Modelling pair distribution functions (PDFs) of organic compounds: describing both intra‐ and intermolecular correlation functions in calculated PDFs

The methods currently used to calculate atomic pair distribution functions (PDFs) from organic structural models do not distinguish between the intramolecular and intermolecular distances. Owing to the stiff bonding between atoms within a molecule, the PDF peaks arising from intramolecular atom–atom distances are much sharper than those of the intermolecular atom–atom distances. This work introduces a simple approach to calculate PDFs of molecular systems without building a supercell model by using two different isotropic displacement parameters to describe atomic motion: one parameter is used for the intramolecular, the other one for intermolecular atom–atom distances. Naphthalene, quinacridone and paracetamol were used as examples. Calculations were done with the DiffPy-CMI complex modelling infrastructure. The new modelling approach produced remarkably better fits to the experimental PDFs, confirming the higher accuracy of this method for organic materials.

[1]  Simon J. L. Billinge,et al.  PDFFIT, a program for full profile structural refinement of the atomic pair distribution function , 1999 .

[2]  Simon J. L. Billinge,et al.  Underneath the Bragg Peaks: Structural Analysis of Complex Materials , 2003 .

[3]  F. Allen.  The Cambridge Structural Database: a quarter of a million crystal structures and rising. , 2002, Acta crystallographica. Section B, Structural science.

[4]  K. Lonsdale.  X-Ray Diffraction , 1971, Nature.

[5]  Andrew L. Goodwin,et al.  Applications of pair distribution function methods to contemporary problems in materials chemistry , 2011 .

[6]  S J L Billinge,et al.  PDFfit2 and PDFgui: computer programs for studying nanostructure in crystals , 2007, Journal of physics. Condensed matter : an Institute of Physics journal.

[7]  S. Billinge,et al.  Toward Phase Quantification at the Nanoscale Using the Total Scattering Pair Distribution Function (TSPDF) Method: Recrystallization of Cryomilled Sulfamerazine , 2013 .

[8]  Simon J L Billinge,et al.  Relationship between the atomic pair distribution function and small-angle scattering: implications for modeling of nanoparticles. , 2008, Acta crystallographica. Section A, Foundations of crystallography.

[9]  T. Proffen,et al.  Measuring Correlated Atomic Motion Using X-ray Diffraction , 1999 .

[10]  J Dressman,et al.  Pair distribution function X-ray analysis explains dissolution characteristics of felodipine melt extrusion products. , 2009, Journal of pharmaceutical sciences.

[11]  M. Laue,et al.  Interferenzerscheinungen bei Röntgenstrahlen , 1913 .

[12]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[13]  Robert Michael Christie.  Industrial organic pigments , 1995 .

[14]  U. Kolb,et al.  Electron diffraction, X-ray powder diffraction and pair-distribution-function analyses to determine the crystal structures of Pigment Yellow 213, C23H21N5O9. , 2009, Acta crystallographica. Section B, Structural science.

[15]  L. Daemen,et al.  Pair distribution function analysis of molecular compounds: significance and modeling approach discussed using the example of p‐terphenyl , 2012 .

[16]  C. Jelsch,et al.  Charge density and electrostatic potential analyses in paracetamol. , 2009, Acta crystallographica. Section B, Structural science.

[17]  S. Larsen,et al.  Charge Density Study of Naphthalene Based on X-ray Diffraction Data at Four Different Temperatures and Theoretical Calculations , 2004 .

[18]  D. Cruickshank,et al.  A detailed refinement of the crystal and molecular structure of naphthalene , 1957 .

[19]  S. Billinge.  Nanoscale structural order from the atomic pair distribution function (PDF): There's plenty of room in the middle , 2008 .

[20]  T. Proffen,et al.  Advances in total scattering analysis , 2009 .

[21]  S. Bates,et al.  Local Structure in Amorphous Phases of Piroxicam from Powder X-ray Diffractometry , 2005 .

[22]  Simon Bates,et al.  Characterization of amorphous API:Polymer mixtures using X-ray powder diffraction. , 2008, Journal of pharmaceutical sciences.

[23]  T. Egami.  Atomic Correlations in Non-Periodic Matter , 1990 .

[24]  Simon J. L. Billinge,et al.  PDFgetX3: a rapid and highly automatable program for processing powder diffraction data into total scattering pair distribution functions , 2012, 1211.7126.

[25]  Simon J L Billinge,et al.  The Problem with Determining Atomic Structure at the Nanoscale , 2007, Science.

[26]  W. Bragg,et al.  The Reflection of X-rays by Crystals , 1913 .

[27]  K. Shankland,et al.  Characterisation of amorphous and nanocrystalline molecular materials by total scattering , 2010 .

[28]  B. Warren,et al.  X-Ray Diffraction , 2014 .

[29]  S. Billinge,et al.  Lattice dynamics and correlated atomic motion from the atomic pair distribution function , 2002, cond-mat/0209603.

[30]  F. Leusen,et al.  Crystal structures of quinacridones , 2007 .

[31]  S. Billinge,et al.  Data Requirements for the Reliable Use of Atomic Pair Distribution Functions in Amorphous Pharmaceutical Fingerprinting , 2011, Pharmaceutical Research.

[32]  Takeshi Egami,et al.  Underneath the Bragg Peaks , 2003 .

[33]  A. P. Hammersley,et al.  Two-dimensional detector software: From real detector to idealised image or two-theta scan , 1996 .

[34]  Simon J L Billinge,et al.  Beyond crystallography: the study of disorder, nanocrystallinity and crystallographically challenged materials with pair distribution functions. , 2004, Chemical communications.