scholarly journals Comparison and evaluation of pair distribution functions, using a similarity measure based on cross-correlation functions

2021 ◽  
Vol 54 (2) ◽  
pp. 612-623
Author(s):  
Stefan Habermehl ◽  
Carina Schlesinger ◽  
Dragica Prill
Keyword(s):  
Similarity Measure ◽  
Correlation Functions ◽  
Cross Correlation ◽  
Barbituric Acid ◽  
Structural Models ◽  
Distribution Functions ◽  
Large Signal ◽  
Small Deviations ◽  
Alternative Approach ◽  
Pair Distribution Functions

An approach for the comparison of pair distribution functions (PDFs) has been developed using a similarity measure based on cross-correlation functions. The PDF is very sensitive to changes in the local structure, i.e. small deviations in the structure can cause large signal shifts and significant discrepancies between the PDFs. Therefore, a comparison based on pointwise differences (e.g. R values and difference curves) may lead to the assumption that the investigated PDFs as well as the corresponding structural models are not in agreement at all, whereas a careful visual inspection of the investigated structural models and corresponding PDFs may reveal a relatively good match. To quantify the agreement of different PDFs for those cases an alternative approach is introduced: the similarity measure based on cross-correlation functions. In this paper, the power of this application of the similarity measure to the analysis of PDFs is highlighted. The similarity measure is compared with the classical R wp values as representative of the comparison based on pointwise differences as well as with the Pearson product-moment correlation coefficient, using polymorph IV of barbituric acid as an example.

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

2015 ◽  
Vol 48 (1) ◽  
pp. 171-178 ◽  
Author(s):  
Dragica Prill ◽  
Pavol Juhás ◽  
Martin U. Schmidt ◽  
Simon J. L. Billinge
Keyword(s):  
Structural Models ◽  
Simple Approach ◽  
Distribution Functions ◽  
Atomic Motion ◽  
Molecular Systems ◽  
Atomic Pair ◽  
Intermolecular Distances ◽  
Supercell Model ◽  
Pair Distribution Functions ◽  
Modelling Approach

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 theDiffPy-CMIcomplex modelling infrastructure. The new modelling approach produced remarkably better fits to the experimental PDFs, confirming the higher accuracy of this method for organic materials.

FIDDLE. Simultaneous Indexing and Structure Solution from Powder Diffraction Data using a Genetic Algorithm and Correlation Functions

2019 ◽  
Author(s):  
Carmen Guguta ◽  
Jan M.M. Smits ◽  
Rene de Gelder
Keyword(s):  
Genetic Algorithm ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Correlation Functions ◽  
Cross Correlation ◽  
Simultaneous Optimization ◽  
Powder Diffraction Data ◽  
Structure Solution ◽  
Matching Technique

A method for the determination of crystal structures from powder diffraction data is presented that circumvents the difficulties associated with separate indexing. For the simultaneous optimization of the parameters that describe a crystal structure a genetic algorithm is used together with a pattern matching technique based on auto and cross correlation functions.<br>

scholarly journals Local structure and distortions of mixed methane-carbon dioxide hydrates

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Bernadette R. Cladek ◽  
S. Michelle Everett ◽  
Marshall T. McDonnell ◽  
Matthew G. Tucker ◽  
David J. Keffer ◽  
...  
Keyword(s):  
Carbon Dioxide ◽  
Exchange Process ◽  
Carbon Dioxide Sequestration ◽  
Distribution Functions ◽  
Atomic Scale ◽  
Mixed Gas ◽  
Pure Compounds ◽  
Dynamics Simulations ◽  
Pair Distribution Functions ◽  
Methane Carbon

AbstractA vast source of methane is found in gas hydrate deposits, which form naturally dispersed throughout ocean sediments and arctic permafrost. Methane may be obtained from hydrates by exchange with hydrocarbon byproduct carbon dioxide. It is imperative for the development of safe methane extraction and carbon dioxide sequestration to understand how methane and carbon dioxide co-occupy the same hydrate structure. Pair distribution functions (PDFs) provide atomic-scale structural insight into intermolecular interactions in methane and carbon dioxide hydrates. We present experimental neutron PDFs of methane, carbon dioxide and mixed methane-carbon dioxide hydrates at 10 K analyzed with complementing classical molecular dynamics simulations and Reverse Monte Carlo fitting. Mixed hydrate, which forms during the exchange process, is more locally disordered than methane or carbon dioxide hydrates. The behavior of mixed gas species cannot be interpolated from properties of pure compounds, and PDF measurements provide important understanding of how the guest composition impacts overall order in the hydrate structure.

Tomographic inversion of measured cross-correlation functions of ocean noise in shallow water using ray theory

2016 ◽  
Vol 62 (4) ◽  
pp. 436-446 ◽  
Author(s):  
V. V. Goncharov ◽  
A. S. Shurup ◽  
O. A. Godin ◽  
N. A. Zabotin ◽  
A. I. Vedenev ◽  
...  
Keyword(s):  
Shallow Water ◽  
Correlation Functions ◽  
Cross Correlation ◽  
Ray Theory ◽  
Tomographic Inversion ◽  
Ocean Noise
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