Non-spherical electron densities
using invarioms
Introduction, applications and examples of
invariom refinement
B. Dittrich
Institute for Inorganic Chemistry,
Tammannstr. 4
37077 Göttingen, Germany
Welcome
2
Dr. Michael Ruf
Product Manager,
SC-XRD
Madison, WI, USA
Dr. Birger Dittrich
Method development in
single-crystal X-ray diffraction
Charge density
research
High-res.
macromolecular
refinement
Antibiotics research
Introduction to
charge density
research
and invariom
refinement (IR)
Examples and
applications of IR:
Flack parameter,
ADPs, H-distances, Properties from ρ(r)
Theoretical background and brief
introduction to charge density research
Least-squares refinement
We refine the parameters of our model (Fc),
which are e.g. positional parameters so that the
model best fits our experimental data (Fo).
The function ε is minimized.
Iterative process, needs good starting positions
from structure solution.
4
Conventional XRD
Structure determination from single-crystals
Uses Independent Atom Model (IAM)
Scattering factor fk obtained by FT from atomic
(i.e. non-interacting) Hartree Fock electron densities
Least-squares refinement gives atomic positions
9 parameters per atom: positions r (xyz) and
the 6 displacement parameters Uij omitted below
5
Residual electron density
We can identify missing atoms or model
deficiencies by calculating residual electron
density Δρ(r) after converged IAM-refinement
The difference between model and observation
is calculated using the model phases.
6
Model deficiencies in the IAM
Antibiotic Ciprofloxacin, residual density Δρ(r) from converged IAM-refinement:
7 Figure generated using free program MolecoolQt:
Hübschle and Dittrich, J. Appl. Cryst., 44, 2011, 238
Isosurfaces with ±0.25 (red/green) e/Å3
Model deficiencies in the IAM
Non-interacting atomic electron density of model
(Fc) does not contain bonding and lone-pair
electron density in fk.
Anisotropic displacement parameters (ADPs)
model parts of the bonding electron density for
low-resolution data.
A considerable number of predominantly small-
molecule data sets contain this extra information.
8
Solution: Charge Density Research
In CD research this additional information is
investigated
Basic ideas and methodology developed
between 1960 and 1980
Combines theory and experiment, with focus on
ρ(r) being an observable (Hohnberg/Kohn)
Usually employs Hansen/Coppens multipole
model
Mature field of research, “coming of age” has been
proclaimed
9 Koritsánszky & Coppens, Chem. Rev. 101, 2001, 1583
P. Coppens, Angew. Chem. Int. Ed. 44, 2005, 6810
Hansen/Coppens’ Multipole model
Combines radial functions jl with spherical
harmonic functions dlm (density-normalized ylm)
Analytical representation of ρ(r)
Fixed core density
Scattering factor fk is different to IAM
Up to 25+2 additional atomic parameters
10 Hansen & Coppens, Acta Cryst. A34, 1978, 909
Spherical harmonics & radial functions
11 Figures courtesy of R. Kalinowski
First X-ray diffraction experiment by
Knipping, Friedrich und Laue 1912
High experimental requirements
12
Good crystal quality
Low temp. (<100 K)
High redundancy (Area detection)
Short exposure
No radiation decay
High resolution (< 0.5 Å or >1.0 sin θ/λ Å-1)
Hard X-rays
Precise intensity measurements
Complete coverage of reciprocal space
Luger, Dittrich, chapter in book by Matta & Boyd on QTAIM, 2007, Wiley
Destro et al., Acta Cryst. A60, 2004, 365
R(F) = 2.9 %
R(F) = 2.6 %
R(F) = 2.0 %
R(F) = 1.3 % R(F) = 0.7 %
R(F) = 0.6 %
What do we model with multipoles?
