scholarly journals The Advent of Quantum Crystallography: Form and Structure Factors from Quantum Mechanics for Advanced Structure Refinement and Wavefunction Fitting

2020 ◽  
Author(s):  
Simon Grabowsky ◽  
Alessandro Genoni ◽  
Sajesh P. Thomas ◽  
Dylan Jayatilaka
Keyword(s):  
Quantum Mechanics ◽  
Structure Refinement ◽  
Structure Factors ◽  
Quantum Crystallography

scholarly journals Exploiting the full quantum crystallography

2018 ◽  
Vol 96 (7) ◽  
pp. 599-605 ◽  
Author(s):  
Lou Massa ◽  
Chérif F. Matta
Keyword(s):  
Quantum Mechanics ◽  
Electron Density ◽  
Mathematical Structure ◽  
Scattering Data ◽  
X Ray ◽  
X Ray Crystallography ◽  
X Ray Scattering ◽  
Fundamental Value ◽  
Quantum Crystallography ◽  
Ray Scattering

Quantum crystallography (QCr) is a branch of crystallography aimed at obtaining the complete quantum mechanics of a crystal given its X-ray scattering data. The fundamental value of obtaining an electron density matrix that is N-representable is that it ensures consistency with an underlying properly antisymmetrized wavefunction, a requirement of quantum mechanical validity. However, X-ray crystallography has progressed in an impressive way for decades based only upon the electron density obtained from the X-ray scattering data without the imposition of the mathematical structure of quantum mechanics. Therefore, one may perhaps ask regarding N-representability “why bother?” It is the purpose of this article to answer such a question by succinctly describing the advantage that is opened by QCr.

scholarly journals The Crystal Structure and Chemical Properties of U2Al3C4 and Structure Refinement of Al4C3

1995 ◽  
Vol 50 (2) ◽  
pp. 196-200 ◽  
Author(s):  
Thorsten M. Gesing ◽  
Wolfgang Jeitschko
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Structure Refinement ◽  
Chemical Properties ◽  
Variable Parameters ◽  
Higher Symmetry ◽  
Structure Factors ◽  
Hydrolysis Of ◽  
Symmetry Space ◽  
Symmetry Space Group

A well crystallized sample of U2Al3C4 was obtained by melting the elemental components in a carbon crucible in a high frequency furnace. The crystal structure of this compound was determined from single-crystal diffractometer data of a twinned crystal: P63mc, a = 342.2(1) pm. c = 2323.0(3) pm. Z = 2 , R = 0.030 for 537 structure factors and 18 variable parameters. The structure can also be described in the higher symmetry space group P63/mmc with one split aluminum position. It consists of close packed layers of uranium and aluminum atoms with carbon atoms at interstitial sites. The structure is closely related to that of Al4C3, which was refined from single-crystal X-ray data to a residual of R = 0.033 for 135 F-values and 11 variables. The hydrolysis of U2Al3C4 with diluted hydrochloric acid resulted in about 74 (wt-)% methane, 8% ethane and ethylene, and 18% saturated and unsaturated higher hydrocarbons.

HgH2 meets relativistic quantum crystallography. How to teach relativity to a non-relativistic wavefunction

2021 ◽  
Vol 77 (1) ◽  
pp. 54-66
Author(s):  
Michal Podhorský ◽  
Lukáš Bučinský ◽  
Dylan Jayatilaka ◽  
Simon Grabowsky
Keyword(s):  
Systematic Error ◽  
Structure Factor ◽  
Relativistic Quantum ◽  
Relativistic Effects ◽  
X Ray ◽  
Structure Factors ◽  
Quantum Crystallography

The capability of X-ray constrained wavefunction (XCW) fitting to introduce relativistic effects into a non-relativistic wavefunction is tested. It is quantified how much of the reference relativistic effects can be absorbed in the non-relativistic XCW calculation when fitted against relativistic structure factors of a model HgH2 molecule. Scaling of the structure-factor sets to improve the agreement statistics is found to introduce a significant systematic error into the XCW fitting of relativistic effects.

scholarly journals Protein structure refinement using a quantum mechanics-based chemical shielding predictor

2017 ◽  
Vol 8 (3) ◽  
pp. 2061-2072 ◽  
Author(s):  
Lars A. Bratholm ◽  
Jan H. Jensen
Keyword(s):  
Quantum Mechanics ◽  
Protein Structure ◽  
Chemical Shift ◽  
Chemical Shifts ◽  
Structure Refinement ◽  
Structural Refinement ◽  
Chemical Shielding ◽  
Protein Backbone ◽  
Protein Structure Refinement ◽  
Comparable Accuracy

We show that a QM-based predictor of a protein backbone and CB chemical shifts is of comparable accuracy to empirical chemical shift predictors after chemical shift-based structural refinement that removes small structural errors (errors in chemical shifts shown in red).

