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Analysis of Distribution of Energy Barriers in Amorphous Diazepam – Based on Computationally Supported NMR Relaxation Data Aleksandra Pajzderska, Marcin Jarek, Jadwiga Mielcarek, and Jan Wasicki J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b08482 • Publication Date (Web): 22 Sep 2016 Downloaded from http://pubs.acs.org on September 29, 2016

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The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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The Journal of Physical Chemistry

Analysis of Distribution of Energy Barriers in Amorphous Diazepam – Based on Computationally Supported NMR Relaxation Data

A. Pajzderska1*, M. Jarek2, J. Mielcarek3, J. Wąsicki1,2

1

Department of Radiospectroscopy, Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614,

Poznan, Poland 2

NanoBioMedical Center, Adam Mickiewicz University, Umultowska 85, 61-614, Poznan, Poland

3

Department of Inorganics and Analytical Chemistry, Poznan University of Medical Sciences, Grunwaldzka 6,

60-780 Poznan, Poland

* corresponding author: email [email protected], telephone number +48 81 8295208

Abstract

The crystalline and amorphous diazepam – a psychoactive drug - was investigated by employing spin-lattice relaxation 1H nuclear magnetic resonance (NMR) along with atomatom calculations of landscape of energy barriers. The activation barriers for reorientation of the methyl group in amorphous diazepam were found in the range of 1.9 kJ/mol to 12.7 kJ/mol. Atom-atom calculations permitted determination of the distribution of energy barriers for reorientations of methyl groups, which was in a good agreement with that obtained on the basis of experimental data. The NMR relaxation combined with calculations provided a quantitative description of the distribution of energy barriers including intra- and intermolecular interactions.

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1. Introduction Many active pharmaceutical ingredients (APIs) in solid state occur in crystalline or amorphous states.1 The amorphous substances show disordered structure but not fully random as there is a short-range ordering. The spatial structure of APIs is very important from the point of view of drug formulation technology. It has been shown that different spatial structure is related to differences in physicochemical properties e.g. different melting points, solubility, density or dissolution rate. Solubility and dissolution rate are known to be the most important features determining the bioavailability of a given therapeutic substance and thus the therapeutic effect.2 If the dissolution rate of an API is smaller than the absorption rate, the stage of dissolution limits the drug bioavailability as it determines the time of its appearance in the blood. This problem is characteristic of the therapeutic substances that show poor water solubility and good permeability through cell membranes, that is belong to class II of the Biopharmaceutics Classification System (BCS).3 The substances in amorphous phase are usually characterized by higher rate of dissolution than those in crystalline phase, which implies the possibility of administration of smaller doses of the drug thus reducing the risk of unwanted side effects.4 Although a wide variety of experimental methods can be applied for physical characterization of solid materials, including thermal analysis (differential scanning calorimetry – DSC, thermogravimetry –TG), infrared spectroscopy (FT-IR), solid state nuclear magnetic resonance (SSNMR) and X-ray powder diffraction (XRPD), investigation of amorphous forms still remains a challenge. Besides the solid state structure, the properties of amorphous substances depend on the molecular dynamics, so analysis of the latter is an important element of amorphous samples characterisation. It is generally believed that determination of reorientations and internal


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mobility of amorphous species can be of key importance for the understanding of their physicochemical properties. NMR relaxation (in particular for low resonance frequencies) is a very sensitive method for investigation of molecular reorientations in crystalline and polycrystalline systems, especially if they contain methyl, tert-butyl or alkyl groups.5, 6 When the molecular and crystal structure of a given system is known, then interpretation of NMR relaxation can be much more precise.7-9 Moreover, on the basis of the crystal structure it is possible to identify the steric hindrances restricting the reorientation and to calculate the energy barriers for reorientation.1013

