Bruker Users Meeting Anharmonic Nuclear Motion in Charge Density Studies

Transcription

1 Bruker Users Meeting 2010 Karlsruhe, 20 th September 2010 Anharmonic Nuclear Motion in Charge Density Studies Regine Herbst-Irmer

2 9-Diphenylthiophosphinoyl-anthracene The molecules absorb UV and emit visible light and so are interesting as photoluminescent materials.

3 Data Sets Four data sets: on a Bruker TXS-Mo rotating anode equipped with INCOATEC Helios mirrors and an APEX II detector at 293 K at 15 K at 100 K at 100 K on an INCOATEC micro source with QUAZAR mirrors and an APEX II detector

4 293 K Resolution Data Theory Compl. Red. <I> <I>/ R int R sigma Inf

5 15 K data Resolution Data Theory Compl. Red. <I> <I>/ R int R sigma Inf Inf

6 100 K - TXS Resolution Data Theory Compl. Red. <I> <I>/ R int R sigma Inf Inf

7 100 K - I S Resolution Data Theory Compl. Red. <I> <I>/ R int R sigma Inf Inf

8 Data Comparison - Rpim 293 K 15 K 100 K TXS 100 K I S

9 SHELXL space group P 1, two molecules in the asymmetric unit P1 P2 S1 S2 100 K 100 K

10 SHELXL space group P 1, two molecules in the asymmetric unit P1 P1 S1 S1 293 K 15 K

11 SHELXL 293 K 15 K 100 K 100 K I S Resolution [Å] [Å] Data Completeness R1 (I > 2 (I) ) I > 2 (I) wr res. Dens. [e/å 3 ]

12 SHELXL 293 K Map levels: 1.63 e/å 3 (1.50 ), 0.18 e/å 3 (3.00 )

13 SHELXL 100 K Map levels: 2.78 e/å 3 (1.50 ), 0.23 e/å 3 (3.00 )

14 SHELXL 15 K Map levels: 3.30 e/å 3 (1.50 ), 0.26 e/å 3 (3.00 )

15 SHELXL 15 K

16 Multipole Refinement with XD N. K. Hansen, P. Coppens, Acta Crystallogr. A34, (1978). A. Volkov, P. Macchi, L. J. Farrugia, C. Gatti, P. R. Mallinson, T. Richter, T. Koritsanszky, XD2006 (2006). = core + sperical valence density + asperical valence density l m lm lm l l l v c c at d P r R r P r P r ), ( ) ' ( ' ) ( ) ( ) ( max

17 Starting model - INVARIOM INVARIOM refinement for all four data sets XD multipole refinement using highest possible symmetry (INVARIOMTOOL) for the high resolution data sets lowering the symmetry where necessary Dittrich B., Koritsanszky T., Luger P., Angew. Chem. Int. Ed. 2003, 43, 314.

18 Comparison of Different Models Problems: High number of refined parameters per atom Correlation problems Convergence problems Criteria: R-values Residual density: flat and featureless Visualisation Residual density descriptors

19 Gross Residual Electrons how much residual density is present in total in the volume under consideration 1 3 e gross 0 ( r) d r 2 This includes model errors, data processing errors and experimental noise K. Meindl, J. Henn, Acta Crystallogr., A64, (2008).

20 Fractal Dimensionality Distribution experimental resolution d residual density grid density model d f log N( 0; ) ( 0; ) lim 0 log(1/ ) d f ( 0 ): featurelessness parabolic shape 0 : flatness K. Meindl, J. Henn, Acta Crystallogr., A64, (2008).

21 INVARIOM 293 K 15 K 100 K 100 K I S SHELX: R1 (I > 2 (I) ) res. Dens. [e/å 3 ] INVARIOM: R(F 2 ) (I > 3 (I) ) res. Dens. [e/å 3 ]

22 Multipole 293 K 15 K 100 K 100 K I S INVARIOM: R(F 2 ) Data / parameter res. Dens. [e/å 3 ] Multipole: R(F 2 ) Data / parameter res. Dens. [e/å 3 ]

23 Residual Density Analysis 293 K 15K 100K TXS 100K I s

24 Residual Density close to S2 S2 S2 S2 S2 P2 P2 P2 P2 293 K 15 K 100 K TXS 100 K I s Map levels: e/å 3 (3.00 )

25 Possible Explanations Problems with the data sets (absorption, twinning, ) Fourier truncation errors Problem with the local coordinate system

26 Multipole Population S versus P 0,400 0,300 0,200 0,100 0,000 D1+ D1- D0 Q0 Q1+ Q1- Q2+ Q2- O0 O1+ O1- O2+ O2- O3+ O3- H0 H1+ H1- H2+ H2- H3+ H3- H4+ H4- -0,100-0,200-0,300-0,400 S P