13
Δρ(r) = 0.01 e/Å3
Δρ(r) = 0.034 e/Å3
Δρ(r) = 0.061 e/Å3
Δρ(r) = 0.072 e/Å3
Δρ(r) = 0.112 e/Å3
Residual density & model sophistication
14
The issue of suitability
Heavier elements pose challenge
Technical: Radial distribution of ρ(r) can deviate substantially from isolated atoms
Experimental: Extinction and absorption occur
Core electrons dominate:
Solutions:
Study lighter elements like Li, B, N, Al, Si, P
Improve the precision of model & data accuracy
Include external information
15 Stevens, Coppens, Acta Cryst. A32, 1976, 915
The problem of parameter correlation
Correlation between parameters is problematic
Recommendation by some researchers: Refinement of parameters in blocks
Blocked refinement has been criticised to not provide a satisfactory solution
Examples: Monopole and Kappa parameters
Quadrupoles and ADPs in similar orientation on fluorine and oxygen
16 Watkin, Acta Cryst. A50, 1994, 411
Background on invariom refinement
Solution: Tabulated multipoles
In invariom ref. the multipole parameters are obtained by FT from theory (DFT/B3LYP), no experimental ρ(r)
Like in IAM only xyz and Uij are refined while multipole parameters are fixed, no extra parameters
Ref. improves geometry, ADPs, and figures of merit
Give better description of chemical bonding in comparison to IAM
High resolution not required
While fatal for charge density, disorder is no big problem in invariom refinement
18 Dittrich, Koritsánszky, Luger, Angew. Chem. 116, 2004, 2773
“An →invariom is a fragment of electron density
that is invariant in a transfer from one molecule to
another (to a good approximation).
For an invariom assigned to an atom, the [next]
nearest neighbors are the same as the chosen
atom in terms of element, bond order and
geometry.
There is a finite number of invarioms for each
element.
→ from invariant pseudoatom
Invariom definition
Dittrich, Koritsánszky, Luger, Angew. Chem. 116, 2004, 2773
Schematic procedure
We partition a molecule into
atomic fragments
We calculate a suitable model
compound to reproduce it
We reconstruct molecular
densities from the reproduced
fragments
Invariom needs to be oriented
20 Hübschle, Luger, Dittrich, J. Appl. Cryst. 40, 2007, 623
Practical procedure
Invariomtool or MolecoolQt identifiy
invariom names
Suitable model compound has been
already calculated for you
Invariom is located in the database
Invariomtool assigns coordinate
system
Process is fully automated when
scattering factors are indeed present
in the database
21 Hübschle, Luger, Dittrich, J. Appl. Cryst. 40, 2007, 623
d is the bond distance, rc the covalent radius and EN the
Allred & Rochow electronegativity.
allows to distinguish single, double and triple bonds.
< 0.0847 = single bond. in between 0.0847 & 0.184 =
delocalized system, > 0.184 = double > 0.27 triple bond.
Schomaker & Stevenson, JACS. 63, 1941, 37
IAM geometry and covalent bonding is evaluated.
We characterize the bonds by subtracting the bond
distance from the result obtained.
Characterization of bonds
22
Scattering factors are organized by invariom name. Local
chemical environment is considered. Atom of interest gets
capital letter, neighbors are listed. Easiest case: single
bonds. H-atoms require next-nearest neighbors.
H1c[1c1h1h]
C1c1h1h1h
C1n1c1c1h
H1c[1n1c1c]
N1c1h1h
H1n[1c1h]
23
Invariom notation for single bonds
1.5 means that the atom is in a de-localized
environment, requiring information on neighbors, 2
means it’s a (more localized) double bond.
H1c[2o1.5n]
C2o1.5n[1h1h]1h
N1.5c[2o1h]1h1h
H1n[1.5c1h]
O2c
24
Invariom notation for de-localized bonds
Next-nearest neighbors are considered for F, but not for S,
since hypervalent atoms can have different direct neighbors
that influence a single-bonded atom next to it.
S1f1f1f1f1f1f
F1s[1f1f1f1f1f]
25
Hypervalent and chiral atoms
Invarioms can be chiral
too (not so common).
Then they get a R- or S-
in front of the name
(CIP-rules).
