CONFERENCE PROCEEDINGS SERIES
`
`EDITED BY
`Allan S. Myerson
`Polytechnic University
`
`Daniel A. Green
`DuPont
`
`Paul Meenan
`DuPont
`
`Proceedings of a conference sponsored
`by E.I. du Pont de Nemours and Company,
`Biosym/Molecular Simulations,
`and American Institute of Chemical Engineers
`Washington, D.C.,
`August 27-31, 1995
`
`American Chemical Society, Washington, DC
`
`Lupin Ex. 1036 (Page 1 of 15)
`
`

`

`Library of Congress Cataloging-in-Publication Data
`
`Crystal growth of organic materials / edited by Allan S. Myerson, Daniel A.
`Green,. Paul Meenan.
`
`p. cm.--(Conference proceedings series, ISSN 1054-7487)
`
`"Proceedings of a conference sponsored by E.I. du Pont de Nemours and
`Company, Biosym/Molecular Simulations, and American Institute of Chemical
`Engineers, Washington, D.C., August 27-31, 1995."
`
`Papers from the Third International Workshop on Crystal Growth of Organic
`Materials.
`
`Includes bibliographical references and index.
`
`ISBN ~?-8412-3382-9 (alk. paper)
`
`1. Crystallization--Industrial applications--Congresses. 2. Chemistry,
`Organic--Industrial applications--Congresses.
`
`I. Myerson, Allan S., 1952- . II. Green, Daniel A~, 1958- . III. Meenan,
`Paul, 1965- . IV. E.I. du Pont de Nemours and Company.
`V. Biosym/Molecular Simulations Inc. VI. American Institute of Chemical
`Engineers. VII. International Workshop on Crystal Growth of Organic
`Materials (3rd: 1995: Washington, D.C.) VIII. Series: Conference proceedings
`series (American Chemical Society)
`
`TP156.C57C79 1996
`661 ’.8--dc20
`
`Copyright © 1996
`
`American Chemical Society
`
`96-1348
`CIP
`
`All Rights Reserved. The appearance of the code at the bottom of the first page of each chapter
`in this volume indicates the copyright owner’s consent that reprographic copies of the chapter
`may be made for personal or internal use or for the personal or internal use of specific clients.
`This consent is given on the condition, however, that the copier pay the stated per-copy fee
`through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, for
`copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent
`does not extend to copying or transmission by any means--graphic or electronic--for any other
`purpose, such as for general distribution, for advertising or promotional purposes, for creating a
`new collective work, for resale, or for information storage and retrieval systems. The copying fee
`for each chapter is indicated in the code at the bottom of the first page of the chapter.
`
`The citation of trade names and/or names of manufacturers in this publication is not to be
`construed as an endorsement or as approval by ACS of the commercial products or services
`referenced herein; nor should the mere reference herein to any drawing, specification, chemical
`process, or other data be regarded as a license or as a conveyance of any right or permission to
`the holder, reader, or any other person or corporation, to manufacture, reproduce, use, or sell any
`patented invention or copyrighted work that may in any way be related thereto. Registered
`names, trademarks, etc., used in this publication, even without specific indication thereof, are not
`to be considered unprotected by law.
`
`PRINTED IN THE UNITED STATES OF AMERICA
`
`Lupin Ex. 1036 (Page 2 of 15)
`
`

