G Wojcik - Intermolecular interactions leading to crystal polymorphism of organic compounds x-ray diffraction and quantum chemical studies of para- and mela-n it - страница 1
ВІСНИК ЛЬВІВ. УН-ТУ VISNYK LVIV UNIV.
Серія хім. 2007. Bun. 48. Ч. I. С. 123-127 Ser. Khim. 2007. No 48. Part I. P. 123-127
PACS 61.10.Nz; 61.43.Bn
INTERMOLECULAR INTERACTIONS LEADING TO CRYSTAL POLYMORPHISM OF ORGANIC COMPOUNDS. X-RAY DIFFRACTION AND QUANTUM CHEMICAL STUDIES OF para- AND mela-N ITROPHENOL
Institute of Physical and Theoretical Chemistry, Wroclaw University of Technology, ul. Wyspianskiego, 27, 50-370 Wroclaw, Poland e-mail: email@example.com
Experimental (variable-temperature X-ray diffraction and rigid-body analysis of the anisotropic displacement parameters) and theoretical (quantum chemical calculations at the MP2 level) studies have been performed for the following four crystal: two polymorphs of p-nitrophenol and two polymorphs of m-nitrophenol. The energies of interactions within molecular clusters -molecular dimers which form building blocks in the studied crystals - have been partitioned into electrostatic, exchange, delocalization and electron correlation terms. The calculated energies may serve as the first-order approximation of crystal properties. The results are discussed in terms of large hysteresis of the metastable polymorphs' occurrence.
Key words: polymorphism, X-ray diffraction, nitrophenol, intermolecular nteractions.
Polymorphism is defined as the occurrence of two, or more different crystal structures for the same compound. The investigation of polymorphic structures enables the crystal structure versus property relationship to be studied. On the other hand the analysis of the crystal structures of isomers may give insight into the mutual dependence between molecular and crystal structures. A comparison of the polymorphic structures of para- and meta-nitrophenol provides an opportunity to explore and to advance our understanding of both problems.
Para-nitrophenol occurs in two polymorphic forms, named a and P forms. Both crystallise in the monoclinic P21/c space group, however their molecular arrangement is quite different. Though in both crystals the molecules form infinite chains through the (N)O...HO hydrogen bonds of similar strengths, the mutual arrangement of the molecules in the chains is different. Briefly speaking, the P crystal corresponds to the stacking type of the molecular packing with one unit cell parameter shorter than 4 A, while the a crystal corresponds to the herringbone type of the molecular packing with almost perpendicular arrangement of the molecular planes of the adjacent molecules [1, 2]. An enantiotropic phase transition from P to a occurs at about 59 oC with an enthalpy equal to, at least, 5 kJ/mol. So the a form is metastable at room temperature .
Two polymorphic forms of meta-nitrophenol: orthorhombic and monoclinic show surprisingly similar molecular arrangements. The molecular chains formed by translationally equivalent molecules linked by hydrogen bonds between the nitro group and the hydroxyl group are almost identical in both crystals. The chains are mutually arranged
© Wojcik G., 2007
in a centrosymmetric way (in the monoclinic form - space group P21/n) or in a non-cetrosymmetric way (in the orthorhombic form - space group P212121). The enantiotropic phase transition from the low-temperature orthorhombic form to the high-temperature monoclinic form occurs at 77 oC with a minor value of enthalpy (about 200 J/mol) . The monoclinic form occurs at ambient as a metastable phase and may be grown from solution.
The question arises why two polymorphs of p-nitrophenol exhibit relatively different molecular arrangements whereas two polymorphs of m-nitrophenol are isostructural in three dimensions. The other question, that results from the previous one, is: to what extent there are similar the structures of the stable forms of p-nitrophenol and m-nitrophenol and, respectively, their metastable forms?
The multi-temperature crystal structure studies [3, 4] enabled to analyse the anisotropic displacement parameters within the TLS formalism. The rigid-body analysis assumes that the amplitudes of the internal (atomic) vibrations are negligible comparing with the amplitudes of the whole molecule's motions. The method uses the atomic displacement parameters to calculate the elements of the molecular libration (L), translation (T) and screw (S) tensors [5, 6]. The internal vibrations of large amplitude (in case of nitrophenol this is the torsional vibration of the nitro group) may be correlated with molecular librations and translations. The results of the rigid-body analysis provide the values of mean square amplitudes of molecular librations and translations (six values of the second-rank tensor) and nine values of the S tensor representing the correlation between librations and translations in non-centrosymmetric molecules. Additionally, the (ф2 +2 АІ'ср) value may be calculated, where ф denotes the amplitude of the torsional vibration of the non-rigidly attached rigid group (the nitro group in case of nitrophenol) and A' is the amplitude of the librational vibration of this group about the same axis. The calculated (ф2 +2 А'ф) value may be treated as the amplitude of the nitro group overall motion about the C-N bond direction and may be compared with A', i.e. the contribution to the motion from molecular libration.
