THE STRUCTURE OF CRYSTALLINE
LITHIUM TRICHLOSOACETATE MONOHYDRATE
DISSERTATION
Presented in Partial Fulfillment of the Requirements
for the Degree Doctor of Philosophy in the
Graduate School of The Ohio State
U niversity
hy
Donald Tuomi, B.S. 1i The Ohio State U niversity
1952
Approved "by:
Adviser ACKNOWLEDGMENTS
I would like to express my appreciation for the advice and encouragement of Dr. P. M. Harris during
this investigation, and to acknowledge with thanks
the support provided hy the Department of Chemistry.
I would also like to express my gratitude for the
assistance provided "by my wife, Ruth, in the com putation of the numerous Fourier series which were
evaluated and for her constant encouragement during
this investigation. I wish to thank Dr. F. H. Yerhoek
and Dr. E. N. L assettre fo r th eir comments during the preparation of the manuscript and Mrs. Carolyn McClure
for typing the final copy.
, i I i
809690 TABLE OF COHTEHTS
page
I. Introduction ...... 1
I I . Summary . 3
III. Literature ...... 9
A. Chemistry ...... 9
B. Bond D i s t a n c e s ...... 17
IT. Experimental Section ...... 37
A. Crystal Growth ...... 37
B. Chemical Composition ...... 39
C. Lattice Constants ...... 1+1
D. Space G roup ...... 1+2
E. Structure Factors ...... 50
T. Patterson Interatomic Vector M aps ...... 72
VI. Structure Determination ...... 113
VII. Discussion: Crystal Structure ...... ll+2
VIII. Discussion: Bond Distance L iterature ...... lllS
IX. Proposals for Further Research ...... 153
X. Appendix ...... 155
1. Lorentz and Polarization Factor Homograph .... 156
2. (hkl) Structure Factors . . 165
3. Structure of Crystalline LiOOCCRj • 2 HgO .... 172
1+. Crystalline Salts of Trichloroacetic Acid .... I 7I+
5. Removal of the O rigin Peak in the
Patterson Series .... 176
i i i XI. Bibliography
XII. Autobio graphy TABLES
page
I. free Energy of Ionization of Chloroacetic Acids .... 11
II. Electron Diffraction Data for Carboxylic Acids .... 19
III. Bond Distances for Crystalline Carboxylic Acids .... 21
IV. Bond Distances for Crystalline Carboxylic Acid Salts . Zk
V. Bond D istances fo r C rystallin e Amino Acids ...... 26
VI. X-Eay D iffra ctio n Carbon-Chlorine Bond D istances . . . 31
VII. Chemical Analyses of LiOOCCCl^ • H20 ...... *K)
VIII. Multiple Film Intensity Seduction Factors ...... 52
IX. Absorption Correction Factors for (hOl)
Structure F actors ...... 59
X. (hOl) Zone Structure F a c t o r s ...... 66
XI. Bragg-Lipson Structure Factors ...... 116
XII. Trial Parameters for Models Obtained from Bragg-Lipson
Charts and from First Fourier Eefinement . . . 119
XIII. Calculated and Observed Structure Factors for
Bragg-Lipson Model ...... 120
XIV. Observed and Calculated Structure Factors for Og-Gc . . 127
XV. Sin Theta Calculated from the Nomograph and from
the Measured Lattice Constants . . 1&J-
v FIGURES page
1 . P ostu lated Model o f the 001^000“ Anion ...... 35
2 .Space Groigo Symmetry ...... U5
3. Structure Factor Distribution
K Average Atomic Scattering Factor Versus Sin 0 . ,
5. Logarithm of Local Scale Factor Versus Sin 0 ...... - 65
6 . Orientation of Patterson Projections ...... 83
7. Patterson Projection - P ^ ^ ......
8 . Patterson Projection - P(ofcl) ......
9. Patterson Projection - P^nirr,^ ...... 10. Patterson Projection - P ^ -j^ ...... l i . Model Suggested hy Patterson Projections ...... 92
12. Patterson-Harker Section - P ^ ^ ......
13. Sharpened Patterson-Harker Section - P ^ ^ . . . c; Ik. Buerger Implication Diagram for P ^ ^ - 0|h“®2/c* . . . 96
15. Patterson Section - ”* Origin Region ....
1 6 . Patterson Section - P^ ^ - Origin Region ....
17. Patterson Section - P> , . - Origin Region .... (u$w) 18. Patterson Section - P. - . - Origin Region .... (uj-w) 19. Patterson Section - P, . v - Origin Region .... (n|w) 20. Three Dimensional Patterson Vector Map ......
21. Projected 01-01 Vectors for Proposed Structure , ,
22. Projected 01-0 Vectors for Proposed Structure , ,
23. Projected Cl-C Vectors for Proposed Structure . .
v i 2ty. Projected 0-0 Vectors for Proposed Structure ...... 112
25. Fourier Series Projection, on the (010) Plane -
Observed Structure Factors and Calculated Phase
Angles ...... 123
26. Fourier Series Projection on the (010) Plane -
Calculated Structure Factors and Calculated Phase
A n g le s ...... 12^
27. Fourier Series Projection on the (010) Plane -
Observed Structure Factors Minus the Chlorine
Contribution ...... 125
2S. The Variation of the Reliability Index with the
Humber of (hOl) Structure Factors Included ...... 132
29 . Flow Sheet for Structure Factor and Fourier Series
C alculations in the Space Crotp c f h - ^ c versus C^-Cc. 135
30. The Structure of Lithium Trichloroacetate Monohydrate
Projected on the (100) Plane ...... 1^3
31. The Change in the Free Energy of Ionization, as
Successive Chlorines are added to Acetic Acid, versus
the C-Cl Bond length in the Chloromethanes ...... 150
32. The Variation of the Molar Magnetic Susceptibility at
Infinite Dilution for the Chloroacetic Acids with the
C-Cl Bond Length in the Chloromethanes ...... 150
33. The Polarization Factor - Sin 9 Homograph ...... I 5S
31!-. The Lorentz Factor Homograph ...... 159
35. The Atomic Scattering Factor Homograph ...... 160
v ii THE STRUCTURE OF CRYSTALLINE
LITHIUM TRICHLOROACETATE MONO HYDRATE
I. INTRODUCTION
In general, the study of the crystal structure of an organic compound is undertaken in order to "be ahle to relate the chemical and physical properties of the compound to its structure as represented "by a set of bond distances. This dissertation reports the results which were obtained in a determination of the crystal structure of lithium trichloroacetate monohydrate.
The trichloroacetate ion has several interesting chemical proper ties. The acid (CCl^COOB) in aqueous solution is highly dissociated.
The dissociation constant at 25° C. is 0.2316 compared to l.S x 10“^ for acetic acid. In solution the anion undergoes a unimolecular de composition with the formation of chloroform and carbon dioxide. In addition, it has been reported that the unimolecular decomposition is accompanied to a small extent by a side reaction involving the production of chloride ions.
The lithium salt rather than the free acid was used in the structure determination for several reasons. In the structural analysis of the acid it would not be possible to locate the hydrogen atoms; however, there was a possibility that the lithium parameters could be determined.
Another factor relating to choice of the lithium salt was that the in tensity of the x-ray reflections would be determined primarily by the trichloroacetate ion. There also does not exist an extensive literature on the structural chemistry o f compounds containing lithium as compared to the other alkali metals. The information for presentation in this report has been organized in the follo\ri.ng manner. The first section presents a "brief summary of the report. In the second section are discussed the chemical character istics of the conpound followed by a discussion of the bond distance results which are pertinent to the structural determination. In the latter section a model of the anion is proposed for use in the structure determination. The experimental phase of the structure determination is then presented. The Patterson interatomic vector maps which were pre pared are discussed in section IV and the actual structure determination in section V. The results of the structure determination and the literature survey are briefly discussed in the Sections VI, VII and VIII.
The nomographic method developed for the confutation of the Lorentz and polarization factors as well as sin theta and the atomic scattering factors for the Weissehberg equi-inclination photographs is discussed in Appendix 1' .
a II. SUMMARY
Crystals of the lithium trichloroacetate were obtained hy the slow
evaporation of water from an aqueous solution of the salt prepared by
the reaction of trichloroacetic acid with lithium carbonate. Chemical analyses demonstrated that the crystals corresponded to the monohydrate
LiOOCCCI^ • HgO. The crystals, which were very deliquescent, were mono
clinic and exhibited the forms ( 100) , (010) , (001) , (110), and (IlO) with
(110) face generally smaller than the (110) . It ms initially assumed
that the crystal class is holohedral Cpy, - 2/m; however, as is later
shorn, the true symmetry class is heiaihedral Cs = m. The measured
density ms 1.8575 g./cm.3 or 1 .910 g./cm.3 after correcting for water
in excess of the stoichiometric amount. The interaxial angle is
107° 27.5' * 6 '.
The lattice constants for the unit cell determined from copper
Kot (1.5^18 A.) "a" and "b" a x is and molybdenum (0.7107 A.) nc" axis rotation photographs are
a 0 = 22.605 ± 0.026 A.
b0 = 5.59*+ ± 0.00^ A.
c0 = 10.80 ± 0.02 A.
Assuming eight molecules per unit cell the calculated density is 1.9101 g./cm .3.
In order to establish the space group oscillation photographs about the three axes were indexed using the graphical method described by Bernal. ^ The indices of the reflections for rotations around the
"b" and "c" axes could not be uniquely assigned. Consequently corres ponding sets of triple film Weissehberg equi-inclination photographs
3 were prepared. The extinction rules observed are (hkl) reflects only i f (h+ k) = 2n, and OiOl) only i f h s 2n and i f 1 = 2n. Consequently the correct space group is the non-centrosymmetric cs ~ and the asymmetric structure unit consists of two stoichiometric molecules.
A set of relative integrated intensities ms obtained for (hkl) reflections by comparing the blackening of the spots using a hand spectroscopic plate measurement contact magnifier. The Lorents and polarization correction factors as well as the associated atomic scattering factors and values of sin© were computed using a new nomo graphic method. After correcting the observed intensities the structure factors were placed on an absolute scale using Harker's procedure.
A complete set of observed magnitudes of (hOl) structure factors was prepared using both the oscillation and Weissehberg films. This set was corrected for absorption and placed on an absolute basis including correction for thermal vibration. The (hOl) zone data were expected to provide good resolution of the molecule.
In the early stages of the structure determination the assumption m s made that the space group was ClK -.C Z/c t the crystal having been assigned the symmetry 2/m on the basis of the observed crystal habit.
To provide a basis for developing the model the Patterson projections on the (a-c) , (b-c s in 0 ) and (b-a sin;® ) planes for and the projection (b-c sin p' ) for 4/c and the Patterson sections and were computed. With the information from these Pattersons it ms not possible ;to derive a model which was consistent with the interatomic vector maps and the observed structure factors. Consequently it ms concluded that the crystal was non-centrosymmetric: space group
- Cc . Further proof was obtained from the positive pyroelectric
tests on small crystals.
For the space group C?- Cc a trial model for the (hOl) projection
was derived by using the Patterson maps and the Bragg-Lipson (hOl)
structure factor charts. The reliability index
for the trial model was 0.4^ over all (hOl) reflections and 0.31 for the
31$ with structure factors greater than 25. The value of E increased
from 0.35 for sin & less than O.^tO to O .63 fo r sin & greater than 0.8.
The results strongly suggested that the model was approximately correct.
The refinement of this model ms attempted using the Bragg-Lipson
structure factor maps for the (hOl) zone with only limited success. The
fu ll three-dimensional Patterson interatomic vector map was then con
structed in order to determine if any alternate model could be readily proposed. In addition, attempts were made to derive an alternate model using the Bragg-Lipson charts and different sets of structure factor
inequalities. The computations consistently resulted in the development
of a model practically identical to the original model. It was con
cluded that the original model was correct. The difficulties encountered
in the refinement attempts were assumed to be related to the problem of
simultaneously refining the 32 parameters. In the computation it was
necessary to consider the contribution of all of the atoms (Cl, 0, and C) because of the extensive cancellation of chlorine contributions.
A Fourier series refinement of the model was made by computing the projection (of the electron density on the x,z plane) using the F (obs.)
and F (calc.) series to eliminate series termination effects. The refinement using the double shift and correcting for the termination of
series changed the parameters 0.006 unit at, the most. The new set of
structure factors confuted from the refined parameters was not signifi
cantly "better than the original set. This result was not too unexpected
in the case of the refinement of a non-centrosymmetric structure since
the Fourier synthesis is dependent upon the assumed atomic scattering
factors as well as on the assumed atomic coordinates. Considering the
amount of labor required to refine a non-centrosymmetric structure with
32 parameters as well as the probable inaccuracies in the final para
meters it was concluded that further work on this structure would not be profitable. Because of the uncertainties in the (x,z) pax-ameters no
attempt ms made to derive a set of y parameters.
The structure proposed for liOOCCCl-j • HgO involves the location
of a two-molecule asymmetric unit in the space group Cg-Cc . The
asymmetric unit corresponds to the close packing of a pair of trichloro
acetate ions writh chlorines opposite carboxyls. The unit is oriented
in a general position so that the chlorines of one molecule and the
oxygens of another are approximately on the same (5o4-) plane. The
c-glide symmetry operation reproduces the molecules along the c
direction so that chains of trichloroacetate ions result. The neigh boring chains in the unit cell are directed in opposite directions.
The water molecules are associated with the carboxyl group to form a
"trioxy” group. Thus along a (4o4) plane the structure consists of a
series of '’trioxy 11 and trichloro groups which are fairly close packed.
Several void regions into which the lithium ion might be placed appear
in the vicinity of the water molecule. The pair of molecules forming the asymmetric unit are approximately related by a two-fold screw axis. The model which gave the best agree ment in the centrosymmetric case was that model of an average asymmetric unit produced by introducing a symmetry center at the center of the cell projection in Cc . Thus the approximate agreement of calculated and observed intensities in C%h~ is not surprising.
The model proposed is consistent with the fracture characteristics of the crystals. The crystals may be readily fractured in a direction parallel to the c axis but not so readily normal to this direction.
This suggests that the bonding along the chains is appreciably stronger than between the chains.
The literature survey provided several results of interest. From a survey of the reported bond distances for the carboxyl group it was concluded that the ion in the solid state is best represented as a fully resonant structure with C-0 distances of 1.25 A. Considering each structure determination as a single determination of the carboxyl ion distances, the average C-0 bond distance was 1.253 ± 0.013 A. for the carboxylic acids, 1.258 i 0.018 A. for the acid salts, and 1.250
± 0.008 A. for the amino acids. It has been reported by Bernstein^) as a result of microwave absorption measurements that the C-Cl bond distance in the chloromethanes is dependent upon the number of chlorine atoms attached to the carbon atom. Assuming that these bond distances could be applied to the chloro group in the chloro acetic acids, it was found that the change in bond length could be linearly related to the
7 change in free energy of ionization of the chloro acetic acids as suc cessive chlorines are added to the acetic acid. In addition, the molar magnetic susceptibility of the acids at infinite dilution are linearly related to the G-Cl bond distances.
8 III. LITERATURE
The crystalline confound lithium trichloroacetate monohydrate has not been discussed very extensively in the chemical literature; however, the chemical and physical properties of trichloroacetic acid and the anion have heen extensively studied. In considering the literature it is convenient to discuss first the chemistry of the acid and its salts, and second to consider the literature pertaining to hond angles and distances present in the crystals of the lithium salt. 3?rom the con sideration of the chemistry and the reported "bond distances a model of the trichloroacetate ion for use in the structural analysis is proposed.
A. Chemistiy. Trichloroacetic acid is a colorless crystalline solid which melts at 52° 0., and hoils at I 960 0. The acid is prepared hy the oxidation of chloral with concentrated nitric acid or hy the direct chlorination of acetic acid using iodine or red phosphorous as the catalyst. An unstable modification of the acid which melted at 50° 0. has heen reported hy Kendall and Carpenter. (5)
In aqueous solution the acid is rather highly dissociated. The dissociation constant of the acid in water has heen reported as 1.21 at 25° 0. hy Landee and Johns^^) , whereas the values 0.2316 ( J) at 25° C. and 0.2159-0• 2185 (.0 at 20° C. are given hy vonHalhan and B rill. (7)
The large dissociation constant of this acid has heen interpreted as heing due to the inductive effect of the electronegative chlorines on the oxygen atoms and to electrostatic interactions.^ H. 0. Jenkins^) has suggested that in the case of the dichloro and the trichloroacetic acids the increase in dissociation constant is due to resonance
9 contributions from structures of the type
ci — C — c Cl'
Shorter and Stubbs^O) , however, report that the effect on the dis sociation constant due to the addition of successive chlorines to acetic acid was greatest for the first chlorine, less for the second chlorine, and least for the third. This is illustrated hy the free energy of ionization data given in Tahle 1 They suggest that the influence of chlorine atoms on the ionisation has a saturation effect, thus carbon- chlorine dipoles within each molecule being in close proximity to each other will he subject to mutual induction effects and each dipole will reduce to some extent the influence of the others on the ionization constant. The free energy change reflects directly the changes in the energy and entropy factors in the molecule.
The molar magnetic susceptibilities of the chloroacetic acids in water have been investigated by frivold and Olsen. Using UOOO and
7000 gauss field strengths and assuming - 0.7200 x 10“^ for the molar susceptibility of water, the following molar susceptibilities were de termined for the acids at infinite dilution: trichloro, - 73.0 x 10” ^; dichloro, - 5S.2 x 10“^; monochfloroacetic acid, -Ug.l x 10“^; and for c acetic acid, - 3 1 .8 x 10” . In the case of trichloroacetic acid the molar susceptibility went through to a minimum at lg$ trichloroacetic acid.
A cryoscopic study of solutions of trichloroacetic acid in vjater, ether, acetone, and methyl acetate by landee and Johns^2) demonstrated
10 IAJB1E I
Free Energy of Ionization of Ohloroacetic Acids
Acid 1C)5k25 A 2ion. A P)
Acetic 1.S2 &50
Ohloroacetic 155. 3^30 -2620
Dichloroacetic 51^0 . 1760 -2070
Trichloroacetic 23,800.. S60 - 900
A (/)P ) 58 Change in free energy of ionization as successive
chlorines are added to acetic acid
11 that the acid is present as a monomer. In addition they demonstrated that in the vapor phase the acid is also a monomer. Bell and Amold^^) studied the behavior of the acid and its hydrate OCI 3OOOH • HgO in dioxane and benzene. The solid phase in the benzene solution was shown to be crystalline benzene with some acid presumably adsorbed on the crystals. Their experimental data indicated that the anhydrous acid is present as a dimer in benzene for the concentration range 0 .0 1 to 1 .5
The hydrate in dilute solution exists as a monomer but at high concen trations it is present as a dimer. In dioxane solutions the acid is present as a monomer due to association with the solvent. The hydrate in dioxane was partially dissociated according to the equilibrium:
CCI3COOH • 0 (OHgCHg) gO + HgO -
CCljCOOH • HgO +■ 0(CH 20H2)20
They also observed that the tendency to form a hydrate.decreased in the order CCI3COOH, HOOlgCOOH, HgCOlOOOH, CH^COOH.
From a study of the vapor pressure as function of the temperature for solutions of the acid in acetone, methyl acetate, ethyl acetate, ether, and benzene, Weissenberger, Schuster and PamerC-1-^) concluded that
1:2 compounds were formed. They suggested the presence of a partial valence character in the trichloro methyl group. Pushkin and Rikovskii^ 15)
studied the melting point diagrams of the acid in benzene, piperonal,
camphor, coumarine, phenol, malonic a cid , ste a ric a cid , p h th alic anhydride and napthalene. They concluded that equimolar add ition compounds o f the acid were formed with benzene, piperpnal, camphor and possible with phenol.
12 With piperonal the compound O - CHi
. ZHOOCCCl3
CHe> and with coumarine the compound
CI3CC OOH • % - < P
were also formed. J. J. Kendall^1^ has reported the formation of equimolar compounds of the acid with benzoic, o-toluic, m-toluic, p -to lu ic and cinnamic acid s.