The lack of far-range ordering in amorphous systems makes it much more difficult to

calculate the energy barrier heights, which becomes a great challenge. In view of the above, the NMR relaxation, besides quasielastic neutron scattering, is the main method providing information on energy barriers for reorientation and determination of local anisotropies in the intramolecular and intermolecular potentials.14 Diazepam belongs to benzodiazepine (BZ) derivatives, a group of medicaments of a a wide spectrum of activity along the four main lines: antianxiety, sedative and sleep-inducing, anticonvulsive and reducing muscle tension.15, 16 Diazepam in crystalline state is poorly water soluble, while in amorphous form much better water soluble,17 for these reasons determination of the inter- and intramolecular interactions in its amorphous form is very important. It is known that in the range from 100 K to the melting point (Tm = 404.5 K) diazepam undergoes no phase transitions,18-20 while after melting and fast cooling a glass transition takes place (Tg = 315.2 K).18 The diazepam molecule is built of a condensed benzodiazepine ring and chlorobenzene ring, with a methyl group attached to the nitrogen atom at position 1 (Fig. 1). The crystalline structure the energy barrier for methyl group reorientation is caused by steric hindrances coming from intra- and intermolecular interactions, so the height of this barrier can provide information on these interactions and be


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used as a probe. Temperature dependence of T1 relaxation time at the frequencies of 58.9 and 200 MHz, performed earlier for crystalline diazepam, revealed a single minimum assigned to the methyl group reorientation.20 The aim of the study presented in this paper was to analyse molecular reorientations in amorphous diazepam in order to get the information on their energy barriers and comparison of the results obtained with the corresponding ones for crystalline diazepam.

2. Experimental Sample Crystalline

diazepam

(7-Chloro-1,3-dihydro-1-methyl-5-phenyl-2H-1,4

benzodiazepin-2-one) from GlaxoSmithKline Pharmaceuticals S.A., Poznań, was purchased in a hermetically sealed container. The quality of the sample was check and described in the previous paper.20 Amorphous diazepam was prepared by melt-quench cooling method. Polycrystalline sample in the form of white powder was placed in a glass sealed ampule. The ampule was then heated at the rate of ca. 10 K/min up to 420 K (~10 degrees above the melting point), kept at this temperature for approximately 10 min and then the melt was cooled down to 100 K. The amorphous sample obtained was colourless and transparent. Methods Powder X-ray diffraction measurements were carried out with an Empyrean (PANalytical) diffractometer, using Cu Kα radiation (1.54 Å), reflection-transmission spinner (sample stage) and a PIXcel 3D detector, operating in the Bragg–Brentano geometry. The 2 theta scans were recorded at room temperature (300 K) for the angles ranging from 5 to 60 degrees (2Theta) with a step size of 0.013 degree (2Theta), using the continuous scan mode.


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Differential scanning calorimetry (DSC) experiment was performed with a DSC 8000 apparatus (Perkin-Elmer, Norwalk, USA) at the heating rate of 10.0 K/min up to 450 K and cooling rate 50.0 K/min to 140 K. The polycrystalline sample for NMR studies was degassed and sealed off under vacuum in glass ampoules of 8 mm inner diameter. The spin-lattice relaxation time (T1) were measured on 1H NMR pulse spectrometers working at resonant frequencies of 25.0 MHz (ElLab Tel-atomic) using the saturation-recovery method in the temperature range 30 – 300 K. The spectrometer was equipped with helium-nitrogen cryostat that permitted measurements to the accuracy of 0.01 K and temperature stabilization was set on the level of 0.1 degree. Temperature measurements of T1 relaxation time were performed at first for a polycrystalline sample, then the sample was was amorphized as described above and similar T1 measurements were carried out. Computational details The potential energy calculations by the atom-atom method21 were made for a crystal block containing 180 elementary cells and for amorphous cluster containing 800 molecules. The crystal block was constructed on the basis of X-ray diffraction (XRD) data,22 and the hydrogen atom positions were corrected to get the C-H bonds length of 1.089 Å. Amorphous cluster of the size 69x69x69 Å3 containing 800 molecules was constructed using Amorphous Cell modules built in Materials Studio package.23 Geometry optimization was performed after the construction of the cluster with the use of the algorithm smart .