Phase determination and structure refinement by density and shift functions

1970 ◽  
Vol 26 (2) ◽  
pp. 230-234 ◽  
Author(s):  
H. Jagodzinski ◽  
D. Philipp
Keyword(s):  
Crystal Structure ◽  
Structure Refinement ◽  
Three Dimensional ◽  
Complete Information ◽  
Shift Function ◽  
Model Structure ◽  
Phase Determination ◽  
One Dimensional ◽  
Structure Factors ◽  
The Right

Any crystal structure may be described in terms of a sublattice of points, each of which represents a certain fraction of the electron density. Multiplying this sublattice by a density function f(x) and applying a shift function s(x), which brings the atoms into the right positions, the correct crystal structure can be given in many different ways. It is shown that the shift function s(x) yields phase relations between the structure factors F(h), which may be evaluated directly, if the coefficients of the Fourier representation of s(x) converge rapidly. This behaviour is demonstrated for the case of a one-dimensional acentric model structure consisting of 50 atoms. Complete information on the structure may be obtained by routine methods with the aid of 5 given phases of the structure factor. This procedure may also be applied to three-dimensional structures, if the corresponding computer programs are available.

scholarly journals On the use of the Obara–Saika recurrence relations for the calculation of structure factors in quantum crystallography

2020 ◽  
Vol 76 (2) ◽  
pp. 172-179 ◽  
Author(s):  
Alessandro Genoni
Keyword(s):  
Recurrence Relations ◽  
Basis Functions ◽  
Future Perspectives ◽  
Recurrence Formulas ◽  
Atomic Nuclei ◽  
Structure Factors ◽  
Modern Methods ◽  
Molecular Integrals ◽  
Chemical Strategies ◽  
Quantum Crystallography

Modern methods of quantum crystallography are techniques firmly rooted in quantum chemistry and, as in many quantum chemical strategies, electron densities are expressed as two-centre expansions that involve basis functions centred on atomic nuclei. Therefore, the computation of the necessary structure factors requires the evaluation of Fourier transform integrals of basis function products. Since these functions are usually Cartesian Gaussians, in this communication it is shown that the Fourier integrals can be efficiently calculated by exploiting an extension of the Obara–Saika recurrence formulas, which are successfully used by quantum chemists in the computation of molecular integrals. Implementation and future perspectives of the technique are also discussed.

Preparation and Crystal Structures of Ternary Rare Earth Silver and Gold Arsenides LnAgAs2 and LnAuAs2 with Ln = La–Nd, Sm, Gd, and Tb

2003 ◽  
Vol 58 (5) ◽  
pp. 399-409 ◽  
Author(s):  
Marcus Eschen ◽  
Wolfgang Jeitschko
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Structure Refinement ◽  
Gold Compound ◽  
Crystal Structure Refinement ◽  
Variable Parameters ◽  
Structure Factors ◽  
Formal Charge ◽  
Gold Compounds ◽  
Silver Compounds

The 14 arsenides LnAgAs2 and LnAuAs2 (Ln = La-Nd, Sm, Gd, Tb) were prepared by reaction of stoichiometric mixtures of the elemental components at high temperatures and characterized by Xray diffractometry. The silver compounds LaAgAs2 and CeAgAs2 and the gold compounds LnAuAs2 (Ln = Ce-Nd, Sm, Gd, Tb) crystallize with HfCuSi2 type structure (P4/nmm, Z = 2). Of these, the structures of CeAgAs2 (a = 408.5(1), c = 1048.2(1) pm, conventional residual R = 0.017 for 261 structure factors and 12 variable parameters) and CeAuAs2 (a = 411.4(1), c = 1015.3(2) pm, R = 0.030 for 428 F values) were refined from four-circle diffractometer data. The silver compounds LnAgAs2 (Ln = Pr, Nd, Sm, Gd, Tb) are isotypic with the antimonide SrZnSb2 (Pnma, Z = 4) as demonstrated by a single-crystal structure refinement of PrAgAs2 (a = 2107.3(4), b = 401.7(1), c = 407.8(1) pm, R = 0.042 for 746 F values and 26 variables). The gold compound LaAuAs2 (I4/mmm, Z = 4, a = 416.9(1), c = 2059.5(3) pm, R = 0.038 for 303 F values and 13 variables) was found to be isotypic with the bismuthide SrZnBi2, again by a refinement from single-crystal diffractometer data. In the structures of CeAgAs2, LaAuAs2, and CeAuAs2 large displacement parameters perpendicular to the four-fold axes were found for one of the two arsenic positions. These structures could also be refined with split positions for these arsenic atoms, which allow for considerable As-As bonding, resulting in a formal charge of −1 for these atoms. Chemical bonding in these compounds can thus be rationalized by a simple model corresponding to the formula Ln+3T+1As−1As−3 (T = Ag, Au), where the superscripts indicate oxidation numbers.

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