Numerous metallic salts of trichloroacetic acid have heen prepared, hut the salts, in general, have not heen very well characterized. The various metallic salts whose preparations have heen described in literar- ture are given in Appendix I . Clermont has described the preparation of crystals of LiOOCCGl-j * 2HgO which were deliquescent prisms. It appears probable that this compound actually was the monohydrate de scribed later in this report. It is interesting that the acid salts
MCOOCCCl-j) • HDOCCCI3 where M i s K, Eh, Cs, T l, and NIfy are formed.
In aqueous solutions the trichloroacetate ion undergoes a decar boxylation reaction with the formation of chloroform and carbon dioxide.
The kinetics of the decarboxylation reaction have been rather exten sively studied by Verhoek and his students. (^7) The reaction was found to be first order with respect to the trichloroacetate ion and dependent upon pH only through the ionization of the acid. In alkaline solution the rate is independent of the pH. The mechanism for the reaction postulated by Verhoek^1?-®) is as follows:
13 Ol^OCOO “ -► CC1^“ -f COg (slow)
c c i f - t HgO CHCl^ H- OH" (rap id ), the rate of the reaction being determined "by the concentration of the trichloroacetate ion. The acid was shown to he stable in the non-basic solvents such as benzene, carbon disulfide, carbon tetrachloride, ethyl ether, acetone, nitrobenzene and acetic acid. In the case of the lithium
salt in the system alcohol-water the decomposition proceeds faster than for the sodium salt for similar concentrations and solvent compositions.
This was due presumably to the higher solvation of the lithium ion as
compared to the sodium ion. The a ctiv a tio n energy o f the reaction in creased as the water concentration increased. This was explained by
the assumption that the trichloroacetate ion became hydrated, the ion being more easily hydrated than alcoholated. The experimental investi gations of Verhoek et al, indicated that the rate of unimolecular de
composition of the ion is determined by the extent of solvation of the
ion and the nature of the solvating substance.
During the solution decomposition of the trichloroacetate ion it
i s observed that the chloride ions are formed. Verhoek^^""3^ has sug
gested that this chloride is formed by the oxidation of chloroform to phosgene which then hydrolyzes to give carbon dioxide and hydrochloric acid. Begeleisen and Allen^^) in a study of the decarboxylation of
1_q12 and 1-0^3 trichloroacetate ions suggest on the basis of their data
that the chloride is produced by a second mechanism of decomposition of
the trichloroacetate ion, namely:
CI3C COO" CI2 C-C = 0 + Cl”
Ik Their in vestigation showed that in the range, zero to 25 percent de composition, the ratio of chloride ion produced to bicarbonate formed was a constant. Thus up to 25 percent decomposition the chloride i s produced with the same half life as the bicarbonate ion. The experi mental data suggested that the chloride was not accompanied by the formation of 0H~ or H* . The reaction given above was postulated to account for the observed data. In the investigations performed by
Verhoek it was reported that a 1:1 correlation existed between the formation of acid and the chloride ion.
The unimolecular decarboxylation mechanism for the carboxylic acids as described above is observed in the acids which have strongly electronegative groups associated with the carbon atom.(19) Fairclough discussed the inductive effect of the chlorines on the electron distri bution in the trichloroacetate ion by the model
5 ! ^ - / Cl ^ S* S - ^ o ^ where $ is the net positive charge on the <£ -carbon atom and S~ the net charge on the carboxyl carbon produced by the inductive effect of the electronegative chlorines. The decomposition is assumed to depend upon a net charge s h ift to the 01^ 0 group, the rate depending upon the localizing of vibrational energy in the C-C bond to produce the activated complex which dissociates.
The thermal decomposition of the trichloroacetic acid and its salts has been investigated primarily with regard to the reaction products formed. The acid does not appreciably decompose at temperatures below
15 190° 0. but using animal charcoal catalyst decomposition to CHCIt; +• COg occurs at 135° C.(2<^ Decomposition of the acid over thoria (210° 0.), china clay ( 230° 0 .), or charcoal (200 - 300° 0 .) catalyst results in the production o f COClg, COgt 00, GHCl^, CgClij., and CgClg.^2-^ The thermal decomposition of the salt HHijPOCCCl^ * 5 H2O at 110° C. the products are HHI 4.CI, CO, COClg. and CHCl^, ^22^ hut the s a lt HaOOCCClj
• 3 HgO on heating decomposes to form HaCl, 00, COg, HCCI 3 .(JMItOjCCl^,
CgOlg, and (COl^CO)^O.^2^ It is rather interesting that trichloro acetic acid reacts rigorously with copper in an aquaous or benzene solution with the formation of the dichloroacetate, whereas in an ether solution the tetrachloro succinate is formed,
Though numerous in v estig a tio n s of the Raman and in fra-red spectra of trichloroacetic acid and its salts have been performed, neither the symmetry of the acid nor the anion has been definitely established.
The symmetry, Cs , for the anion has been suggested by W ittek ,( 25) how ever , a complete normal coordinate analysis of the spectra has not been performed. Prom an investigation of the infra-red spectra associated with the carboxyl group of the univalent salts of ca.rboxylic acids,
Duval, Lecompte, and Douville^2^ conclude that the anion of the metallic salts exists as the resonating carboxyl ion. In the case of the trichloroacetates of Li, Ha. Mg, Ca, Zn, Hi, and Ba, it is reported that the metal has little effect on the infra-red spectra as a whole. (^7)
Hua-Chih Cheng and Lecompte^2^ have in v estig a ted the Raman and infra-red spectra of compounds of the form CHgCl - R, CHClg ~ R, and
CCI3 - R where R was OH, OHO, 0001, 000H, 0OOCnH2if+ 1. In the case of
16 CH2OI - R the substituent R had very little effect upon the frequencies assigned to the C-Cl group; in CHClg - R an appreciable effect was ob served; whereas in CCI 3 - R the substituent R had a predominant effect.
The frequency which they associated with the C-C bond vibration was observed to increase as the number of chlorines increased but decreased in the above order of (R). Rennet and Daniels(29) have reported that for the ser ie s CE-jCOOE, CC1H2C00E, CC12EC00E, and CCI3COOE a strong absorption band occurs in the neighborhood of vflaich is shifted to shorter wave len gth s as Cl atoms are added: namely, 1697. 1709, 172^,
1739 cm“l respectively. This band probably is related to the C = 0 bond stretching vibration at 1700 cm rl.^O)
In the case of lithium trichloroacetate the infra-red absorption maxima have been reported^31) as occurring at 66S, 622, 739, SUo, 922, llOty, 13^+1, and 1666 cm"*-*-. The polarizations of the Raman lin es of sodium trichloroacetate have been reported by G-upta^^ as being
^3U cm"1 (0 .0 2 ), 232 ( 0 .7 ) , 1330 (0.2U) , and 1667 (0 . 7). From a study of the effect of dilution on the Raman spectra of the ohloroacetic a cid s, Saksena^3) assigned the lines at 102, *+50, 676, and 1^3^ cm“l to the undissociated trichloroacetic acid, and the lines at V+ 3 , 695 ,
735, S33, 1322, and 175S cm-1 to the monomer and the ion. The lines at
695 and 735 cm- 1 appeared on dilution and were assigned to the ion.
B. Bond Distances. In the process of determining the crystal structure of a compound it is advantageous, when possible, to propose a model for the structure of the molecule which may be used in the initial trial stages of computation. In the following sections the literature data
17 relating to the inter- and intramolecular distances to he reasonably expected in the lithium trichloroacetate monohydrate crystal are surveyed.
1. Garhoxyl group. The structure of the carboxyl group in organic compounds has been studied by electron diffraction and x-ray diffraction methods. Prom-the electron diffraction results informa tion is obtained on the structure of the isolated acid molecules in the gas phase, whereas the x-ray diffraction results provide data on the structure of the carboxyl group in a crystal where the group may interact with the surrounding atoms.
The results of the electron diffraction studies of formic, acetic, and trifluoroacetic acids are given in Table II . The carboxyl oxygen bond distance for formic and acetic acid monomer is reported by Karle and Brockway as 1.24 A. , with the hydroxyl oxygen at 1.1+2-1.1+3 A. in the monomer and at I .3 6 A. in the dimer. In the case of the formic acid monomer the bond distan ces have been rein v estig a ted by Schomaker and
Gorman using electron diffraction methods and by Williams using spectro
scopic data. The in v estig a tio n by Schomaker and Gorman i s the b est determination of the carboxyl bond distances in formic acid monomer.
The carboxyl group for the isolated acid is characterized by the 0-0 bonds 1.213 and I .368 A. In thioacetic acid the carbonyl oxygen bond
d istan ces i s reported as 1.21+A. by Gordy. The carboxyl bond distances s’ in trifluoroacetic acid (1.30 A.) are exceptionally long and this
structure should be reinvestigated.
IS TABLE XI
Electron Diffraction Data for Carboxylic Acids.
Acid C-C 0=0 C-0 Z.0-C-0 O-H-O Ref
Formic (mono) 1 .2*1- 1 .U2 1 1 7" 1
Formic (dimer) 1.25 1.36 121 2.73 1
A cetic (mono) 1.5^ 1 . 2*1- i M 117 1
Acetic (dimer) 1.5^ 1.25 1.36 13° 2.76 1
Trifluoroacetic (dimer) 1.^7 1.30 1.30 130 2.76 1
Formic (mono) 1.213 1 . 36s 123.5 2
Formic (mono) 1.225 i.*!-i 125 3 T hioacetic 1.5^ 1. 2** ------125 4
Methyl formate 1.22 1.37 123 a 5 Methyl acetate 1.52 1.22 1.36 125 a 5 Methyl chloroformate 1.19 1.36 125 a 5
References
1. J. Karle a n d ! . 0 . Broclcway, J . Am. Chem. S o c., 66, (19^4)
2. V. 0 . Schomaker and J. M. Gorman, J.Am.Chem.Soc., 69 , 263S ( 19 I+7)
3. Spectroscopic value. V. Z. Williams, J.Chem.Phys., 1^, 232 (19^7)
k. W. J. Gordy, J. Chem. P h y s., lU,560 (19*16)
5. J- M. Gorman, W. Shand Jr. and V. Schomaker, J.Am.Chem.Soc. ,
72, k222 (1950)
(a.) methoxy hond distances were l.*+7, 1.U6, and 1.^7 A. respectively
19 On the 'basis of the covalent single and double bond radii given by-
Pauling^^) t the single bond carbon-oxygen distance is 1.43 A ., whereas the double bond distance is 1.21 A. The double bond distance for the carbonyl group is also reported by Pauling as 1.24 A.(35) which is the value normally observed in the solid state studies of compounds con taining ketonic oxygen.
The electron diffraction results suggest that the structure of the carboxyl group in the isolated molecules is represented by the model
- c/(? S 0 -H ^ O-H + where the carbonyl distance is 1.22 A., the hydroxyl distance is 1.37 A., and the bond angle (O-C-O) equal to 125°.
The crystal structure investigations of the carboxyl group may be
conveniently considered under three classifications: carboxylic acids, earboxylic acid salts, and amino acids.
Por the carboxylic acids whose structures have been determined the pertinent intermolecular and intramolecular bond distances are given in
Table III . It is interesting to note that the structure of only one monocarboxylic acid (lauric acid) has been determined. The crystal
structures of these acids are determined primarily by the hydrogen bonding of carboxyl groups through a proton or by hydronium ions (water molecules).
Prom the data for the carboxyl bond distances given in Table III ,
it would appear that there may be a difference in the oxygen bond distances. Actually in the most reliable structure detex-minations the
two bonds have heen found to be equivalent with C-0 distances of 1.24 A.
to 1.27 A. The differences reported are probably within the experimental 20 TABLE III
Bond D istances fo r C rystallin e Carboxylic Acids : o Acid S.G. C-C c=o C-0 ^.O-C-O O-H-O &
CH -O xalic pcab 1.57 1.22 1.29 Oxalic acid dihydrate 1.46 1.24 P2./a. 1.25 2.50 p -S u ccin ic 1.25 1.30 122* 2.6S ?*i la. 1.51 p -g lu ta r ic la. 1.53 1.23 1.30 122 2. 6s or Iz/A
Adipic P2i/a 1.52 1.2 3 1.29 126 2. 6s 5
Pimelic I2/i 1.44 1.2S 1.38 122 2.69 6
Sebacic 1.51 1.24 1.27 124 2. 6s 7
Acetylene dicarboxylic P *,/*. 1.43 1.27 1 .2 6 2.56 2 .S- S dihydrate 2.9
Diacetylene dicarbox- P^./a, 1.45 1.25 1.25 123.5 9 ylic dihydrate cU. -Laurie /a. 1.17 1.38 2.56 10
dl-Tartaric dihydrate pi 1.44 1 .2 2 1.2S 120 2.72 2 .9 - 11 1.52 1.20 1.33 124 3.1
Tartaric 1.53 1.17 1.20 124 12 1.49 1.21 1.24 123 p-Chlorobenzoic pi 1.50 1.2 2 1.24 2.62 13
21 TABLE III (cont.)
References
1. S. B. Hendricks, Z. Krist., gi, kS (1935)
2. J.O.Dnnitz and J.Monteath Robertson, J.Chem.Soc., 11^5 (19^7)
3. J.D.Morrison and J.Monteath Robertson, J.Ghem.Soc., 9^0 (19*+9)
U. J.D.Morrison and J.Monteath Robertson, J.Ghem. S o c., 1001 (19^9)
5. J.D.Morrison and J.Monteath Robertson, J.Ghem.Soc., 9S7 (19^9)
6. C.H.MacG-illavry, G.Hoogschagen, and F.L.J.Sixma, Rec.Trav.Chim. P a y s., 67, S69 (1 9 ^ )
7. J.D.Morrison and J.Monteath Robertson, J.Chem.Soc., 993 (19^+9)
S. J.O.Dunitz and J.Monteath Robertson, J.Chem.Soc., l^S (19^-7)
9. JLMd. 111*5 (19^7)
10. V.Vand, W.M.Morley, and T.R.Lomer, Acta C ry st., 32k (1951)
11. G-.S.Parry, Acta Cryst., H, 131 (1951)
12. P.Stem and C.A.Beevers, Acta Cryst. 3» 3^1 (1950)
13. J.Toussaint, Acta Cryst. 71 (1951)
22 error of the structure determinations. In the case of oxalic acid dihydrate, the earlier structure determinations gave hond distances of
1.2U A. and 1.30 A. for the carboxyl "bonds; however, further refinements have shown that the "bonds are equivalent within the experimental error of the determination.
The reported bond angles for the carboxyl group vary from l l 6° to
12^° for the 0- 0=0 bond angle compared to 117° 22' predicted, and the
0=0-0 angle varies from 120° to 126° compared to 125° 1 7 * predicted.
The bond angles are within the experimental error equal to the predicted values.
The bond distance data for the salts of the carboxylic acids are
given in Table 17 . The carboxylic salt structural reports have been
restricted primarily to the salts of formic and oxalic acids. For these
salts the average bond distance is 1.26 A. for the carbonyl oxygen and
1.22 A. for the hydroxyl oxygen. The results in the case of the more
careful studies indicate that the carboxyl bonds are equivalent with the
0-0 distances 1.25 £ 0.01 A.
The carboxyl bond distan ces for the amino acids are summarized in
Table V . For the amino acids the average carbonyl bond distance is
1.22±0.02 A., and for the hydroxyl-oxygen 1.22 * 0.02 A. In the
£ -threonine structure determination considerable care was used in the
accumulation of an accurate and precise set of self-consistent structure
factors and in this compound the carboxyl bond distances were equivalent
with the bond distances 1.2^ — 1.25 A.
23 EABLI IY
Bond Distances for Crystalline Carboxylic Acid Salts Space Salt Group C-C 0=0 C-0 ^ o -c -o Ref
Gd(HCOO) 3 E5n 1.27 1.33 . 1
Ha(ECOO) 1 .2 7 1 .2 7 124* 2
Sr(ECOO) g" (HCOO) j 1 .2 6 1.25 126 3
(HGOO)jj 1 .2 5 1.25 127 ! Ca(HD00 ) 2 p cab 1.2 4 1.25 124 4
Ba(HCOO) 2 1.24 1 .2 6 5 p P'b(HCOO) g 1.24 1 .2 6 5 • m 8 o
ro* 1.60 l . l 4
ro 0 -zic 1.30 6 kh( coo) 2 EXl/c. 1.59 1.30 1 .3 2 6
(HHi^ 2(C00)2 • Pa, a,a, 1.5S 1.25 1 .2 3 129 7
Ea((/02) ( CH3COO) 3 1 .6 2 1.30 1.32 s
Ba(Ca) 2 (C2H5C00)g 1.24 1.24 9
Kfc^CgOij) 2 ^ 2^ 21 * 3HgO 1.39 1 . 2s 1.30 125 10
1.19 1.3 2 125 aiESTa fCOOCHOHCHDHCOOj • 4 E^Q P i 1.5S 1 . 2s 1 . 2s 125 11
1.5S 1 .2 9 1.19 124 CABLE 17 (co n t.)
References
1. A. PaLst, J. Chem. Phys., 11, 1^5 (19^3)
2. W. H. Zacharisen, Phys. Rev., ££, 917 (±938)
3. I. Uitta and Y. Saito, X-Sen (X-Rays), jj, S9 (19^9)
k. I. llitta and X. Osaki, X-Sen (X-Rays), 37 (19^8)
5. T. Sugav/ara, M. Kakudo, Y. S a ito , and I . ITitta, X-Sen (X-Rays^, 6 , 85 (1951)
6. S. B. Hendricks, Z. K rist., Agl, kZ (1935)
7. S. B. Hendricks and M. 1 . Jefferson, J. Chem. Phys., 102 (1936)
8 . I. Fankucken, Z. Krist., Agl, ^73 (1935)
9. L. P. Biefeld and P. M. Harris, J. Am. Chem. Soc., 57, 396 (1935)
10. J. H.. van Elekerk and P. R. L. Schoening, Acta. Cryst., 35 (1951)
11. R. Sadanaga, Acta. Cryst., 3. ^16 (1950) SABH V
Carhosyl Bond Distances for Crystalline Amino Acids
Amino Acid Space C-C 0=0 C-0 / o-C -0 Ref. Group
cL Glycine fa. 1.52 1.25 1.27 122 1
ct-JL Alanine Pna 1.54 1.23 1.25 125 2
f t - Glycylglycine A* A. 1.53 1.21 1.27 124.5 3 (Hi)Glycine Dihydrate P*/c 1.50 1.25 1.29 122 4 Cysteylglycine - Hal A^ 1.59 1.23 1.28 126 5
H - Acetylglycine P.,/c 1.51 1.19 1.31 124 6
JL - Threonine 1.52 1 . 22+ 1.25 127 7
IL - Hydrosyproline 1.52 1.18 1.29 129 8
J & - Alanine ^na 1.54 1 .2 1 1.27 125 9 EABLE V
References (Amino Acids) ,
1. G. A. Albrecht and R. B. Corey, J. Am. Chem. Soc., 6l, 1087 (1939)
2. H. A. le v y and R. B. Corey, J. Am. Chem. Soc., 63 , 2095 (19^1)
3. E. \I. Hughes and W. J. Moore, J. Am. Chem. Soc., 71. 26lS (19^9) 1
K A. J. Stosick, J.Am. Chem. Soc., 67, 36 5 ( I 9 U5 )
5. H. B. Dyer, Acta. Cryst., k, k2 (1951)
6. G. B. Carpenter and J. Donohue, J. Am. Chem. S oc., 72, 2315 (1950)
7. D. P. Shoemaker, J. Donohue, ?. Schomaker, and R. B. Corey, J. Am. Chem. Soc. J2, 232S (1950)
8. J. Zussman, Acta. Cryst., **-93 (1951)
9. J. Donohue, J. Am. Chem. Soc., 72, 9^9 (1950) In the determination of the reliability of a particular crystal structure considerable emphasis has been placed by various individuals on the value of "reliability index," R, namely:
ST )l Fojtc.}~)F&*/c. I ) R - - ~ohs. where F ^ is the observed- structure factor, F ^ is the calculated structure fa c to r , and the summation i s made over the observed r e fle c tio n s in some cases, and in others over the observable reciprocal space. This cri terion places undue emphasis upon the agreement between calculated and observed structure factors. Too frequently the question of the accuracy of the observed data is completely negLeeted. Considering the diffi culties in obtaining structure factors to 20$, the reporting of reliability indices of 15$ and less for the final structure in many instances raises the question of the significance of the bond errors estimated by conventional methods. The model structure may represent the observed data very precisely but it may not represent the "true" bond distances to the accuracy frequently reported.