`

`The Application Of Computational Chemistry to the Study Of Molecular
`Materials.
`
`R. Docherty, Zeneca Specialties Research Centre, Hexagon House, Blackley,
`Manchester England M9 8ZS.
`
`An understanding of the specific arrangements of molecules in the solid
`state allows the chemist to manipulate the solid state to optimise the performance
`characteristic of interest. In this paper the application of molecular modelling and
`computational chemistry techniques to the study of molecular materials will be
`described including lattice energy calculations, crystal shape prediction property
`estimation methods and crystal structure prediction/determination. The potential
`and limitations of these methods will be discussed.
`
`Introduction
`
`An understanding of the specific
`arrangements adopted by molecules within the
`crystal lattice allows the solid state chemist to
`manipulate the crystal chemistry to optimise the
`performance characteristic of interest.
`Given the importance of crystal
`engineering and polymorph control to the
`development and production of a vast range of
`speciality chemicals (i.e. pharmaceuticals,
`agrochemicals, pigments, dyes, opto-electronic
`materials and explosives) it is not surprising that
`many techniques are applied to improve our
`understanding of the solid state structure of such
`materials. Over recent years molecular modelling
`and computational chemistry have played and
`increasingly important role in this field.
`The solid state arrangement(s) adopted by
`a molecules depends on the subtle balance of
`intermolecular interactions that it can achieve for
`a given conformation in a particular packing
`arrangement. Crystallisation and the properties of
`the solid state are dependent on a process which
`is essentially molecular recognition on a grand
`scale. Polymorphism and changes in properties
`are due to the recognition of different balances of
`these subtle interactions. In this paper the use of
`molecular modelling to establish the link between
`molecular structure, intermolecular interactions
`packing motifs and solid state property will be
`illustrated.
`
`Molecular Modelling
`
`Molecular modelling and computational
`
`chemistry methods operate on three levels. Firstly
`
`molecular modelling is almost unique in it’s
`ability in allowing the examination of the
`detailed, complex and often elegant arrangements
`of molecules, proteins, fibres, polymers, surfaces
`and solid state structures. Secondly in
`conjunction with computational chemistry
`molecular modelling permits the determination of
`structure activity relationships (SAR’s) linking
`calculated properties and hence molecular
`structure to performance characteristics.
`Ultimately it enables (based in these SAR’s) the
`design of novel molecular/solid state structures
`with improved properties and performance
`characteristics.
`
`The Crystal Chemistry Of Molecular Materials
`
`The structures and crystal chemistry of
`molecular materials are often classified into
`different categories according to the type of
`intermolecular forces present. These include;
`
`* simple Van der Waals attractive interactions,
`* classical hydrogen bonding (Taylor, 1982),
`* electrostatic interactions,
`* C-H:::::O non classical hydrogen bonding,
`* short directional contacts (Desiraju, 1989).
`
`Molecules can essentially be regarded as
`impenetrable systems whose shape and volume
`characteristics are governed by the molecular
`conformation and the radii of their constituent
`atoms. The general uneven, awkward shape of
`molecular structures tends to result in unequal
`unit cell parameters being adopted during
`crystallisation. The vast maj ority of the structures
`
`1054-7487/96/0002512.00/0 @ 1996 American Chemical Society
`
`Lupin Ex. 1036 (Page 3 of 15)
`
`

