An Electron Diffraction Investigation of the Structure of Octafluorocyclobutane, Methylcyclobutane, and 1,1,2,2-Tetramethylcyclopropane

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An Electron Diffraction Investigation of the Structure of Octafluorocyclobutane, Methylcyclobutane, and 1,1,2,2-Tetramethylcyclopropane

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PURDUE UNIVERSITY

THIS IS TO CERTIFY THAT THE T H E SIS PR EPA R ED U N D E R MY SU P E R V ISIO N

Henry Paul Lemalre

BY

ENTITLED

An Electron Diffraction Investigation

of the Structures of Octafluorocyclobutane, Methylcyclobutane and 1,1,2,2-Tetramethylcyclopropane COMPLIES WITH THE UNIVERSITY REGULATIO NS O N GRADUATION T H E S E S

AND IS APPROVED BY ME A S FU LFILLIN G THIS PART O F THE REQUIREM ENTS

FO R THE DEG R EE OF

Doctor of Philosophy

P ro fesso r

H

ead o f

S

in

Charge

chool or

TO THE LIBRARIAN:----IS THIS TH E SIS IS NOT TO B E REGARDED A S CONFIDENTIAL.

GJEAD. SCHOOL FORM 9—3 .4 9 — 1M

of

Th e s is

D epartm ent

AN ELECTRON DIFFRACTION INVESTIGATION OF THE STRUCTURES OF OCTAFLUOROCYCLOBUTANE, METHYLCYCLOBUTANE AND 1,1,2,2-TETRAMETHYLCYCLOFROPANE

A Thesis Submitted to the Faculty of Purdue University

"by

Henry Paul Lemaire

In Partial Fulfillment of the Requirements for the Degree

of Doctor of Philosophy

June, 1950"

ProQuest Number: 27712260

All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is d e p e n d e n t upon the quality of the copy subm itted. In the unlikely e v e n t that the a u thor did not send a c o m p le te m anuscript and there are missing pages, these will be noted. Also, if m aterial had to be rem oved, a n o te will ind ica te the deletion.

uest ProQuest 27712260 Published by ProQuest LLC (2019). C opyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States C o d e M icroform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106 - 1346

AC KNOWLEDGMENT I wish to express my sincere gratitude to Dr. R. Livingston for his guidance and assistance in directing this research. I am also very grateful to Dr. H. J • Year!an of the Physics Department for his helpful advice in several aspects of the work. Thanks are extended to Mr. T. T. Broun and to Mr. J . W. Coutts for their assistance in the analysis of the dif­ fraction photographs. Thanks are due also to Professor S. E. Wirt and Miss : B. Bradley of the Tabulating Division for their help and cooperation in carrying out the International Business Machine calculations. I wish to state my indebtedness to the Research Corporation for the financial support of this work.

TABLE OF CONTENTS Page ABSTRACTS..............................................

i

I. Evidence for a Non-planar Carbon Ring in Octafluorocyclobutane............

i

II. The Molecular Structures of Octafluoro­ cyclobutane and of Methylcyclobutane. III.

iv

The Molecular Structure of 1,1,2,2-Tetramethylcyclopropane...................

xx

A SUMMARY OF THE THEORY AND METHODS OF ELECTRON DIFFRACTION............

1

Introduction.................. Experimental Procedure.

-.

..........

3

The Apparatus.......................

3

Recording of the Diffraction Pattern.........

5

Measurements and Calculations................

6

Elastic Scattering by Molecules........

10

The Visual Correlation Method.........

12

The Radial Distribution Method

16

......

Methods of Evaluating the Theoretical Intensity Curves and the Radial Distribution Function... Sources of Error and Accuracy of Results....... THE MOLECULAR STRUCTURE OF OCTAFLUOROC YCLOBUTANE....... Introduction

..........................

23 26 29 29

Experimental................................... •••

30

Interpretation of Pattern......................

31

1

TABLE OF CONTENTS (Cont.) Page The Radial Distribution Function...........

31

Theoretical Intensity Curves and Calculations.

38

Discussion of Results..........................

50

THE MOLECULAR STRUCTURE OF METHYLCYCLOBUTANE........

58

Introduction

.........

58

Experimental................ Interpretation of Pattern.

59 .............

60

The Radial Distribution Function............ .

60

Theoretical Intensity Curves and Calculations.

62

Discussion of Results..........................

76

THE MOLECULAR STRUCTURE OF 1,1,2,2-TETRAMETHYLC YCLO­ FROPANE........................................

78

Introduction........

78

Experimental......................

79

Interpretation of Pattern.................

80

The Radial Distribution Function..........

80

Theoretical Intensity Curves and Calculations. Discussion of Results........ BIBLIOGRAPHY........................................

82 90

93

VITA................................................ ..

LIST OF TABLES

Table

Page

1. Experimental Data for C4F8 .........

32

2. q(calc )/q(obs) Ratios for G4F8 Models..............

51

3 . Acceptable Models and Interatomic Distances

in C4FQ......................................... 4.

53

Comparison of R. D. Data and Results of the Visual Correlation.........

54

5 . Experimental Data for Methylcyclobutane...... ...

61

6. q(calc)/q(obs) Ratios for Planar Models of Methylcyclobutane. 7*

.......................

q (calc)/q(obs) Ratios for Non-planar Models of Methylcyclobutane.............

8.

72

Acceptable Models and Interatomic Distances in Methyl cyclobut ane...............................

9.

71

73

Experimental Data for 1,1,2,2-Tetramethylcyclopropane.....

81

10.

q(calc)/q(obs) Ratios for Tetramethylcyclopropane..

11.

Acceptable Models and Interatomic Distances Tetramethylcyclopropane

91

for

......................

92

LIST OF FIGURES Figure

Page

1. Radial Distribution Functions, Diatomic Molecule*

.......................

34

2. Radial Distribution Curves, C^Fg............. 3. Types of Models Constructed for C^Fg;..............

40

4. Parameter Chart for C^Fg;

43

5*

...................

R* D. Function and Theoretical Intensity Curves for Planar Models of C^Fg................

6. Visual Curve and Theoretical Intensity Curves: for Non-planar Models of C^Fg....................

455

7* Types of Models Constructed and Parameter Chart for Methylcyclobutane.......................

64

8. R. D. Function and Theoretical Intensity Curves for Models of Methylcyclobutane.

.........

66

9» Theoretical Intensity Curves for Non-planar Models of Methylcyclobutane..................... 10.

Types of Models Constructed and Parameter Chart for 1,1,2,2-Tet rame thylcyclopropane..............

11.

68

83

Theoretical Intensity Curves for Tetramethyl­ cyclopropane .....................................