3. RESULTS AND DISCUSSION Preliminary characterizations of amorphous sample Fig. 2 presents the diffraction spectra recorded for the crystalline (powder) sample and amorphous sample. The spectrum of the crystalline diazepam shows diffraction peaks whose


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positions correspond to those generated on the basis of crystallographic data.22 For the amorphous sample, as expected, no diffraction peaks appear but only a broad peak at about 20 deg. Fig. 2 also presents the DSC curve recorded upon rapid cooling, showing the glass transition temperature (315.4 K). This temperature is in agreement with literature value.18 The above data confirmed that diazepam in amorphous form has been obtained by melt-quench cooling. T1 relaxation time measurements Fig. 3 presents the spin-lattice relaxation time measured for crystalline and amorphous diazepam over a wide temperature range. For crystalline diazepam the curve of lnT1 on 1000/T shows a symmetric minimum of 77.7 ms at 104 K. Analysis of molecular and crystalline structure of diazepam indicates that all molecules, so also all methyl groups, have the same surrounding in the crystal lattice. Therefore, the spin-lattice T1 relaxation time for protons for this system can be described by the BPP formula with a single correlation time τ:24

1 = C ⋅ [J (ω ,τ ) + 4 J (2ω ,τ )] T1

(1)

where C – is the relaxation constant, while the spectral density function J(ω,τ) in the BPP model is described as:

J (ω , τ ) =

2τ

(2)

1 + ω 2τ 2

E  where τ = τ 0 exp A  is the correlation time (the Arrhenius relation), τ0 is a constant, Ea is  RT 

the activation energy, R is the gas constant, and ω is the resonance frequency. The activation parameters obtained from the best fit of eq. 1 to the temperature dependence of T1 relaxation time are given in Table 1. The obtained activation energy of 8.5 kJ/mol is in agreement with the value reported in,20 calculated earlier from T1 measurements at the resonance frequencies


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58.9 and 200 MHz. Thus, analysis of the temperature dependence of T1 relaxation time confirmed that the only process responsible for the minimum is the methyl group reorientation, and the dominant is the intramolecular 1H – 1H interaction. The latter conclusion was confirmed by the calculations of energy barrier for methyl group reorientation in the diazepam crystal by the atom-atom method.20 Similar measurements for the amorphous sample revealed a minimum T1 of 251 ms at 90 K. However, in contrast to that for the crystalline sample, the T1 minimum for the amorphous diazepam is broad and asymmetric, the slop of its linear section from the side of high temperature is much greater than that on the low-temperature side. In the hightemperature range, the T1 relaxation time values and the slope of lnT1 versus 1000/T are similar for the two samples. The broad minimum suggests a distribution of correlation times and/or activation energies.25,26 Therefore, the temperature dependence of T1 was fitted with the formula comprising the Davidson-Cole distribution for which the spectral density function is expressed by:27

J DC (ω ,τ , β ) =

2  sin (β arctan(ωτ ))    ω  1 + ω 2τ 2 β 2 

(

)

(3)

where: parameter β characterizes the distribution and may assume values between zero and one. The parameters of the fit are collected in Table 1. However, as shown in Fig. 3, this fit is not satisfactory, especially in the low-temperature range. Therefore, we decided to use a few BPP functions described by formula (1) to fit the temperature dependence of T1 relaxation time in the entire temperature range. The best fit was obtained for 7 functions, as shown in Fig. 4, and the activation parameters of particular processes are given in Table 2. It should be noted that the value of C constant is proportional to the fraction of mobile methyl groups. The activation energies vary in a wide range from 1.9 to 12.7 kJ/mol. Moreover, the depths of particular minima, directly proportional to the value of C constant so to the number of


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reorienting methyl groups, are different. The deepest minimum corresponds to the activation energy of 5.4 kJ/mol which is lower than the activation energy obtained from T1 measurements for the crystalline sample. The result indicates that for the amorphous sample the energy barriers for methyl group reorientations make a distribution of values.

Calculations To give a detail interpretation of the experimental results the energy barrier for methyl group reorientations were calculated for the crystalline and amorphous diazepam. Fig. 5 presents the crystalline block and amorphous cluster for which the calculations were performed. The energy E is a sum of Eij calculated for all pairs of interacting atoms:21 E = ∑ Eij = ij

 1  Aij − 6 + Bij exp(− Cij ⋅ rij ) ∑ 2 ij  rij 

(4)

where: rij is the distance between atoms i and j; Aij, Bij, Cij are the constants characteristic of given atoms. The calculations were performed for the constants given in28 used for the calculations for the crystalline diazepam.20 The constants A and B between different types of atoms were calculated according to the geometric rule, while constant C – to the arimthemtic one. The methyl group was rotated with a step 5 deg (in the range -180 deg to 180 deg) and at each its position the energy was calculated using eq. (4). The results provided a potential energy landscape illustrating the dependence of potential energy on the angle of rotation of the methyl group. The height of the energy barrier was calculated as the difference between its maximum and minimum values. As the molecules on the surface of the crystalline block or amorphous cluster are in incomplete surrounding, in further analysis these molecules were left out. The calculations included the intramolecular part of energy (for distances between a given methyl group atoms and the atoms of the molecule to which it belongs) and the