`

`reported prefer the triclinic, monoclinic and
`orthorhombic crystal systems.
`A useful parameter for judging the
`efficiency of a molecule for using space in a
`given solid state arrangement is the packing
`efficient (PC). This model assumes that the
`molecules within the crystal will attempt to pack
`in a manner such as to minimise the amount of
`unoccupied space (Kitaigorodskii, 1973).
`In general there is a rough correlation
`between higher PC values and increasing size of
`large flat aromatic molecules i.e perylene (0.8).
`Once even slight deviations from planarity are
`introduced the effective packing ability falls. For
`benzophenone, an aromatic ketone (Ph2C=O) the
`phenyl groups are twisted to 54° with respect to
`each other and the PC falls to 0.64. One of the
`most interesting features of such a model is the
`low PC for hydrogen bonded systems such as
`urea (0.65) and benzoic acid (0.62). This rather
`surprising feature is due to the rather open
`architecture of hydrogen bonded structures which
`is the result of a need to adopt particular
`arrangements to maximise the hydrogen bonded
`network (Etter, 1991).
`In general it is probably safe to suggest
`that in the majority of cases with molecular
`materials it is the desire to pack efficiently is the
`single biggest driving force towards selected
`structural arrangements. The notable exceptions
`will be in cases where the need to form complex
`hydrogen bonding networks will override this
`need. Weaker interactions such as special
`hydrogen bonds and polar interactions are
`probably not primary movers in the arrangements
`adopted but will tend to be optimised within a
`given efficient arrangement.
`
`Lattice Energy Calculations
`
`In order to understand the principles
`which govem the wide variety of solid state
`properties and structures of organic materials it is
`important to describe both the energy and nature
`of interactions in specific orientations and
`directions. As a result of the pioneering work of
`Williams (1966) and Kitaigordskii (1968) in the
`development of atom-atom potentials it is now
`possible to interpret packing effects in organic
`crystals in terms of interaction energies. The
`basic assumption of the atom-atom method is that
`the interaction between two molecules can be
`
`considered to simply consist of the sum of the
`interactions between the constituent atom pairs.
`The lattice energy E~ (often referred to as
`the crystal binding or cohesive energy), can for
`molecular materials be calculated by summing all
`the interactions between a central molecule and
`all the surrounding molecules. If there are n
`atoms in the central molecule and n’ atoms in
`each of the N surrounding molecules then lattice
`energy can be calculated by Equation (1).
`
`k=l i=l j=l
`
`(i)
`
`Vkij is the interaction between atom i in
`the central molecule and atom j in the k’th
`surrounding molecule. Each atom-atom
`interaction pair consists of a Van der Waals
`attractive and repulsive interaction, an
`electrostatic interaction and in some special cases
`a hydrogen bonding potential. Figure 1 shows the
`profiles of the calculated lattice energy as a
`function of summation limit for ~-glycine,
`anthracene, B-succinic acid and urea. These plots
`show the same general trend, on increasing the
`summation limit there is an initial increase in the
`lattice energy is recorded. This is followed by the
`reaching of a plateau region beyond 20~. Further
`increase in the summation limit has no effect on
`the calculated lattice energy.
`The validity of the potentials can to some
`extent be tested by comparing the theoretical
`values against the experimental sublimation
`enthalpy. Table 1 contains a selection of
`calculated lattice energies and experimental
`sublimation enthalpies. Figure 2 shows a plot of
`calculated against experimental lattice energies
`for a range of around eighty compounds. The
`molecular classes reported include a wide range
`of molecular materials. The excellent agreement
`between theory and experiment is clear, the mean
`error is 1.5 kcal/mol and the maximum error 3.5
`kcal/mol. The average difference between
`calculated and experimental less than 6%.
`
`Intermolecular Interactions
`
`A particular advantage of the calculated
`lattice energy is that it can be broken down into
`the specific interactions along particular
`directions and further partitioned into the
`constituent atom-atom contributions.
`
`,e solid
`[’mance
`ing and
`will be
`roperty
`3tential
`
`)st unique in it’s
`maination of the
`~gant arrangements
`polymers, surfaces
`Secondly in
`tional chemistry
`te determination of
`s (SAR’s) linking
`hence molecular
`characteristics.
`a these SAR’s) the
`[d state structures
`and performance
`
`lecular Materials
`
`cstal chemistry of
`m classified into
`g to the type of
`These include;
`
`:tive interactions,
`(Taylor, 1982),
`
`’ogen bonding,
`~esiraju, 1989).
`
`dly be regarded as
`shape and volume
`by the molecular
`f their constituent
`awkward shape of
`result in unequal
`adopted during
`.ty of the structures
`
`Lupin Ex. 1036 (Page 4 of 15)
`
`

