146
`
`Acc. Chem. Res. 1983, 16, 146-153
`
`Systematic Analysis of Structural Data as a Research
`Technique in Organic Chemistry
`
`FRANK H. ALLEN, OLGA KENNARD,* and ROBIN TAYLOR
`
`Crystallographic Data Centre, University Chemical Laboratory, Cambridge CB2 1EW, Great Britain
`
`Received April 20, 1982 (Revised Manuscript Received November 1, 1982)
`
`Crystallography is the most powerful method avail-
`able for studying molecular structures. It has become
`increasingly important in recent years with the intro-
`duction of automatic diffractometers and new methods
`of structure solution and refinement. There are now
`more than 30000 organocarbon structures (i.e., organics,
`organometallics, and metal complexes) in the literature,
`a number that is likely to double within 5-7 years.
`Unfortunately, this wealth of information has not been
`greatly exploited; detailed discussions of individual
`crystal structures are commonplace, but systematic
`studies of large numbers of related structures are rarely
`undertaken.
`The purpose of this Account is to illustrate how the
`systematic analysis of crystallographic data can be a
`versatile research technique in organic chemistry.1
`Examples are taken from many areas, including studies
`of bonding theories, conformational analysis, reaction
`pathways and hydrogen bonding. Many of the studies
`were carried out with the aid of the Cambridge Struc-
`tural Database (CSD),2 which is described briefly below.
`
`Cambridge Structural Database (CSD)
`CSD contains results of X-ray and neutron diffraction
`studies of organics, organometallics, and metal com-
`plexes. The information stored for each entry (Table
`I) may be divided into three categories: bibliographic
`information (BIB)? chemical connectivity information
`(CONN), and crystallographic data (DATA). CSD is
`fully comprehensive from 1935 onward, and is also a
`depository for unpublished atomic coordinates.4 The
`database is available in 22 countries and on January 1,
`1982, contained 31631 studies of 28978 different com-
`pounds. About 4000 new entries are added each year.
`The information in CSD is searched and analyzed by
`a system of computer programs;2 examples of program
`input and output are given in Figure 1. The two main
`search programs are BIBSER and CONNSER. BIBSER uses
`the bibliographic information fields italicized in Table
`I to locate entries on the basis of their chemical name,
`
`After graduating from Cambridge University, Olga Kennard worked at the
`Cavendlsh Laboratory and subsequently joined the Medical Research Council
`In London. She returned to Cambrldpe in 1961, as a member of M. R. C,
`External Staff, to build up an X-ray crystallographic unit In the University
`Chemical Laboratory. The Cambridge Crys~aliographio Data Centre (CCDC)
`was established there, under her direction, In 1965. Olga Kennard’e research
`is concerned with biological structures, particularly ollgonucleotides and their
`Interaction with drugs and proteins. She was awarded an Sc,D. (Cantab) in
`1971 and the Structural Chemistry Prize of the Chemical Society In 1980,
`Frank Allen obtained a Ph.D, from London University and did postdoctoral
`crystallographic work at the University of British Columbia. He Joined the
`CCDC in 1970 and has been involved in many aspects of Its development; he
`is a member of the Data Commission of the International Union of Crystal-
`lography. Current research interests Involve applications of the Structural
`Database In physical organic chemistry.
`Robin Taylor obtained a B.A. from Oxford and a Ph.D. in chemical crys-
`tallography from Cambridge University. He held postdoctoral positions in
`York and Pittsburgh before joining the CCDC in 1980. His research interests
`include the structure and energy of hydrogen-bonded systems and the appli-
`cation of statistical methods to crystallographic data.
`
`Table I
`Principal Information Held in the
`Cambridge Structural Database (CSD)
`
`Bibliographic (BIB)
`Compound name(s); qualifying phrase(s) [e.g., neutron
`study, low-temperature study, absolute configuration
`determined]; molecular formula, literature citation;
`chemical class(es) [e.g., 15 = benzene nitro compounds,
`51 = steroids, 58 = alkaloids, etc.]
`
`Chemical Connectivity (CONN)
`Chemical structural diagrams are coded in terms of atom
`and bond properties. Atom properties: atom sequence
`number (n); element symbol (el); no. of connected non-H
`atoms (nca); no. of terminal H atoms (nh); net charge
`(ch). Bond properties: pair of atom sequence numbers
`(n = i, ]); bond type for bond i-j (bt); [see Figure 1, b and
`c].
`
`Crystallographic Data (DATA)
`Unit-cell Parameters; space group; symmetry operators;
`atomic coordinates; accuracy indicators [mean estimated
`standard deviation of C-C bonds, R factor] ; evaluation
`flags [indicating: presence of disorder, presence of errors,
`method used for data collection, etc. ] ; comment text
`[e.g., describing any disorder, or errors in the original
`reference ].
`
`molecular formula, chemical class, etc. (e.g., Figure la).