85

EVIDENCE FOR A NON-PLANAR CARBON RING IN OCTAFLUOROCYCLOG BUTANE (1) (1)

From the Ph. D. thesis of H. P. Lemaire, Research Corporation Fellow In Chemistry, Purdue University.

by H.

P. Lemaire and R. L. Livingston

Department of Chemistry, Purdue University, West Lafayette, Indiana ABSTRACT I Preliminary results of an electron diffraction investi­ gation of the structure of octafluorocyclobutane have led to the conclusion that the four-membered carbon ring Is nonplanar. Electron diffraction photographs were prepared from a highly purified sample which weasobtained from the Central Research Laboratories of the Minnesota Mining and Manufacture ing Company.

The photographs showed diffraction patterns

extending to q = about 75* Models having a planar carbon ring ( D ^ symmetry) gave rise to intensity curves which are in disagreement with the visual appearance of the diffraction patterns.

Non-planar

models were then constructed from planar models in the following way;

One pair of diametrically opposite carbon

atoms was raised above the plane while the other pair was lowered to the same extent keeping the CFg groups oriented

il

so that a plane through the carbon atom of this group and the two adjacent carbon atoms bisected the PCF angle of the GFg group.

These models have

(V^) symmetry.

Agreement

with the diffraction data is obtained with models having this configuration and parameters within the following limits: C-F = 1.31 to 1.34 A.; 0-0 = 1.57 to 1.62 A, Z.FOF s 107° to 112°, oC (angle between planes which bisect opposite OFg groups) = 157° to 163°.

Further work is neces­

sary in order to choose the best models and to estimate un­ certainties but the final results should fall within the ranges indicated. It is Interesting to compare this compound with cyclobutane and hexafluoropropene.

In the former, spectroscopic

evidence (2 i favors a planar carbon ring indicating that the (2)

T. P. Wilson, J. Ohem. Phys., 11, 361 (1943).

non-planar ring in O^Fg may be attributed to repulsions be­ tween fluorine atoms attached to different carbon atoms. These repulsions may also be responsible for an increase in the G-G distance above the value of about 1 .54 A which is observed in many hydrocarbons.

In the case of hexafluoro-

propene, evidence has been obtained (3 ) for the fact that (3)

F. A. M. Buck and R. L. Livingston, J . Ghem. Phys. , 00. OOO (OOOO).

(To be published in the same issue of

this Journal.) the closest approach of fluorine atoms attached to different

Ill

carbon atoms is about 2.70 A, which is twice the van der Waala radius of fluorine.

This same value appears in the

acceptable models of C^Fg as the shortest distance between fluorine atoms attached to different carbon atoms.

It thus

appears likely that twice the van der Waals radius of fluorine does represent the closest distance of approach of fluorine atoms which are not attached to the same carbon atom.

This Is not the case with the other halogens. Independent evidence for the non-planar carbon ring in

C^Fg

has been obtained from spectroscopic studies by Edgell

and Weiblen (4). (4)

W. F. Edgell and D. G-. Weiblen, J. Ghem. Phys., 00. 000 (0000).

(To be published in the same issue of J.

Ghem. Phys.) The authors wish to thank the Research Corporation for financial support of this work.

They are grateful to Pro­

fessor Edgell of the Chemistry Department who suggested the problem, and to Professor H. J.Yearian of the Physics Depart­ ment for the use of his diffraction equipment and for many stimulating discussions.

iv

Department of Ghemistry and Purdue Research. Foundation, Purdue University, Lafayette, Indiana.

THE MOLECULAR STRUCTURES OF OCTAFLUOROCYCLOBUTANE AND OF METHYLCYCLOBUTANE :(l) (1)

From the Ph. D. thesis of H. P. Lemalre, Research Corporation Fellow in Chemistry, Purdue University, 1949-50. by H. P. Lemaire (2) and R. L. Livingston

(2)

Present address:

Department of Chemistry, St. Michael's

College, Winooski Park, Vermont.

ABSTRACT II INTRODUCTION The preliminary results of an electron diffraction in­ vestigation of the structure of octafluorocyclobutane have been described in a previous article (3)* (3)

It is the purpose

H. P. Le ma ire and R. L. Livingston, J. Ghem. Phys. , 18, 569 (1950).

of this paper to present the final results of this investi­ gation and the results of thmstudy of methylcyclobutane. An electron diffraction investigation of hexafluoropropene (4) has led to the proposal of a strained configur-

V

(4)

F* A. M. Buck and R. L. Livingston, J. Ghem. Phys. , 18, 570 (1950).

ation for this molecule; this apparently results from re­ pulsions between fluorine atoms which are attached to dif­ ferent carbon atoms.

It appeared possible that the fluorine

atoms in O^Fg would exhibit the same property and that the effect could be experimentally detectable.

It is also sig­

nificant that Edgell and Weiblen (5) have raised some doubt (5$

W. F. Edgell and D. G-. Weiblen, J. Ghem. Phys. , 18, 571 (1950).

as to the correctness of the interpretation of spectroscopic data on the basis of a

configuration as given by Glaassen

(6 ). (6)

H. H. Glaassen, J. Ghem. Phys., 18, 543 (1950). The conclusive evidence, obtained in this investigation,

for a non-planar carbon ring and an unusually long G-G bond distance in the perfluoro derivative of cyclobutane led to the study of methylcyclobutane ; It seemed possible that the carbon ring in the methyl derivative might also be nonplanar.

A theoretical intensity curve was calculated for

a non-planar model of me thylene eye 1obut ane in order to make a comparison with the published data on this compound (7> 8). (7)

S. H. Bauer and J. Y. Beach, THIS JOURNAL, 64, 1142 (1942).

Vi

(8)

W. Shand, V* Soîiomaker and J. R. Fischer, THIS JOURNAL, 66, 636 (1944).

The results showed that a non-planar structure is also compatible with experimental data, indicating that the exact structural nature of the ring In this compound is difficult to determine by diffraction methods.

Calculations for

methylcyclobutane showed that the intensity pattern was more sensitive to the folding parameter and its study was under­ taken in the hope of obtaining information on the ring structure and the C-C distances. EXPERIMENTAL The sample of octafluorocyclobutane (b.p. -6.1° to -6.0°) was obtained from the Central Research Department of the Minnesota Mining and Manufacturing Company; the estimated purity was 99* 5^ on the basis of infrared spectroscopy. The sample of methylcyclobutane was prepared In the NAGA Cleveland Laboratories and made available to us by Dr. Greenlee of Ohio State University.