`

`-a UREA
`-+ ANTHRACENE
`- ~ SUCCINIC ACID
`
`1 4 ,.~ GLTCINE
`
`30
`Summation Limit Radius (Angstroms)
`
`Figure 1 The calculated lattice energy as a
`function of summation limit for anthracene, urea,
`
`succlnic acid and glycine
`
`Table 1 Calculated and ’experimental’ lat-
`tice energiess for a range of molecular ma-
`
`terials. This is a subset of the data
`presented in Figure 2.
`
`Material
`
`n-Octadecane
`Biphenyl
`Napthalene
`Anthracene
`Perylene
`Benzophenone
`Trinitrotoluene
`Glycine
`L-alanine
`Benzoic acid
`Urea
`g-succinic acid
`
`Lattice Energies (kcal/mol)
`Calculated Experimental
`
`-35.2
`-21.6
`- 19.4
`-24.9
`-32.5
`-24.5
`-25.1
`-33.0
`-33.3
`-20.4
`-22.7
`-30.8
`
`-37.8
`-20.7
`- 18.6
`-26.2
`-31.0
`-23.9
`-24.4
`-33.8
`-34.2
`-23.0
`-22.2
`-30.1
`
`As a result it is possible to build up an
`understanding of the interactions which contribute
`to particular packing motifs. The study of the
`strength and geometry of intermolecular
`interactions remains an area of active research as
`it is a key element in molecular solid state
`chemistry (as described in the elegant work by
`Etter, 1991), in the design of molecular
`aggregates and in the understanding and
`construction of molecular recognition complexes
`for biologically interesting substrates (Chang and
`Hamilton, 1988).
`
`Urea (see Fig 3) has a three dimensional
`arrangement of hydrogen bonds where each urea
`molecule is surrounded by six other urea
`molecules. This cluster is responsible for 85% of
`the total lattice energy. The important
`intermolecular interactions are given in Table 2.
`The calculated intermolecular interactions,
`in particular the weaker ones, can be further
`examined to determine their relative importance,
`geometry and strength by using the vast amount
`of experimental data available in the Cambridge
`Crystallographic Database.
`
`Lupin Ex. 1036 (Page 5 of 15)
`
`

`

`Lattice Energies for Organic Materials
`Theory -vs- Experiment
`
`6O
`
`50
`
`40
`
`30
`
`20
`
`[]
`
`[]
`
`o
`
`lO
`
`20
`
`30
`
`40
`
`50
`
`60
`
`Theoretical (kcal/mol)
`
`Figure 2 The calculated lattice energy against the
`experimental lattice energy derived from the
`
`experimental sublimation enthalpy
`
`The Cambridge Crystallographic Database
`
`Over the past ten years total number of
`structures stored in the Cambridge
`Crystallographic Database has increased from
`40,000 to over 130,000. There has also been a
`noticeable improvement in the quality of the
`structures reported and in the complexity of the
`structures solved. The crystallographic
`discrepancy factor R has fallen from an average
`of 12% in 1965 to a present value of 5%. At the
`same time the number of atoms in the structures
`being investigated has increased from about 20 to
`50 (Allen et al, 1983).
`The database stores and can be searched
`on, three main categories of information for each
`entry including the bibliographic summary, the
`two dimensional chemical structure, and the full
`three dimensional structure details. The full three
`dimensional crystal structure information includes
`the unit cell dimensions, the space group
`
`symmetry and the individual atomic fractional co-
`ordinates. A specific full three dimensional query
`can now be introduced. This allows particular
`intermolecular bonding patterns to be examined
`both within molecules and between molecules.
`Clearly this is a powerful search facility which
`increases value of the information already within
`the database.
`The occurrence, relative importance,
`strength and geometry of different intermolecular
`interactions can be assessed. An example of such
`an analysis concerns the role of weaker
`interactions such as special hydrogen bonds (e.g.
`C-H:::O=C interactions). They have been
`considered in detail (Taylor and Kennard, 1984
`Desiraju, 1989). These ’special’ hydrogen bonds
`are generally weaker than traditional hydrogen
`bonds and spectroscopic, crystallographic and
`theoretical investigations continue to probe their
`magnitude and directionality. An analysis of the
`database suggests that the strength of the
`
`[]
`
`~0
`
`f the data
`
`three dimensional
`ls where each urea
`six other urea
`onsible for 85% of
`The important
`given in Table 2.
`ecular interactions,
`,~s, can be further
`~lative importance,
`~g the vast amount
`; in the Cambridge
`
`Lupin Ex. 1036 (Page 6 of 15)
`
`