`CONNSER is used to search for compounds containing
`specific chemical fragments. Program input consists
`of a coded representation of the desired fragment (e.g.,
`the coding in Figure lc would be used to find com-
`pounds containing the substructure shown in Figure
`lb).
`Output from both BmSER and CONNSI~,R consists of a
`listing of all structures in the database that satisfy the
`search criteria, together with the corresponding litera-
`ture references (e.g., Figure 1, parts d and e). The
`RETRIEVE program may now be used to create a file of
`crystallographic data for entries located by the search.
`This DATA subtile can be processed by the programs
`PLUTO78, which produces plots and illustrations (e.g.,
`Figure lf), and GLOOM78, which is used for geometrical
`analysis. GLOOM78 will calculate the intra- and/or in-
`termolecular geometries of all entries in a DATA subtile
`or provide systematic tabulations of selected geome-
`trical parameters for a specific chemical fragment.
`Figure lg is a tabulation of R factor, five independent
`bond lengths, and the torsion angle O(1)-C(2)-C(3)-X
`(X = midpoint of C(4)-C(5)) for the fragment shown
`
`(1) This Account complements an earlier paper that was primarily
`concerned with the chemical interpretation of individual structures:
`Wilson, S. R.; Huffmau, J. C. J. Org. Chem. 1980, 45, 56C-566.
`(2) Allen, F. H.; Bellard, S.; Brice, M. D.; Cartwright, B. A.; Doubleday,
`A.; Higgs, H.; Hummelink, T.; Hummalink-Peters, B. G.; Kennard, O.;
`Motherwell, W. D. S.; Rodgers, J. R.; Watson, D. G. Acta Crystallogr.
`Sect. B 1979, B35, 2331-2339 and references therein.
`(3) Bibliographic information is also published annually in:
`=Molecular Structures and Dimensions~, Kennard, O., Watson, D. G.,
`Allen, F. H., Bellard, S., Eds.; D. Reidel: Dordrecht, The Netherlands.
`(4) Journals involved in this scheme since 1977 include Chemical
`Communications, Tetrahedron, and Tetrahedron Letters.
`
`0001-4842/83/0116-0146501.50/0
`
`© 1983 American Chemical Society
`
`Lupin Ex. 1061 (Page 1 of 8)
`
`

`

`Vol. 16, 1983
`
`Organic Chemistry from Crystal Structures
`
`147
`
`(s)
`
`BIBSER : sample ~uestion]
`
`(i) Find all steroids :
`
`0 *CLASS ’51’
`
`Note ~ Chemical class 51 = steroids
`
`(ii) Find all penicillins published between
`1970 and 1980 inclusive :
`
`O *COMPND ’PENICILL’ and *YEAR ’70-80’
`
`Note : The string PENICILL will locate
`penicillin, penicillanic, penicilloic,
`etc.
`
`(iii) Find all compounds for which absolute
`configuration has been established by
`X-ray methods :
`
`Q *COMPND ’ABSOLUTE CONFIGURATION’
`
`CONNSER : Search ~uery
`[for fragment in (b)]
`
`O Cyclopropyl-carbonyls
`
`Atom
`only
`
`properties:
`nca is specified :
`
`ATI O
`AT2 C
`AT3 C
`AT4 C
`AT5 C
`
`I
`2
`3
`2
`2
`
`properties :
`Bond
`C node numbers, bond-type,
`C and Acyclic/Cyclic flag :
`C
`BO i 2 2 A
`BO 2 3 i A
`BO 3 4 i C
`80 4 5 1 C
`BO 3 5 1 C
`END
`
`(d) BIBSER : Sample Output from Question (a,i)
`
`~e) CONNSER : Sample Biblio@raphic Listin~
`for Search Quer[ (c)
`
`AAMAND
`
`ABAXES
`
`16alpha-Acetyl-3beta-methoxy-CD-cis-D-
`norandrostane
`C21 M34 02; Class 51
`J.Meinwald,A.J.Taggi,P.A.Luhan,
`A.T.McPhail
`Proc.Nat.Acad.Sci.U.S.A., 71, 78, 1974
`
`2alpha-Bromo-17beta-acetoxy-9-methyl-
`5alpha,gbeta,10alpha-estran-3-one
`C21 H31 Srl O31 Class 51
`J.C.A.Boeyens,J.R.Bull,J.Floor,
`A.Tuinman
`J.Chem. Soc.,Perkin I, 808, 1978
`
`CORAMA
`
`(-)-Coronamic acid N-acetate
`(absolute configuration)
`C8 HI3 N1 03; Class 48,20
`A.Ichihara,K.Shirsishi,S.Sakamura,
`A.Furusaki,N.Hashiba,T.Matsumoto
`Tetrahedron Lett., 365, 1979
`
`CPCOHA Cyclopropanecarbohydrazide
`C4 H8 N2 O1; Class 20,9
`D.B.Chesnut,R.E.Marsh
`Acts Crystallogr., ii, 413, 1958
`
`CPRPCXI0 Cyclopropanecarboxamide
`C4 H7 NI Oli Class 20,1
`R.E.Long,N.Maddox,K.N.Trueblood
`Acts Crystsllogr.,Sect.B, 25, 2083, 1969
`
`~fl PLUTO78 : Sample Plc~s for C~clopropanecarboh[drazide [CPCOHA in (e)]
`
`(i) ’stick’ diagram
`
`(ii) ’ball-and-spoke’ style with
`shading and perspective
`
`(iii) ’space-filling’ model with
`shading and perspective
`
`(9) GEOM78 : Example of Geometry Tabulation for Fragment (b)
`CSD code
`
`Notes :
`
`*RFACT C4-C5 C3-C4 C3-C5 C3-C2 C2-O1
`
`TAU
`
`Distances in Angstroms,
`angle (TAU) in degrees.
