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.
Keywords Atomic displacement parameters · Crystal structure refinement · Least
squares · Leverage analysis · Restraints · Structure factor · Validation
Abbreviations
Convolution operator
ADP
Anisotropic displacement parameter
DFT
Density functional theory
F c
2
Calculated structure factor squared
FFT
FAST Fourier transform
F o
2
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
σ
2 (F o
2 ) Estimated variance of the observed structure factor
1 Introduction and Background of Crystal Structure
Refinement and Analysis
X-ray crystal structures have been determined from a diverse range of materials,
spanning metals and minerals, through small-molecule organic and metal-organic
compounds, including covalent and metal-organic extended frameworks, to crystallized proteins and even virus particles. This chapter focusses specifically on the
determination of chemical information based on X-ray or neutron scattering
techniques.
Structure solution algorithms based on direct methods or charge flipping can be
run in parallel, in order to provide a high chance of finding a reasonable trial
structure solution. Such solutions, despite being derived directly from the experimental data, should be considered as untested hypotheses. The accuracy of the
structure can be improved, and the hypothesis tested, by fitting the model to the
experimental data using weighted non-linear least squares algorithms. This
approach provides several internal measures of quality including the goodness of
fit to the data, estimates of precision of the parameters and convergence of the model.
44
R. I. Cooper
useful information from joint X-ray and neutron data and from mixed ground-state
and excited-state X-ray data from pump-probe experiments.
Keywords Atomic displacement parameters · Crystal structure refinement · Least
squares · Leverage analysis · Restraints · Structure factor · Validation
Abbreviations
Convolution operator
ADP
Anisotropic displacement parameter
DFT
Density functional theory
F c
2
Calculated structure factor squared
FFT
FAST Fourier transform
F o
2
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
σ
2 (F o
2 ) Estimated variance of the observed structure factor
1 Introduction and Background of Crystal Structure
Refinement and Analysis
X-ray crystal structures have been determined from a diverse range of materials,
spanning metals and minerals, through small-molecule organic and metal-organic
compounds, including covalent and metal-organic extended frameworks, to crystallized proteins and even virus particles. This chapter focusses specifically on the
determination of chemical information based on X-ray or neutron scattering
techniques.
Structure solution algorithms based on direct methods or charge flipping can be
run in parallel, in order to provide a high chance of finding a reasonable trial
structure solution. Such solutions, despite being derived directly from the experimental data, should be considered as untested hypotheses. The accuracy of the
structure can be improved, and the hypothesis tested, by fitting the model to the
experimental data using weighted non-linear least squares algorithms. This
approach provides several internal measures of quality including the goodness of
fit to the data, estimates of precision of the parameters and convergence of the model.
44
R. I. Cooper