`

`C
`
`Figure 3 The ~hree dimensional s~ruclure of a urea cluster involving six surrounding molecules
`
`Table 2 The important intermolecular interactions in urea.
`
`Position
`UVW
`
`Interaction Energy Bond Fraction
`Type (%)
`Z
`(kcal/mol)
`
`001
`00-1
`
`100
`-110
`000
`010
`
`1
`1
`
`2
`2
`2
`2
`
`-3.64
`-3.64
`
`-3.00
`-3.00
`-3.00
`-3.00
`
`a
`a
`
`b
`b
`b
`b
`
`16.1
`16.1
`
`13.2
`13.2
`13.2
`13.2
`
`Lupin Ex. 1036 (Page 7 of 15)
`
`

`

`~ndlng molecules
`
`interaction depends on the acidity of the
`hydrogen involved and so the strength order
`C(sp)-H > C(sp2)-H > C(ar)-H > C(sp3)-H
`(Desiraj u, 1989).
`
`Crystal Shape Calculation
`
`Early crystallographers were fascinated by
`the fiat, plane and symmetry related external
`faces in both natural and synthetic crystallised
`solids. This led them to postulate that the ordered
`external arrangement was a result of an ordered
`internal arrangement.
`Morphological simulations based on
`crystal lattice geometry were proposed by
`Bravais, Friedel, Donnay and Harker (1937). This
`work spans over seventy years but is often quoted
`collectively by modem workers as the BFDH
`law. Hartman and Perdok (1955) were the first
`to extensively quantify the crystal morphology in
`terms df the interaction energies between
`crystallising units. They used the assumption by
`that the surface energy is directly related to the
`chemical bond energies and identified chains of
`’strong’ intermolecular interactions called periodic
`bond chains (PBC). The strength of a PBC is
`determined by the weakest link in that chain.
`They also characterised fiat, stepped and kinked
`faces according to the number of PBC’s that are
`present in these faces.
`Attachment and slice energies can be
`determined from a PBC analysis or calculated
`directly from the crystal structure by partitioning
`the lattice energy calculated from each
`symmetrically independent molecule in the unit
`cell into slice and attachment energies
`(Berkovitch-Yellin, 1985). The slice energy is
`defined as the energy released on the formation
`of a growth slice of a particular thickness
`(Hartman and Bennema, 1980). The attachment
`energy is defined as the energy released on the
`attachment of a particular growth slice onto the
`surface in a specified orientation. Faces with the
`lowest attachment energies will be the slowest
`growing and therefore will be the
`morphologically most important.
`Figure 4 shows a precursor in the
`manufacture of the agrochemical paclobutrazol
`(Black et al, 1990). The molecule crystallises in
`the orthorhombic space group P212121 with four
`molecules in a unit cell of dimensions a=5.799,
`b=13.552 and c=19.654~. The packing of the
`molecule is dominated by chains of C-H::::O
`
`A Paclobutrazol Intermediate
`
`1 -(4-C hlo rophenyl)-4,4-dimethyl-2-
`(1 H-1,2,4-tdazol-l-yl) pentan-3-one
`
`0
`
`Observed
`
`Calculated
`
`(11o)
`
`1012)
`
`Figure 4 The molecular structure and experi-
`mental and calculated morphologies for the in-
`termediate in the manufacture of paclobutrazol.
`
`interactions running in the b-direction and a
`cascade of edge to face interactions rurming down
`the a--direction. The calculated crystal shape
`based on attachment energies shows excellent
`agreement with the observed morphology as
`shown in Figure 4. The only major differences is
`the prediction of the (012) faces which are not
`usually observed.
`It has been established over a number of
`years that impurities can have drastic effects on
`crystal shape. The elegant work of the Weizmann
`Institute (Lahav et al, 1985) has shown that for
`molecular crystals this can be accounted for
`through structural explanations.
`Tailor made additives can be broken down
`into two different categories, the ’disruptive and
`’blocker’ types (Clydesdale et al, 1994).
`Disruptive additives are generally smaller than
`the host system. They are structurally similar to
`the host and use this similarity to enter a surface
`site where there difference is not recognized.
`Additional on-coming molecules encounter a
`normal surface except in an area on a particular
`face where the disruptive molecule is situated.
`This is shown in Figure 5. For disruptive
`additive this results in a failure to complete the
`proper intermolecular bonding sequence normally
`
`Lupin Ex. 1036 (Page 8 of 15)
`
`