`
`TAU is the torsion angle :
`O(i) - C(2) - C(3) - X(1),
`where X(1) is the mid-point
`of the bond C(4) - C(5).
`
`CORAMA
`CPCOHA
`CPRPCXI0
`CPEPCXI0
`DCFEDO
`DMCPRC
`MBCFC×
`NPCPMK
`PMCPRCI0
`SDPPCX
`
`0.059
`1.491
`1.534 1.503
`1.502 1.216 28.04
`0.130
`1.478 1.520 1.493
`1.478 1.213
`4.52
`0.087
`1.467 1.485 1.501
`1.484
`1.238 -7.74
`0.087
`1.450
`1.489 1.493
`1.470 1.249 -4.67
`0.047
`1.475 1.515 1.510
`1.456 1.213
`3.19
`0.085
`1.477 1.521
`1.510
`1.456 1.246 -7.30
`0.062
`1.488 1.531
`1.508
`1.480
`1.210 30.07
`0.092
`1.474 1.513 1.488 1.469 1.235
`8.64
`0.037 1.490 1.548 1.505 1.484 1.205 -21.17
`0.042
`1.482 1.533 1.510
`1.470
`1.201 -5.47
`
`STD. DEVN. is the standard
`deviation of each sample.
`The standard deviations of
`the means are 0.004, 0.006,
`MEAN
`0.003, 0.005 and 0.006.
`STD. DEVN.
`Figure I. Examples of input and output for the CSD program system.
`
`1.477 1.519 1.502
`0.012 0.020 0.008
`
`1.475 1.223
`0.014 0.018
`
`in Figure lb. The DATA subfde may also be processed
`by the user’s own programs.
`Systematic Analysis of Intramolecular
`Geometry
`Mean Geometries. The results of early X-ray
`analyses were used to derive mean bond lengths,~ co-
`
`valent radii, etc., which were important in the devel-
`opment of structural chemistry and bonding theories.
`As the number of structural studies increased, it became
`possible to determine the mean geometries of complete
`
`(5) Sutton, L. E., Ed., "Tables of Interatomic Distances and Configu-
`ration in Molecules and Ions~; The Chemical Society: London; Special
`Publication 11 (1958) and 18 (1965).
`
`Lupin Ex. 1061 (Page 2 of 8)
`
`

`

`148
`
`Allen, Kennard, and Taylor
`
`Accounts of Chemical Research
`
`Table II
`Angular Deformations in Substituted Benzenes (IV)a’ b
`
`~(mean),
`
`Linear regression values, degd
`
`X
`
`degc
`
`As
`
`A~
`
`A~
`
`A6
`
`chemical residues. Thus, the average dimensions of
`furanose,~ pyranose,7 and nucleic acid base residuess
`have all been determined. Given these mean values,
`together with their standard deviations, it is easys to
`derive orthogonal coordinates for "standard residues".
`Apart from a variety of crystallographic uses, standard
`geometries are invaluable in model building, paramet-
`erization of empirical force fields, and interpretation
`of new structural data.
`Substituent and Hybridization Effects. Early
`bond length tabulations5 were subdivided on the basis
`of gross differences in hybridization and environment.
`For example, hybridization changes at C* in I-III cause
`
`C-- ~ 1’538C/-- C’--~1’507C/-- C~--~-1"464C~
`
`appreciable bond length alterations, which are easily
`recognized in any individual crystal structure. Smaller
`changes in electron distribution--due, perhaps, to
`substitution and slight rehybridization--produce cor-
`respondingly smaller geometric variations, which are
`often close to the error limits of individual structure
`determinations. These are only discovered by the
`systematic analysis of many related structures. Studies
`of this type provide results that can be correlated with
`theoretical calculations, reactivity, spectral properties,
`and other physical phenomena. Two examples are
`discussed below.
`Substituent-Induced Ring Deformations in Benzene.