Considering each structure determination as a single determination of the bond distance in the carboxyl ion, the average carbon-oxygen distan ce was computed for the various groups o f compounds. For the carboxylic acids this distance was 1.253 - 0.013 A., for the acid salts 1.25S “£ 0.018 A., and for the amino acids 1.250 +• 0.008 A.
These results suggest that for a model of the carboxyl group the bond distances may be adequately represented by the model in which the oxygens are equivalent with the bond distance 1.25 — 0.01 A. , and the
0- 0-0 angle 125° 171. 28 2. Trichloro-G-roup. In considering the trichloromethyl group two questions arise with regard to the postulation of a model for the tri- chloroacetate group. The first is the question of the length of the carbon-chlorine bond and the second the orientation of the trichloro group r e la tiv e to the carboxyl group.
Eumerous electron diffraction results have been reported for the carbon-chlorine bond length in various types o f compounds. The in ter atomic distances obtained prior to September, 19*49» from electron diffraction studies of various compounds in the gas phase have been
summarized by A llen and S u t t o n . (36) With the aid of this tabulation the average carbon-chlorine bond length observed in different intrar- molecular environments has been computed. For chlorine atoms substi tuted on saturated hydrocarbons the average carbon-chlorine bond distance was 1.766 £ 0.010 A., the average for 29 determinations. For chlorines attached to an ethylene group (13 determinations), and to a benzene ring (S> determinations) , the average bond distances were the same, namely: 1.70 £ 0.0,2 A. A recent determination of the structure of chloroacetylene by Westenberg, Goldstein, and Wilson, Jr.(37) provides the value 1 .6 3 2 j£ 0.001 A. for the carbon-chlorine distance in the presence of a triple bond. In the case of the fluorochloro- methanes and methyl fluorochloromethanes, the average for seven determinations of the carbon-chlorine distance was 1.75 i 0.0 2 A.
The average bond length for chlorine in the acid chloride group was
1.71 - 0.02 A. (3 determinations).
29 In considering the above data it is of interest to note some of
the results obtained from the microwave investigations of methyl
chloride and chloroform. Gordy, Simmons, and Smith^^) have reported
that the carbon-chlorine bond length in methyl chloride is 1.779 A.
Smith and Untenberger^39) have reported that for chloroform the carbon-
chlorine distance is 1.75 2- 0 .02 A. They suggest th a t, though the
above values are within esperimental error, the carbon-chlorine bond
distance may actually decrease when more than one chlorine is attached
to a carbon atom. On the other hand, Hastings and Bauer^^ in aa
electron d iffra ctio n stxtdy o f neopentyl chloride (CHj^CCHgCl and
silico-neopentyl chloride (CH^^SiC^Cl report the carbon-chlorine bond
lengths as 1.7^ £ 0.03 and 1.73 ■£ 0.03 A. resp ectiv ely .
A partial summary of the crystal structure results on the carbon-
chlorine bond distances is given in Table YI . The mean reported bond
distance for the monochloro substituted conpounds is 1.78 2" 0.02 A.
The bond distance for octachlorocyclobutane where there are two chlorines per carbon is 1.7^ 0.01 A., the average of 5 observed values. For
this compound the average bond distance before correcting for the
termination of series errors was 1.77 ^ O.OU A. In the case of the
other chloro compounds the errors due to series termination were care
fully considered only in the case of b amino- 2 , 6 , dichloro pyrimidine
in which the average carbon-chlorine distance was 1.7&3 ~ 0.006 A. This
difference in the lengths of the carbon-chlorine bond with the number of
chlorines attached may be significant.
\
30 CABLE 71
X-Ray Diffraction Carbon-Chlorine Bond Distances Space Compound Group C-Cl 01-01 C1---C1 Rej
2 2‘ cLichloro"benzidine mClCgH-jDHg g Pnea 1.72 3.36 3.27 1 ------P-chloro iodoxy benzene PCl-CgHtyJOg Pa./e. 1.S0 3.75 2 Octo chlorocyclobutane CijClg 1.7^ 2 . S3 3
3 .3 8
3.10
C6H5015 1.S2 3.2** 3.55 b Tetrachlo ro cyclohexane C gHgClij. P 2.1(2, 1.79 5
2 amino 1* methyl 6 chloro pyrimidine P*./«S 1.76 2 amino U, 6 dichloro pyrimidine PA(/tfL 1.78 3 .bb- 6 1.79 3.85
4 amino 2 , 6 dichloro pyrimidine P^./4 1.757 3.1*7- 7 1.770 3.78 (TABLE 71 (con t.)
References
1. D. L. Smare, Acta. C ryst., 1, 150 (I 9 US)
2. E. M. Archer, iM d., 1, 0+ (19^3)
3. T. B. Owens and J. I. Hoard, iM d., k, 172 (1951)
k. R. A. Pasternak, iM d., 316 (1951)
5. 0 . Hassel and 1. W. Lund, ih i d ., 2, 309 (19^9)
6. C. J. Clews and ¥. Cochran, ihid., 1, k (19^g)
7. Ihid.', 2, 1^6 (19^9) It is interesting to note that in HClTC^f HCF 2CI, and OPgClg
C-01 distance is reported as 1.73 “ 1.7^ A. Pauling^2) has suggested that in the fluoroehloromethanes the "bond shortening from I .77 A, i s a result of the C-Cl "bond developing partial double bond character in the presence of the strongly electronegative fluorine. The resonance hybrid postulated was _ X~
1 tt where X is a halogen atom. For the trichloroacetate ion it would appear that the carbon-chlorine bonds have appreciable ionic character. This is indicated by the production of chloride ions during its decomposition in solution; the fact that in attempting to prepare the mercurous salt mercurous chloride is precipitated. The silver salt may be prepared but it readily undergoes an explosive decomposition when heated. In ad dition, the acid readily reacts with copper in water or benzene solution to form a compound which on acidification with HOI forms dichloroacetic acid and cuprous chloride quantitatively. Thus the carbon-chlorine bond distance may be significantly shortened by an effect such as re ported fo r the fluoro compounds.
In considering a possible model for the trichloroacetate ion the question of the orientation of the carboxyl group with respect to the trichloromethyl group arises. The spectroscopic studies of the acid and its derivatives have not been sufficiently complete to define its con figuration. In the electron diffraction study of trifluoroacetic acid^3) the model with the carbon-fluorine hond oriented at 15° with respect to the carboxyl plane gave the hest fit for calculated and observed scat tering curves. The other models in which the trifluoromethyl rotated freely or vibrated with large amplitudes resulted in scattering curves which were almost identical to the 15° model and no d e fin ite conclusion could be made. From a consideration of the van der Waal radii of the chlorines and oxygen in the anion, the model in which the carboxyl plane is rotated at an angle of 30° to the carbon-chloride bond is postulated.
3. Postulated Model of the Trichloroacetate Ion. For the crystal structure study of lithium trichloroacetate monohydrate the following trial model for the structure of the anion was considered. The carboxyl group is represented by the resonating ion structure in which the carbon- oxygen distance is 1.25 A. and the 0 C 0 angle is 125°. For the carbon-carbon bond distance the value of 1.51 A. is suggested by the observed distances for the carboxylic acids. The trichloromethyl group was considered as tetrahedral with the chlorines at 1.7^ A. as observed in Oi^Clg, and the carboxyl plane at 30° to a carbon-chlorine bond. The proposed model is shown in Fig. 1 . The effective length of the mole cule, assuming van der Vfaal radii of 1. SO A. for the chlorines and l.Ho A. for the oxygens, was 5*9 A. The slightly shorter distance of
5.6 A. corresponds to the packing of the molecules chlorine to oxygen with one carboxyl oxygen nested in the trichloro group base. For the trichloro group the maximum packing dimension as shown in Fig. 1 is
6.^ A. (Cl-^ - 01^). The packing dimension normal to the (Cli - CI 3) — *-
~ T <
... j — Pos tu fsuf&cL Mode! for the CC/jCO O Anion 35 group and in the trichloro plane is 6.1 A ., which is reduced to 5.6 A. for close packing of the trichloro groups (OI 2 of another molecule nested "between Clj_ and CI3 as indicated in Pig. _i ). In the model the intramolecular distances are as follows: 0 ------C2 = 1.25 A. 0 1------C2 I 1.51 A. 01------Ox = 1.7^ A. 01------o2 = 2 . 6 6 A. 01 01 3 2 .gk a . Clx Ox - CI 3—0 2 ~ 3.06 A. ci2— ox = ci2—o2 i 3.4 o a. 0 I 3 Ox 3 C l x ~ 0 2 I I4-.09 A. 36 IV. EXPERIMENTAL SEOTION (The discussion of the experimental -work performed in the study of the crystal structure of lithium trichloroacetate monohydrate may he conveniently considered in six sections, namely: crystal growth, chemical analysis, lattice constant determination, space group determination, intensity estimation, and the calculation of structure factors from the observed intensity data. A. Crystal Growth. The crystals of lithium trichloroacetate mono hydrate were prepared by the slow evaporation of water from a saturated solution containing excess trichloroacetic acid. The salt was prepared by the reaction of reagent grade, Coleman and Bell Co., trichloroacetic a c id w ith C. P. Baker and Adamson lith iu m carbonate; u sin g as sm all a volume-of water as possible. The excess trichloroacetic acid was used to eliminate the possibility of the formation of lithium carbonate crystals as a result of the decarboxylation reaction of the trichloro acetate ion. The solubility of the lithium trichloroacetate monohydrate in water is quite high. The saturated solution at room temperature has a syrupy consistency. The crystals form as very deliquescent mono clinic plates exhibiting the forms (100), (001), and (110). The ex terna! form of the crystal is very dependent upon the growth rate. At high growth velocities needles elongated in the "c" direction with a very small "a" dimension are formed; but at slow growth rates approximately equal development of crystals in all three dimensions is obtained. At no time were forms other than (100) , (001) , and (110) 37 o b s e r v e d ; however, numerous specimens exhibited only the ( 100) , (001), (110), and (110) faces. In general, the surface areas of the faces are in the order ( 100) la r g e s t, ( 110) and ( 110) equal, ( 110) and ( 110) equal, and the (OOl) smallest. The crystals are usually veiled and rather soft. The crystals formed at high growth rates exhibit a fibrous character suggesting cleavage planes parallel to the ( 100) and (010) planes. The presence of definite cleavage planes could not readily be established because of the veiling and deliquescent character of the crystals. The small crystals (*' 0.5 mm) are converted to a drop of saturated liquor by just exhaling near them. This characteristic of the compound was a constant source of difficulty in the experimental work. The a:b axial ratio computed from goniometer data is 3.865:1.000, which is in good agreement with the values, ajbsc s 3.856:1:1.6S15» computed from the la t t ic e constants. The goniom etric in ter a x ia l angle (a to c) is 107° 27. 5 * t 6 «. On the basis of the crystalline forms observed it was initially assumed that the crystals belonged to the monoclinic holohedral class 2/m. Later it was found that the true symmetry is mono clinic hemi- hedral - Cs Z m, and the c ry sta ls do not have a center o f symmetry. This ivas also suggested by the differing growth rates of (110) and (IlO), but which had been interpreted as being related to the tabular habit of the crystals. 38 The density of the crystals was determined hy the pycnometer method, using carbon tetrachloride as the immersion liquid. The volume of the pycnometer was determined with water at 29° 0. The weight of the pycnometer containing CClij., and CGl^ plus a known weight of the salt was determined. From this data the density of the salt at 29° C. was calculated as 1.3575 g/cm^. The crystals which were used in this determination were appreciably veiled and had a moist surface due to the deliquescence of the compound. B. Ohemical Composition. In order to determine the composition of the crystals, the loss in weight on drying at 100° C. and the percentage lithium were determined. The samples were first partially desiccated over P 2O5 then heated to constant weight at 100° C. The residue was analyzed gravimetrically for lithium by repeated evaporation with concentrated sulfuric acid to convert the lithium to lithium sulfate which was then weighed. For this analytical work it was not readily possible to obtain crystals completely free of the mother liquor. The anals’-tical results presented in Table VII indicate that the crystals may best be described as lithium trichloroacetate monohydrate. Assuming that the compound is actually the monohydrate, the water analyses indicate the presence of 2.04- percent excess water on and in the crystals. The percentage lithium for the anhydrous acid was k.Okffi as compared to ty-.09S$ calcu lated , a d ifferen ce o f 0.051$. Though the difference is within the experimental error of the determination, 39 TABLE VII Chemical Analyses of HOOCCCI 3 • HgO Sample 1 2 Ave. J6 H^O (kS h r. over P 20 5) 7 . 06$ 6.19$ 6. 62$ $> HgO (100° C. toy) 1 1. Ug 11.23 11.65 $ l i (O riginal Sample) 3.52^ 3.560 3.572 $ Li (Dried Sample) U.O52 ^.0^3 I4-.0I+7 56 L i (LiOOCCC^) 4-. 092 $ $ Li (1.0 H20) 3.70H $ L i (1 .5 HgO) 3.53k $ Li (2.0 H^) 3.379 $ H^O (1 . 0 H2O) 9.61 $ $ HgO 1 ( . 5 HgO) 13.76 $ H^O (2 .0 H20 ) 15.59 40 several factors which, would contribute to lowering the experimental value for percent lithium are as follows: (l) incomplete dehydration of the salt at 100° 0 . , ( 2) occlusion of mother liquor containing excess trichloroacetic acid, and ( 3) the possible loss of lithium by spattering during the ignition of the anhydrous salt with sulfuric acid. It is of interest to note that the crystals, after dehydration, were pseudomorphs of the original crystals. 0. Lattice Constants. The lattice constants for the crystals were determined from single crystal rotation photographs around three crystal- lographic axes. The film holder for the 57.3 radius rotating crystal camera used in th is work has a p a ir of h o les d r ille d in the base at 90 ° and 270° so that during an exposure fid u c ia l marks are produced on the film edge by the diffuse scattered radiation. The measurement of the distance between the marks provides a means for the accurate calculation of the camera radius for each film. Using the values 1.54l8 A. and 0.7107 A. for the CuK^ and MoK^ wavelengths respectively, the calculated lattice constants are as follows: a 0 ■ 22.605 ± 0.026 A. b0 I 5.594 ± 0.004 A. c0 = 1 0 .SO ± 0.02 A. p = 1070 27. 5 « X 6 ' X - 1 ,302.7 a3 z 0.07151 C 1 0.2756 <£ z 0.1497 f = 720 3 2 .5 ’ 4 i Since there were no systematic variations in the lattice constant with the layer line number, all layer lines were given a weight of unity in the lattice constant computation. Using the data on the volume of the unit cell and the density ( 1.8575 g/cm3) , the calculated number of molecules per unit cell was 7.7S. Thus there are eight molecules of LiOOCCCl^ • H20 in the unit cell and the calculated density is 1.9101 g/cm3. If it is assumed that the crystals used for the density determination contained 2. 0$ water in excess of the stoichiometric amount as observed in the chemical analysis, then the corrected experimental density is 1.910 g/cm^. The latter is in very good agreement with the value calculated for eight molecules of the monohydrate per unit cell. P. Space Group. In general the possible space groups for a compound are determined by the extinction rules obeyed by the observed reflections. Where more than one space group is possible a choice must be made by the use of supplementary information. For the indexing of reflections on the rotation photographs about each axis, sets of 15° oscillation photographs with 3° overlap for 180° angles were prepared. The ]f and ^ coordinates for the spots appearing in the oscillation photographs were determined by using a Bernal chart for a 57*3 111311 radius camera. Eeciprocal lattice nets were prepared for the a-—b*, b-—c*, and a-— c* planes; and the (hkl) indices were assigned to the spots observed on the oscillation photographs using h2 the graphical method described "by B ernal.^ Unfortunately, due to the l|l short a vector, the indices for numerous reflections appearing in the b and c axis photographs could not be definitely assigned. In addition, the crystal size (^ 0 . 5 nun) used for the rotation photographs -was too large and the spot shape indicated that absorption v/as appreciably affecting the intensities. In the rotation photographs there was con siderable overlapping of reflections, thus making accurate intensity determinations difficult. This may be illustrated by the fact that in the "b" axis rotation photograph the (? 02 ) , (U0 0 ) , and ( 0 0 2 ) form one elongated spot; and the (S 0 2 ) , ( 2 0 ^), (800) , (^ 0 *+), ( 6 0 2 ) , and ( 0 0 ^) form a second strong spot. To overcome these difficulties the following series of Ueissenberg equi-inclination photographs were prepared by using DuPont Type 50S film : (hOl) , ( h ll) , (h21) , (hkO) , (hid) , (hk 2 ) , (hk3) , (hk^) , and (hk5). The Weissenberg equi-inclination photographs were indexed by using the reciprocal lattice projection net method described by Buerger.Prom the indexing of the photographs the following extinction rules were ob tained: (hkl) observed only if (h-*- k) - 2 n (hOl) observed only if h = 2n and 1 s 2n. The extinction law (h f k) - 2n implies that the Bravais lattice is c-centered; and the hOl extinction 1 = 2n implies the presence of a c-gLide plane. Thus the space group is either noncentrosymmetric O5 - Cc or centrosymmetric Pk - 0*/c • Since well-formed crystals exhibiting holohedral symmetry were observed and there were eight molecules per u n it c e ll compared to eight equivalent p o sitio n s in 0%/ and only four in Cc, i t was i n i t i a l l y assumed th at the space group was Ci - ° m >- The symmetry elements ch a ra cteristic o f th ese two space groups (Cc and 0 ^ ) are shown in Fig. 2 . Equivalent points for the space groups are as follows: c iw ~ C*/c C l ~ C x y' z ) ^ 2 0 tx .y,* ) (JC}Y, H) , (''*-*• 2 -> Cxy fyyfir*) , C'*--*> Vi+>0 Vir^ 0/x-t*,'/a+y,?) C *,?,*+*) ((*+*> fe-y,vfc+s) The form of the geometrical structure factor equations for the two space groups^^ are given below. In the expressions F is the structure factor; fi the scattering factor for the i th atom; Ai and Bi the phase contribution fo r the ith atom o f the asymmetric u n it and the summation is for the asymmetric unit of structure with the parametric coordinates (*!» y^» 23) • th® centrosymmetric space group C*H - C?/c the expressions are F= 2: f; A; / where for 1 : 2 n and (h +- k) - 2n A; - # CoS* ft (hy;+4b; ) ccs*.7T ky; fane.) ■** ^Ck ksl) = _ FCh kV and for 1 : 2n + 1 and (h + k) Z 2n A) - ~ S s/rr 1 (hx; +£&;) slu'xTThy F(* k£.)~ ~ FCWk.Ji') ^ ' F(u w£.) Group Symnte For the noncentro symmetric space group cjf - Cc the expressions are: I f W ’ t where fo r 1 = 2n and (h + k) - 2n c Ai = V c&s zTT (hXt + £*;)cos zvkyy B i - V S,* *n CKX!+*l;) CovxT'Ky; — ^ C 5 k7 ) - -^ c k k ? ) = ~oiChke) ^ of(hK') and for 1 “ 2n t 1 and (h ■+- k) Z 2n Ai - — HSiH £Ti SfM».rrky; Bl - ^ Cos air ( K>C/+•?«;) S»* = ~ 7r+ ~ "-0< fkRlJ ~ ,,*’*C'*Tix) ^ In the Fourier synthesis of a crystal structure on the "basis of the observed structure factors it is necessary to know the phase angle for each term, namely: ^ hJe. = In the centrosymmetric case the phase angle is 0 or IT and cos a$kk4J =. ±. / and the Fourier re finement of a structure is primarily dependent upon the observed data. In the noncentro symmetric Fourier series the terms ~ ^ CoS ^Chk«) ~ ^ ^Cwk*)! -S'* ^CKK*; appear as coefficients. Thus, for the noncentrosymmetric case, the Fourier refinement process is dependent upon the assumed atomic co ordinates and upon the assumed atomic scattering factors for the atoms. The form of the Fourier synthesis of the electron density function will markedly depend upon assumed coordinates and the convergence of this series will tend to be slow. U6 Initially it was assumed that the correct space group was with the eight m olecules in general p o sitio n s. A fter numerous calcu lations for models which satisfied the Patterson interatomic vector maps it was concluded that no arrangement in C*/* , which was compatible with the Patterson maps and the (hOl) structure factors, would simultaneously satisfy the requirements imposed "by the general (hkl) reflections. It was therefor concluded that the correct space group was noncentrosym metric C* - Cc. This conclusion was then substantiated in several ways. The f i r s t confirmation o f the noncentro symmetry m s obtained throuth the use of the pyroelectric tests given by Bunn.