`

`E ~tt’
`
`Figure 5 Schematic representation of the growth
`of crys~s in the presence of tailor made
`
`adopted by the pure host system. Altering a
`particular bonding sequence in a certain direction
`affects the growth rate along that direction
`relative to the unaffected faces and consequently
`alters the relative growth rates.
`Blocker type additives are usually bigger
`than the host system. Again the additive is
`structurally similar to the host but normally with
`an end group that differs significantly from the
`host structure. The part of the additive that is
`structurally similar to the host is then accepted
`into certain faces. These faces again recognise the
`similarity regions of the impurity and not the
`differences. The differing units in the blocker
`then sit on the respective crystal faces and
`prevent on-coming molecules getting into their
`rightful positions at the surface. This is shown in
`Figure 5.
`In order to model these changes in
`morphology induced by these additives a number
`of new parameters must be calculated. The
`difference in binding energy for the additive
`compared to the host molecule (in a particular
`site) can be used as a measure of the ease of
`incorporation of the impurity. The effect of the
`impurity on subsequent growth can then be
`considered.
`This can be illustrated by considering the
`effect of toluene on the morphology of
`benzophenone (Roberts et al, 1994). Figure 6
`shows the morphology of benzophenone grown
`from the melt and from a toluene solution. The
`
`E nff" ~ Blocking
`
`disruptive and blocker additives.
`
`most dramatic effect is the considerable increase
`in the importance of the {021} face. Figure 6
`also shows the benzophenone structure down the
`a-axis with a toluene molecule fitted on the
`{021} plane.
`
`Sublimation EnthalpT Estimation
`
`Measurement ofthermochemical data such
`as the sublimation enthalpy can be a costly and
`time-consuming process. Prediction of solid state
`properties before a compound is synthesised
`would obviously be of considerable use.
`Recent applications of statistical methods
`including neural networks include the
`determination of structure-activity relationships in
`drug design and the classification of spectra.
`Thermochemical data such as solubilities and
`boiling points of organic heterocycles have also
`been the subject of investigation. There are also
`a number of reviews of the use NNs in chemistry
`(Lacy, 1990 and Zupan and Gasteiger, 1993).
`The work of a number of authors
`including (Gavezzotti, 1991) has shown that the
`lattice energy (and consequently the sublimation
`enthalpy) can be predicted based upon linear
`regression studies on molecular crystals. The
`heat of sublimation can be estimated from the
`packing potential energy (PPE) (Gavezzotti,
`1991) which correlates with molecular descriptors
`such as molecular weight, Van der Waals’
`surface, volume and molecular outer surface.
`
`Lupin Ex. 1036 (Page 9 of 15)
`
`