`Early microwave and X-ray investigations showed that
`the regular hexagonal geometry of benzene is perturbed
`when the ring is substituted by strong electron-with-
`drawing or -donating groups. With reference to IV,
`
`\
`
`/
`
`deformations due to electron-withdrawing groups in-
`volve an increase in the ipso angle a, a decrease in the
`ortho angles B, and shortening of bonds a with respect
`to bonds b. Deformations due to electron-donating
`groups are in the opposite sense. Only groups with
`strong electronic effects produce deformations that are
`consistently larger than the error limits of individual
`structure determinations.
`The angular deformations (Aa, A~, A% A~ from 120°;
`see IV) in more than 100 mono- and para-disubstituted
`benzenes have been analyzed. Early results9,l° showed
`that Aa is the largest deformation, and that its value
`for a particular substituent X is unaffected by para-
`substitution; A~ was found to be ~---Aa/2. Values of
`a were determined for a variety of substituents (Table
`II) by averaging relevant fragment geometries. It was
`recognized that a-effects predominate in determining
`Aa values.1°,11 This is consistent with the observed
`correlation between a and the electronegativity (X) for
`
`(6) Arnott, S.; Hukins, D. W. L. Biochem. J. 1972, 130, 453-465.
`(7) Arnott, S.; Scott, W. E. J. Chem. Soc., Perkin Trans. H 1972,
`324-335.
`(8) Taylor, R.; Kennard, O. J. Mol. Struct. 1982, 78, 1-28. Taylor, R.;
`Kennard, O. J. Am. Chem. Soc. 1982, 104, 3209-3212.
`(9) Domenicano, A.; Vaciago, A.; Coulson, C. A. Acta Crystallogr.,
`Sect. B 1975, B3I, 221-234.
`(10) Domenicano, A.; Vaciago, A.; Coulson, A. A. Acta Crystallogr.,
`Sect. B 1975, B31, 1630-1641.
`(11) Domenicano, A.; Mazzeo, P.; Vaciago, A. Tetrahedron Left. 1976,
`1029-1032.
`
`N(Me)~
`Ph
`Me
`CH=CHR
`COMe
`COOH
`OMe
`CN
`C1
`NO~,
`F
`
`117.2
`117.6
`118.1
`118.0
`118.8
`119.8
`119.9
`121.8
`121.4
`122.1
`123.4
`
`-2.4 (3)
`-2.3 (2)
`-1.9 (2)
`-1,8(2)
`-1.0(2)
`0.1 (2)
`0.2 (2)
`1.1 (2)
`1,9 (2)
`2.9 (2)
`3,4 (2)
`
`1.4 (2)
`0.6 (2)
`1.0(1) 0.6 (1)
`1.0 (1) 0.4 (1)
`0.3 (1)
`0.8 (1)
`0.4 (1) 0.2 (1)
`-0.2 (1) 0.1(1)
`1.1 (1)
`-0.6 (1)
`-0.8(1) 0.3 (1)
`-1.4 (1) 0.6 (1)
`-1.9 (1) 0,3(t)
`-2.0 (1) 0.5 (1)
`a Standard deviations in c~ (mean) are in the range 0.1-
`0.2o. b Substitution reduces perfect D6h ring symmetry to
`C~v;henceA~ + 2A/3+ 2A7+ A6 =0, c Reference 11.
`d Reference 13.
`
`-1.7 (3)
`-0.9 (2)
`-0.8 (2)
`-0.4 (2)
`-0.3 (2)
`0.2 (2)
`-1.1 (2)
`-0.1 (2)
`-0.2 (2)
`0.4 (1)
`-0.4 (2)
`
`first-row functional groups11 and second-row elements1°
`(Figure 2a,b). Later,12 it was realized that substituents
`that interact with the benzene ~r-system also produce
`significant deformations (A% A~). Factor analysis
`showed that all substituent-induced deformations can
`be ascribed to two independent effects, which were in-
`terpreted as a- and ~r-interactions.~3 Values of A~, A~,
`AT, A5 for 21 functional groups were derived by linear
`regression, the geometries of 71 mono- and para-di-
`substituted benzenes (Table II)~4 being used.
`The marked sensitivity of a to a-effects, evidenced
`by the a-x plots, is confirmed by the plot~,~ of Aa
`against the Taftzs inductive parameter, a~ (Figure 2c).
`The sensitivity of ~/to ~r-effects is shown by the A-r-aa°
`plot13 in Figure 2d (aao = Taft resonance parameterlS).
`These correlations suggest that A-values may be a useful
`addition to traditional reactivity parameters, since they
`measure substituent effects on the ring in the ground
`state, do not depend on the choice of a suitable reaction
`series, are independent of solvent effects, and can be
`related to conformational changes.