(^7) Crystals without a center of symmetry, when cooled or warmed, develop oppositely charged faces. Several crystal were placed in a silver spoon which was then cooled with liquid air. When the cooled spoon was inverted, the crystals momentarily adhered to the spoon, indicating that the crystals were pyroelectric. In another experiment two crystals suspended by silk threads were cooled with liquid air. While warming to room temperature the crystals exhibited a marked tendency to adhere to each other. The pyroelectric tests thus indicated that the crystals do not have a cen ter o f symmetry and the cry sta l c la ss i s m and the correct space group is Cc. In passing it is of interest to note that the crystal growth data a c tu a lly suggests that the symmetry i s m i f the small area o f (110) compared to (110) i s considered as being due to symmetry rather than growth conditions. A further te s t o f the symmetry of the c ry sta ls i s obtained by con sidering the statistical distribution of the intensity data. The procedure involves the division of the intensity data into several **7 equal groups as a function of sin© . For each group the average value of the in te n sity i s computed and the fra ctio n X " or i f a center o f symmetry i s present ‘fay where erf i s th e error fu nction. An a ltern a tiv e procedure i s to compute the Wilson ratio ^9) 11 g" which is e - where F is the absolute value of the structure factor, I the squared structure factor, and the symbol< > representing the average value of the enclosed function. This ratio should be 0.785 for noncentrosymmetric structures and 0.637 for centrosymmetric structures. For the (hOl), (hkO), (Hll), and (h21) reflections the Yftlson ratios .were 0.635 *■ 0 .017, O.63I t 0.009, 0.435 * 0 . 01 5 , and 0.4l4± 0.015, respectively, using the sin© ranges 0.3-0.5, 0.4-0.6, O. 5-O.7 . The corresponding intensity distribution curves are shown in Fig. 3 « Rodgers and Stanley^50) have reported that experimental errors ( up to 30$) in the intensities have very little effect on the distribution curves. In addition, departures of experimental curves from one or the O hot □ h U & h & t 1 F„.JL 'Structure factor Distribution 1*9 other of the theoretical curves indicate either gross errors or the presence o f pseudo symmetry in the structure. Thus, though the (hOl) and (hkQ) Wilson ratios would suggest the presence of a center of symmetry, the distribution curves indicate that the intensities do not follow a normal distribution and the statistical ratio test is not a significant te s t for the determ ination o f the presence o f a center o f symmetry. I t is interesting to note that the shape of the curves between 10 and 50 percent are very similar to the distribution for the noncentrosymmetric case. The differences between the centro symmetric and noncentro symmetric distribution curves are most marked between zero and fifty percent . E. Structure Factors. The determination of the experimental structure factors for the observed reflections may be considered as a four step process. The first step is the estimation of an integrated intensity for a reflection; second, the correction of the value for the polar ization and Lorentz factors; third, correcting for the effect of absorp tion; and finally, the calculation of a set of absolute structure factors. Intensity Estimation. In the determination of the structure factor from observed intensities it is necessary to determine the integrated intensity for the reflection. Thus the integrated intensity to be assigned to a given reflection is dependent upon the total black ening of the spot as well as the area of the spot. For the structure factor determination equi-inclination Weissenberg photographs about the "b" and "c11 axes were prepared by using the multiple film technique. (5^) In this method the range of intensities which may he recorded in a single exposure is extended hy using several layers of film in the camera, the intensity of a reflection heing reduced hy a constant amount hy each successive layer of film. For the determination of the relative blackening of the spots a tr ip le film standard blackening sca le was prepared on DuPont type 50S film . This sca le con sisted o f a row of M-2 uniform circular spots corresponding to exposure times ranging from eight seconds to twelve minutes. Assigning the twelve minute spot a value of 100, the other spots were assigned a fractional value of 100 based on the relative exposure time. The faintest spot (S sec.) was barely perceptible to the eye while the strongest spot corresponded to almost 100$ blacken ing. The scale proceeded by unit intervals in the range 1 to 20, by units of two in the range from 20 to Ho, units of four in the range Ho to 75» ^d by units of five in the range 75 to 100. Using the scale, the blackenings of all the reflections appearing on the triple film sets of Weissenberg photographs were determined, and the average intensity reduction factor for each set of films computed. The reciprocal reduction fa c to r s, summarized in Table 71II , show that the scale factor may vary from film set to film set. All of the re duction factors calculated were reproducible to at least 3$. ®be factors listed in column 1+ for the hil sets correspond to a determina tion made approximately three months after the first sets of data were obtained. The relative blackenings determined on the second and third films were converted to corresponding values for the first film by 51 iEARLE VIII Multiple Film Intensity Reduction Factors Film Set I l / I 2 12/13 i i / i j i j / i 2 bOJ! 2 .0 7 2.06 If. 26 2.01 b U 2.0 7 2.06 ^ .26 2.06 h2JL 2.07 2.06 ij-,26 2 . 0^ hkO 1 . 8 H 1.83 3.37 hkl 2. 0^ 2.03 U.lH hk:2 2. 0U 2. 01+ U.1 6 hk3 2.05 2.05 U.20 2.00 2.00 U.00 hk5 2.20 2.1S H.so (b) determined three months after first s e t. 52 using the tabulated factors. For the reflections whose intensities could he estimated on all three films the relative blackenings referred to the first film did not differ hy more than 10$. The deviations for reflections with blackening greater than. 100 were from 12 to 15$; fo r those in the range 10 to 100, the average deviation m s from 5 to 10$; and for those below 10 it was 10 to 50$ . To estimate the area factor for the reflections, the assumption was made that the area for the ellipsoidal shaped spots was proportional to the product of the length and breadth of the spots as measured with a spectroscopic plate contact hand magnifier. The estimation of this factor was quite important since the relative areas of the spots varied in some cases by a factor of 2 to 3 times. The accuracy of the relative integrated intensities was determined by the accuracy of the measurement of the area factor correction. In the preparation of the photographs it was observed that the equi-inclination rotation axis did not coincide with the intersection of the axis of rotation of the goniometer head and the pinhole system. Consequently in the (hil) photographs the crystal position, with respect to the incident beam, varied with the layer line. This effect was cor rected in the hki photograph series. Thus the problem of obtaining a set of relative intensities was resolved into the determination of the blackening of the spots, the estimation of the area of the spots, and the determination of conversion factors to place the structure factors from different films on the same relative scale. A self-consistent set of data was finally obtained by applying the condition that the relative squared structure factors appearing on two different sets of films (hil) and (hki) should he linearly related. The final sets of data used in the comparisons were weighted according to the reliability of the area factor determination. Actually it was found rather difficult to make objective measurements of the area and the blackening; however, after considerable practice a set of relative struc ture factors, which were self-consistent, was determined. The data for the hki series of films was found to be self-consistent but for the bn films referred to the hki films the conversion factors for the squared structure factors were 2.00 for (hOl), 3.2 for (hll) , and 1+.2 for (h21) . From the graphs relating the structure factors estimated on the two different film sets (hil) and (hki) it was possible to estimate the degree of self-consistency. For the strong reflections the discrepancy between the two sets of squared structure factors was no greater than 25$ and for the majority of the data was less than 15$. In the case of the weak reflections with structure factors between 5 and 10, the dis crepancy in F^ was less than 30$ and for the majority of the reflections was less than 20$. In the case of the weak reflections with structure factors less than 5.0, the discrepancy in F^ was as large as 50$ Intensity Correction Factors. For the calculation of a set of relative structure factors from the integrated intensities it is neces sary to apply certain correction factors which depend upon the geometry of the experimental method used to obtain the data. For Weisseriberg equi-inclination photographs the integrated intensity is related to the crystal structure factor by the expression IH oC (P) (L) (A) J3PH| 2 or Xrr cl [ i-tCo*T-ze) ( — j— — ) (A) IFhI*~ H ot L i; } \ Ct. sys In the expressions & is the Bragg scattering angle, the equi- inclination angle, and the off-axis angle for the reflection H. For LiOQCCCl-j • HgO the Lorentz and polarization correction factors for the Weissenberg equi-inclination photographs were calculated using the nomographic method described in Appendix 1 , In conjunction with this computation a nomographic method was used to calculate sin© and the atomic scattering factors for the observed reflections. The effect of the absorption of x-rays on the intensity of a diffracted ray is to diminish the intensities of reflections at small angles much more than those for the back reflection region. For lithium trichloroacetate monohydrate the linear absorption coefficient for copper OuE ^ radiation is 119.0 em“^ calculated using the Internationale Tabellen data for the mass absorption coefficients of 01, C, 0, Li, and H. (52) In the in itial set of photographs which were prepared the crystal size ms approximately a 0.5 x 0.3 s 0.2 mm and the diffraction spots exhibited an irregular form corresponding to appreciable absorption by the crystal. Consequently the Weissenberg photographs were prepared using as small crystals as could be mounted with the available equipment. The reflections appearing on these photographs did not exhibit any 55 absorption effects. Using Albrecht's method of absorption, correction^53) i t was computed that fo r these samples the maximum deviation due to absorption should be less than 30$. In addition, the self-consistency of the final integrated intensities as estimated on the (hil) and (hki) photographs indicated that the absorption error due to the crystal geometry could not be very large for the two different crystals which were used. The crystals were both approximately the same size (^ 0.15 mm), but had different geometries for the different axes. Another factor affecting the observed intensities is the reduction of the intensities of strong reflection by extinctions. The extinction correction may be divided into two factors; primary and secondary extinction. ^5^) in primary extinction the lower layers of the crystal are screened from the radiation at angles at which they would normally reflect, because of the reflection from the upper layers of the same crystal. In secondary extinction a certain fraction of the incident radiation is reflected at each layer in the crystal. From this dif fracted ray another fraction is, by a second reflection, reflected back into direction of the incident beam; and there is an energy interchange between the incident and diffracted radiation. Since it is rather difficult to apply corrections for these effects, the usual procedure in structure determinations is to estimate the intensities of the strong- reflections on powder photographs where extinction is considerably re duced because of the small crystal size. In the case of LiOOCCCl^ * HgO this could not be done because of the extensive overlapping of re flections even in the small glancing angle region. Thus the structure factors for the strong reflections could he low if appreciable extinction was present. The structure factor data for the observed (hki) reflections are presented in Appendix 2 . This data was not corrected for absorption but was placed on an absolute basis using the procedure discussed in the following sections relating to the (hOl) structure factors. The three dimensional Patterson interatomic vector map was computed using th is data. (hOl) Structure Factors. In the very early stages of the struc tural work it became evident that the (hOl) zone should provide good resolution of the atoms. Por the other projections it was evident that Pourier refinement of a model would be impractical due to overlapping of the atoms. Consequently an effort was made to obtain a complete set of self-consistent (hOl) structure factors. These were derived from three sources: the (hOl) and (hki) equi-inclination Weissenberg photo graphs; and, for weak reflections not appearing on the Weissenbergs, from the "b" axis oscillation for which a larger crystal had been used. The structure factors calculated from the oscillation data were placed on the Weissenberg film scale by calculating the average conversion factor for three to six spots which appeared at approximately the same sin£ and which were not very intense. The relative structure factors obtained are given as 3P^ and P^, the latter value is the P divided by the average atomic scattering factor. An approximate absorption correction was applied to this data. Por the (hOl) Weissenberg photographs a crystal, which could he approxi mated hy a cylinder with a diameter o f 0.017 cm or a radius of 0.002 cm, was used. The absorption factor, A, for a cylindrical rod with a radius, r, and an absorption coefficient, A* , is given in the Inter nationale T abellen^5) as a function of ( A‘IM and the Bragg reflection angle O . The absorption factor "A" is the ratio of transmitted in tensity with absorption to that for no absorption. This factor for Z 0.002 x 119.0 - 0.952 was used to correct the complete set of (hOl) data. The values o f A as a function o f sin & are given in Table IX ., and the absorption corrected (hOl) structure factors Fg and Pg are given in Table X . Por the structure determination it is very desirable to have the structure factors on an absolute basis. The conversion factor for relative to absolute structure factors may be most accurately determined by measuring the absolute intensities for a series of reflections with an x-ray spectrometer. Alternatively, a set of approximate absolute structure factors may be calculated from the observed results using a method suggested by Harker.In the first procedure for calculating the scale factor the thermal vibration correction factor is neglected or is included in the atomic scattering factor curves used for the computation. In the second procedure the thermal vibration factor and the scale factor are computed simultaneously. The first procedure was used to compute the absolute structure fa c to r s fo r the (hki) data used in the Patterson sections and the second was applied to the (hOl) zone data. 58 !EABM IX Absorption Correction Factors for (hOl) Structure Factors © 0 22.5° 45° 67.5° 90 ° sin © 0.000 0.323 0.707 0 .9 2 4 1.000 A 0.1995 0.209 0.24-2 0.272 0.294 1/2.25 A 1.00 0.973 0.902 0.853 0.822 59 The structure factor for a crystal may "be written in the general form *5- r •/*; f~U ~ where fi is the atomic scattering factor for the ith atom, is the reciprocal lattice vector to the plane (hki) = H, ai is the vector from the origin to the ith atom, and the summation i s over a l l o f the atoms in the unit cell. For the squared structure factor which is proportion al to the intensity for the ideally imperfect crystal the expression is i ant (0h *A^is ) - Z i j ' # j For the calculation of the absolute structure factors for the (hki) data it was assumed that the atomic scattering factor for an atom could be represented by f,- f where Z\ is the number of electrons associated with the i th atom and f is a unitary average scattering factor. Making this substitution the expression for the structure factor squared becomes J j 1 {Z H* +-2 rz‘2/?y or How the average value of cos 2 H ( b H'A«,-j) summed over H approaches zero as the number of H terms are increased, provided that the -£>i J terms correspond to general terms in inter-atomic vector srpace. The terms are precisely the vectors represented hy the three dimension a l Patterson function for the c r y sta l. Performing the summation over H and noting that the actual P differs from the true value hy a constant K the expression becomes z. or where n^ is the number of reflections H, and the symbol < > represents the average value. Harker has shorn that the above formula is invalid if the values of Bjj are all integers or all zeros for the planes used in the averaging. Therefor, if not many co-zonal reflections are used in the averaging, the procedure is satisfactory. Harker has also shown that the probable error in this procedure for the evaluation K is where Q is the number of reflections used to obtain the average. The procedure described above was used to place the original set of structure factors upon an absolute basis. The average atomic scat tering factor curve, shown in Pig. _J+_, was computed using the Inter nationale Tabellen atomic scattering factors for atoms at rest. Por the (hki) data the calculated sum of was 133>563 with n^ equal to 996. The calculated value of K was 2.IS when the structure factor was based on a two molecule structural unit. The values for the hki structure factors are given in Appendix Z. . Por the calculation of the (hOl) structure factors the structure factor expression with an isotropic temperature factor included was used. The correct foim of the structure factor expression when thermal 0 8 0 6 ay oz 0.2 0.6 r.o Fig. A verage A forme Seatiering Factor Versus Sin& 62 vibrations are considered is -«.* -a/7/ Oh ' JH : Z f i e JL| is the vector distance from the origin in the unit cell to the mean position of the ith atom. For a first approximation the temperature factor is expressed as an isotropic term multiplying the calculated structure factor, namely: p _ e'Q z: -f: a Bfiiz* • J1- v jl ' _ -rtti i Z' or / rw' ' >• H Thus the graph of for small ranges of sin G versus sin 2 fi i s a straight line with a slope of**/)?- and the intercept at sin2^ = 0 is » * (0 . 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PATTERSON INTERATOMIC VECTOR MAPS In order to determine the crystal structure of a compound from the observed structure factor data it is necessary to determine "by some procedure the phase angles \ddch are associated with the most important spectra. Once a set of approximate phase angles has been obtained, the structure may be refined by successive approximations using Fourier series or an equivalent procedure. In the problems where a direct ap proach by the use of phase inequalities is not readily feasible a trial and error process for determining the phase angles is necessary. In applying the trial and error process the number of models that need to be considered may be considerably reduced by the use of Patter son interatomic vector maps.