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Recent Developments in the Refinement and Analysis of Crystal Structures

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21st Century Challenges in Chemical Crystallography I

Part of the book series: Structure and Bonding ((STRUCTURE,volume 185))

Abstract

Crystal structure refinement and analysis is a powerful method for determination of crystal structures and finds widespread application in determination of structures of crystals of small molecules and frameworks at atomic resolution. The independent atom model is used to describe atomic scattering for routine use, while more accurate aspherical scattering factors are increasingly available. The structure factor is presented as the Fourier transform of convolutions of scattering and probability densities in the crystal structure to clarify how aspherical scattering factors and alternative displacement probabilities can be introduced into refinement methods. Non-linear least squares fitting of the crystal structure parameters in the structure factor equations is described using matrix algebra notation which enables simple derivation of the extensions required for discussion of crystallographic restraints and leverage analysis. Finally, combined analysis of multiple single-crystal experiments is discussed highlighting the potential of refinement tools to extract useful information from joint X-ray and neutron data and from mixed ground-state and excited-state X-ray data from pump-probe experiments.

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Abbreviations

⊗:

Convolution operator

ADP:

Anisotropic displacement parameter

DFT:

Density functional theory

Fc2:

Calculated structure factor squared

FFT:

FAST Fourier transform

Fo2:

Observed structure factor squared

FT:

Fourier transform

IAM:

Independent atom model

r.m.s.:

Root mean square

SCF:

Self-consistent field

TAAM:

Transferable aspherical atom model

TLS:

Translation-libration-screw

u(x):

Estimated uncertainty of a model parameter, x

λ:

Wavelength

σ2(Fo2):

Estimated variance of the observed structure factor

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Authors and Affiliations

  1. Chemical Crystallography, Department of Chemistry, University of Oxford, Oxford, UK

    Richard I. Cooper

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  1. Richard I. Cooper
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Correspondence to Richard I. Cooper .

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Editors and Affiliations

  1. Inorganic Chemistry Laboratory, University of Oxford, Oxford, UK

    D. Michael P. Mingos

  2. Department of Chemistry, University of Bath, Bath, UK

    Paul R. Raithby

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Cooper, R.I. (2020). Recent Developments in the Refinement and Analysis of Crystal Structures. In: Mingos, D.M.P., Raithby, P.R. (eds) 21st Century Challenges in Chemical Crystallography I. Structure and Bonding, vol 185. Springer, Cham. https://doi.org/10.1007/430_2020_76

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