`Conjugation and Hybridization in Three-Mernbered
`Rings. Cyclopropane is unusual among cycloalkanes in
`that it conjugates with ~r-acceptor substituents,~ as is
`shown by spectroscopic results17 and the stabilization
`of carbonium ions by cyclopropane. Molecular orbital
`theory suggests~s that conjugation involves transfer of
`electron density from the cyclopropane 3e’ orbitals to
`the ~r* orbitals of the substituent (V). This would be
`
`v
`
`Vl
`
`R2
`VII
`
`(12) Domenicano, A.; Vaciago, A. Acta Crystallogr., Sect. B 1979, B35,
`1382-1388.
`(13) Domenicano, A.; Murray-Rust, P. Tetrahedron Lett. 1979,
`2283-2286.
`(14) A similar independent analysis is described by: Norrestam, R.;
`Schepper, L. Acta Chem. Scand. Sec. A 1981, A35, 91-103. The two sets
`of angle deformations have a correlation coefficient of 0.966 and a root
`mean square deviation of 0.22%
`(15) Ehrenson, S.; Brownlee, R. T. C.; Taft, R. W. Prog. Phys. Org.
`Chem. 1973, 10, 1-80.
`(16) Charton, M. "The Chemistry of Alkenes’; Zabicky, J., Ed.; In-
`terscience, London, 1970; Vol. II, pp 511-610.
`(17) Pete, J.-P. Bull. Soc. Chim. Ft. 1967, 357-370.
`(18) Hoffmann, R. J. Chem. Phys. 1964, 40, 2480-2488. Hoffmann R.;
`Stohrer, W.-D. J. Am. Chem. Soc. 1971, 93, 6941-6948.
`
`Lupin Ex. 1061 (Page 3 of 8)
`
`

`

`Vol. 16, 1983
`
`(a)
`
`~(o)
`124
`
`122
`
`120
`
`116
`
`4.0
`
`0’0
`
`(c)
`
`Organic Chemistry [rom Crystal Structures
`(b)
`
`149
`
`120’,
`
`p III
`
`Si
`
`/=
`AI
`
`(d)
`
`A ~ P1
`
`1.o.
`
`0.5¸
`
`o.oo o’,~o o:,o o:so o, - o:,~o -o:2o o:oo o:zo o~
`
`Figure 2. Correlation of substituent-induced angular deformations in benzene with electronegativity (x) and Taft parameters (~).
`The ipso ang.le (a in IV) is plotted (a) against x for first-row functional groups (Reprinted with permission from ref 11. Copyright
`1976, Pergamon Press Ltd.) and (b) against × for second-row elements (Reprinted with permission from ref 10. Copyright 1975, International
`Union of Crystallography). In (c) the deformation Aa is plotted against the inductive parameter ai (Reprinted with permission from
`ref 13. Copyright 1979, Pergamon Press Ltd.),while in (d) the deformation A? is plotted against aR° (Reprinted with permission from
`ref 13. Copyright 1979, Pergamon Press Ltd.). We gratefully acknowledge permission to reproduce these plots from Dr. Aldo Domenicano
`and the copyright holders.
`
`expected to shorten the distal (2-3) bond by ~ and in-
`crease the vicinal (1-2,1-3) bonds by ~/2. However,
`the degree of conjugation will depend on the extent of
`orbital overlap, which is maximized in the cis- and
`trans-bisected conformations (Newman projections VI
`and VII, respectively).19
`In order to quantify these effects, Allen2° analyzed
`results from 146 X-ray studies of cyclopropane deriva-
`tives. The mean geometry of nonconjugated cyclo-
`propanes was established by using purely C(sp3) de-
`rivatives (VIII). Substituent-induced bond length
`
`C----C1__R
`
`VIII
`
`IX
`
`X
`
`XI
`
`asymmetries were consistently observed in the geome-
`tries of derivatives involving the ~-acceptor substituents
`--C---~O (ketones, acids, esters; see Figure lg for a typ-
`ical geometrical tabulation), --C-~C, and --CN. It was
`found that multiple substitution produces net distor-
`
`Table III
`Asymmetry Parametera for
`CyclopropaneRingsHaving ~-Acceptor Substituents
`
`subst.
`c=o
`C=C
`Ph
`
`~, A
`-0.026 (5)
`-0.022 (4)
`-0.018 (-)
`
`subst.
`N=C
`CN
`N:N
`
`~, A
`-0.0~S (-)
`-0.017 (2)
`-0.014 (-)
`
`a Reference 20.
`
`tions that can be approximated by simple sums of in-
`dividual substituent effects. The bond length asym-
`metry parameters (6 in the preceding paragraph) due
`to some representative substituents are given in Table
`III. The variation of bond length asymmetries with
`conformation suggests2°,2~ that conjugative overlap of
`ring and accepter orbitals is effective for --C~O and
`C----C conformations within 30° of the bisected positions
`(VI, VII). These results are in agreement with ultra-
`violet spectral data}7
`Cyclopropane is also unusual because its protons
`exhibit vinylic properties.1~ This is consistent with the
`
`(19) Hoffmann, R. Tetrahedron Lett. 1970, 2907-2909. Hoffmann, R.;
`Davidson, R. B. J. Am. Chem. Soc. 1971, 93, 5699-5705.
