^{·:·.. .. '}

· .. '. ;.

····.

''·

... ·

. .....

:•=

.· .

'· ^{. : i}

··.··.

'.•

...

. ; ·.•.:

,_·.·

: •. ···

::-.. ^·.·

• .. • .· .····

.... ^·

· ...

•.:

~'.

..

... ^~

-^•,'

.'':-'

I

' .•

. I .. .· _I