(56) uhe tjjree-dimensional Patterson inter atomic vector map *presents in one form all of the information which is obtainable from the observed x-ray diffraction data. In some cases, by the proper use of the function, it has been possible to obtain a unique trial model. For a structure to be correct it necessarily must account for the observed interatomic vectors present in the Patterson map. A model which accounts for the interatomic vectors present in a Patterson map may be incorrect unless its Fourier representation converges to the correct structure with a corresponding improvement in the agreement between calculated and observed structure factors. Since a complete solution to the structure problem has not been obtained, it is of interest to discuss the Patterson interatomic vector function for lithium trichloroacetate monohydrate and the restrictions 72 which it imposes on any proposed structure. In the following sections the general characteristics of the Patterson representation and its application are discussed. Porms of the Patterson Series. The general forn of the Patterson series is as follows: v = _ L 2 1 IF"** 1^* cx>sxnlBn 'A) (uvw) V H where P(uvw) = value of the series at the point (u, v, w). u,v,w - parametric distances along the a, b, and c axes. V - volume of the unit cell H = (hkl) CO Z z Z Z Z H fc R 4 -60 Pg - crystal structure factor for plane (hkl) Bg - ha* + kb* +■ lc* R = ua + vb + wc The significance of the series may be shown by substituting for the value o f % H 2 z £ where i s the interatom ic vector function ' An.'S * C*. -*i)3L + (W- yj) y •* c in which (X^ - Xj) , (Yj - Yj) , and (Z^ - Zj) are the differences in the parameters for atoms i and j. Thus the Patterson series is /S*VM = V » 1 “ ” Ir|0,'''') + $ I f ' x fi(„| tiH ) t ' J M _ The first series in this function P(UTW) produces a large peak at the multiples of the unit cell edges corresponding to an origin peak which represents the vectors from an atom to itself. The height of this peak is proportional £ Z > In the case of a c-centered space group the origin peak is reproduced at the equivalent point at (l/2, l/2 #0) automatically hy the operation of the extinction rule present in H, namely: (h + k) - 2n. The first series thus produces a peak at the points uat-vb-fwc = n a * m b pc ^ 2 where n, m, p are integers and (n+ m) is even. Secondary maxima may he produced in the synthesis at points other than the origin regions be cause of the termination of the series before the coefficients are negligibly small. The second series which involves the atoms i and j produces maxima at R = n ± A ft; j or ua*Tb twc Z nt[(x^-Xj)a ♦•(yi-yj)b ♦ where n is an integer. Thus the positions of the peaks produced by the second series correspond to vectors' ua vb wc which represent inter atomic vectors in the actual crystal. The height of the peak associated 7^ with a given &fl\\ is proportional to the 2: f,•<#, In actual practice the fu ll three-dimensional Patterson function Fq.ivw) is not usually computed during the initial stages of a structure determination unless computational aids such as IBM machines are avail able or the c e ll constants o f the cry sta l are sm all. The amount of labor involved in such a calculation is the usual deterrent to the full utilization of the Patterson function since it requires the use of a conplete set of three-dimensional structure factors summed in a three-dimensional series. The simplest form of the Patterson series corresponds to the projection of the three-dimensional vectors onto a line (which normally corresponds to an axial direction). The series in the case of the projection on the a axis has the form %to«l * JL * ^*06^ £o»»7»*»« * where "a" is the interplanar spacing of the 100 plane, and uis the fractional distance along this line. The notation ^ ^ in stead of ^UVWjis used here for Pattersons which involve the projection of vectors onto a plane. This series, in general, is of value only in the analysis of structures vrhich are not complex or where a layer structure exists that is related to a principal direction in a crystal. However, even with complex structures this series may be completely evaluated with the aid of Patterson and Tunnel strips(57) and plotted in one hour. A more general form of the series is the projection of the vectors in the three dimensional space onto a plane. In this case the series 75 assumes the form = 2T 21 IFq**,)! cosa 71 (M«. + k v) •* k K where (a h) is the area of plane normal to the (hko) zone axis. This synthesis is primarily useful in two cases: when a few heavy atoms dominate the structure, or when there is sufficient resolution in the origin region to determine the orientation of the molecule in the unit cell "by the intramolecular vector peaks. The intermolecular vectors are generally greater than 3.0 * 0.5 A., whereas the intramolecular vectors are less than 3.0 A. The resolution of the projection may he increased hy subtracting the origin peak fromi the synthesis. This operation may he conveniently performed hy using the data from the absolute intensity determination. The desired structure factors are / a t . . * / ’-- This calculation may he readily performed after the derivation of absolute structure factors, since the quantity ^ f^ is used in these calculations, and consequently the contribution of the origin peak may conveniently he subtracted from the final tabulated absolute structure factors. This procedure would not disturb the convergence of the series. The introduction of false maxima in the series by this process might be reduced since the calculated temperature factor could be applied to the f; terms. For complex structures the various projections which may be cal culated are generally of not too great value because of the coincidence of vectors resulting in a maze which is impossible to interpret. In these cases it is necessary to utilize the three-dimensional series to 76 calculate the full three-dimensional interatomic vector map, or the Patterson-Harker sections.These sections correspond to regions (planes or lines) in the three-dimensional Patterson synthesis where the vectors related to the symmetry operation of the space group should appear. For the space group C C/ the interatomic vectors between four equivalent points are as follows: No. of v e cto rs V ectors k 0, 0, 0 h 1/2, 1/2, 0 2 0, 2y, 1/2 = 0, v, 1/2 2 0, 2y, 1/2 = 0, v, 1/2 2 l/2,2y-l/2,l/2 = 1/2,v,1/2 2 l/2,l/2-2y,l/2 = 1/2,V,1/2 Here the Patterson-Harker synthesis PCov^w ill contain the terminii of the vector distances corresponding to the atoms related by the c-glide operation. The value of v in the neighborhood of the peaks appearing in fliay be used to limit the y coordinates for the atoms related by the c-glide since v = 2y for these vectors. Though the line synthesis may prove to be of little value, the computational time involved is quite small. The computation of the three-dimensional Patterson function P | COS nil (HU- + kir +-4 UJ) is usually performed by the computation of sections at various levels perpendicular to the shortest dimension in the crystal. The series in this case may be written in the form 1 g *21 c -fr sannir) cosf.tr (Vttt+Mut) (im i) V for sections perpendicular to the b axis. The computation of the sections involves considerably more labor than the corresponding pro jections, especially if the zone data involves an extinction rule such as (h-t k) = 2n and 1 = 2n for C_, since a ll in d ices appear in the three-dimensional computation. In the case of Cc, using Patterson- Tunnel strips for the calculation, the minimum time for calculation of a section was 30 hours, the h index running from 0 to 2k and the 1 index from 0 to 12. The i n i t i a l sectio n which was computed required a total time of 100 to 120 hours .1 By proper organization of the work the time was rea d ily reduced to 2$% of the initial calculation. The practice of preparing several carbon copies of master tables for use in each computation considerably reduces the total time required. In ad d ition , the use o f tracin g paper mounted on top o f a master u n it c e ll net for preparing the final projection results in a further saving of tim e. In the three-dimensional Patterson for C the vectors appearing c at 0 , 0 , 0 ; 1/ 2, 1/ 2 , 0 ; 0 , v , l / 2 ; and 1/ 2, v , 1 /2 arise from the following operations of the space groups: identity, c-centering, c-glide planes, and net glide planes. Thus all the other vectors appearing arise from the in tera ctio n o f atoms not d ir e c tly rela ted by symmetry elem ents. For two atoms located at (x^, y^, z^) and (x2, y , zg ) in the space group Cc the following interatomic vectors w ill occur: No. Vectors Coordinates 2 2 AJTj AX jAZ 1 AX ;4y-'4j>S4 i <3* , sy j avr+ki. 1 -& scy / 1 AY jTY-ltLiA z ' ' / 2- 1 2: y - / i l A y , / - r y , A •?-*-'/*. 1 AX'^;4V^/i.; A* 1 ^ Jr-4-i, Z y -'/a.y^ 2 1 &.‘A y j * 2 1 A x-'^z. J t/i-^yjA *+',/z. 1 A y-'/i, ri/-^ -Aa-'/*. i a x-t- '/-Lj ’/2~Tyj **+<4. where A X ~ = y /- y * .y -d 5? — 2 ,- 2 1 . and Siy - y/+y*~ . The negative of the listed vector also appears, giving a total of 32 vectors "between two atoms in general positions in Cc> or 22 non-identical vectors. In the case of lithium trichloroacetate monohydrate there are two molecules LiOOCCCl^ • HgO located in general positions, neglecting the hydrogens a total of 12 atoms. In the three-dimensional Patterson there would be a total of n(n-l) = 72 ( 71) r 5112 interatomic vectors. 79 This group consists of HS 96 vector interactions between atoms in general p o sitio n s and. 216 which are rela ted to the space group symmetry. The k &36 vector interactions are composed of the following number of vectors; Cl-Cl 0 - 0 IfSO C - c 192 L i-li 32 01 -0 1152 01 -c 768 Cl-Li 38 k 0 - c 76s 0 -Li 38k C -Li 256 Thus there are more than twice as many Cl - 0 and approximately 1 .5 times as many Cl - 0 as Cl - Cl vectors. Considering the number of vectors a priori it would appear inprobable that the Patterson function could be interpreted. That this is not the case is demonstrated by the subsequent discussion of the observed Patterson functions. Prior to the discussion of the Patterson maps it is desirable to consider first the lengths of the intermolecular and intramolecular* vectors which may appear in the Patterson function. Por the model of the molecule presented in the bond-distance section, the intramolecular vector distances were as follows: 0-0 = 1.25 A. - ° l - ° 2 1.51 A. Ol-Oi - 1.7^ A. ci-c2 - 2.66 A. Cl-Cl - 2.SU A. O rH o ii f<~\1 C li-O i K"\ 3 .o 6 a . O li-O i - o i 2-o 3 = 3 M a . Cl3-° 1 ci^—o 2 — ^.09 A. For the chlorine-water oxygen distance it would appear reasonable to assume that the distance would "be comparable to the values 3 .2 5 and 3.30 A. observed in EgS^Clg * 6 HgO and KgSnClty • HgO./*^) respectively. For the chloro compounds discussed in the literature section the chlorine- chlorine intermolecular distances varied from 3.2 to 3.9 A. Ihe litera ture on the hydrated carboxylic acids indicated that the water oxygen- carboxyl oxygen distance may vary from 2.5 to 3.1 A. Using the ionic radius of lithium 0,60 and the van der Waal radius of 1.8 for chlorine and l.^K) for oxygen/^ the minimum Li-01 and Li-0 distances would be 2.*+ and 2.0 A ., respectively. In the Patterson maps the heights of the peaks are proportional to 2T fvfji which may to a first approximation be replaced by the product Zj_Zj where Z^ and Zj are the number of electrons associated with the atoms 11 i 11 and "j". 81 The individual vectors would thus have the weights Cl - Cl 17x17 239 Cl - 0 17x3 136 C l - C 17x 6 102 Cl - Li 17x 2 3^ 0 - 0 8x3 6k 0 - C 3x6 k& 0 - Li 8 x 2 16 C - C 6x 6 36 C - Li 6x 2 12 Li - Li 2x 2 k In the Patterson map the chlorine-chlorine interactions would produce the largest peaks, while the 01-0 and Cl-C would have heights pro portional to l/2 to l/3 those for Cl-Cl. Actually "because of overlap ping of vectors it would "be probable that the small interaction terms involving atoms other than Cl-Cl, 01-0, and Cl-C could appear in the Pattersons only as a perturbation on these vectors, and would not readily be detected. Patterson Projections. In the course of the investigation of lithium trichloroacetate monohydrate the Patterson projections , P ( ,k l ) , P (6ku) » 8114 were prepared. The Patterson projection ^(oki.) is ^ile Pr°Jec'bion ^he interatomic’vectors on the £ b + tGs+bJ«£j] plane. The spatial relationship betv/een the various projections is shown in P ig . 6 . The Patterson maps are drawn to a scale of 1.0 cm x = 1.0 A. In the calculations the Poeo term was omitted and the dotted lines correspond to the zero contours of the resultant series. 32 /7y. 0 rien fa fion o / pa t te r son P ro j ec fions The Patterson projection P(j,*0) ~ ^(uv) E*own Pig* 7 exhibits a series of rather "broad maxima which in the 90 s,Hp direction are separated "by a distance of 3.2 1. 0.4 A. The elongation of the peaks in the "b 11 direction suggests that there are a large number of coincident vectors which have lengths ranging from approximately 2.6 to 3*6 A. The peaks nearest to the origin define an hexagonal array about the origin. Since the vector map should exhibit primarily the 01-C1 and 01-0 interactions, the peaks may be associated with the trichloro group oriented with the plane of the trichloro group approximately parallel to the b 0 - 8 ^ sinj* plane and with one pair of chlorines approximately parallel to the •'a 11 d irectio n . For the trich loro group the 01-01 distance is approximately 2.29 A ., and for adjacent chlorines the van der Waal distance is approximately 3*6 A ., the average vector distance being 3.2 i 0.4 A. If the trichloro group has the postulated orientation the shape of the peaks suggests that the oxygens of the carboxyl group plus the water oxygen form a triangular array above the trichloro group, I.e. the tricbloroacetate ion has the postulated structure and a water molecule may be associated with the carboxyl group to produce a triangu lar array o f oxygens. The Patterson projection P^©^) = shown in Fig. 8 exh ib its maxima a t 0 , 0 ; l / 2 , 0 ; 1 /4 , 1/ 2 ; l/4, 3/^ which are elongated in the "c" direction. The vector distance from the origin to the zero contour of the origin peak is 2.3 A. The vector distances to the (1/4, l/2) peak region are from 3*3 "to 7.5 A. while the vector distances to the 84 Figure _7_ Patterson Projection - P^Mco) Figure 8 Patterson Projection - 86 peak (l/2, 0) aret 1 .9 to 3.6 A. with the longest rectors haring components of approximately (l/2, l/U) - 3. 6 A. The results may be interpreted on the assumption that the trichloro plane as defined hy ]?(hko) is inclined at an angle with respect to the (001) plane. The chloro groups for the two different molecules in Cc howerer probably do not hare rery different Z coordinates, i.e. the Az chlorines are le s s than l/h c®sin^ . Considering the peak at (l/^, l/2) as arising from Cl-Cl in tera ctio n s in ro lrin g the 11 c" and "n" glide operations, the chlorines would be located approximately midway between the "c" and Hn" g lid e plan es. The Patterson projection of the rectors on the plane defined by b0 and (a0+ cj x bc= &(ioi) is sllowti in Fig. 9 « This is the pro jection on c 0 sinp' - bQ for the space group Ic obtained from Cc by the transformation ao' = a0 * co I b„ - bQ 1 _ c - 'c„ In this projection it is clear that there are a large number of rectors which hare components approximately parallel to bQ with d(ioi) cora“ ponents of 0, t- l/b, and ±. l/2. The major terms in correspond to P 2 o f (5o^) and ( 606) with = 2.72 A. and - 1.82. A. If the chlorines are located in the (^OU) then the continuity of rectors along bQ may readily be accounted for if an edge of the trichloro group is not quite parallel to a 0 and the arerage parameter of chlorines is l/S and 3/S. With these conditions the operation of the net glide 1*Q * io + O Y Figure 9 Patterson Projection - P (OKU 0 Figure 10 Patterson Projection - plane would produce a second set of chloro groups at the 3 /8 and 7/8 bQ positions, thus effectively filling the space across h 0 with vec tors. The hand parallel to h 0 at wrnld result from 01-0 and 01- molecule "1M to 01- molecule "S" interactions. This latter re su lt i 3 suggested hy the fa c t that *s smal l compared to and F - _ and therefor there must he some phase cancellation of ( 60b) chlorines associated with the (202) planes. For the trichloroacetate ion a configuration in the solid state in which all the chlorines and all the oxygens are in separate layers does not seem very prohahle a p r io r i. The Patterson projection P. . - P is shown in Fig. 10 . v*0®) (u\n) From the uostulated configuration derived from P.,, , P. , and (,hlc0; ( 0hl) P(0]a) the molecule should he fairly well resolved in an (hOl) zone projection. The vectors in the projection, h o w e v e r, are not well re solved. I t i s clear that there are numerous vectors term inating on the (202) plan.es, i.e. (u - w) and (u-l/2 - w). The region 6L appears to he composed o f three peaks a t 1 . 9 , 2 . 7 5 » 3 .1 A .» while the corres ponding peak is related to vectors 3.0, 3.2, and 3.7 A. The peak ^.involves vectors which may vary from 2.0 to 2.8 to 3.^- A. This peak has heen interpreted as arising from the 01-01 intramolecular vectors corresponding to the trichloro plane oriented approximately parallel to the 101 planes. The region S i s composed o f vectors o f length s greater than 3 .2 A. w ith the peak at ^-.3 A. This peak i s assumed to a r ise from the intermolecular vectors between trichloro group planes. The region S which involves vectors of ^.3 to 6 .6 A. is presumed to be related to 90 intermolecular 01-0 vectors. The peaks G* and /3 on the hasis of these assumptions involve the superposition of a large number of Cl-0 inter actions corresponding to intramolecular vectors and to intermolecular vectors 01-0 between molecules related by the c-glide operation. An approximate model for the structure projected on the (010) plane which is consistent with the Patterson projections is shown in Pig. 11 . Using this approximate model an effort was made to fit the (hOl) struc ture factors using (hOl) Bragg-Lipson structure factors graphs drawn to a scale of ^ cm - 1.0 A. The structure factor calculations were re stricted to the (hOl) zone since it was evident that the Fourier series refinement procedure would readily provide resolution in this zone. A model which gave good fit to the observed data could not readily be found. The three-dimensional Pattersons discussed in the following sections were then used to try to derive an alternate model. Patterson Sections. As the investigation proceeded, it became increasingly evident that the Patterson projections did not provide sufficient data to permit a solution to the structure. During the trial structure calculations in space group c£K - 0%/c the Patterson-Harker sections associated with the twofold and the twofold screw axes, respectively, were prepared. Finally the sections P ^ /g ^ > P (i4/ty) and P, (uys;w) , v were calculated so that a three-dimensional model of the interatomic vector space could be studies. The results obtained from these calculations are discussed in the following sub sections. 91 <0 * A* £ VI C7 v 5: <& w "b U <* b O s Os a 0 - 0 ' to ■* *s o 92 Patterson-Harker Section Bfrow). The Patterson-Harker section Pteow)was computed originally on the "basis of the assumption that the correct space group ms q£k - G ^ . In this space group the section P(uow) cou^ Pr0Ti&e inform ation on the x and z coordinates o f the chlorines relative to the twofold axis since, for the tvro atoms related by a twofold axis, the interatomic vector (uvw) is (2x, 0, 2y). The Patterson may thus resolve the molecule on a 1:2 scale in the P, « (uow) section . The Patterson-Harker section P, N is shown in Pig. 12 . Because (now) ° ------of the apparent lack of resolution in this section the corresponding sharpened synthesis shown in Pig. 13 ms computed. This sharpened er I2' / ~ synthesis was prepared "by using the coefficients lfwy / , where f is the average atomic scattering factor for plane (hkl) . This pro cess is equivalent to assuming a point atom scattering factor and actually produces a nonconvergent Pourier series. It has the effect of sharpening the maxima but may introduce some spurious peaks. In the synthesis a series of large peaks appears along the "a" direction with "w" conponents from 0 to £ 3/S. The distances be tween successive peaks correspond to 3*5 A. This value is very close to the value of 3.6 A. for the chlorine-chlorine intermolecular vector. The series of peaks suggests that for chlorines the z coordinates do not d iffe r by more than 3 /8 2. Por the se r ie s o f numbered peaks the asso cia ted approximate vector distances are as follows: 93 figure 12 Patter so n-Earker. Section - P. . (now) Co Figure 13 Sharpened Patterson-Harker Section - 0 g figure lU Buerger Implication Diagram for - 0^ = ^g/c Peak Ho. 1 ---- 2.S i 0 .7 2 3.0 * 0. 