`(20) Allen, F. H. Acta Crystallogr., Sect. B 1980, B36, 81-96.
`
`(21) Allen, F. H. In "Molecular Structure and Biological Activity";
`Griffin, J. F., Duax, W. L., Eds.; Elsevier Biomedical: New York, 1982;
`105-116.
`
`Lupin Ex. 1061 (Page 4 of 8)
`
`

`

`150
`
`Allen, Kennard, and Taylor
`
`Accounts of Chemical Research
`
`Table IV
`Variation in the C(I )-R Bond Lengtha in IX-XI due to
`Changes in Hybridization (h)and to Conjugative Effects (c)
`fragment
`X
`
`R
`
`IX
`
`XI
`
`h(~x )b h(sp~)b
`
`This is illustrated by the following example.
`The relative rates of condensation with benzaldehyde
`of a series of 3-keto-5a steroids (XII) were determined
`Ph
`
`XII
`
`XIII
`
`C8
`
`OH
`
`XIV
`
`XV
`
`by Barton et al.~s The 2-benzylidene ketone XIII is
`exclusively formed by elimination of OH-, the reaction
`involving rehybridization of C(2) from sp3 to sp~. The
`presence of ethylenic links and/or substituents at
`positions remote from the reaction center was found to
`produce large differences in reaction rates. It was
`therefore inferred that gross conformational changes at
`remote sites produce small changes--here at C(2)--by
`"conformational transmission". This influences the rate
`of condensation, r, which may be expressed as2s
`r = r0II.]i
`where r0 is the rate for saturated XII and the fi are
`~group rate factors" for remote substituents or double
`bonds.
`The crystal structure2~ of cholest-6-en-3-one (XIV),
`which has the highest reaction rate (r = 645), shows an
`unusually flat A ring, with a mean ring torsion angle
`~ (=~]~o~/6 in XII) of only 50.4°. The flattening is
`especially pronounced at C(2), where w12 (=(o~z + o~)/2
`in XII) is 42.2°. The ring bond angle at C(2), v, is
`correspondingly high at 114.4 (8)°. In contrast, the
`structure3° of 17&hydroxyandrostan-3-one (XV), which
`has a much lower reaction rate (r = 188), shows ~ =
`54.1°, Wl~ = 51.7°, and v = 110.7°. Clearly, C(2) is more
`prepared to undergo rehybridization in XIV than in
`XV.~ An analysis~1 of several other A-ring conforma-
`tions confirmed that the reaction rate tends to increase
`as the ring becomes flattened at C(2). The parameter
`~ = w~2 - a~ was used to express the relative puckering
`in each ring (negative a represents flattening at C(2)).
`For steroids with r = 33, 188, 235, and 645, the corre-
`sponding mean values of ~ were 2.6, -2.8, -3.3, and
`-8.3°. Although the data are limited, the r--~ correlation
`is qualitatively acceptable.
`Systematic Analysis of Intermolecular
`Interactions
`Hydrogen-Bonding Studies. Systematic analyses
`of crystal structures have made a significant contribu-
`tion to our knowledge of hydrogen bonding. Studies
`of O-H...O and C-H...O bonds are discussed below.
`
`(28) Barton, D. H. R.; Head, A. J.; May, P. J. J. Chem. Soc. 1957,
`935-944. Barton, D. H. R.; McCapra, F.; May, P. J.; Thudium, F. J.
`Chem. Soc. 1960, 1297-1311.
`(29) Guy, J. J.; Allen, F. H.; Kennard, O.; Sheldrick, G. M. Acta
`Crystallogr., Sect. B 1977, B33, 1236-1244.
`(30) Courseille, C.; Precigoux, G.; Leroy, F.; Busetta, B. Cryst. Struct.
`Commun. 1973, 2, 441-446.
`
`Lupin Ex. 1061 (Page 5 of 8)
`
`1.538
`1.507
`
`1.512
`
`1.514
`
`C sp3
`C=C
`
`C=O
`(keto)
`
`1.507 -0.019 -0.031
`1.519
`h
`1.472 -0.027 -0.035
`1.480
`h
`1.458
`1.470
`h + c
`-0.010 -0.014
`c
`1.489
`1.482 -0.023 -0.030
`h
`1.474
`!.460
`h + c
`-0.015 -0.022
`c
`1.504
`1.497 -0.010 -0.017
`C=O
`h
`1.484
`1.470
`h + c
`(acids,
`-0.020 -0.027
`esters)
`c
`a Reference 22. b h(A)=h(X)-h(IX),h(sp~)=h(XI)-
`
`h(IX) for each substituent R (see text).