The constants given for

the sample are: f.p., -161.51°; b.p., 36.98° (755 mm.) and 37*18° (760 mm.); n25D 1 .3878 . Electron diffraction photographs were prepared in the customary manner (9) using an apparatus built by Dr. H. J. (9)

L. 0. Brockway, Revs. Modern Phys. , 8, 231 (1936).

Yearian of the Purdue Physics Department.

The camera dis-

vil

tance was about 10.8 cm. and the electron wave length, as determined from photographs of zinc oxide, was about 0.055 A.

The recorded pattern for octafluorocyclobutane extended

to a q value of about 75 and the pattern for methylcyclo­ butane to a q value of about 93* Octafluorocyclobutane Interpretation of Pattern.—

The radial distribution

method (10, 11) and the visual correlation method (9, 12) (10)

P. A. Shaffer, V. Schomaker and L. Pauling, J. Ghem. Phys., 14, 659 (1946).

(11)

L. Pauling and L. 0. Brockway, THIS JOURNAL, 2L, 2684

(1935:)* (12).

L. Pauling and L. 0. Brockway, J. Ghem. Phys. , 2,? 867r

(1934). were used in the interpretation of the recorded pattern. The radial distribution function was calculated from the equation qmax rD(r) = 2 I(q) exp(-bq2 ) sin (^Qr) q s 1,2..» by the use of punched cards (10).

(l)

I(q) is the visual inten­

sity curve ( Curve vis. Figure 6), which is drawn assuming no falling off of intensity with increasing q.

The constant:

b was chosen so that exp(-bq2 ) - 0.10 at q = 100.

The

resulting curve (Figure 5) shows major peaks at 1.34, 2.47 and 3.38 A,

vlii

The theoretical intensity curves were calculated from the simplified expression ^(q) = ZT zEI *

i

(2 )

sin (ffe*i iq) *1 3

Curves were calculated for planar models of type A, Figure 3; in these models the ^ FOF is bisected by the plane of the carbon ring and the symmetry is that of the point group.

The scale of all models was fixed by choosing

C-F s 1.33 A while the C-C distance was varied from 1.48 to 1.64 A and the FOF angle was varied from 104.5® to 114.5° in increments of 2*5°Intensity curves for representative planar models are shown in Figure 5.

Most of them are in such complete: dis­

agreement with the visual curve (Curve vis, Figure 6) that a detailed correlation is impossible.

Curves A^q q , C^qqi

d180 an 49)

photographic so t h a t

as t h e

A n intensity pattern thus microphotometer and the

ob­

a rotating

which, w h e n

p l a t e , can be

cut

such that

t h i r d p o w e r of the

thereby compensating

s h o w no

made

it is a p p r o x i m a t e l y

s e c t o r is u s u a l l y

radius

for the decreasing

obtained

in­

o f t h is,

may be visually

In o r d e r to o b t a i n quantitative data,

introduced to

is

on a background,

fourth p o w e r of the

maxima

c o n t r i b u t i o n to t h e

scattering

intensity varies

microphotometer traces real

the t o t a l

inde­

its

angular

o f th e

intensity.

can be measured w i t h a

results used to

e v a l u a t e th e

inte­

g r a l i n E q u a t i o n 1 4 to a g o o d a p p r o x i m a t i o n . Ph o tographs t a k e n without the use cannot be m e a s u r e d with objective

intensity data

to e v a l u a t e t h e

a microphotometer.

b e a p p r o x i m a t e d to

must b e made

ey e

compensates

and h o w the apparent

s^T ( s ).

If this

for the

intensity can

s u b s t i t u t i o n is m a d e

in

a n d the expression further modified by i n tro­

ducing the Dëgar d reducing the

of

r a d i a l d i s t r i b u t i o n function.

in background

E q u a t i o n 14,

In the absence

certain approximations

It h a s b e e n d e s c r i b e d h o w t h e rapid fall

of a sector, ho we ver ,

factor

relative

(exp(-as^))

which has the effect

c o n t r i b u t i o n of the

outermost

of

intensity

19

peaks

(a is u s u a l l y

c h o s e n so t h a t

^x P ( - a s ^ m a x ) = 0 .l)

one

(15)

o where

I Q ( s ) is

Since the the

the apparent

i n t e n s i t y as v i s u a l l y o b s e r v e d .

d i f f r a c t i o n p a t t e r n does

i n t e g r a t i o n is m a d e

not

f r o m zero t o

extend to

infinity,

sma:x.

S e v e r a l methodsVh®ve b e e n d e v i s e d to e v a l u a t e this integral,

all

of w h i c h

involve certain approximations.

is f i r s t n e c e s s a r y t o a p p r o x i m a t e it as a s u m m a t i o n o v e r t h e was m e a s u r e d .

range

the of

It

integral by writing

s for w hich the p a t t e r n

We get

(16) where,

in the

original work

(3 1 ) > I k r e p r e s e n t e d the

intensity of the kth m ax i m u m and o f s.

the corresponding value

T h e m e t h o d was l a t e r extended to

both maxima The use

and minima

include terms

method of computation

d esc r i b e d In the next

section has

a series

one hun d r e d terms without

This

lifts the

the

summation,

the

integral

in this

It w a s

provided a means of summing undue

effort.

r e s t r i c t i o n on the n u m b e r of terms u sed in making

for which

it p o s s i b l e t o a p p r o x i m a t e m o r e it w as

investigation has

and Pauling

for

( 6 ).

of the p u n c h e d cards

of e i g h t y t o

estimated

substituted.

been described by

closely

The method used Shaffer,

Schomaker

(3 5 ). found convenient,

in the a p p l i c a t i o n of p u n c h

20

cards

to t h e s e

r e l a t e d to this

s u m m a t i o n s , to define a n e w quantity

s by the

simple relation,

q u a n t i t y i n t o E q u a t i o n 16,

rD(r) is the

obtained

in which

from the

integral values the

^

(1%)

q is n o w t h e v a r i a b l e

angle.

The terms

for the

intensity curve b y taking values of q«

I n this way,

p a t t e r n and not by the Since the

it is

innermost

from theoretical

including the discussed

damping

factor,

i n t e n s i t y curves.

shown,

exp(-bq^)

resolution obtained

the

terms

rD(r)

fluctuating

is m a d e

clear

f u n c t i o n are

of

d i s t r i b u t i o n is

obtained

at t h a t

time,

for octa-

a definite

that

changing the

effect

if no c o n v e r g e n c e

in the

on the

The use

of a finite

curve.