1+ 3 ---- 3 .2 * 0.1+ k 6.7 * 0.8 5 10.0 t 1 .0 6 — 9.^ ±0.7 Prom a comparison of these vector distances with expected values it was concluded that Peak Ho. 1 did not correspond to any Cl-Cl inter actions which could he consistent with large peaks 3. *+> 5> and 6. It ms therefor concluded that this peak was produced hy the superposition of a series of Cl-0 interactions. Peak Ho. 2 ms interpreted as rep resenting intramolecular Cl-Cl interactions since, if it was assumed that 3 was associated with intramolecular Cl-Cl terms, the chlorines would he out of phase for the (lK)l+) reflection which is very strong. The vectors to 3> *+» 5» &n Cl-Cl and Cl-0 interactions. In considering these maps it is of interest to note that P, ■, N is obtained from P. . hy translating the (ufw) (uow) origin to (l/2, l/2, 0). Thus the section also contains the vectors having components of ( l/ 2b ). In the introduction it was stated that was originally prepared for use as a Patterson-Harker section in space group C*K - C . By reducing the scale of the map 2:1 the Buerger implication diagram shown in Pig. lH ms prepared. The size of the circles in the drawing is proportional to the height of the peak. It is evident that in C xie, 97 the implication diagram strongly lim its the allowed chlorine parameters as indicated hy the large peaks near z - l/U. Using alternative inter pretations of the large peaks, a series of "allowed" models was tried in C i/t with only very limited success. For the more promising models (agreement of F observed to F calculated) the Fourier refinement was carried to the point where no more sign changes occurred on recycling and the se r ie s had converged to a r e su lt. A fter numerous such attempts it was concluded that the centrosymmetric space group could not he correct. Three-Dimensional Patterson Series. In order to obtain the maximum information from the observed structure factor data, a three- dimensional Patterson synthesis was made, using the sections at v equal to 0, l/S, 1 /M-, 3/8» and l/2. In the preparation of the syn thesis the u and w directions were divided into six-degree units corresponding to 0.308 and 0.18 A. while the v direction was divided into forty five-degree units corresponding to 0.7 A. One procedure for interpreting a three-dimensional Patterson series is to investigate the distribution of the vectors \d.thin 3.0 A. of the origin peak. This region, in general, contains principally the intra molecular vectors without the ambiguities arising from intermolecular vectors. The oi’igin region ( * a°/V j ^e°/z.) for the three-dimensional Patterson series is shown in Figs. 13 through 19 . In Fig. 15 » the v = 0 section, the shorter vectors associated with the formation of the peak at (l/ 3 0 , l/H) are definitely related to the intramolecular 9S '5fc figu re 13 Patterson Section - - Origin Region 001 i e l re u fig (u3/Sw) 6 atro Scin , . rgn Region Origin - . , P, - Section Patterson Figure 17 Patterson Section - P. . „ - Origin Segion w) -i-C. <2 Figure 18 Patterson Section - - Origin Region 102 M O V>J Figure 19 Patterson Section - “ Origin Region vectors. This peak which undoubtedly involves the super-position of numerous vectors is at the correct distance to correspond to Cl-0 intramolecular vectors and to Cl-0 intermolecular vectors from a car- boxyl-water triad to the chloro group directly above it which is pro duced by the c-glide operation on the molecule with which the oxygens are associated. In addition, it is possible that Cl-Cg vectors of lengths 2.66 A. also contribute to the peak. The origin peak conceals any bond distance vectors (less than 2.0 A.) which might be resolved by the terms in the series. The form of the peaks around the origin region suggests that diffraction effects due to the origin peak are actually present. The computation of these sections using the Patterson series with the origin peak removed might be rather illuminating. The section v - l/S in Pig. 16 has a rather oddly shaped origin peak region which suggests the presence of vectors of lengths of ap proximately 1.5 A. which are directed along aQ, at ^5° to s© > and along e0. These vectors might be related to Cl-C^ vectors of lengths 1.7^ A. which are concealed by the origin peak. The peak region at (l/l6 , l/H) is interpretable in terms of the 01-0 interactions considered for the zero level. The intramolecular Cl-0 vectors range from 3.0 to 4-.1 A. The v = l/b section (Pig. 17 ) does not exhibit any peaks in the origin region which are associated with intramolecular vectors. The region at z equals l/z has, however, a series of maxima which is asso ciated with vectors between molecules related by the c and net glide planes. The peak at (0, 1/2) corresponds to the maximum in a synthesis, vddch indicates that the mean distance of the chlorines from 1 0 k the c and n planes must he l/S bQ. If chlorines are located at 1/8, then on the operation of c-glide the pair of chlorines in the trichloro group which are assumed to he approximately parallel to the aQ direction should exhibit cross vectors in the l/2 c0 region. In deriving a model it was assumed that the peaks oL were associated with these cross Cl (molecule l)-Cl(molecule 2) vectors. The distance 2.S jr0.3 A. is in agreement with 2.89 A. postulated for the intramolecular Cl-Cl distance. These peaks combined with similar peaks appearing in the next section (v = 3/S) were assumed to indicate that the orientation of the trichloro- acetate plane postulated in the first model was essentially correct. In the section at v = 3/S (Fig. 18 ) the peaks associated with the intramolecular interaction of Cl^ and 01^ with Clg, and 01)^ and Clg with Clpj as well as the intermolecular chlorine vectors begin to appear. The peaks marked were assumed to a r ise from the intram olecular chlorine interactions whereas the peaks marked were produced by intramolecular and c -g lid e rela ted m olecule Cl -0 and Cl-C v ecto rs. The peaks S and 6 near ( 0 , l / 2) vrere assumed to be associated c-glide chlorine-chlorine vectors and c and n glide chlorine-oxygen vectors, respectively. The Patterson section at v - l/2 shown in Pig. 19 is very similar to in the region between (u, ± w/U). In this map the p peak o f the 3/8 level becomes very large corresponding to a large number of vectors of lengths 3*6 * 0.6 A. This peak is assumed to be a composite of the intramolecular chlorine interactions since the vectors from Clp-Clg, Gig—Gl^, ClipClij, and 01^-Clg would all fall into this general region in three-dimensional space with the net effect of building a 105 large composite peak. Similarly the peak Y of P^^g^ appears in ]?(u/w) and i s interpreted as a consolidation o f 01-01, C l-0, and Cl-C interactions. Thus from a consideration of the three-dimensional Patterson sec tions about the origin region it is possible to interpret the results consistently with the general model proposed on the basis of the pro jections. However, due to the superposition of vectors it is not readily possible to obtain parameters directly from the Patterson sec tions. It is possible that by removing the contribution of the origin peak the resolution would be increased so that more concrete data on intramolecular vectors could be obtained. Unfortunately, at the time these calculations were performed the reliability with which an origin peak might be removed was not appreciated by the writer. The composite three-dimensional Patterson synthesis shorn in Fig. 20 was prepared by using only the zero and 100 contour lines of the various sections. In this figure the alternation of large peaks between v = 0 and l /2 along the a 0 direction and between jt 3/ l 6 w i s very evident. Because of this distribution of peaks it was concluded that the chlorines for the two molecules in general position must be approximately parallel to the ( 101) planes, but the two trichloro groups must be on different (5o4) planes or the high concentration of 3.6 A. vectors as indicated would not be possible. That this interpretation is correct is also indicated by the character of the sections along the w - l/2 line. The vectors appearing in this region would not involve many 01-0 and Cl-C interactions, and the Cl-Cl terms should dominate the 0-0 and C-C terms. 106 In Pigs, 21 through 2^ are shown the positions for the vector peaks produced hy Cl-Cl, Cl-0, Cl-C, and 0-0 interactions for the model discussed in the next section. These diagrams illustrate the extent to ■which the final proposed structure is consistent with the Patterson series previously discussed. It is worthwhile to note in considering the Patterson maps that the gross features of the three-dimensional Patterson may he readily obtained hy just considering the addition of the Bragg-Lipson drawings for the following strong reflections; ( 712) , ( 710) , ( 021) , (% 0 , ( 606) , ( 602) , ( 100U) , and ( 1006) . ' 107 UOW-- — • Ui/sw x U i/4 W= — ■ U 3/8 W * + Ui£W* ▼ Figure 20 Three Dimensional Patterson Vector Map 0 Figure 21 Projected Cl-Cl 'Vectors for Proposed Structure o U . Figure 22 Projected Cl-0 Vectors for Proposed Structure 110 Ill iue 3 rjce 0- Vcos or rpsd Structure Proposed r fo Vectors 01-C Projected 23 Figure 0 0 • • • • i Figure 2b Projected 0-0 Vectors for Proposed Structxire VI. STRUCTURE LETEBMIHATIOU U tilizing the information which was derived from the Patterson interatomic vector maps and Bragg-Lip son structure factor graphs an approximate model for the ( 010) plane-projection has teen obtained. The unit cell in this model contains chains of trichloroacetate ions directed normal to the (^ 01) planes with neighboring chains directed in opposite directions. It is postulated that the water molecule is associated with the carboxyl group, forming a trioxy- group above the trichloro- group. Thus, along a (hO^) plane there is a close packing of trichloro- trioxy-trichloro-groups. The development of this model by the use of the Bragg-Lip son charts and the Fourier series refinement is discussed in the following sections. Bragg-Lipson Model. For centrosymmetric space groups it is frequently quite feasible to refine a trial model which satisfies the Patterson vector map and agrees fairly well with the strong observed reflections (strongest 10 to 20$ of all reflections) by repeated struc ture factor calculations and Fourier refinement. This method of calcu lation for LiOOOCOl^ • HgO in the centro symmetric space group was extensively used. Models for the centrosymmetric case we re rejected only when further Fourier refinement did not produce any sign changes and there had not been any significant improvement in the agreement of observed and calculated structure factors. For the (hOl) zone a com plete refinement cycle could be performed in twelve hours. In the 113 non-centrosymmetric case such a cycle required at least 300 hours. Therefore, in considering any model in - Cc it was necessary to use graphical methods of calculation as much as possible, For the space group C* -0 the structure factor for the (hOl) c zone has the form 1 Fl = t A2 ■»* B2 ) ^ where & Z *f Z- £■ c«« and B I -V Z f ,* S«n.%.H Cnx,-*A*i) Bor the calculation of the phase angles for the (hOl) reflections, the (hOl) Bragg-Lip son structure factor chart coa and s t h aiTthx+eaj were prepared on tracing paper using a scale o f 1 cm = 0,25 A. and fo r the range x c°Jt- . To calculate the phase angles for a model the Bragg-Lipson chart was placed underneath the model chart and the phase angles for the model measured. To evaluate approximate structure factors it was assumed that for chlorine seventeen electrons contributed, for oxygen eight, and for the carbon six elec trons. The data were then compared to the observed structure factors divided by an average atomic scattering factor (B). Brom the calculations in space group 0 ^ - G ^ it was evident that certain restrictions could be placed on the development of a model for Cjf - Cc. The initial restrictions used to derive a Bragg-Lipson model were as follow s: 1. All atoms partially contribute to the (7X2) reflections. 2. Net contribution of all atoms to the (712) reflection must be sm all. 3. All atoms contribute to the (5oH). '4. At least four chlorines contribute to the (lOOH) and (1006) f reflections. 5. All atoms contribute to (602) and (802) with the restriction that the chlorine parameters still satisfy condition 1 . These restrictions are suggested by the values of the corresponding sharpened structure factors, namely: 0$ of electrons f (712) 0 = — 108.2 = 59$ P(712) 121.1 = 66$ ^3(5o*9 = •^ (looty 99.6 = 5 ¥ ^3 (1006) -U 6. l = 63$ ^3 ( 602) 99.9 _ 5 ¥ F3 ( £>02) - 78. ^ = 1+3$ After obtaining a set of approximate parameters for the two molecules (01, 0, and C) , the model was refined by using the(hOl) Bragg-Lipson charts. A model was finally obtained which seemed to fit the observed data fairly well. Using the Bragg-Lipson charts a set of (hOl) struc ture fa cto rs was computed fo r r e fle c tio n s which appeared to be c r it ic a l. This group of reflections (Table XX ) had a reliability index r = 2 )1 Fot,J-Vu 115 T sh /e _ZL D raycj - 1/pjion S fro c tv re factors for the t~r/& / rr? o ale / hOA A J3 'ftCc*u) 066 +2. +/o /O ? 7o7 0 + /7 17 s 207 + IS + 77 SO 73 ^oy + H - 2 // s Z 0 6 -V? -32 S8 77 20 6 i-ie - 7 20 12 7oz + /? -28 3V 72 *JOS +3) 7 3/ 3) 7° 7 -33 136 12/ 70 6 + 77 -31 S 7 6 3 yas + )o 0 to /S 6oz + 77 +61 77 Joo Zo z - 3o + 7 3/ 72 6o*f + 3 -7 2 7 2 6 2 6 0 V + S3 - i s 27 116 of 0.26H, and. it appeared that the model was worthy of Fourier refinement. During the development of the trial model it was observed that extensive phase cancellation occurred so that it was necessary to con sider the contribution of the carbons and oxygens as well as the chlorines. Thus there are very few reflections in ifdiich the chlorines make a large contribution to the observed structure factor. This point is illustrated for the postulated model by the values of A and B struc ture factor terms in Table XT . The maximum value of A and B when the two molecules are in phase is 17^-. Several attempts were made to further improve the agreement between the calculated and observed structure factors by means of the Bragg- Lipson charts. This proved to be very difficult and consequently attempts were made to derive an alternate model based upon different initial structure factor conditions. These calculations consistently resulted in the same model and it was concluded that the model must be approximately right. It should be emphasized that the proposed model was derived by using the requirements imposed by the experimental structure factors and not by using a molecular model. The only spatial requirements imposed were that the trichloroacetate group must appear as a bonded ion (CGI 3COO-) and that the intermolecular distances must be large enough to satisfy packing requirements, i.e. two different atoms may not occupy the same space at the same time. Furthermore, in the initial stages only relative structure factor inequalities \rere used. 117 Using the Bragg-Lipson model parameters (Xg_^, Table X3j the structure factors for the observed reflections were confuted, using the Internationale Tabellen scattering factors for 01, 0, and 0. The cal culated structure factors are compared to the temperature-corrected observed values in XIII« The value of the reliability index for these data was as follows; Classification Ho. of Reflections R Good 0.186 F a ir 21$ 0.551 Good & F a ir 65$ 0.270 Poor 23.5$ O.SSO Good & F a ir & Poor 88 $ 0.389 Very Poor 12$ 1.187 A ll o .ift 3 ¥ 0.31 The low value of R for the 3^$ of the reflections with structure factors greater than 25 strongly suggests that the model is approximately cor rect. The value of R increased from 0.35 sin & less than 0.U- to O.63 for sin© greater than 0 . 8 . This agreement between calculated and observed structure factors indicated that a Fourier refinement of the- structure should be performed. Refinement of the model by means of the Bragg-Lipson would be quite difficult because there are 32 parameters and their associated phase angles which must simultaneously be adjusted. 118 Tai/e M . 7y/&/ p&ramefers f o r mod fy^nt 3rA$q -Lipson charts ( B-L) & Hat frtyn first Fourier re fine Men! ( F. ) fifo t *1 X b -L x F 3~L Z p C// 0.080 0 . 08 C 0.2 6? 0.26/ ciz 0.136 0 ./3 7 0.233 0 .2 3 5 C h 0.209 0.201 0.360 0 .379 0.3)5 c /i 0.313 OJ 8 ! 0.776 c /s 4.3V 8 0.350 0.23V 0 . 2Z6 C/6 0 .1 3 ? 0.138 0 . 3 0 0 0 . 3 0 2 o, (hzo) o .o se 0.130 o . u s 0 . 3 7 0 ° g 0.15 S ^O .lsS ' O . / y o 0./?2 C 3 0 ./8 3 ^0,/B 3 - 0 . / s o G .!? 2 O y 0. 32. / 0 . 3 3 9 0 . 1 S’ 3 0 . 1 7 3 O s 0 .3 7 8 0.381 O .S V 6 0 .0 0 9 0 6 (/ho) 0.160 0 . 0 7 3 0 . 1 7 S Q . / 8 1 0.0/3 O.H! cy O. IS! 0.22? Cz 0./67 0 . / 7 S 0 .1 0 7 0.068 0.3 7 3 0.307 C3 0 .36S 0,302 0.36S C y 0 .3 1 8 0-163 0.977 119 Table m Calculated drtd Observed Structure Factors J3ra^^- L-fpson Model S)n & ho £ F3 (obs.) F(c*/e. Si*, S ho/ Fj(pMsJ F(C»!e.) /39 9 0 0 28-9 579 529 Ho 6 5.8 77-3 !6>o zoz 3 0.9 //,? 99/ gcg 99.0 29.2 I 66 Voz Z99 2 9 .5 597 TzoV / 0.9 92 2 (6B 0 0 z. 57.3 35.7 950 COG 9/ / 5.6 Mb z o z /O'Z /o> 3 560 0 0 6 7.1 /S.Q Z/9 £ > o o Z5.9 Z9.9 5 6 2 809 29S /6.7 z z s Z ' o z 30./ /<,.? 57/ 2 0 6 3/ 7 33.9 S3 5 5 0 2 29.2 Z7-3 9 73 5 /0 2 29.9 29 3 2.8/ W o z ZO.Q 33.0 580 To 0 6 99.5 30.5 £03 BOO Z/.8 3 8S 980 /zoa 2 3.8 /€>■/ S 87 lev 3.7 15.0 69 9 /9 0 0 /BJ 22.9 2 90 602 63.0 96.0 S'00 75 0 9 /7.9 31.6 29/ 9 09 7 5 .6 5/8.5 5 0 9 9 0 6 2 5 ? 265 3o2 coy 3/S 32.8 6/7 /0 0 9 /Z.l 7 .0 326 ZOV 17.5 29.3 5 2 0 7k oG 9-6 2 5 , 5 33 2 6 0 V 3 9 5 / 8 .5 59/ M0 2 9 0 .0 9-8 3 V 3 76e>z 2 7 .3 75.2 599 / 9 0 2 37.6 38.2 3 5 0 902 52.0 39.9 550 606 7.7 Z0.8 3 5 0 W o y 17.3 9 .5 565 50B 272 / 3. 7 360 /oo o / 2.&> 20.1 56 5 79 0 6 50./ 35/ 3 6 5 50 9 2.5 /9.Z 5 6 6 Z.0 6 /0.7 /?.? 3 7 6 7 3 0 5 59. 3 5 5 .? 566 &OS /o.7 32.5 A//o 6 0 9 3 0.3 3 9 .5 568 /6 0 0 1 o.z z 7.0 7 /3 JO 0 2 5 . 9 2 3.8 579 808 //.O / 8.1 525 /Z oo //. 1 9.6 580 /209 /3.9 6.9 9 £5 9 06 7.0 /Z.9 588 008 zo.z 3.5 120 121 6 'S Z 9 ’8 / o/C? /r OOQ /f'Z / 1 8 / O/o 9£ /6L h ’£ 2 '-6 (7/C7 2 7 LS 6 8 'S 6 ' 8 / 9 0 Z Z 'S*C / 6 8 ‘3 8 0 rz S/r/j Z Z i 7 ’Q/ ooze ZBL E ‘9 2 O'Z ( 9 0 0 / S £ 6 6 ' / 2 9 ' 6 0/0 A/ £?L 9' IE 6 02 809/ £ £ 6 O ’l /' / ' £ (>'£/ 9 0/,/ Z9L a"Z/ S 'ft 9/0 hj? 2/6 f t ?'£/ 0/0 0 2 / t*'£Z Z’SZ hQZZ 2 /6 /•fiZ -2-6 0 / 0 o. 02/. 1, 'tr. r z f 0 /0 0/ <7/6 S '/r / S'O/ q/ o X 0 2 L o/ozj. a /6 £ '0 / 1 8 0 /0 8_ S//8 s i t £ 7 / Zo/rZ 60 6 O'Zl A>'& /rO 9/ 2 /Z (8 8Q hZ o{>8 O'B £ ’Q/ 2 0 8 / 0 0 / Z'S 6'02 Z/O /r/L 388 O ’// £ '£ ./ 9 0 2 / S 69 S ' 8 / •/? /y09Z 918 8 '2 / S ’ 8 20 ox 2 8 9 9 £ £ 0 9 / o/o & S L 8 6'9 2 £ 'S Z ATOO2 £ 9 3 S ’S Q'£f- Z/OA_ 2 1 8 t'6 O'Z/ 9 08£ 6 9 9 3C t o f f o/ OOZ QL> 8 ! ‘0Z h /j 0 0 0 / 8 £9 9 ? oohZ /r98 S'VZ 0 1 2 9 0 0/ OA9 OZB C’Qf Z /o + | r i /W jJ S'K A V% A where ^ke<) is the phase angle associated with the structure factor F(hol) ‘ ^lle ^our3'er series coefficients lf^ o x l e « ^^and 1Fha * l s i k . correspond to the A and B terms in the structure factor equation. The first refinement attempted corresponded to using only the terms fo r sin 9 less than 0.50. This projection did not produce any appreciable changes in the parameters of the atoms. A second attempt at refining the structure was performed by com puting the Fourier projections corresponding to the following coef ficients: first, the observed structure factors multiplied by the calculated phase factors; second, the calculated structure factors multiplied by the calculated phase factors; and third, the observed structure factors minus the contribution made by the chlorines. The series calculations were performed on the IBM machines by J. Beltzer. The observed and calculated structure factor Fourier series projections are shown in Figs.. 2 $ and 2 $ . The parameters for the calculated series were not appreciably different from the postulated values in dicating that series termination errors were small. The parameters derived from the projection by doubling the indicated correction.