`
`abnormally short exocyclic C-C bond in derivatives of
`the type VIII (cf. I, II).2°,22 Theoretical models23 in-
`dicate that the C(ring) hybrid involved in the exocyclic
`C-C bond in VIII is ~sp~, whereas those involved in
`the ring a-bonds are ~,-sp5. Hybridization in cycle-
`propane was studied in details~ by comparing the C-R
`distances in the related fragments IX-XI (R = C(sp3),
`vinyl, keto, acid, ester). In those cases where conjuga-
`tion can occur (i.e., X and XI with R -- --C----C or
`--C~O), two C-R distances were obtained, for (i)
`conformations outside the ranges established for ef-
`fective conjugation (this is a measure of hybridization
`effects (h)) and (ii) conjugative conformations, where
`C-R is further shortened by ~r-effects (c). Represent-
`ative results are given in Table IV. The relative bond
`length contractions due to hybridization, defined by
`h(A) -- [R-C(cyclopropane)]h- [R-C(sp3)]
`
`h(sp2) = [R-C(sp2)]h- [R-C(sp3)]
`
`can be used to infer the hybridization of the cycle-
`propane ring atoms. Values of h(A)/h(sp2) range from
`59 to 77 %. The mean, 69%, corresponds to sp2’~s hy-
`bridization (30.8% s character) in exocyclic bonds;
`hence, ring ~-hybrids are sp4’20 (19.2% s). Table IV also
`permits comparison of the relative conjugative abilities
`of cyclopropane and the vinyl group,is The ratios
`c(A)/c(sp~) average to 71%, which compares well with
`a UV bathochromic shift ratio of ~60%.17
`Conformational Analysis. Comparative reviews of
`steroids,~4 alkaloids and terpenes,z5 and medium rings26
`illustrate the extensive application of crystallographic
`data to conformational analysis.~7 In the present re-
`view, we are particularly concerned with the systematic
`analysis of solid-state conformations. Although some
`molecules are known to adopt different conformations
`in solution and in the crystalline state, it has been
`shown that solid-state conformational data can be
`successfully related to solution properties, provided that
`a sufficient number of crystal structures are studied.
`
`(22) Allen, F. H. Acta Crystallogr., Sect. B 1981, B37, 890-900.
`(23) Bernett, W. A. J. Chem. Educ. 1967, 44, 17-24 and references
`therein.
`(24) Altona, C.; Geise, H. J.; Romers, C. Tetrahedron 1968, 24, 13-32.
`Duax, W. L.; Norton, D. A. "Atlas of Steroid Structures~; Plenum:
`London, 1975. Duax, W. L.; Weeks, C. M.; Rohrer, D. C. Recent Prog.
`Herin. Res. 1976, 32, 81-116.
`(25) Mathieson, A. McL. Perspect. Struct. Chem. 1967, 1, 41-108.
`(26) Dunitz, J. D. Perspect. Struct. Chem. 1968, 2, 1-70.
`(27) The correlation of crystal structure conformations with pharma-
`ceutical activity cannot be covered adequately here. Interested readers
`are referred to: Griffin, J. F.; Duax, W. L., Eds., "Molecular Structure
`and Biological Activity’; Elsevier Biomedical: New York, 1982.
`
`

`

`Vol. 16, 1983
`
`Organic Chemistry [rom Crystal Structures
`
`151
`
`15
`
`0-~., .0 ~0~
`O...H
`Figure 3. Distribution of 0...H distances (A) and O-H...O angles
`(o) in O-H...O hydrogen bonds (ref 31).
`
`O-H...O Hydrogen Bonds. The distributions of O-.-H
`distances and O-H...O angles were determined in a
`survey of the neutron diffraction geometries of 74 O-
`H...O< bonds (Figure 3).31 The mean values are 1.818
`(9) A and 167.1 (8)°, respectively. The latter is in good
`agreement with the most probable value predicted by
`molecular orbital calculations (163°).82 For hydrogen
`bonds with O...H < 1.812 A (the median O...H distance
`of the sample) the mean O-H...O angle was 168.4 (9)°,
`compared with 165.8 (12)° for bonds with O...H > 1.812
`A. The difference between these means is statistically
`significant at the 92.5% level, which suggests that short
`hydrogen bonds tend to be more linear than long ones.
`This can be ascribed to the unfavorable van der Waals
`interaction between the oxygen atoms in short, non-
`linear O-H...O bonds.8s
`In the same study?1 it was found that the proton in
`XVI tends to lie in, or near to, the plane containing the
`
`0/R1
`\R~
`
`xvI
`lone-pair orbitals of the acceptor atom (assumed to be
`the plane bisecting the R1-O-P~ angle). However, there
`was no evidence of a preferred direction within the
`plane. Apparently, hydrogen bonding does not occur
`preferentially along the directions which correspond to
`idealized spa lone-pair orbitals. This finding is con-
`sistent with charge density studies?4 which show the
`lone-pair electron density of sp3 oxygen atoms to be
`rather diffuse, bearing little resemblance to the simple
`"rabbit-ear" model. The directional influence of the
`lone pairs may be more important in hydrogen bonds
`that involve carbonyl acceptors3s because the angular
`separation of sp2 lone pairs is greater than that of sps
`lone pairs.