Prelog, Helmchen, Angew. Chem. Int. Ed. 21, 1982, 567
Name gets modified if the atom is planar, e.g. =–N1c1h1h
Is the atom part of a 3,5,6- or 7-membered ring? Then
# means that atom is part of a de-localized ring environment.
More information from geometry
26
H@6c
6-C#6c[#6c1o]#6c[#6c1h]1h
6-C#6c[#6c1h]#6c[#6c1h]1o
O@6c1h
H1o[@6c]
An overview of empirical rules in IR
Single bonds:
Nearest neighbors Hydrogens:
Next-nearest
neighbors Delocalisation:
Best suited
mesomeric system Bonded to heavier
Nucleus:
Next-nearest
neighbor Heavier nucleus:
Nearest neighbor
27
benzylalcohol
Model compounds provide local chemical environments
(NNA/NNNA) based on empirical rules
Entries obtained via G09 geometry optimization
Fourier Transform of ρ(r) (program TONTO) gives Fsim
Multipole refinement (program XDLSM) against Fsim gives
database entry
Currently > 2000 scattering factors and growing
Koritsánszky et al., Acta Cryst. A58, 2002, 464
Dittrich, Hübschle, Luger, Spackman, Acta Cryst. D62, 2006, 1325
The invariom database
Applications of invariom refinement (IR)
What did we miss in the IAM again?
Antibiotic ciprofloxacin, residual density after
converged IAM-refinement:
Isosurfaces with ±0.25 (red/green) e/Å3
Dittrich, Hübschle, Holstein, Fabbiani, J. Appl. Cryst. 42, 2009, 1110 30
What is included in the model
Antibiotic ciprofloxacin, imposed deformation
density from invariom database (frozen core)
J. Appl. Cryst. 42, 2009, 1110
Units: e/Å3
31
Residual density after invariom ref.
Ciprofloxacin Hexahydrate, residual density after
invariom refinement:
J. Appl. Cryst. 42, 2009, 1110
Isosurfaces: 0.1 e/Å3
32
R(F),IAM 3.13 % R(F), INV 2.05 %
Effect on residual density: DL-Serine
33 Dittrich, Hübschle, Messerschmidt, Kalinowski, Girnt, Luger,
Acta Cryst. A61, 2005, 314
sin / [Å-1]
Hirshfeld, Acta Cryst. A32, 1976, 239
“[...] the relative vibrational motion of a pair of bonded
atoms has an effectively vanishing component
in the direction of the bond.“
The difference of the mean-square displacement
amplitude (DMSDA) should be zero (< 10-4Å2).
2
,
2
, ABBA zz
The Hirshfeld test
34
Effect on the ADPs for DL-Serine
35 Acta Cryst. A61, 2005, 314
sin / [Å-1] sin / [Å-1]
n
i
iDMSDAn
y ||1
in 1
0-4
Å2
Effect on the ADPs, L-Hydroxylysine HCl
In the IAM the bonding density is partially
absorbed by ADPs
This is corrected for by imposing ρ(r) in IR
Picture shows ADP difference of IAM minus IR
and was generated by program Peanut
36 Dittrich, McKinnon, Warren, Acta Cryst. B64, 2008, 750
Hummel, Hauser, Buergi, J. Mol. Graphics 4, 1990, 214
Changes in geometry after IR
Higher accuracy, better precision (e.s.d.s)
Corrects asphericity shifts from IAM
H-Atoms move most
Changes for other atoms often within standard deviation for normal resolution data
Example: L-ornitine HCl, ∆1 IAM-IR, 2 IAM-mult
37 Coppens, Acta Cryst. A25, 1969, 180
Dittrich, Munshi, Spackman, Acta Cryst. B63, 2007, 505
H-bond distances, DL-serine @ 298K
38
Bindung Neutronen Röntgen
(Invariome)
Normale
SFAC
N1-H11,
H12,
H13
1.037(1)
1.045(1)
1.041(1)
1.048(9)
1.03(1)
1.03(1)
0.96(2)
0.95(2)
0.94(2)
C2-H2 1.101(1) 1.080(7) 0.956(9)
C3-H31,
H32
1.095(1)
1.095(1)
1.096(9)
1.12(1)
0.97(2)
1.00(2)
O4-H4 0.981(1) 0.95(1)
R(F) = 2.2 %
0.92(2)
R(F) = 3.3 %
Energy –398.90 Ha –398.86 Ha
Acta Cryst. A61, 2005, 314
Flack parameter ESD after IR
Higher accuracy, better precision (e.s.d.s)
Example: Paeciloside, new polyketide
R-Factor improves from IAM: 2.91 % to IR: 2.36%
Flack-parameter from IAM: 0.02(14), IR: 0.01(11)
39 Dittrich, Strumpel, Schäfer, Spackman, Koritsánszky,
Acta Cryst. A62, 2006, 217
Changes in energy
Changes in geometry lead to dramatic changes
in the single-point energy
After fixing X-H distances ~100 KJ/mol difference
Extra -0.25 KJ/mol improvement for asphericity
shifts for serine
For modelling purposes accurate structures are
absolutely necessary
40
Properties from invarioms
Dipole moments and electrostatic potential
(Study by Holstein on 9 different Fluoroquinolones, 12
structures, Cryst. Eng. Comm.14, 2012, 2520 )
Units: e/Å on 0.0067 e/Å3 isosurf.