The val u e

converge

integral

o ne

instead

rise to

a

of using a convergence

i n Figure 1 in which two plots

s hown;

It

f a c t o r at a l l

s u m m a t i o n w o u l d not

i n t e g r a t e d f r o m zero to i n f i n i t y gives

spurious factor

radial

effect

i n t h e r a d i a l d i s t r i b u t i o n curve.

s ufficiently rapidly. of one

The

intensity

33).

has

s h o u l d b e p o i n t e d out t h a t were used,

in

of the recorded

it t o q = 0 b y t a k i n g

(See p a g e

also be

o f I at

the number of terms

i n rela.tion to t h e r e s u l t s

It w i l l

ob­

p a t t e r n is e s s e n t i a l l y u n o b s e r v a b l e ,

inner pattern on the

fluorocyclobutane.

upon

n u m b e r of f e a t u r e s w h i c h a p p e a r u p o n

c u s t o m a r y to ext e n d

values

dependent

summation are

s u m m a t i o n is d e t e r m i n e d b y t h e e x t e n t

it.

Introducing

a similar expression

expC-bq^) sln

scattering

tained

q = l^s.

q

of the

is c a l c u l a t e d w i t h a n d t h e

21

22 p other without

the use

of* t h e d a m p i n s t e r m ,

exp( - b q

rD(r)

function was

obtained from a theoretical

curve

e x t e n d i n g to

q = 120 and calculated

diatomic power

molecule

consisting

separated by unit

intensity of coherent the

expression I(q)

which

the

For such a molecule, can then be

the

represented by

(1 8 )

q = 5 , 2 5 , 45,

q = 1 5 , 35, 5 5 , etc.

c o r r e s p o n d i n g to t h e

six minima

in the

the

q * 120.

a convergence

first

i n t e n s i t y curve;

convergence

convergence

- 0 . 1 at

including

spurious

scattering

T h e r D (r)

t h e n calculated using a total of twelve terms

curve B with the

that

for a simple

of u n i t

s i n c u r v e w i t h m a x i m a at

calculated without

exp(-bq2)

intensity

= sin^H q .

summation,

first

scattering

a n d m i n i m a at

function was in the

distance.

The

(See E q u a t i o n 19)

is a s i m p l e

6 5 , etc.,

of atoms

).

factor,

factor,

six maxima and curve

A

was

e x p ( - b q ^ ) , and

choosing b

such that

A c o m p a r i s o n of A a n d B s h o w s f a c t o r not

fluctuations b u t , in addition,

t h e t r u e p e a k a p p e a r i n g a t r = 1 A;

o n l y d a m p s ou t

th e

broadens and flattens

t h i s , o f c o u r s e , is w h a t

one w o u l d e x p e c t . Walter

and Beach

(46) h a v e u s e d a r a d i c a l l y d i f f e r e n t

m e t h o d o f a p p r o x i m a t i n g the ra d i a l d i s t r i b u t i o n integral. Instead of replacing the assumed that cosine

the

shapes

integral by a summation,

they

of maxima a n d m i n i m a are those

of

functions.

Very recently,

Karle

and Earle

(18) h a v e

extended the

23

t h e o r y for c o m p u t i n g r a d i a l d i s t r i b u t i o n c urves to pe r m i t accurate

curves

to b e

obtained from scattering data extending

to o n l y a r e l a t i v e l y

small

a means

not

of

obtaining

s value.

only equilibrium distances but

a me t h o d of e v a l uating the motion bet w e e n pairs

Methods

magnitude

of atoms

of Evaluating

Their method provides also

of t h e v i b r a t i o n a l

in a molecule.

the Theoretical Intensity Curves

and

the Radial Distribution Function The

e v a l u a t i o n of t h e s e two

s u m m a t i o n of s e v e r a l t e r m s , ly l a b o r i o u s

The Strips

first

(37)

of these

w h i c h are

inch wide and two values

val on each i ng s t r i p s

of 0.02 strip

simply paper

these

entries

for the

The

summation,

-— — ^ sr

of s u p to 20.

Calculations

The

are made by

s inter­ select­

in the assumed model and

si d e o n a n a p p r o p r i a t e h o l d e r so t h a t s value

lie

in the

same ho r i z o n t a l

s u c h as r e p r e s e n t e d b y E q u a t i o n 11,

each value

to a limited extent

approximately an

interva-ls o f 0 . 0 1

c a n t h e n be made by using the p r o p e r t e r m - b y - t e r m at

calculations.

a n d fo r r b e t w e e n 4 . 0 0 a n d 8 . 0 0

is 0.20.

same

Two methods

o n w h i c h are t a b u l a t e d

for values

side b y

extreme­

of Sherman-Cross

strips

c o r r e s p o n d i n g to e a c h r^ j

placing

row.

involves the use

o f s u p t o 40,

intervals

which would be

for making these

feet long,

involves the

m e c h a n i c a l aids.

f o r r b e t w e e n O . 5 0 a n d 4 . 0 0 at

for values at

a process

if d o n e w i t h o u t

are n o w commonly employed

functions

in this

of s.

j factors and summing

This m e t h o d was used only

laboratory,

u sually to c h eck the

24

results

obtained by the punched card method which

is d e s ­

c r i b e d below. In the these

a d a p t a t i o n of t h e u s e

summations

it w a s

scattering expression, q, w h e r e the

q =

.

found

If t h e

1 1 , one

obtains

It a l s o

for s i n x r a t h e r t h a n for —

sin

in the latter the

c urve.

in Equation

this gives

(1 9 )

1 1 a n d 19 is t h a t

no t a p p e a r i n t h e d e n o m i n a ­

rise to a n u n d a m p e d i n t e n s i t y

(When comparing theoretical and experimental

s i t y c u r v e s , it

is t h e n m o r e

curve with a n average

Ÿ

qr^^ )

quantity q does

s i n term;

s in the

a p p e a r e d a d v a n t a g e o u s to m a k e

essential difference between Equations

t o r of the

replace

n e c essary modifications are made

1 (0.) = k

The

c o n v e n i e n t to

in making

given by Equation 1 1 , by a new variable

summation calculations

terms.

of p u n c h e d cards

convenient to plot

amplitude

independent

inten­

a visual

of q . )

For a d e t a i l e d d e s c r i p t i o n of the p u n c h e d - c a r d files and their use to the

in making these

original article

liminary calculations the

interatomic

on the

are those

distances

t h e n tabulated with their (5AEj)

calculations subject

(35)•

is m a d e

The only p r e ­

involved in obtaining

i n a n a s s u m e d model.

These

all are

corresponding amplitudes

an d submitted for the machine

If t h e

reference

intramolecular vibrations

summation. in the

I n v e s t i g a t e d are b e l i e v e d to be a p p r ec iab le

compound being it b e c o m e s

neces—

25

s a r y to

consider non-rigid models.