`

`"ow,h
`,ocking
`
`~siderable increase
`1} face. Figure 6
`structure down the
`~ule fitted on the
`
`,chemical data such
`m be a costly and
`ction of solid state
`nd is synthesised
`~rable use.
`statistical methods
`:s include the
`rity relationships in
`cation of spectra.
`Ls solubilities and
`rocycles have also
`~n. There are also
`,~ NNs in chemistry
`asteiger, 1993).
`mber of authors
`~as shown that the
`fly the sublimation
`based upon linear
`tlar crystals. The
`~stimated from the
`PPE) (Gavezzotti,
`~lecular descriptors
`Van der Waals’
`r outer surface.
`
`PURE BENZOPHENONE
`
`\
`
`BENZOPHENONE GROWN WITH TOLUENE
`
`,(oat)
`
`\
`
`\
`
`\
`
`\
`\
`
`CRYSTAL PACKING OF BENZOPHENONE
`
`Hgure 6 The morphology of pure benzophenone,
`benzophenone grown in toluene and the packing
`
`of benzophenone
`
`Recently a feed forward Neural Network
`(NN), has been trained to reproduce sublimation
`enthalpies for 62 molecules including aliphatic
`hydrocarbons through to amino acids (Charlton et
`al 1995). The results are compared both with
`calculated values from traditional crystal packing
`techniques and with a multilinear regression
`analysis (MLRA) model. The molecular
`descriptors input to the NN was kept as simple as
`
`possible to facilitate the prediction of values for
`novel molecules. The parameters are the number
`of carbon atoms (C), the number of hydrogen
`atoms (H), the number of nitrogen atoms (N), the
`number of oxygen atoms (O), the number of x-
`atoms (PI), the number of hydrogen bond donors
`(HBD) and the number of hydrogen bond
`acceptors (HBA). The MLRA uses the same
`input data as the NN, although some covariance
`
`Lupin Ex. 1036 (Page 10 of 15)
`
`

`

`was found between the input p~rameters,
`indicating that the number of inputs could be
`reduced. It is therefore concluded that a simple 3-
`parameter MLRA model fitted the data used. A
`plot of calculated values of sublimation enthalpy
`based on Equation 2 is shown in Figure 7. The
`mean and maximum errors are given in Table 3
`for the various methods.
`
`SE = 3.47 + 1.41C + 4.55I-[BD + 2.7HBA (2)
`
`Crystal Structure Prediction
`
`The generation by computational methods
`of reliable solid state structural details and solid
`state properties on novel materials from only
`molecular descriptors remains both a major
`scientific goal and the subject of some
`controversy (Maddox, 1988 and G-avezzotti,
`I994). It is often difficult!impossible to obtain
`crystals of sufficient size and quality, in the
`
`Plot of MLRA prediction vs.
`experimental sublimation enthalpy
`
`5O
`
`@
`
`+ + ++
`
`10
`
`0
`
`0
`
`~,~
`; -~-~ -~ ~ and H BA =~---------~
`[] HBD=0andHBD>0
`~
`+ HBD > 0
`¯ /
`
`40
`30
`20
`10
`Experimental sublimation enthalpy
`
`50
`
`Figure 7.
`
`The plot of the sublimation enthalpy determined from equation (2) against experiment.
`
`Table 3 A summary of the predicted sublimation enthalpy results
`
`MLRA°
`
`Max. Error
`Mean Error
`r2
`
`3.5
`1.4
`0.97
`
`10.1
`2.5
`0.87
`
`8.9
`1.8
`0.92
`
`Theoretical prediction using crystal packing.
`Neural network prediction (Leave One Out Experiment).
`Multilinear Regression Analysis prediction
`
`10
`
`Lupin Ex. 1036 (Page 11 of 15)
`
`

