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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