This

entails using an

i n t e n s i t y e x p r e s s i o n s u c h a s E q u a t i o n 12 i n w h i c h a vibration by

q, t h e

f a c t o r , exp(-as^).

intensity

Kq) =

out

t e r m a r e no t ly

chosen for b ^

a

Variable

b u t i o n of interatomic atomic vibrations

coefficientsof

coefficients

expressed by the

r2 Dij(r)

by

the

f o r its b a s i s t h e

each

are compari t i v e S t rips;

when

is n e c e s s a r y

fact t h a t

distances which occurs

can be

d i s t r i b u t i o n about

ca,n b e

atom

a n o t h e r procedure.

This p r o c e d u r e has

It

on the

t h e e x p o n e n t i a l fa,ctors i n v o l v e s

t h e p u n c h e d - c a r d m e t h o d of s u m m a t i o n it

to a d o p t

distri­

as a r e s u l t

represented by a normal

error

r Q , the equilibrium distance.

This

of

curve is

equation

= K exp

- ° ^ ( ^ .

^)2

(21)

shown that o C . is r e l a t e d to b; i n E q u a t i o n 20 3- J -L J

formula

05

The

again depends

s u m m a t i o n in w h i c h the

constant.

(20)

simple to h a n d l e by the use of Sherman-Gross

using

s is r e p l a c e d

f u n c t i o n is r e p r e s e n t e d b y t h e f o r m u l a

involved. Introducing

carrying

included

h E j exp(-bijq2 )'sin

in which the value pair

If t h e v a r i a b l e

is

actual

= 4

(IO/tD^ b

calculation

k n o w n or assumed value

is m a d e b y

(22) first

finding

o G from a

of b and t h e n evaluating the exponential

26

■term i n E q u a t i o n 2 1 of about

0 .05 A

for values

of r^ ^

i n th e n e i g h b o r h o o d

d i s t r i b u t i o n of

interatomic

s p a c e d at

of r Q .

distances

I n this w a y the

is o b t a i n e d so t h a t

to each distance

can be assigned a constant

efficient .

i n c r e a s e s t h e n u m b e r of t e r m s

This

m a t i o n b u t , as d i s c u s s e d b y can be

scattering

its o r i g i n a t o r s

i n the

co­ sum­

(3 5 )> t h i s

c o n v e n i e n t l y h a n d l e d b y th e p u n c h e d - c a r d method.

To apply this

me tho d to

E q u a t i o n 17 must b e because

the

lations

with

to

in steps

5* 0 0

needed 100.

intervals

is It

factor, of cards

modified

slightly.

This

m e t h o d was d e s i g n e d for intensity cards

available

o f 0.01.

for terms

usually

2 0 , to

available.

= ^q^I^

Sources

for r v a l u e s

The radial

c o r r e s p o n d i n g to

is n e c e s s a r y ,

rD(r)

a radial distribution summation.

q values

t h e r e f o r e , to d i v i d e t h e make

these

exp(-bq^)

compatible

sin^*

from 0.01

f r o m 1 to

^

say

q's b y a

with the range

E q u a t i o n 17 » w h e n m o d i f i e d ,

of the results

a c c u r a c y of t h e v i s u a l

Errors

ranging

distribution summation

becomes

2 Or

(2 3 )

obtained by the visual

c o r r e l a t i o n m e t h o d d e p e n d s m o s t l y o n two

parameters

curve c alcu­

of Err o r and Accuracy of Results

The uncertainty

of theore t i c a l

is n e c e s s a r y

intensity

intensity

factors :

c u r v e , and 2 ) the

c u r v e s to

changes

in the

l) t h e sensitivity structural

of the assumed models. in the visual

c u rve, commonly

called the

qQ

27

function,

may arise

ation of the

q_o' s f o r e a c h

wave

l e n g t h , the

Buck

(8 ) h a s

ing

calculated the

a n d the

electron wavelength

and the

in measuring

in camera

the

in s r e s u l t ­

camera distance

geometry measurements,

e r r o r i n m e a s u r i n g t h e d i a m e t e r of t h e 1 0 5 l i n e This

line

w i t h i n less

t h a n 0 .2 ;^; t h e

thus

o r d e r o f 0.5^-

in the

maximum error in wavelength Measurements

of t h e gas p a t t e r n are the most

error.

F o r a w e l l - d e f i n e d r i ng,

can be made with rings,

but

quantitative

error in the usually

of the ring likely

it is

the

c u s t o m a r y to

correlation.

To

one

from the visual

exclude

p o s s i b l e to

make

a direct

interpretation.

d i f f r a c t i o n r e s u l t s to t h o s e methods has experimental

afforded

of the

the

in

subjective

The

most

are ques­

an intensity

pattern.

It

is i m ­

of the reliability

c o m p a r i s o n of e l e c t r o n

obtained by other experimental

such a test

e r r o r is a b o u t

can become

several observers

objective test

However,

of

these values

involved in plotting

appearance

source

fluctuations

minimize the

diameter estimations,

s t e p is t h e

di­

For asymmetric

called u p o n to analyze the pattern.

tionable

is

diameter measurements

0.5% m a x i m u m deviation.

or p o o r l y d e f i n e d rings,

appreciable

in

is s h a r p a n d c a n b e m e a s u r e d t o

ameters

of the

camera geometry.

can be obtained with a n accuracy

u p o n the e r ror

the ZnO pattern.

curve

on the e l e c t r o n

maximum uncertainty

errors

Evalu­

c a m e r a u s e d i n t h i s w o r k to b e a p p r o x i m a t e l y 0 . 3 ^«

dependent

the

sources.

feature depends

ring diameters

from instrumental

of the The

from several different

1%

(6 , 24).

i n t h e mo s t

The

over-all

favorable

cases.

28

The limits of uncertainty of the results to a very large extent depend upon the nature of the compound being studied*

This is best understood if one recalls that the

intensity expression is essentially a summation of terms, each term having a different coefficient*

The magnitude of

each coefficient depends on the scattering power of the atom pair to which the term corresponds.

It is evident, therefore,

that certain interatomic distances, which have small scattering power, will contribute relatively little to the total diffraction pattern.

Such distances can then be changed

over a considerable range of values without producing a sig­ nificant effect in the calculated curve; distances involving H atoms are naturally of this type,

in compounds requiring

the determination of more than one parameter therefore, all interatomic distances cannot usually be determined with the same accuracy.

This means that for some compounds, only a

partial structure determination can be made.

It is often

necessary to assume values for certain parameters bearing in mind that the validity of the conclusions will depend upon these assumptions. In a final presentation of results, the limits of uncertainty assigned to any one parameter depend upon two factors.