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intermolecular part of energy (for distances between a given methyl group and the atoms of neighbouring molecules). The sum of these components gives the total energy. Fig. 6 presents the total energy curves for CH3 groups reorientation in the diazepam crystal and its amorphous cluster. As expected, the energy barrier for reorientation of all CH3 groups from the crystalline block was the same and equal to 11.6 kJ/mol. For the methyl groups from the amorphous cluster the energy barrier for methyl group reorientation was found to take values from a range comprising lower and higher values than the one for the crystal. The energy barrier for reorientation of methyl group in the crystalline block is composed of two parts, the one related to intramolecular interactions and the other one related to intermolecular ones, equal to 10.3 kJ/mol and 1.3 kJ/mol, respectively, which means that in the crystal the intermolecular interactions bring a very small contribution to the barrier. In a similar way the contributions to the total energy barrier coming from intra- and intermolecular interactions in the amorphous cluster were calculated. The intramolecular contribution varied from 2.0 to 10.0 kJ/mol, while the intermolecular contribution varied from 0 kJ/mol to as much as 24 kJ/mol. As follows from the above, the intramolecular component to the energy barrier for methyl group reorientation in the amorphous cluster are lower or much lower than in the crystal, while the intermolecular component can be much higher than in the crystal. As the energy barrier heights calculated for the amorphous cluster vary in certain ranges, the histograms were made, illustrating the number of molecules versus the total energy barrier as well as the intra- and intermolecular components of this barrier. The histograms are presented in Fig. 7. The distribution of energy barrier heights related to intramolecular interactions (Fig. 7a) is rather narrow, symmetric and shows a maximum for 5 kJ/mol. The distribution of energy barrier heights related to intermolecular interactions reaches a maximum in the energy range 1- 2 kJ/mol (which means that for about 40% of


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methyl molecules the contribution to energy barrier related to intermolecular interactions is small and comparable to that in the crystal) and decreases with increasing values of energy barriers. The distribution of total energy barriers (Fig. 7b) is asymmetric and shows a distinct maximum at about ~6 kJ/mol, much lower than the energy barrier calculated for the methyl group reorientation in the crystal block. The same figure also presents the experimental distribution of energy barriers obtained on the basis of the data from Table 2, that is the activation energy and the corresponding C constant proportional to the number of reorienting methyl groups. The shape of the calculated distribution is in good agreement with that obtained from the experimental data. The wide distribution of energy barriers related to intermolecular interactions reflects the local anisotropy of these interactions. In order to explain the reasons for the distribution of energy barrier heights related to intramolecular interactions and their values lower than in the crystal, a detail analysis of molecular conformations in the amorphous cluster and in the crystal block was made. To make a comparison, the following four planes were chosen: the first passing through the benzene ring atoms, the second passing through C2, C3 and N4 atoms, the third passing through C2, N1 and C7 atoms and the fourth passing through C6, C5 and N4 atoms. For the crystal the angle between the first and the second plane is 83.8 deg, the angle between the first and the third is 129.2 deg, while the angle between the second and the fourth plane is 75.2 deg. In the amorphous cluster, the angles take different values, on average by 10 deg greater or smaller than the corresponding value in the crystal. Therefore, the conformation of the molecules in the amorphous cluster has changed with respect to that in the crystal, which implies a change in the torsion angles in the condensed benzodiazepine ring with respect to those in the crystal. The change resulted in the increase in the distances between the methyl group atoms and the other atoms from the molecule and therefore caused


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a decrease in the energy barrier. That is why the energy barrier heights related to intramolecular interactions are lower than for the crystal. To sum up, it can be concluded that the distribution of molecular conformations reflects that of the heights of energy barriers related to intramolecular interactions. The increase in the total energy barriers even by 10-15 kJ/mol is related to intermolecular interactions and to their anisotropy.