41
Strongly dipolar molecule, 38.9 D
Spackman, Chem. Rev. 92, 1992, 1769
Spackman, Munshi, Dittrich, ChemPhysChem 8, 2007,2051
Complex example of IR: Vitamin B12
Vitamin B12 chemistry:
Benzimidazole, corrin
ring-, CN-, PO4-, and
(3d6)-Co3+
Starting invariom model
was crucial for
convergence of
multipole refinement
Modified radial
functions were tested,
influence d-orbital
populations
Dittrich et al. Angew. Chem. 119, 2007, 2993 42
Vitamin B12
Test next version of invariom data base
Current stage: Extension, validation and testing
Beta-testers welcome
Send your shelx data or try it yourself
Structure should be non-disordered, fulfilling Acta
C standards
No elements heavier than C,H,N,O,F,Cl
S and P deprecated but possible
Next release of the database at the end of the
year
Licensed XD-users can get InvariomTool,
MoleCoolQt is free
Dittrich, Hüschle, Holstein, Pröpper, Stolper, to be published, 2012 43
Summary
We can construct an accurate non-spherical
electron density from invariom database
fragments, covering a vast area of chemistry
Better structures (accuracy and precision,
Figures of Merit, ADPs)
Lower parameter esds, (incl. Flack parameter)
Properties available directly from ρ(r)
More insight in bonding for organic compounds
44
Further reading (also see articles cited before)
45
Brock, Hirshfeld und Dunitz, Acta Cryst. B47 1991, 789 Pichon Pesme et al., J. Phys. Chem. 99, 1995, 6242 Koritsánszky et al., Acta Cryst. A58, 2002, 464 Volkov et al., J. Phys. Chem. A 108, 2004, 4283 Dominiak et al., J. Chem. Theory Comput., 3, 2007, 232 Zarychta et al., Acta Cryst. A63, 2007,108 Jelsch et al., Acta Cryst. D54, 1998, 1306 Volkov et al., Acta Cryst. D63, 2007, 160 Johnas et al., Acta Cryst. D65, 2009, 284 Holstein et al., Acta Cryst. B66, 2010, 568 Dittrich et al.,Phys. Chem. Chem. Phys.11, 2009, 2601 Dominiak et al., Acta Cryst. D65, 2009, 485 (electrostatics of
neuraminidase complex) Dittrich et al.,Cryst. Eng. Comm.12, 2010, 2419 Hathwar et al.,Cryst.Growth Des., 2011, 2419 Holstein et al.,Cryst. Eng. Comm.14, 2012, 2520 (application of
new invariom database to fluoroquinolones) Jelsch et al., Acta Cryst. A68, 2012, 337 (ELMAM2) Jarzembska et al., Acta Cryst. A68, 2012, 139 (UBDB2011)
Funding: DI 921/3-1,2, SPP1178
‘Australian Synchrotron Deutsche
Research Program’ Forschungsgemeinschaft
C.B. Hübschle, D. Stalke, G.M. Sheldrick, F.P.A. Fabbiani, J.J. Holstein, K. Pröpper, R. Ghadwal, H.W. Roesky, E. Balcazar, C. Orben, C. Volkmann, J. Lübben
M.A. Spackman, D. Jayatilaka, B. Corry,
G. Koutsantonis, A. Sobolev
P. Luger, T. Koritsánszky, M. Strumpel,
D. Zobel, M. Weber, all others for interest
J. Bak, P. Dominiak, K. Wozniak
Acknowledgement
46
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