The first is the extent to which that parameter

can be varied before definite disagreement between the theoretical and experimental intensity curves is obtained. The second factor takes into account the maximum experi­ mental error in determining the q(obs) values.

29

II.

T H E M O L E C U L A R S T R U C T U R E OF O C T A F L U O R O C Y C L O S U T A M E

Introduction

The

i n ve stigation of the

molecular structure

fluo r o cyclobutane was und e r t a k e n because connection with the

structure

o f its

of f l u o r o c a r b o n s

interest

c a r b o n ring.

Livingston

(8 ^ 9)

shown that the

of the

fluorine

in d e t e r m i n i n g the obtained

for the

of f l u o r i n e 2 .7 0 A,

atoms

which

It b e c a m e

structure

of interest atoms

quite likely that the of a lengthening

of a b o u t

(7)

some doubt

as t o t h e

(1 1 ).

a-nd t h a t

radius

is a b o u t

of fluorine.

exhibited this t h e n it

distance above

the

same, ap­ seemed form either

frequently

or in a twisting or folding It a p p e a r e d s i g n i f i c a n t ,

interpret

of a p l a n a r

successful

carbon atoms

would appear in the

1 .54- A

to

of approach

therefore to determine whether

c a r b o n ring.

attempts

data on the basis

Glaassen

effect

effect

Evidence was

distance

If t h e y did,

of the 0 - 0

of the f o u r - m e m b e r e d

spectroscopic

closest

in C^Fg

parently u n i q u e , property.

t hat p r e v i o u s

compound.

attached to different

fluorine

observed value

a very remarkable

of this

fact that t h e

four-

o f h e x a f l u o r o p r o p e n e has^

atoms have

structure

of the

investigation b y Buck and

is t w i c e t h e v a n d e r W a a l s

a point

or not the

A recent

in

in general

and to a s c e r t a i n the pl an ar it y or n o n -p la na ri t y membered

of o c t a -

electron diffraction

carbon ring h a d proved u n ­

Edgell

and Weiblen

correctness

data on the basis

of the of a

(17) h a v e p l a c e d

i n t e r p r e t a t i o n of m o d e l as g i v e n b y

30

I n "bhiis i n v e s t i g a t i o n ,

conclusive

for a non-planar carbon ring distance. approach

It is a l s o of fluorine

carbon atoms

evidence

is p r o v i d e d

a nd a n u n u s u a l l y long 0-0 b o n d

found that the

closest

distance

of

a t o m s -which a r e b o n d e d t o d i f f e r e n t

is at l e a s t

2 .T O A.

Experimental

The

sample

v i d e d b y Drs.

of C^Fg u s e d

Hals

in this wo r k was kindly p r o ­

a n d P e a r l s o n of t h e C e n t r a l R e s e a r c h

Department

of the M i n n e s o t a Mining and Ma n u f a c t u r i n g C o m ­

pany.

sample

The

was p repared by the pyrolysis

tetrafluoroethylene main products (b.p.

-29°)

(2 2 ) a n d s e p a r a t e d

of the

reaction,

by means

CgP^

f r o m the

(b*p.

o f a P o d b i e l n i a k still.

was trea t e d wi t h b r o m i n e

o f 1 3 mm.

(38).

The

and was packed with

3/64-inch

The

- 6 . 0 ° at 7 4 5

mm.

Hg.

A

dicated that

the

c o m p o u n d wasat least

the

major

fraction patterns

sample

study

contaminant

Several attempts

a n d C-^Fg

The

fractional

c o l u m n of t h e t y p e

was

c o l l e c t e d at

of t h e

being

stainless

obtained.

steel -6.1 to

infrared spectrum in­ 9 9 • 3% p e r f l u o r o c y c l o -

C^Fg.

were necessary before

could be

compound

column h a d a n inside diameter

single t u r n helices.

butane,

other two

and further purified by

d i s t i l l a t i o n i n a 2^ - f t . l o w t e m p e r a t u r e described by Simons

- 7 6 °)

of pol y -

acceptable d i f ­

Six measurable

photo­

graphs were p r e p a r e d u s i n g E a s t m a n K o d a k 33 and E a s t m a n Kodak Super Ortho Press both types

of plates.

plates; The

D K d e v e l o p e r was

patterns

were

used

for

o b t a i n e d at a n

31

electron wavelength approximately duced

0.6 microamp.

into the

which the Hg.

The

0.4

sec.

1.6

sec.

gas

of 0*0554- A,

using

The gaseous

diffraction apparatus pressure was

a b e a m current sample was

of

intro­

from a reservoir in

m a i n t a i n e d at

100 to

125

mm.

of

measured patterns were obtained using multiple exposures

Three

;

the t o t a l time was v a r i e d

photographs

remove the

subjective

other observers server making

(J. W.

were

The

qualitative

the

above

Goutts,

a n d R.

sixteen measurable

of the s e

a n d T.

T.

measured b y two

Broun) , each o b ­

of t e n measurements

appearance

persons

m e a s u r e d b y t h e a u t h o r an d , t o

e l e m e n t , two

an average

L.

f r o m 1 . 2 to

o n each feature.

of t h e p a t t e r n w a s d e t e r m i n e d b y Livingston.

f e a t u r e s , the

The pattern showed

outermost

maximum corres­

p o n d i n g to a q of 7 5 * 3 1 ; m e a s u r e me nt s o n e l e v e n o f t h e s e features were tative

s u f f i c i e n t l y r e l i a b l e to be u s e d i n the

quanti­

c o r r e l a t i o n procedure.

The

q(obs)

values given in Table

the measured ring diameters

using the

I were

calculated from

customary procedure.

Interpretation of Pattern The Radial bution curves

were

shown in Figure

rD(r) = In order to

D i s t r i b u t i o n F u n c t i o n .— T h e

^

obtained from the visual

5 by means of the

radial distri­ intensity

equation

I(c^exp(-bqk2 ) sin ( ^ q kr) ;

evaluate the

cu r v e

function by the

I.B.M.

(25) m e t h o d of

32

Table

1.

Maximum

Data

for V i s u a l P a t t e r n of Octafluorocyolobufcane

Minimum

2

11*36

3 3 4 4a 4b

(s h e l f ) 5

5 6 6

7 7 8 8

9 9

q(obs)

D(diameter) mm.