The results of the multi-temperature rigid-body analysis performed for four crystals under consideration point to a similar molecular mechanism of the enantiotropic phase transition in p-nitrophenol and m-nitrophenol. The transformations are driven by thermally induced molecular librations about the direction of the intermolecular hydrogen bonds. The librations are coupled with torsional vibrations of the nitro groups about the same axis. In both high-temperature forms the internal torsional vibrations of the nitro group are damped making impossible the reverse transformation below the transition temperature. This phenomenon seems to be responsible for the large hysteresis of the metastable forms and persistent metastability of the high-temperature polymorphs.
A crystal structure of an organic compound results from numerous, mainly weak interactions between molecules. The energy of interactions strongly depends on a distance between interacting molecules and atoms, so the contribution from the nearest neighbours is dominating. The statement is at the origin of our approach to the quantum chemical (MP2) calculations of the energy of interactions in the crystals under consideration. The experimentally determined crystal structures were assumed in the calculations. The two-body interactions were considered to represent the many-body interactions in the real crystal. Quantum chemical calculations of interactions for molecular clusters that modeled polymorphic crystal structures have been performed. We analysed molecular clusters, i.e. dimers formed by H-bonded and n stacked molecules in the polymorphs of para- and meta-nitrophenol [3, 4].
The intermolecular interactions were studied using the interaction energy decomposition scheme in which the interaction energy is partitioned into the first order
Heitler-London exchange eHL, and the higher order delocalization
+ C +AEd
The AEHF component accounts for the charge-transfer and induction effects
associated with the relaxation of the electronic densities of monomers upon interaction,
whereas the Heitler-London terms (0) and £Н) represent the electrostatic interactions
and exchange repulsion between subsystems of which electron density distributions are unperturbed by the presence of a neighboring molecule. The electron correlation effects are
taken into account by means of the M0ller-Plesset perturbation theory. The interaction
energy term, which includes the dispersion contribution and correlation corrections to the Hartree-Fock components, is calculated in the supermolecular approach as the difference between the appropriate second order MPPT energy corrections.
Є(2) = E (2) CMP ^ AB ^2)
The interaction energy decomposition scheme was implemented in the GAMESS program .
Fig. 1 and 2 show the molecular dimers considered in the calculations. Tables 1 and 2 report the calculated energies for p-nitrophenol and m-nitrophenol, respectively. Assuming the additivity of the energy of the molecular interactions and taking into account the closest contacts between molecules in the crystals under consideration, the crystal energies have been calculated. The crystal energies of two polymorphic forms of m-nitrophenol turned out to be almost equivalent. The energy of the stable, orthorhombic crystal is lower by the value of about 200 J/mol when compared with its metastable counterpart.
Fig. 1. The molecular dimers of hydrogen bonded molecules in the stable (on the left) and the metastable (on the right) polymorphic forms of p-nitrophenol and m-nitrophenol
Fig. 2. The molecular dimers of overlapped molecules in the stable (on the left) and the metastable (on the right) polymorphic forms of p-nitrophenol and m-nitrophenol
The interaction energy components for the molecular dimers occurring in two p-nitrophenol polymorphs. Energy in kcal/mol. See the text for the meaning of headings
The interaction energy components for the molecular dimers occurring in two m-nitrophenol polymorphs. Energy in kJ/mol. See the text for the meaning of headings
Such an excellent agreement with the experimental value of the transition enthalpy is rather accidental. The approximations made do not justify such quality of theoretical predictions. The crystal energies of the p-nitrophenol polymorphs differ by the value about 14 kJ/mol. This value exceeds the experimental value of the transition enthalpy, nevertheless the polymorph stable at ambient has been properly found by the crystal energy calculations.
The comparison of molecular interaction energies and dynamics in polymorphs has been considered in terms of the large hysteresis of the metastable phase occurrence. The calculated energies of the intermolecular interactions within the clusters rationalise the polymorphic structures and may serve as a first-order approximation of crystal properties.
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4. Wojcik G., Holband J., Szymczak J., Roszak S., Leszczynski J. Interactions in polymorphic crystals of m-nitrophenol as studied by variable-temperature X-ray diffraction and quantum chemical calculations // Cryst. Growth Des. 2006. Vol. 6.
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МІЖМОЛЕКУЛЯРНІ ВЗАЄМОДІЇ, ЯКІ ПРИЗВОДЯТЬ ДО ПОЛІМОРФІЗМУ КРИСТАЛІВ ОРГАНІЧНИХ СПОЛУК. РЕНТГЕНІВСЬКА ДИФРАКЦІЯ ТА КВАНТОВО-ХІМІЧНЕ ВИВЧЕННЯ пара- І .««яяя-НІТРОФЕНОЛІВ
Інститут фізичної та теоретичної хімії, Технологічний Університет Вроцлава, вул. Виспанського, 27, 50-370 Вроцлав, Польща e-mail: firstname.lastname@example.org
Розглянуто поліморфізм пара- і мета-нітрофенолів, зумовлений міжмолекулярними взаємодіями. Кожна із цих сполук може існувати у двох модифікаціях, що інтерпретується з використанням даних рентгеноструктурного аналізу і квантово-хімічних обчислень.
Ключові слова: поліморфізм, рентгенівська дифракція, нітрофенол, міжмолекулярні взаємоді .
Стаття надійшла до редколегії 28.05.2006 Прийнята до друку 01.11.2006