experimental data. The validity of models can be assessed using traditional least
squares metrics. Increasingly, DFT calculations can provide a theoretical check on
results, while leverage analysis can check the influence of restraints on the fit of
model parameters.
I would like to acknowledge the feedback and contributions of users and developers of the CRYSTALS software – in particular Pascal Parois, Bruce Foxman and
David Watkin – which have led to investigations of many of the refinement features
described in this chapter.
References
1. Brown PJ, Fox AG, Maslen EN, Keefe MA, Willis BTM (2006) Intensity of diffracted
intensities. In: International tables for crystallography. International Union of Crystallography,
pp 554–595
2. Sanjuan-Szklarz WF, Hoser AA, Gutmann M, Madsen AØ, Woźniak K (2016) Yes, one can
obtain better quality structures from routine X-ray data collection. IUCrJ 3:61–70
3. Sheldrick GM (2015) Crystal structure refinement with SHELXL. Acta Crystallogr Sect C
Struct Chem 71:3–8
4. Wilson AJC (1976) Statistical bias in least-squares refinement. Acta Crystallogr Sect A
32:994–996
5. Dominiak PM, Volkov A, Li X, Messerschmidt M, Coppens P (2007) A theoretical databank of
transferable aspherical atoms and its application to electrostatic interaction energy calculations
of macromolecules. J Chem Theory Comput 3:232–247
6. Fugel M et al (2017) Probing the accuracy and precision of hirshfeld atom refinement with
HARt interfaced with Olex2. IUCrJ 5:32–44
7. Schröder L, Watkin DJ, Cousson A, Cooper RI, Paulus W (2004) CRYSTALS enhancements:
refinement of atoms continuously disordered along a line, on a ring or on the surface of a sphere.
J Appl Crystallogr. https://doi.org/10.1107/s0021889804009847
8. King MV, Lipscomb WN (1950) The X-ray scattering from a hindered rotator. Acta Crystallogr
3:155–158
9. Reilly AM, Morrison CA, Rankin DWH, McLean KR (2011) Using molecular-dynamics
simulations to understand and improve the treatment of anharmonic vibrations.
II. Developing and assessing new Debye-Waller factors. Acta Crystallogr Sect A Found
Crystallogr 67:346–356
10. Betteridge PW, Carruthers JR, Cooper RI, Prout K, Watkin DJ (2003) CRYSTALS version 12:
software for guided crystal structure analysis. J Appl Crystallogr. https://doi.org/10.1107/
s0021889803021800
11. Binns J et al (2017) Phase transition sequences in tetramethylammonium tetrachlorometallates
by X-ray diffraction and spectroscopic measurements. Acta Crystallogr Sect B Struct Sci Cryst
Eng Mater 73:844–855
12. Bailey PJ et al (2010) A new synthesis of charge-neutral tris-pyrazolyl and -methimazolyl
borate ligands. Chem Eur J 16:2819–2829
13. Barrett ES, Irwin JL, Edwards AJ, Sherburn MS (2004) Superbowl container molecules. J Am
Chem Soc 126:1
14. Anderson E, Bai Z, Bischof J, Blackford S, Demmel J, Dongarra J, Du Croz J, Greenbaum A,
Hammarling S, McKenney A, Sorensen D (1999) LAPACK users’ guide. Society for Industrial
and Applied Mathematics, Philadelphia
15. Wang Q, Zhang X, Zhang Y, Yi Q (2013) AUGEM: automatically generate high performance
dense linear algebra kernels on x86 CPUs. In: International conference for high performance
Recent Developments in the Refinement and Analysis of Crystal Structures
65
squares metrics. Increasingly, DFT calculations can provide a theoretical check on
results, while leverage analysis can check the influence of restraints on the fit of
model parameters.
I would like to acknowledge the feedback and contributions of users and developers of the CRYSTALS software – in particular Pascal Parois, Bruce Foxman and
David Watkin – which have led to investigations of many of the refinement features
described in this chapter.
References
1. Brown PJ, Fox AG, Maslen EN, Keefe MA, Willis BTM (2006) Intensity of diffracted
intensities. In: International tables for crystallography. International Union of Crystallography,
pp 554–595
2. Sanjuan-Szklarz WF, Hoser AA, Gutmann M, Madsen AØ, Woźniak K (2016) Yes, one can
obtain better quality structures from routine X-ray data collection. IUCrJ 3:61–70
3. Sheldrick GM (2015) Crystal structure refinement with SHELXL. Acta Crystallogr Sect C
Struct Chem 71:3–8
4. Wilson AJC (1976) Statistical bias in least-squares refinement. Acta Crystallogr Sect A
32:994–996
5. Dominiak PM, Volkov A, Li X, Messerschmidt M, Coppens P (2007) A theoretical databank of
transferable aspherical atoms and its application to electrostatic interaction energy calculations
of macromolecules. J Chem Theory Comput 3:232–247
6. Fugel M et al (2017) Probing the accuracy and precision of hirshfeld atom refinement with
HARt interfaced with Olex2. IUCrJ 5:32–44
7. Schröder L, Watkin DJ, Cousson A, Cooper RI, Paulus W (2004) CRYSTALS enhancements:
refinement of atoms continuously disordered along a line, on a ring or on the surface of a sphere.
J Appl Crystallogr. https://doi.org/10.1107/s0021889804009847
8. King MV, Lipscomb WN (1950) The X-ray scattering from a hindered rotator. Acta Crystallogr
3:155–158
9. Reilly AM, Morrison CA, Rankin DWH, McLean KR (2011) Using molecular-dynamics
simulations to understand and improve the treatment of anharmonic vibrations.
II. Developing and assessing new Debye-Waller factors. Acta Crystallogr Sect A Found
Crystallogr 67:346–356
10. Betteridge PW, Carruthers JR, Cooper RI, Prout K, Watkin DJ (2003) CRYSTALS version 12:
software for guided crystal structure analysis. J Appl Crystallogr. https://doi.org/10.1107/
s0021889803021800
11. Binns J et al (2017) Phase transition sequences in tetramethylammonium tetrachlorometallates
by X-ray diffraction and spectroscopic measurements. Acta Crystallogr Sect B Struct Sci Cryst
Eng Mater 73:844–855
12. Bailey PJ et al (2010) A new synthesis of charge-neutral tris-pyrazolyl and -methimazolyl
borate ligands. Chem Eur J 16:2819–2829
13. Barrett ES, Irwin JL, Edwards AJ, Sherburn MS (2004) Superbowl container molecules. J Am
Chem Soc 126:1
14. Anderson E, Bai Z, Bischof J, Blackford S, Demmel J, Dongarra J, Du Croz J, Greenbaum A,
Hammarling S, McKenney A, Sorensen D (1999) LAPACK users’ guide. Society for Industrial
and Applied Mathematics, Philadelphia
15. Wang Q, Zhang X, Zhang Y, Yi Q (2013) AUGEM: automatically generate high performance
dense linear algebra kernels on x86 CPUs. In: International conference for high performance
Recent Developments in the Refinement and Analysis of Crystal Structures
65