I(obs)

19.07

20

13.55'

22.69

-14

14.90

24.92

10

16.56

27.69

- 9

17-96

30.02 :

2 2 .3 8 :

37.37

7

24.00

40.04

- 6

25.68

42.87

4

27.32

45.74

- 6

29-27

48.73

13

33-39

55.51

-10

35-26

58.53

7

38.05

63.09

- 2

40.10

66.40

13

43.00

71.08

-13

45.69

75.37

10

12

c a l c u l a t i o n it w a s n e c e s s a r y t o r e w r i t e E q u a t i o n 25 i n t h e more

suitable

form

rD(r)

2 , I ( q k ) e x p (- b q 1 2 ) s i n qk

=

For purposes

of calculation,

and 20r becomes

(^* ^

q.^/20 b e c o m e s

i d e n t i f i e d w i t h q.

The

20r )

(26 )

identified with r

significance

of t h i s

33

p r o c e d u r e lias b e e n o u t l i n e d p r e v i o u s l y . recalled that intensity does

not As

were

the values

curve fall

in which

ar e o b t a i n e d

sho w n in Figure the

of including,

should also be from a visual

it is a s s u m e d t h a t t h e

off with increasing

calculated,

effect

1(d)

It

2, t h r e e

intensity

q. radial d istribution curves

o b j e c t b e i n g to d e t e r m i n e

1) t h e

i n t h e R, D.

terms

calculation,

from

the

i n n e r m o s t p o r t i o n o f t h e d i f f r a c t i o n p a t t e r n a n d 2)

the

effect

o n r e s o l u t i o n of c h a n g i n g t h e d a m p i n g

The thr ee

curves

intensity

c u r v e b y t h e a p p l i c a t i o n o f e q u a t i o n 25 i n ;

three

were

factor.

obtained from the visually estimated

slightly different

taking values q = 76;

the

of

I at

ways.

O u r v e A wa s

integral values

r e g i o n for values

o f q f r o m q = 19 to

of q l e s s t h a n 19

which reliable

intensity measurements

value

chosen such that e x p ( - b q ^ )

of b w a s

0 . 1 0 at

q - 80.

Ourve B was

factor but b y t a k i n g v a l u e s extended portion of the to s t r u c t u r e

values q = 100 q s 80 A

of q f r o m q = 1 t o

pattern which

of q f r o m 1 to 7 6 a n d

setting

curve)

0 was

is t h e n e q u a l t o

T he

same d a m p i n g q = 76.

is q u i t e

The

insensitive was

obtained

calculated using

exp(-bq^)

i n s t e a d o f at q = 8 0 ; t h e v a l u e

„ 0 . 1 at

of e x p ( - b q ^ )

at

0 .2 3 -

c o m p a r i s o n of c u r v e s A a n d B i n d i c a t e s t h a t t h e

i n c l u s i o n or e x c l u s i o n of the has

Ourve

in

is e q u a l t o

obtained using the

curves.

is on e

c a n n o t b e made.

(dotted p o r t i o n of v i s u a l

from the theoretical

calculated by

little

or no

effect

inner part

o n the positions

of the inner pattern of the m a i n peaks

RADIAL

D ISTR IB U TIO N ,

C4 Fe

CD

FIG. 2

34

o

35

in the

resulting

significant part

dif f e r e n c e s , however,

readily

T here are a few

and these are

in the most

explainable.

The most the

r a d i a l d i s t r i b u t i o n curve.

obvious difference

average height

of pea ks

is t h e o v e r a l l

in Curve

B.

This,

increase

in

of c o u r s e ,

results

fro m the extra terms which were used in obtaining * it, t h e s e t e r m s b e i n g r e l a t i v e l y i m p o r t a n t s i n c e t h e y are

taken from the the d a m p i n g however,

factor

is t h a t

other have nearly

inner part

is small.

the heights

positive

increase

significant,

o f t h e p e a k s r e l a t i v e to e a c h

character,

in h e i g h t

relative to the three 4 . 2 4 A,

is e a s i l y

which have gone We h a v e

Curve B has now

extending be l o w the

This

feature has is l e d to

from the

added terms

I n its

calculation

inner intensity pattern,

a large I and has very little damping e x p e c t , t h e r e f o r e , that terms taken

q = 4 woul!d h a v e a n a p p r e c i a b l e

such terms give

It

can be

effect

zero v a l u e s

of including these terms

on

shown b y a simple

r i s e to a f u n c t i o n c h a r a c t e r ­

i z e d b y a m a x i m u m at r = 2 . 5 ^ w h i c h t h e n s l o w l y d r o p s side to

the

at a q a p p r o x i m a t e l y e q u a l to

the r a d i a l d i s t r i b u t i o n c u r v e . calculation that

p e a k at r = 2 * 4 6 A,

f o r m a t i o n of B.

maximum appearing

one

of the

explained by considering the

into the

from say q = 1 to

on each

ze r o

o t h e r m a j o r p e a k s at 1 . 3 3 » 3 -38 a n d

included terms

innermost

o n it;

is m o r e

I is l a r g e a n d

a very minor extent.

The

2.

What

changed appreciably and that

complete

line to

of the p a t t e r n where

at r = 0 a n d r = 5-

i n t h e R.

D.

off

The effect

c a l c u l a t i o n is t h e r e f o r e

36

"fco i n c r e a s e "the freights peaks

at

smaller and larger values

t h e p e a k at 2 . 4 7 A at

of p e a k s a r o u n d 2 . 5 A rela t i v e to

1.33 a n d 3-38,

can be

easily

while

of t h e

seen by

of t h e v e r t i c a l to t h e a m o u n t tance

T h u s , i n C u r v e A,

is w e a k e r t h a n t h e t w o p r o m i n e n t p e a k s i n C u r v e B,

ment i o n e d l o w frequency terms were higher than any

o f r.

ot h e r s .

in which the aboveincluded,

That this

comparing heights

t h i s p e a k is

is as it s h o u l d be

of p e a k s

to t h e l e n g t h

lines which are d r a w n roughly proportional

of s c a t ter ing m a t t e r s e p a rat ed b y the d i s ­

indicated. T h e p e a k at

nevertheless, ing p e a k s

2.75

is p o o r l y r e s o l v e d i n B b u t

clear that

and relative

is c l o s e r t o

the

i ts h e i g h t ,

to the

this peak relative to the so r e a d i l y e x p l a i n e d .

should

of t h e v e r t i c a l lines,

a d j o i n i n g p e a k at 2 . 4 7 A

It m a y be,

zero d e c r e a s e s the

errors

surround­

Why

inclu­

increase the height

of

is n o t

of c o u r s e , t h a t extending "diffra c t i o n effects"

mentioned by Yiervoll and Cruickshank systematic

rela t i v e to the

e x p e c t e d v a l u e t h a n it is i n A.

sion of low f r e q u e n c y terms

the p a t t e r n to

lengths

it is,

resulting from the

(44), finite

w h i c h are

simply

r a n g e of i n t e ­

g r a t i o n r a t h e r t h a n f r o m 0 t o o£>. E x p l a n a t i o n has b e e n g i v e n for the has

less negative

this difference intensity

the

c h a r a c t e r t h a n C u r v e A.