4. Conclusions The results obtained by NMR relaxation and atom-atom potential energy calculations for amorphous diazepam permit drawing the following conclusions. 1. Reorientations of methyl groups provide interesting information on the local anisotropy of interactions in the system studied. 2. The local anisotropy of interactions is manifested as a distribution of energy barriers for methyl group reorientation; the heights of the barriers vary from 1.9 to 12.7 kJ/mol with a maximum for 5.5 kJ/mol. 3. The calculated energy barriers for the reorientation of the methyl group also show the distribution of their values, which are in good agreement with experimental results 4. The calculated landscape of potential energy permitted evaluation of the distribution of total energy barriers as well as the distributions of their components related to intra- and intermolecular interactions. The character of distribution of the energy barrier component related to intramolecular interactions indicates a modification of diazepam molecule conformation in the amorphous system.


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Acknowledgements The work has been partially financed by the National Science Centre of Poland, Grant No. 2015/17/B/ST5/00104. A.P. would like to thank the Institut Laue Langevin (France) for an invitation as a visiting scientist. Dr Miguel A. Gonzalez (ILL) is acknowledged for the helpful discussions on the use of the Materials Studio package.


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spectroscopy, differential scanning calorimetry, and x-ray diffraction of two polymorphs of 2,6-di-tert-butylnaphthalene, J. Chem. Phys. 2000, 113, 1958. 8. Beckmann, P. A.; Conn, K. G.; Mallory, C. W.; Mallory, F. B.; Rheingold, A. L.; Rotkina, L.; Wang, X. Distributions of methyl group rotational barriers in polycrystalline organic solids, J. Chem. Phys. 2013, 139, 204501.


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28. Daszewski, W.G. Conformational analysis of organic molecules, Izdat. Acad. Nauk Moskwa 1982.


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Table 1 The activation parameters obtained from fitting BPP and Davidson-Cole models to T1 relaxation-spin time measured at 25 MHz for crystalline and amorphous samples crystalline sample

amorphous sample

BPP model

Davidson-Cole model

C [1/s2]

1.431*109

1.240*109

τ0 [ps]

0.20

16.80

Ea [kJ/mol]

8.5

6.26

β

0.26


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Table 2 The activation parameters obtained from fitting seven BPP processes to T1 relaxation-spin time measured at 25 MHz for amorphous sample

Ea [kJ/mol]

τ0 [ps]

C [1/s2]

12,7

0.095

0.052*109

10,4

0.13

0.124*109

7,5

0,70

0.234*109

5,4

1,70

0.291*109

4,7

0,06

0.167*109

3,2

2,70

0.153*109

1,9

9,20

0.029*109


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Fig. 1. The shape of diazepam molecule


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Fig. 2. Powder X-ray diffraction spectra of crystalline and amorphous diazepam. Insert; DSC curve showing glass transition.


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Fig. 3. Temperature dependencies of the relaxation time T1 of crystalline (▲) and amorphous (●) diazepam. The solid lines are the best fit to the experimental points using BPP and Davidson-Cole models.


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Fig. 4. Temperature dependence of the relaxation time T1 of amorphous (●) diazepam. The solid lines are the best fit to the experimental points using several BPP models.


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Fig. 5. The crystalline and amorphous clusters used in the calculations


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Fig. 6. The total energy curves corresponding to the reorientation of methyl group – for crystalline cluster (blue triangle) and for representative molecules from amorphous cluster (red circle)


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a)

b)

Fig. 7. a) The calculated distributions of intramolecular (blue rectangular) and intermolecular energy barriers (dash rectangular) b) the calculated distribution of total energy barriers (left axis) for amorphous cluster and the experimental distribution based on fitting BPP functions to temperature dependence of spin-lattice relaxation time T1 (right axis).


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Graphical abstract


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Figure 1 52x52mm (96 x 96 DPI)



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Figure 2 201x141mm (300 x 300 DPI)


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Figure 3 200x139mm (300 x 300 DPI)



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Figure 4 200x139mm (300 x 300 DPI)


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Figure 5 left 224x197mm (96 x 96 DPI)



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Figure 5 - right 222x164mm (96 x 96 DPI)


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Figure 6 201x141mm (300 x 300 DPI)



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Figure 7a 201x141mm (300 x 300 DPI)


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Figure 7b 201x141mm (300 x 300 DPI)



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graphical abstract 254x190mm (96 x 96 DPI)


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Analysis of the Distribution of Energy Barriers in ... - ACS Publications

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