`Theoretical calculations~ suggest that the length of
`an O-H...O bond should be dependent on its environ-
`ment. Specifically, hydrogen bonds belonging to infinite
`¯ ..O-H...0-H... chains should be stronger, and therefore
`shorter, than isolated O-H...O bonds (the so-called
`"cooperative effect"). This is due to the changes that
`occur in the electron densities at the oxygen and hy-
`
`(31) Ceccarelli, C.; Jeffrey, G. A.; Taylor, R. J. Mol. Struct. 1981, 70,
`255-271.
`(32) Newton, M. D.; Jeffrey, G. A.; TAIr~, S. J. Am. Chem. Soc. 1979,
`101, 1997-2002.
`(33) Taylor, R. J. Mol. Struct. 1981, 73, 125-136.
`(34) For example, Diercksen, G. H. F. Theor. Chim. Acta 1971, 21,
`335-367.
`(35) Olovsson, I.; JSnsson, P.-G. In =The Hydrogen Bond--Recent
`Developments in Theory and Experiments"; Schuster, P., Zundel, G.,
`Sandorfy, C., Eds.; Elsevier North-Holland: Amsterdam, 1976; Vol II
`416-420.
`(36) Del Bene, J. E.; Pople, J. A. J. Chem. Phys. 1973, 58, 3605-3608.
`
`drogen atoms upon hydrogen-bond formation. The
`mean 0...H distance of hydrogen bonds belonging to
`infinite chains was foundsl to be 1.805 (9) A, compared
`with 1.869 (23) A for isolated hydrogen bonds. The
`difference between these means is statistically signifi-
`cant at the 99.5% level, thus confirming the theoretical
`prediction. Many of the hydrogen-bond patterns ob-
`served in carbohydrate crystal structures can be ra-
`tionalized by the cooperative effect.37 For example, all
`of the hydrogen bonding in sugar alcohol structures is
`of the favorable infinite chain variety. These structures
`are ideally suited to this type of arrangement because
`they possess only hydroxyl groups; i.e., there is a 1:1
`ratio of hydrogen-bond donor and acceptor atoms.
`Thus, it is possible for infinite ...O-H...O-H... chains to
`incorporate all of the oxygen atoms in the structure.
`This is not the case in cyclic pyranoses, where the ring
`oxygen atom can accept but not donate hydrogen
`bonds. It therefore acts as a chain stopper and is often
`completely excluded from the hydrogen-bonding
`schemes in pyranose crystal structures.37
`C-H...O Hydrogen Bonds. The hydrogen-bonding
`schemes observed in the structures of other biologically
`important molecules (e.g., amino acids, nucleosides) are
`more difficult to interpret. Nevertheless, some useful
`results were obtained in a recent survey of hydrogen-
`bond patterns in amino acid structures.~ Among these
`was the observation that short C-H...O contacts are
`relatively common in amino acid crystal structures,
`particularly when the C-H group is adjacent to a +NH8
`group. Thus, C-H...O hydrogen bonding may be a
`significant factor in determining the conformations and
`crystal-packing arrangements of amino acids. This
`conclusion was supported by an analysis39 of the crys-
`tallographic environments of 661 (C-)H atoms (i.e.,
`hydrogen atoms covalently bonded to carbon), observed
`by neutron diffraction in 113 organic crystal structures.
`Fifty-nine C-H...O contacts (of which 41 were inter-
`molecular) were found with H...O < 2.4 A and C-H...O
`> 90°; 2.4 A is 0.3 A shorter than the sum of the van
`der Waals radii of H and O, using the values of Bondi
`and Kitaigorodsky.4° In contrast, short C-H...C and
`C-H...H contacts were found to be extremely rare: it
`was established that (C-)H atoms have a statistically
`significant (> 99.9%) tendency to form short intermo-
`lecular contacts to oxygen rather than carbon or hy-
`drogen. The proton in the majority of short C-H...O
`contacts lies within 30° of the plane containing the
`oxygen lone pairsJ9
`The (C-)H atoms involved in the 10 shortest C-H...O
`contacts found in the above survey are underlined in
`XVII-XXVI. Eight of them are immediately adjacent
`to nitrogen; the other two belong to nitrogen-containing
`aromatic molecules. Presumably, the inductive effect
`of nitrogen decreases the electron density at nearby
`(C-)H atoms, thereby enhancing their ability to form
`short C-H...0 contacts.
`Inference of