^3) are (Xg,, in Table X I I I . The parameter changes produced by the ja. Figure 23 Fourier Series Projection on the (010) Plane Observed Structure Factors and Calculated Phase Angles Figure 2.6 Fourier Series Projection on the (010) Plane Calculated Structure Factors and Calculated Phase Angles Figure 27 Fourier Series Projection on the (010) Plane Using Observed Structure Factors Minus the Chlorine Contribution refinement were rather small. In the projections the carboxyl group and the water molecule for the second trichloroacetate molecule located "between aand &0j 2 poorly resolved. This suggests that the parar- meters for these atoms may "be appreciably in error. This is also sug gested "by the appearance of the (Fol3S - Fq]_) synthesis in this region. The projection (F^g - v in Fig. 2n shows that the chlorine para meters for Olg, Oly 01^, and Olg are nearly correct since the slope of the contours at the postulated positions for these a toms is s m a ll.T h e parameter of Cl^ would appear to "be the most in error, the Z coordinate o f the atom "being too large. In the Fourier projections the location of Og, the water molecule associated with molecule u2n, could not "be definitely established. Con sequently a set of structure factors was conputed omitting the water oxygen 0g; a second set with the oxygen at ( 0 . 01 3 , 0 . 1^1) ; and a third set with the oxygen at (0.^75» 0.1SH). These structure factors corres pond to F]_ (calc.) , Fg (calc.) ^ and F^ (calc.) in Table XIV . The structure factors given in Table XIV are the calculated values multiplied by a combination temperature factor and scale factor. This correction was determined by a least mean square fitting of the calcu lated data to the absorption corrected (hOl) structure factors (Fg^-^g ^) using the equation /©* ■=. /a 126 Jo / Gbs&y-v&cJ a net Ca/cut a fed Structure factors for C$- Cc ~ Observed St mature factors. ~ Fourier /lode/ Less Ot f^Cci/c.) ' faun& v t t o t e l - df (0.0/3 ^ a.l^l) F^(Cs^c') ~ Fbvr/er Fotet ~ Qg at (^a.‘f7S’jO‘i8i) Fp-l_ ~ Sy&JJ- Lfp son ttoJe/ . (£ ff) v N o ^ X Vi VS 0 x N *n ' ' N ffj $1 S ' . ■ V , I '* N» c \ j Q (*V 03 ^ £ ^ 00 > n * o n «. N *3 X ■v *Nf * - s N fN m N ^ !n to is <3 N N yi n x * o t_> 1 n . t> <«S »N . "* ^ M "0 *) N N f, N N1 i. o« 6„ ^ * U S ^ V a <5 fN \ N4 In <3 V i O s U <3 N N © f Oti N 1^ VS WJ . . ^ x \fl os v» (\ NN n» V'* ,VJ M rN| .>• V3 >1 N • ^ fs O' fN N N} t\f V\ V} &o fN N ^ O' ^ ^ b X Vi N © M > (T\ on m VS N <3 On 0 i Vs ■s OQ n W! \» r*> \ s N V i fM •N \ S N 3 » Sn O O s 1 * v© > . *N <3 * s Vj Vi ■n iN 0 •» *S *N N Vi C U« v s N fo *N on X Os N Os in © r*i ID «0 ^ s ff> X 00 N N On to •s ~s VI S3 JVS * N V Ns - s •*> <>> N X 3 . « Co v« > m ■N <*) u N N O s V i n >S ^V >• f s . r> N N ~s ■s. «3 M n 03 N U t Ns \ N X H 03 N N (3 fN ^ v <33 N (Sl f n s >s On 3 3 N X N s Vi N - s V i m N» X /V, X ©« 0 Ck O © S 0 <3 Q N VO <£> N N O © O <3 <3 Q O S3 < i <3 0 0 N S' NS <3 <3 <3 0 <3 !»n V* N >« s» <*3 X V ■*s» N N N 'N <3 O C 0 I2 g Os CQ V> v £ /V ) CN5 ' t^ <0 ', *• 'fi, ^ *S f\j S^ I> \Tj > «® in ^ N Vs itl N ! > OV O- M UN s ^ •* n °0 £ \3 vo ^ ^ ^ V} i ff) ^ ^ -S -N -N ^ Os N % " £ 51 S •< * ^ *• * s ^ N V£ fc Os Oo c O Ci Cl £. S: >; c In ''V Cs G C *s J* ,s (N ^ (B D Vl QSSv- N «*4 Vs u> s. 129 ^ ", ^ V. "V. ^ ^ *s MM N X f\f ^ N fc ^ ^ _ N "■ ? rf\ ^ *s m N N U. *55 - X 3 m -v J * r^ 'as '<* fn <& c N l“J ^ <1 N (\ Ci r r>. * <* <0 *> m •*• tito O. 5 oa £ r5 5: ° v bo Oq Oo 0-. •S • 0 ^ 5 in Jc fr\ 'Jv 'N M ft \q ft ny. ^ ^ Vi 'x /N *5 (V ro * V\ 5 * v V* ft rn iv \a L ^, « vo O' •v 5 *'• W UN ^0 *• m ^ vs 'vo 0s I J5 * v* \0 V> C* ft f't) Qj \g VO \o tn ^■o r»n. o (\j ^ vo 5 .?.» !? i» r- Vvfv ro *s * ft *5 x ® J'v *n \a «0 > N ^ \r> N Q Q V 130 Model K B (A .2) ^ (c a lc .) 1.121 2.21 I 2 (c a lc .) 1.12k 2.3k F-j (calc.) 1.074 2.47 1 *111 2 ‘ 57 The values of K and B obtained in the Hanker calculation of temperature- corrected absolute structure factors were 0.86 and 4.07 A.2, respectively. Owens and Hoard report that a value of B - 2.97 A . 2 gave the best fit of calculated and observed structure factors for 0ctachlorocyclobutane.^ 5) The r e lia b ilit y index computed for the models F-j_, Fg> ^ 3 > and were 0.440, 0.442, 0.435, and 0.424, respectively. The Fourier refine ments thus resulted in an increase in R of 0.02 units. If, in the computation of R, the F's for the (400) , (4o4) , (006), (204) , (802), (804) , ( 1002) , (1006) , ( 1602) , and’(2408) are omitted, the values of R decrease to 0.352, 0.372, 0.348, and O. 36I, respectively. The variation of R with the percentage of (hOl) reflections considered is shown in Fig. 2$ . For the strong reflections (F 20) which constitute 24$ of the (hOl) reflections the values of R were 0.401, 0.39^, O.4o6, and 0.327 for F-^, Fg, F^» and respectively. Thus, in terms of the r e lia b ilit y index, there was no marked improvement in the agreement be tween the calculated and observed values as a result of the Fourier refinement. Though the absence o f improvement on the f i r s t Fourier refinement was discouraging it was by no means unexpected. For a non-centrosymmetric Fourier refinement the values of phase angles used in the series depend 131 Sty. The V6*rfaftt>*r o f th e reliability index w ith th e n u m ber of of ber m u n e th ith w index reliability V6*rfaftt>*r e The th f o Sty. /fe/ioftt/ity fat/ex ( % ) O S Structure Structure f- . Ffr-L - V d n a fa cto rs rs cto fa ecn Observed (O)Stuct e act s r to c fa re tu c tru S (hOf) d e v r e s b O Percent inciuded. . . 0'S,ccth4 y A ' f z «*k.) , a-r3(Csic.iM , «*k.) z f ' A 0'S,ccth4y 7S 8S (hO£) depend directly on the assumed parameter and on the assumed theoretical scattering factors. Because of this dependence the Fourier synthesis prodaces a representation of the model proposed rather than an appreci able refinement of this model. This point has been illustrated by James^^ for the case of two ideal atoms located with the origin at the center of symmetry, and with the origin displaced from the center of symmetry. The Fourier refinement for the centrosymmetric case using a 5^° parameter rather than the correct one of 60° resulted in a peak at 58°; and a second refinement completed the process. The Fourier refine ment for the non-centrosymmetric case using 108° instead of 120° for the parameter of one atom resulted in a peak at approximately 111°. Thus the Fourier refinement process resulted in a better representation of the approximate model than the true structure. Seller and Hoard^^ have determined the crystal structure of trimethylamine-boron trifluoride which crystallizes in the space group 0 with one molecule per unit cell. This structure determination, which, as they stated, involved a non-centrosymmetric structure of almost trivial simplicity, proved to be a problem out of all proportion to the apparent difficulties. It was found that the Fourier refinement pro cess was a very slowly convergent one. In the first two stages of refinement the parameters of the atoms changed at most only 0 .0 0 6 u n its. After considerable labor a refined structure was obtained for which the r e lia b ilit y index was 0 .2 3 . In d iscu ssin g the problem G eller and Hoard conclude that the principle sources of difficulty in determining this structure arose from the slow rate of convergence of the Fourier series 133 and the errors introduced by the assumption of spherically symmetric atom form fa cto rs. B o o th ^ 8) t in discussing the methods for obtaining approximate structures, states that "For any extensive an alysis the absence o f a center o f symmetry in the space group, u n less compensated by in tern al Symmetry of a different kind, is an almost complete contra indication to the analysis on account of the great increase in labor of computation." This statement is well illustrated by the case of LiOOOCGl^ • HgO for which a Fourier refinement cycle in the centrosymmetric case required only 12 hours, but the non-centrosymmetric case involving similar cal- culational methods required some 300 hours. Thus, the labor of refining the structure without the full use of fast computing machines is pro hibitive. This is illustrated by the block diagram for the structure factor computation and Fourier series refinement shown in Fig. 29 . The computations in the general (hkl) zone become cotrpletely prohibitive for manual methods o f computation. 13^ * * ^7 | F" f; (Cos*.irJlx ZJT/f y» > £ c* > V t> ' * t ** h m V) II 5?5 135 ? ! •? •si * V, <0 v—^ o * £ -~N *5 %> n> s 5 Xs •! * N * c >* CO ’ o If * <* V> H1 X' l tc o < K - $ u7 $ A ■* "A ■k ^ct f '• tf' •5: * ^ O' * Vl £ % » ^ J» ts? X. X >?JJ k > " Q o' VI. ' O ?*< *0 ^ ’A K s < v 5i ^ =» U <✓> ■i. X £ t« J-t s> * r o Or 137 I +: s* c u V-l *] ^i U: « V •K X £ V 4 * -* X -C X O If -* Uj u t 138 C/> Kl W •f- sr c U ■w ff! M I «r> 1C “9 It 139 i \ C O or?! * 5 u lo i4o * Vj 05 H\ 1C Ikl V II. DISCUSSION: CRYSTAL STRUCTURE Though a complete analysis of the structure of crystalline lithium trichloroacetate has not "been feasible, the general features of the structure have been established. A scale drawing of the proposed struc ture projected on the (010) plane is shown in Pig. 30 . The radii assigned to the atoms are the generally accepted van der Yfeal radii of 1.S0 A. for chlorine and l.llO A. for oxygen. Using a scale model of the anion (1.0 cm = 1.0 A.) , it was found that there is adequate space for close packing of the model as indicated in the figure. In addition, there are several voids in the region of the water molecules where the lithium ion can be located. It ms not possible to pack the molecules so that there would be sufficient space for the lithium ions to be directly associated with the carboxyl group. The model thus suggests that the structure is ionic in character, the lithium ion not being bonded to a s p e c ific carboxyl group. Since precise values for the projected bond distances within the molecule were not obtained no attempt was made to calculate the y coordinates o f the atoms from the (x , z) parameters. The Patterson- Harker section P^ovi^ suggests that the average of the chlorine para meters corresponds to chlorines lying between the glide planes. In the proposed structure the two molecule asymmetric unit is re produced by the c-glide operation to form a chain of trichloroacetate ions, one chain directed in the positive c direction and the neighborihg chain in the negative c direction. The pair of chains in the scale 1U2 F, (l/2, y, z) . The voids appearing in the vicinity of z = 0 and 1/2 form a continuous tunnel through the structure parallel to the y axis. It is possible that the water of hydration (which may be removed very easily) is zeolitic in character. During the composition determination it was observed that the crystals after drying were pseudomorphs of the hydrated crystal; however, no x-ray diffraction photographs were prepared from these samples. In the model it is of interest to note that the packing of the molecules along a (HoU) plane corresponds to a packing of alternate trichloro- and trioxy- groups, the latter being formed from the asso ciation of the water molecule with the carboxyl group. The actual pack ing of these groups along a (1401+) plane appears to be partially deter mined by the orientations of the trichloro- groups in the asymmetric u n it. The structure of the asymmetric unit as well as the chain structure which requires close packing of the anions in the c direction suggests that there exists in the solid state a strong chlorine to oxygen inter action. This is also suggested by the physical properties of the crystals. Under rapid growth-conditions the crystals develop as needles which may be split into fibers elongated in the c direction. The crys tals do not exhibit definite( 010) nor ( 100) cleavage planes, but the single crystals grown slowly from the mother liquor may be easily fractured along a direction parallel to the c axis. If it is assumed 12& that the chain structure of the ions is partially maintained in solution, the relatively high viscosity of the saturated solution and the difficulties in inducing crystallization in the saturated liquor are understandable. The crystal structure of lithium trichloroacetate monohydrate definitely does not involve the formation of dimers in the chemical sense. This is consistent with the observation that the acid exists as a monomer in aqueous solutions.The crystal structure deter minations of carboxylic acid salts have clearly demonstrated that the carboxyl group is present as an ion and that the structures are ionic in character. The formation of carboxyl group dimers in the chemical sense has been observed only in certain crystalline modifications of the anhydrous crystalline acids. The actual structures of the crys talline acids are dependent upon the nature of the hydrogen bonding present, i.e . whether the hydrogen bonding occurs between opposed carboxyl groups (dimers) or between neighboring carboxyl groups. In general the crystal structures of the carboxylic acids and their salts are determined by the character of the hydrogen bonding present and the three-dimensional packing configuration of the anion. A detailed comparison of the proposed structure to the struc tures reported for other acid salts is not valid. The three dimension al packing of the trichloroacetate ions would not be comparable to the packing of either formate, oxalate, or acetate ions. It is interesting that the r ela ted c r y sta llin e compounds LiOOGC(CH^)^ and LiOOCCH^ * 2 H^O both are pyroelectric and therefor form crystals isomorphous with non-centrosymmetric space groups., The unimolecular decomposition, of the anion to form chloroform and carbon dioxide has been carefully studies by Yerhoek and his students^^ The rate of the decomposition is dependent upon the concentration of the trichloroacetate ion. Consequently the reaction is postulated to pro ceed according to the mechanism: CI3COO" CCl^” -+- C02 (slow ) CC13“ f BH — CCI3H + B“ (rapid) For the lithium salt in water-alcohol mixtures the activation energy for the decomposition increases as the water concentration increases. This increase in activation energy was explained by the assumption that the anion is more easily hydrated than alcoholated. From a consideration of the bond distances which have been reported for compounds containing the carboxyl group i t was concluded that in the solid state the carboxyl group exists as the resonating ion with equi valent carbon-oxygen bonds of 1.25 A. The complete equivalence of the bonds is most certain in the cs.se of the metallic salts. If this is the case, then, according to the unimolecular decomposition mechanism, there could occur some decomposition in the solid state. For the proposed structure of crystalline lithium trichloroacetate monohydrate it would be conceivable that such a reaction could occur without a too large distortion of the structure. In the decomposition the carboxyl group would be transformed to COg, a linear molecule with an overall length of 5.1 A. conpared to the Mb" cell dimension of 5*6 A. 1U6 A proton from the water molecule could then he transferred from the water molecule to the trichloromethyl ion, while the COg molecule re acts with the water to form a "bicarbonate ion. If such a condition did exist, it would be exceedingly difficult to evaluate by x-ray diffraction methods. The x-ray photographs did not indicate the presence of gross disorder. The water of hydration in the crystalline lithium trichloroacetate may actually be associated with the carboxyl group rather than the lithium ion. Since the trimethylacetate ion has approximately the same size as the trichloroacetate ion, it was predicted that the lithium salt would be isomorphous with the trichloroacetate salt. This salt, however, crystallizes from an ace tone-vjater mixture as anhydrous needles which are pyroelectric. It is rather interesting to note that chloral (OOl^CHO) is characterized by the formation of a stable hydrate. ^9) V III. DISCUSSION: BOND DISTANCE LITERATURE The interpretation of the relationship between the structure of the trichloroacetate ion and its chemical properties is rather diffi cult. The model for the trichloroacetate ion must account for the unimolecular decomposition to form carbon dioxide and chloroform* for the decomposition to form chloride ions and a product* and for the large acid dissociation constant. Though a complete determination of the structure of the lithium salt was not obtained* results of other chemical investigations provide some insight into the problem. Bernstein has discussed the relationship of the bond distances in the chloro methane series to their physical properties.^ From a study of the microwave absorption spectra of chlorinated methanes (70) it has been established that the carbon-chlorine bond distance depends upon the number of chlorines attached to the carbon atom. The reported bond distan ces are as follow s: methyl chloride — 1.780 + 0.002 A. methylene chloride ' —■ 1.772l| + 0.0005 A. chloroform — 1.761 t O.OOU A. carbon tetrachloride — 1.755 £ 0.005 A. The value for CCl^ corresponds to the electron diffraction determina tio n by Brockway (71). Bernstein suggests th at on the b a sis of the "Badger's" Rule rela tio n sh ip between force constant and bond distance that the C-H bond distance increases linearly as chlorines replace hydrogens in the methane molecule. 14S In the chloroacetic acids the physical and chemical properties are undoubtedly related to the characteristics of the carbon-chlorine bonds. Assuming that the carbon-chlorine bond lengths in the chloro acetic acids are similar to those in the methane series several interesting correlations have been obtained. As shown in Figure SI the carbon-chlorine bond distance may be linearly related to the suc cessive decrements in the free energy of ionization which occur as successive chlorines are added to acetic acid (data from. Table JT). Thus the change in the ionization constant may be directly related to changes in bond distance within the molecule. It has been observed that a linear relationship exists between the dissociation energies and the carbon-halogen bond lengths in the acetyl halides, methyl halides, allyl halides, and the t-butyl halides(72). (The molar magnetic sus ceptibility for the chlcroacetic acids at infinite dilution may also be related to the carbon-chlorine bond lengths as shown in Figure 3&.) It would appear to be worthwhile to consider what characteristics of the bonds in the ion may be related to its chemical properties. On the basis of the differences in electro-negativities (chlorine 3 .0 and carbon 2 . 5 ) the carbon-chlorine bonds have $% ionic character. * This estimate probably is low if the decrease in bond distance with the number of chlorines attached to the carbon is due to resonance structures of the form * c _ c» - c Cle) where there is a contribution due to the formation of double bonds. The net effect of these structures would be to reduce the inductive effect llf-9 3.0 * 2.0 -c * 3 <3 J.0 \ tri. di. mono. W 1! i n “ ' TT& C-Cl Bond Lentff~h (A-) Plg|3#j 'The Change in fha Free Energy of Ionization,as Successive Chlorines are added to A c e t i c Acid ,Versus the C-Cl Bond Length in the C’ -lev 7:ietV,n-,\% SO X X 1.77 C-C! ESond LexytkiA) Fig«i_?jLl The Variation of the Volar Magnetic Susceptibility at Infinite Dilution for the Ghloroacetic Acids with the C-Cl Bond Length in the Chloromethanes* 150 of the chlorines in producing a polarization charge on the &. carbon atom. The contribution of such structures may be related to the saturation effect in the change of the free energy of ionization as successive chlorines are added to acetic acid. Pauling has discussed the structure of the normal carbonyl group in relation to its dipole moment. In order to account for the observed dipole moment, it was necessary to postulate the resonance structures . ^ , > e = o «-*■ > c where the ionic structure contributes k7% ionic character to the normal state of the bond. The normal carbonyl bond distance is l,2l|A. Degard has investigated the structure of chloral by electron'diffrac~ t±on.Kl.