To

Curve B

some e x t e n t

r e s t s u p o n t h e m e t h o d of c a l c u l a t i o n o f t h e

curves.

function was

fact that

To o b t a i n t h e s e , an approximate

assumed

( E q u a t i o n 11)

a t o m i c n u m b e r s , Z ^ Z ., as

intensity

using the products

coefficients

of

i n s t e a d of th e

37

products F,

of th e

the X - r a y

values

scattering

f o r m factor, has

coefficients,

the

pattern,

of the

pattern.

which gives positive

a resulting

innermost

too large

p o r t i o n of maximum appearing

of p r o p o r t i o n to t h e it

is t h i s

feature

character.

certain amount

from the

i n t h e R.

inner part

D.

calculations

of t h e p a t t e r n a

o f r e s o l u t i o n h a s b e e n lost.

It must

follow

o u t e r p a t t e r n is t h e r e b y g i v e n r e l a t i v e l y l e s s

and

since

sensitive to

it is t h i s

distances

part

of t h e p a t t e r n w h i c h is

with a small weighting

of t h e m may not

appear well

To

this p o i n t , Curve

the

zero.

r a d i a l d i s t r i b u t i o n C u r v e B its n e a r l y a l l

low frequency terms

weight

and the

just p o i n t e d out,

It is e v i d e n t t h a t b y i n c l u d i n g

that the

for small

Z aa q approaches

i n t e n s i t y out

As

- F j).

an appreciable value

as a p p l i e d to t he

are therefore

q s 2 has

rest

(Z^ - Fj_)(Zj

of q an d rapidly approaches

The

at

factors

substantiate damping

was

in exp(-bq^).

r e s o l v e d i n t h e R. C was

decreased by assigning The

D.

so m e

curve.

calculated in which a larger value to b

o u t e r p o r t i o n of the d i f f r a c t i o n p a t t e r n

is t h e r e b y a s s i g n e d a l a r g e r w e i g h t i n g an improvement

fac t o r ,

f a c t o r and,

i n r e s o l u t i o n is o b t a i n e d .

as e x p e c t e d ,

It h a s b e e n shown,

h o w e v e r , w h e n d i s c u s s i n g the radial d i s t r i b u t i o n m e t h o d , that b cannot be peaks

appearing

made too in the

large

curve

a compromise between too many r e s o l u t i o n is t h e r e f o r e F o r the

i f th e

n u m b e r of spurious

is t o b e k e p t t o a m i n i m u m ; spurious peaks

and loss

in

desirable.

interpretation of the

radial distribution p e a k s ,

38

reference

is m a d e t o F i g u r e

non-planar model• following

The peaks which occur c o r r espond to the

interatomic

1.33 1*61 2.17 2.47

Ci 0 -i Ft Ci

- Fi — Cp - Fp — F-^

2.75

Fi

- F3

3.38

Fi

- F4

°1 - f 5 F 2 - Fg

4.24

Fi

— F3

F1 - f6

The peaks most p rominent

3 i n which, is d r a w n a t y p i c a l

distances:

(bonded) (bonded) ( b o n d e d to s a m e 0 atom) (shortest n o n - b o n d e d 0 - F distance) (s h o r t F - F d i s t a n c e f o r F a t o m s b o n d e d to a d j o i n i n g G atoms) (long F - F d i s t a n c e f o r F atoms b o n d e d to adjoining C atoms ) (long n o n - b o n d e d C - F d i s t a n c e ) (s h o r t e s t F - F d i s t a n c e f o r F atoms b o n d e d to d i a g o n a l l y op p o s i t e C atoms) (Long F - F d i s t a n c e f o r F a t o m s b o n d e d to d i a g o n a l l y oppo s i t e C atoms) (longest F - F distance for F atoms b o n d e d to d i a g o n a l l y o p p o s i t e C atoms)

o c c u r r i n g at 1 .33,

2 . 4 7 a n d 3 * 3 8 A are th e

ones and probably the most reliable;

those

at 1 . 6 1 a n d 2 . 7 5 A a r e p o o r l y r e s o l v e d a n d m u s t b e c o n s i d e r e d unreliable. Theoretical Intensity Ourves

The

theoretical

tion procedure were

and Calculations

intensity curves used calculated from the

in the

correla­

simplified expression

39

This

e x p r e s s i o n represents the d i f f r a c t i o n patt e r n for

an essentially rigid molecule. t h e r e f o r e , that

the displacements

intramolecular vibrations appreciable,

do

no t

cation will become

o ne

in which

which

it

significantly affect the That this

assumption had

carbon ring Two

one having

not.

as P l a n a r T y p e A diagram, of the

justifi­

types

other in

o f lfp l a n a r rt m o d e l s w e r e

s y m m e t r y a n d the

other

is t h a t

The

models are

of each model are

diago n a l l y opposite GF^ groups

p aper.

It

Is e v i d e n t t h a t

3

In the

s h o w n w i t h the p l a n e

ring d r a w n p e r p e n d i c u l a r to t h e plane

the two

former

in t h e

shown in Figure

and Pla n a r Type B r e s p e c t i v e l y .

si d e v i e w s

(^gd^ '

i n th e

of t h e r i n g b i s e c t s t h e F G F a n g l e w h i l e

l a t t e r it d o e s

of

main classes,

is p l a n a r a n d t h e

the essen t i a l difference b etween these the plane

appearance

c o n v e n i e n t l y g r o u p e d into two

the

caused by

m o l e c u l a r configurations assumed for the

is n o n p l a n a r .

considered,

of t h e a t o m s

e v i d e n t later.

The different can be

a s s u m p t i o n was made,

are negligibly small or t h a t , if

the d i f f r a c t i o n pattern.

compound

The

of t h e p a p e r and

in the plane

of t h e

i n the Type B s t r u c t u r e , the

i n t e r a t o m i c , n o n - b o n d e d distance G^-F^ will be different f r o m 0^_-F4;

will be

different

the T y p e A m o d e l t h e p l a n e

of t h e

and these d i s t a n c e s are

a l l equal.

corresponds to the most

prominent

bution curve.

This

peak

i n w i d t h , at h a l f h e i g h t ,

is

f r o m G g - F g , etc.

ring bisects

the F G F angle

This distance p e a k in the

In

( 2 .46 A)

radial d i s t r i ­

s h a r p , well defined and equal

t o t h e p e a k at 1 . 33 w h i c h we

can

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Table 11.

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