`

`mputational methods
`~ral details and solid
`naterials from only
`~ins both a major
`subject of some
`18 and Gavezzotti,
`mpossible to obtain
`and quality, in the
`
`;ainst experiment.
`
`desired polymorph in order to study a structure
`by conventional single crystal methods.
`The lack of a general approach enabling
`the prediction of the solid state structure solely
`from molecular structure has been described as
`’one of the continuing scandals in the physical
`sciences’ (Maddox, 1988). Progress has been
`hindered due to problems with global
`minimisation and force-field accuracy. The
`electrostatic component of the force-field has
`received much consideration (Price and Stone,
`1984). These problems have limited the routine
`application of such methodologies to industrially
`important molecules. The methods being
`developed for structure prediction usually involve
`three stages;
`
`- trial structure generation,
`- clustering of similar trial structures,
`- refinement of trial structures.
`
`A systematic efficient search/structure
`generation algorithm is needed to generate all the
`potential structures. It is important that a
`sufficient sample of structural space is covered so
`that not only local minima are located but the
`global minimum as well. A reduction in these
`trials is achieved by either a similarity clustering
`procedure or filtering approach to remove the
`similar or unlikely candidates. Finally refinement
`of the potential structures is carried out using
`lattice energy minimisations. During refinement
`the lattice energy is refined with respect to the
`structural variables. The unit cell dimensions
`(a,b,c, c% fl and 30 are allowed to alter along with
`translational
`the molecular orientation and
`parameters.
`difficulties,
`Despite the inherent
`predictions from first principles remains an
`admirable scientific goal and the subject of much
`investigation reflected in the elegant work of
`Gavezzotti (1992), Holden (1993), Pedstein
`(1994) and Karfunkel (1992).
`Gavezzotti (1992) and his co-workers
`have pioneered the concept of the ’molecular
`nuclei’. Given a molecular structure clusters of
`molecules (nuclei) are built using various
`symmetry operators. The relative stability of each
`of these nuclei is appraised through a calculation
`of it’s intermolecular energy. When these clusters
`(nuclei) have been selected a full crystal structure
`can be generated using a systematic translational
`search. The translational search is carried out in
`
`a systematic manner with lines, layers and full
`three dimensional structures being built. A further
`selection process is used based on packing
`efficient and packing density limits to filter out
`the most likely structures. These are then refined
`using lattice energy minimisation techniques. The
`results for this approach are very impressive.
`A similar process was described by
`Holden (1993) who considered an approach in
`terms of molecular co-ordination spheres. From a
`detailed examination of the Cambridge
`Crystallographic Database they identified co-
`ordination numbers for various space groups.
`They restricted the search to molecules containing
`just C,H,N,O and F with only one molecule in
`the asymmetric unit (i.e. no solvates or
`complexes).
`The construction of possible full crystal
`packing patterns follows in three stages. Initially
`a line of molecules is established by moving a
`second molecule towards the central molecule
`until a specified interaction criteria is meet. A
`two dimensional grid is then organised by
`moving a line of molecules towards the central
`line. The final step involves moving a two
`dimensional grid parallel to the central grid. The
`orientation of the molecules within the two
`dimensional grids and the three dimensional
`packing arrangement depends on the symmetry
`operations within the space group being
`investigated. In a number of cases the lowest
`energy theoretical structure is in good agreement
`with the experimental arrangement.
`In recent publications Perlstein (1994) has
`used a Monte Carlo cooling approach to describe
`the packing of one dimensional stacked
`aggregates including perylenedicarboximide
`pigments. Starting aggregates are generated using
`five identical molecules randomly orientated at
`set separation distances along a defined axis. The
`Monte Carlo cooling is carried out from 4000K
`to 300K. Each Monte Carlo step involves
`randomly rotating the central molecule and
`regenerating the other molecules along the axis at
`the set distances. The energy of this arrangement
`is then computed and compared against the
`previous energy and either accepted or rejected
`based on the acceptance criteria of the Monte
`Carlo algorithm. This process is repeated twenty
`times for both rotational angles and then the
`separation distance r. The temperature is then
`cooled by 10% and the process repeated. At a
`temperature of 300K the lowest energy structure
`
`11
`
`Lupin Ex. 1036 (Page 12 of 15)
`
`

`

`found is accepted as a local minima. This whole
`procedure is repeated until a number of local
`minima (sufficient to include the global
`minimum) have been found.
`The results show good agreement between
`predicted and experimental values for the
`interplanar separation distance, and the
`longitudinal and the transverse displacement.
`Although this is not three dimensional structure
`prediction it is a technique which has potential to
`contribute to the problem of predicting three
`dimensional structures. It is of particular interest
`that these results have been obtained for
`molecules with flexible end groups with non-
`bonded interaction and torsional terms taken into
`account during the simulation.
`Recently Karfunkel (1993)has described
`an approach to the crystal