(7%) J The observed bond distances are as follows: C-C = 1.52 * 0.02 A. C-Cl * 1.76 t 0.02 A. C-0 = 1.15 .± 0 .0 2 A. The corresponding bond distances reported for acetaldehyde are as folloitfs: C-C . = 1.50 - 0.02 A. C-0 = 1.22 1 0.02 A. If the errors are not greater than reported then the difference in carbonyl bond distances, 1.15A. compared to 1.22A., is significant. Thermal decomposition of chloral results in the formation of CCl^H and CO. The reported bond distance for the carbonyl group is not very different from the accepted value of 1.13 A. in carbon monoxide. The bond shortening could arise from the inductive effect of the trichloro 151 group reducing the ionic character of the carbonyl group. The re duction of the ionic contribution to the carbonyl bond by the induc tive effect may also be considered as increasing the resonance con tribution in the carboxyl group. The undissociated carboxyl group is represented by the resonance structures — e *+ — e + For undissociated formic acid the bond distances are 1.213 A. fo r carbonyl oxygen and 1.368 A. for hydroxyl oxygen. (77) The normal bond distance for a hydroxyl oxygen is 1.1*2 A., thus there is appreci able shortening of the hydroxyl bond as a result of the resonance hybrids. A reduction in the ionic character of the carbonyl group by the inductive effect may facilitate the resonance in the undissociated carboxyl group, thereby increasing the acid dissociation constant. Bernstein reported that the C-H bond length in the chloromethanes increases with the number of chlorines attached to the carbon atom. It is possible that the C-C bond distance in trichloroacetic acid may be increased relative to the bond in acetic acid. In addition, there could be a contribution to the C-C bond stretching by the van der Waal repulsive interaction of the chlorines and oxygens. If the carboxyl bond distances were decreased by the presence of the chlorines, then the formation of the activated complex from which CO^ is removed would be facilitated. The normal bond distance for the carbon dioxide mole cule i s 1.1^ A. 152 IX. PROPOSALS FOR FURTHER RESEARCH From the discussion in the previous section, it is very- evident that a very precise structural determination would have to be performed to obtain results which could be reliably correlated with the chemical properties of the trichloroacetate ion. The structural determination would require an accurate determination of the electron density distribution in the anion. The determination of the electron distribution in lithium trichloroacetate monohydrate with the required accuracy would be an exceedingly difficult task. For a precision bond distance determination without a prohibitive amount o f la b o r, th e s a l t used must s a ti s f y some ra th e r s trin g e n t requirements. The compound must form crystals isomorphous with a space group which has a center of symmetry, or which has at the very least a center of symmetry in a projection where the molecule is well resolved. The cation associated with the carboxyl group should have a low atomic number so that the contribution of the anion to the scattering is as large as possible. It would be of interest to investigate the pyro electric properties and the space groups of the acid, its hydrate, the anhydrous lithium salt, and the basic beryllium salts. The analysis of the structures of chloral and its hydrate would also be of interest. For the structure determination of the trichloroacetate ion in a centrosymmetric compound, it would be desirable to obtain Geiger counter x-ray spectrometer intensity data which could be corrected for the con ventional geometric factors including absorption and extinction. For 153 the Fourier series refinement the (F obs.-F calc.) synthesis developed by Cochran could profitably be used. With this refinement pro cedure it is possible to simultaneously refine the atomic scattering factors as well as the atomic parameters. In addition, the termination of series errors normally present in a Fourier refineanent are elimin ated. The correct choice of scale factor for observed and calculated structure factors, atomic coordinates, and atomic scattering factor parameters is indicated at the atomic centers by the condition that the function and its first and second derivatives be zero. 15U 551 xiatraadv *x APPENDIX 1 NOMOGRAPHS FOR USE WITH WEISSENBERG EQUI-INCLINATION PHOTOGRAPHS The P olarization Factor and Sin Nomograph. A nomographic method for the calculation of the polarization factor for Weisseriberg equi- ( 76^ inclination photographs has been developed by W. L. Bond.' ’ For the equi-inclination method, the diffraction direction described by the off axis angle, 0T (longitude), and the equi-inclination angle /*< (latitude) is related to the scattering angle 2® by to s'L e - Co*T — SIM*/*. The final result for cotzo given by Zachariasen for the general case of a rotating crystal is in error. The result given is a Ct>*pcos(f*o*x •* am(p Sim x where P and latitude of the diffraction direction relative to the rotation axis and the direct beam plane, and X is the inclination of the incident beam, to the plane perpendicular to the rotation axis. The correct form of this expression is c o sze - Cosp co co*x - 9 /* The nomograph for the polarization factor prepared by W. L. Bond was expressed in the standard determinental form /■#- COS%/*- l + • - o I COST -cotxe 156 and since the polarization factor was related to 2 © by Co* the ® curve was marked in terms of the correction factor l/P instead of 0 Since cos (2© ) is related to sin© by Cosz&*. i- s s " - 1® the nomograph was modified by the addition of a sin O sc a le . The re su ltin g nomograph, as shown in Figure 33 . , using the observed values of T and^' , makes possible the direct calculation of the polarization factor and sin & for all reflections. Lorentz Factor Nomograph. For the eq u i-in clin a tio n method the Lorentz factor (1) is related to the off-axis angle ( T ) and the in clination angle ( f*- ) by L - s i n r j ( or the correction factor is W' ~ 'T since cos = /— Si*7-/*. . Applying the methods devel oped by Bond*' ^ for the preparation of nomographs, the determinant for l/L which must be reduced to the standard form i s o o multiplying the first row by l/l,r^ , and the last by L gives - o Now m ultiplying the second column by sin , the th ird column by l/L , and adding the first row to the third, the determinant becomes o I 157 F 'S .33 1.00-r LOO PoJartjatton factor - •S/n 6/VomograpA .20 110 F o r Weissenbery Fyui-mcfination ■30 Photographs 1.20 -0 .9 ? -40 1.30- l.fO -rSO 0 9 0 1.50- 1.60 ■60 170- -a a s 180- *5 r 70 -0.80 \ 4 0 1.90- V* \ 3 0 -80 -Q 7 S o . '£ 5 yP S in e A *X T :: ZJOOA X*>\ o -■90 0.70 ■ -Q-65 i/0 0 m - _ ■-0.60 1j80\ - 110 r 0.55 1.70-i 1£0-rQ&O --&o 1*50- :a ?5 1-40- 7-/3 0 70.4-0 130- \-0.35 -A/fO ISOzAO30 \0.25 \lSO 1J0- zr0.20 yeo i-0./Q i /70 1.00-h0.00 *180 I5ff 090 O | | 3 8 § I I Ip I I I | M l I \ I II I | H-n -t-H- i 11 11 11 i i £ <3 V. Oo 0u) § 1 5 O- 3 Vo S!> 51, *D to •Sfc It^ JS. 0r * § «« 2' ? ■* y |»l|t t I I | ) 1 1 I—|--1--1- - t - 1----1----1---- 1---- 1---- 1-----1—--1---- c-----H H 1---- 1 COO to 091 s VK3*0H \ s s \ \ r o e s s 8 ejgei s s, 8 e S 8 § ggssg.gggsss I 8 I S SmgsiapgSM dividing the first column, and transferring to the standard form gives 3i * T siw*. v- /+ S'm 'T* /t-Sf-T •= o I S /x > Thus, by plotting = 'A X, = * , X/ girt f si« r X i “ !* Sin T , KZ = li-S.nT s ' - / K * 3 • ' , in terms of l/L, 'T , and , a nomograph for the calculation of l/L may be prepared. Since the usual range of /•< is c»< /-c ^ V 5"° the lim it on Y^ for the determinant is 0.5>, while the maximum value of l/L equals Y^ is 1 . 0 , it is desirable to expand the scale to Y^ equals 1 . 0 . To accomplish this the determinant is multiplied by the post-factor determinant I a o to give 5 i*\ T c si«. T l+Sm'f' i+ s■/« r c +/ '/L L etting p = , dividing the first row by + 0 , the second by (c.+-i ), then /3 C&tl C/bi-t now for f* = h5°, sin^ M = O.fjO and it is desirable to have = 1, thus o,«r 1 j ' C^o.5 " c + f and after reduction to standard form the determinat becomes S im . T Z S>~'T ?.+ si„r 2 - t S . k 'T 1 z Thus the nomograph for the Lorentz factor correction, as shown in Figure 3 f , was obtained by plotting V, = o Y t c ' / i - in terms of l/L, /*- , and *T . Atomic Structure Factors. In the calculation of the structure factors for various reflections, values of the atomic structure factor as a function of sin & and the atomic number are required. Since the value of sin © may be readily calculated from ^ and A , it seemed desirable to be able to calculate all of the required atomic structure factors for all reflections at the same time. Using the atomic scattering factors from the Internationale Tabellen ^SZ\ the Cu atomic structure factor curves for Li , Cl, C, and 0 as a function of sin & were drawn. Using the data from these curves, the sin®"'- structure factor nomograph shown in Figure 3 & was constructed. Angle Measurement. Since most Weissenberg equi-inclination photo graphs may be indexed by inspection, i t i s desirable to have a rapid method for the measurement of , the off-axis angle. For the Weissenberg camera at this laboratory the film-holder diameter is 5>7.3 mm., therefore the off-axis angle in degrees is twice the m illi meter distance of the spot from the center of the direct beam line. A plexiglass plate slightly larger than the film (3" x 7") was ruled with parallel lines spaced 1.00 mm. apart, and the lines graduated in terms of the off-axis angle T . By planing the Weissenberg equi- inclination photograph on the plate with the direct beam, line centered on the T-0 line, it is possible to estimate rapidly the values of t? directly to o.2 for all the observed reflections. These values com bined with the known inclination angles may be used to calculate quickly the Lorentz and polarization correction factors, sin © , and the atomic scattering factors. The procedure -was checked by the cal culation of sin© for a series of (hOl) reflections observed on a series of (hki) Weissenberg equi-inclination photographs by using the nomographs and ty using the known lattice constants. The results of the calculation given in Table show that the method fox- measuring is capable of giving sin® values accurate to 1%. The nomographs for the Lorentz and polarization factors are accurate to better than while the atomic structure factor nomograph permits the estimation of the atomic structure factor to 0.1 units. 163 o TABLE /S' Sin© calculated from the measured using the nomographs, and from the observed lattice constants. sin O sin & hkl ■/* nomograph calculated hoo 0 0.139 0 .1 i*3 600 0 0 . 211* 0.215 800 0 0.283 0°.286 1000 0 0.360 0.358 602 8.2 0.290 0.292 1202 8.2 0.1*87 0-1*92 1602 8.2 0.633 0.63U 113 12.It 0.278 0.27U 1113 12 .U 0.515 0.522 313 12.k 0.306 0.308 60k 12.k 0.1*ll* 0.1*17 80U 12.h 0 .1*68 o.ii7l 606 25.U5 O.khl 0.1*33 206 25.U5 0.1*71 0.1*75 1006 25.1*5 0.509 0.505 !&*■ Appendix g (hkl) Structure Factors Fi * Absolute structure factor per Wo molecule unit calculated using Marker’s method ex cluding the temperature factor. Squared data used to prepare the Patterson maps. F2 - Absolute structure factor per Wo molecule un it calcu lated using Marker’ s method in clu d - the temperature factor. 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In this structure determination it was assumed that the crystals were isomorphous with the holohedral orthor hombic crystal class D2h - mmm. The crystals grox'm from aqueous solu tion exhibit the forms (100), (001), and (110) and exhibit cleavage planes parallel to the (110) planes. It is observed, however, that the (100) and (100) planes do not appear equally developed. In the majority of the crystals only one (100) pinacoid is observed. The pyroelectric properties of the crystals x^ere investigated using the techniques described by Bunn. The tests xtfere all positive and the crystals do not have a center of symmetry. The data thus suggests that the crystals are actually isomorphous with the hemimorphic hemihedral orthorhombic crystal class G^ - 2mm. From rotation photographs for the three principle axes of the crystal M iller concluded that the orthorhombic unit cell dimensions x^ere as folloxtfs: a0 = 6.7k 0,0k A. b0 = 10.81 ± O.Ol; A. c 0 = 6.U8 ± O.Olt A. This unit cell contained four molecules of LiOOCCH^.PHgO. The ob served extinction rule (h +lc) = 2n indicated that cell was based on 172 a c-centered Bravais lattice. The crystals were therefore con- sidered to be isomorphous with the holohedral space group — C The noncentrosymmetric space group — C_ was rejected because 2v 2 mm of the assumption that the crystals were holohedral. A series of Weissenberg equi-inclination photographs for the three principal axes have been prepared using small crystals obtained by cleavage from a large crystal. In the (hko) reflection series the following weak reflections indexed using M iller's unit cell was observed: (hOO) — (1.5,0,0); (2.5,0,0) (OkO) — (0,2.5,0)5 (030); (050) (hkO) — (2.5, 2.5, 0) Thus, to eliminate the fractional indices, the cell edges in the a and b directions must be doubled, and the extinction rule (h 4 k) - 2n is eliminated. The revised unit cell dimensions are a0 = 2x 6.7k - 13.1*8 A. bQ = 2x 10.81 = 21.62 A. c 0 = 6.1*8 A. The true space group for the crystals examined is — ^2mm k general positions and 16 molecules of LiOOCCH^^HgO per unit cell. Before further work is performed on the determination of the crystal structure of this compound, x-ray diffraction photographs of numerous different crystals should be prepared in order to establish conclusively that the occurrence of the weak reflections described above i s a general fa c t for th is compound. 173 APPENDIX k CRYSTALLINE SALTS OF TRICHLOROACETIC ACID DESCRIBED IN THE CHEMICAL LITERATURE (B) = (00CCC13)“ Compound. R e fe re n c e Li (B)*2H20 Clermont, Compt. Rend. 7h, 9kb (1 8 7 0 ) Na (B)*3H20 Clermont, Compt. Rend. 73>, 302 ( I 8 6 9 ) K (B) ‘iH^O Clermont, Corpt. Rend. 73, 302 ( I 8 6 9 ) K (B)*HB F.M.Jaeger, Z. Krist. 3 0 , 2l& (1 9 1 1 ) Rb (B)*HB F.M.Jaeger, Z. Krist. 3 0 , 2l<7 (1 9 1 1 ) Cs (B)-HB F.M.Jaeger, Z. Krist. 30, 2h8 (1 9 1 1 ) T1 (B)*HB Clermont, Corrpt. Rend. 7b, 1^92 (B)*HB F.M.Jaeger, Z. Krist. 30, 232 (1 9 1 1 ) Be (B)2*2H20 C.L.Parson and G.T.Sargeant, J.Am.Chein.Soc, 1203 (1909) .Mg (B)2 *itH20 Clermont, Compt. Rend. 7k, 9k3 (1 8 7 0 ) Ca (B)2 *6H20 Clermont, Compt. Rend. 73, 302 (1 8 6 9 ) Ba (B)2*6H20 Clermont, Conpt. Rend. 73j 302 ( 1 8 6 9 ) Sr (B)2‘6H20 Clermont, Conpt. Rend. 7_3, 302 ( I 8 6 9 ) Zn (B)2*6H20 Clermont, Compt. Rend. 7 6 , 773 (1 8 7 1 ) Cu (B)2'3H20 W.G.Bateman and D.B.Conrad, J.Am.Chem.Soc. 2333 (1913) 17^ Compound Reference Hg (B)2 unstable Ib id . Cd (B)2 -lfH 20 L.Fogel, T .Rubinoztein, and A. T aura an ^ Roczniki Chem. 9, 3hQ (1929) Mn (B )2/3tH 20 Ib id . Co (B)2*3|H20 Ib id . Co (B)o *liH90 A.Ablov, Bull.Soc.Chim, 6, U91 (1939) 2 Co(B)2 *Co(OH)2 *iiC2H^OH Ib id . 175 APPENDIX 5 REMOVAL OF THE ORIGIN PEAK IN THE PATTERSON SERIES As discussed in the section on the Patterson interatomic vector maps, the large origin peak frequently masks the interatomic vectors in the origin region. In addition, the Patterson map in the origin region may be distorted by diffraction effects produced by the large origin peak. A procedure for removing the origin peak has been de scribed by Patterson The coefficients for this modified series are derived from the absolute structure factors by the relationship where I is the desired coefficient, /fw / the absolute struc ture factor, and •£» the atomic scattering factor. It is frequently stated that the origin peak may not be readily removed because of the dependence on the theoretical scattering factor curves Actually this is not the case. ( z ) It has been demonstrated by Harker ' that the local average structure factor is related to the atomic scattering factor by the relationship 1 ce) where-the symbol < > denotes the average value of the enclosed func tion, the averages being computed for a range of theta as denoted by the subscript. This relation is used to derive absolute structure factors corrected for thermal vibrations as discussed in .the experi mental section. 176 The expression relating the observed structure factors to the atomic scattering factors is where k is the scale factor used to convert the observed values to absolute values. The desired coefficients for the Patterson series with origin peak removed are or and /< u Thus the Patterson series with origin peak removed may be computed by evaluating the series where the value of the series at any point (uvw) differs from the true value by a scale factor. This procedure for the computation of the series does not require the assumption of any theoretical values for the atomic scattering factors. The only restriction imposed is that the statistical relation for the average structure factor be correct.. It is of interest to note that the resultant series is a convergent series and it is not necessary to introduce any artificial function to produce convergence. 177 BIBLIOGRAPHY 1. J. D. Bernal, Proc. Roy. Soc., London All3, 123 (1926). 2. D. Harker, Am. Mineralogist, 33, 764 (1948). 3. H. J. Bernstein, J. Phys. Chem., 56, 351 (1952). 4. L. F. Fieser and M. Fieser, "Organic Chemistry," D. C. Heath and Co., Boston, (19140, P. 116, 173-74. 5. J. Kendall and C. D. Carpenter, J. Am. Chem. Soc. 36, 2505 (1914). 6. F. A. Landee and I. B. Johns, J. Am. Chem. Soc., 63, 2891 (1941). 7. H. von Halban and J. B rill, Helv. Chim. Acta, 27, 1719 (1944). 8. L. Pauling, "Nature of the Chemical. Bond," Cornell Univ. Press, Ithaca, N. Y., (1942), P. 202. 9. H. 0. Jenkins, Nature, 145, 625 (1940). 10. J. Shorter and F. J. Stubbs, Nature, 163, 65 (1949). 11. 0. E. Frivold and N. G. Olsen, Avhandl. Norske Videnskaps Akad., Oslo I Mat.-Naturv. Klasse No. 7 30 pp. (1944). 12. F. A. Landee and I. B. Johns, J. 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Miller Dissertation: The Determination of the Structure of the Crystalline Lithiam Acetate Dihydrate by means of X-Rays., The Ohio State University, Columbus, Ohio (1938). 82. A. L. Patterson, Phys. Rev. I46, 372 (193l|). 83. R. W. James, "Optical Principles of the Diffraction of X-Rays" G. Bell and Sons, Ltd., London, (I 9 I48 ), P. 377. 183 AUTOBIOGRAPHY I, Donald Tuomij was born in Willoughby, Ohio, September 12, 1920. I received ny secondary education in the public schools of the city of Ashtabula, Ohio. My undergraduate training was obtained at The Ohio State University from which I received the degree Bachelor of Science in June 19i|3. In June 19U3 I received an appointment as a graduate assistant in the Department of Chemistry, The Ohio State University, where I specialized in the field of Physical Chemistry. During the period from January 191*1* to June 191*6, I was employed as a Research Associate and Research Scientist at the Manhattan D istrict, SAM Labora tories at Columbia University, and with its successor, the Carbide and Carbon Chemical Corporation in New York City. In June 19U6 I returned to The Ohio State University to continue ny academic education. During th e Summer, W inter, and Spring Q uarters of 191*6-191*7 I held a Develop ment Fund Fellowship. The Fall Quarter of 191*6 I was an assistant in Analytical Chemistry in the Department of'Chemistry. From June 19h7 to September 191*8, I was an assistant in the Physical Chemistry division of the Department of Chemistry. During the period from September 191*8 to March 19b9, I held the position of Research Assistant on an investi gation of crystal habit modification sponsored by the Office of Naval Research through The Ohio State University Research Foundation. For the period from March 1 9h9 to April 1, 1 9 .3 0 , I was granted a Research Fellowship by the Department of Chemistry. In April 1 9 3 0 I accepted ry lgl* present full-tim e position as a Research Associate of The Ohio State University Research Foundation for the investigation of infra-red photoemissive surfaces, sponsored by the Engineer Research and Development Board, Fort Belvoir, Virginia. 185