27 Possible Explanations Problems with the data sets (absorption, twinning, ) Fourier truncation errors Problem with the local coordinate system Disorder Principal problems with the multipole model concerning S Anharmonic motion

28 Gram-Charlier Expansion implemented in XD its Fourier transform is reduced to a simple power series expansion about the harmonic temperature factor T(H) = (1 3 i C jkl h j h k h l + 4 i D jklm h j h k h l h m + )T 0 (H) C jkl : 3 rd order: 10 additional parameter per atom D jklm : 4 th order: 15 additional parameter per atom

29 293 K data set harmonic S 3 rd order S, P 3 rd order S, P 3 rd and 4 th order S2 S2 S2 S2 P2 P2 P2 P2

30 Comparison for 293 K data Refinement harmonic 3 rd S 3 rd S + P 4 th S + P R(F 2 ) min. res max.res Goof data:param e gross

31 15 K data set harmonic S 3 rd order S, P 3 rd order S, P 3 rd and 4 th order S2 S2 S2 S2 P2 P2 P2 P2

32 Comparison for 15 K data Refinement harmonic 3 rd S 3 rd S + P 4 th S + P R min. res max.res Goof data:param e gross

33 100 K TXS harmonic S 3 rd order S, P 3 rd order S, P 3 rd and 4 th order S2 S2 S2 S2 P2 P2 P2 P2

34 Even some Carbons?? C47 C48 C49 C50 some C 3 rd order C52 C51 some C 3 rd and 4 th order C48 C49 C48 C49 C47 C52 C51 C50 C47 C52 C51 C50

35 Comparison for 100 K data TXS Refinement harmonic 3 rd S 3 rd S, P 4 th S, P 3 rd C 4 th C R min. res max.res Goof data:param e gross

36 Residual Density Analysis 293 K 15K 100K TXS 100K I S

37 Multipole 293 K 15 K 100 K 100 K I S INVARIOM Harmonic: R(F 2 ) Data / parameter res. Dens. [e/å 3 ] Anharmonic: R(F 2 ) Data / parameter res. Dens. [e/å 3 ]

38 Interpretation Gram-Charlier expansion coefficients C jkl and D jklm have (in general) no direct physical meaning examine the derived pdf (probability density function): Negative regions physically meaningless however due to the limited accuracy of the refined coefficients, the pdf may have some negative features far from the center, with small absolute values If negative regions are found close to the center of the pdf, especially if they are surrounded by positive areas, it is likely that the refined anharmonic coefficients are meaningless. K. N. Trueblood, H.-B. Bürgi, H. Burzlaff, C. M. Gramaccioli, H. H. Schultz, U. Shmueli, S. C. Abrahams Acta Cryst. A52, (1996).

39 PDF of S2-100 K harmonic 2 nd and 3 rd 3 rd 2 nd, 3 rd and 4 th 3 rd and 4 th Hübschle, C.B., Luger, P., J. Appl. Cryst. 2006, 39, 901.

40 Temperature Dependence

41 Required Resolution 15 K minimum data resolution required for meaningful refinement of anharmonic thermal parameters (Gram-Charlier coefficients), for each anisotropic atom: Q n = 2n ½ (2 ) -½ (2ln2) ½ <u 2 > ½ Kuhs, W. F. (1992) Acta Cryst A48, Atom Principal M.D.A's (A) Min. resolution Qn sin( )/ [Å -1 ] (res. [Å]) n = 3 n = 4 S(1) (0.35) 1.63 (0.31) S(2) (0.38) 1.50 (0.33) P(1) (0.29) 2.01 (0.25) P(2) (0.30) 1.91 (0.26)

42 Required Resolution 100 K Atom Principal M.D.A's (A) Min. resolution Qn sin(theta)/lambda n = 3 n = 4 S(1) S(2) P(1) P(2) C(45) C(46) C(47) C(48) C(49) C(50) C(51) C(52)

43 Arguments against Anharmonic Refinement XD manual: It should always be remembered that there is a close mathematical resemblance between the formalisms used to describe non-gaussian pdf's and aspherical electron densities, see for example Mallinson et al. There are likely to be high correlations between the Gram- Charlier coefficients and the multipole populations for the same atom in the least-squares refinement, and great care should be taken to ensure that a true minimum is reached. P. R. Mallison, T. Koritsanszky, E. Elkaim, N. Li, P.Coppens, Acta Cryst. (1988), A44, R. Restori, D. Schwarzenbach, Acta Cryst. (1996) A52,

44 Correlations above x, y, z, C iii C ijk C ijk U ij D ijkl D ijkl D ijkl M1 C ijk, D ijkl multipoles under 0.3

45 pdf 3 rd order 4 th order Gaussian probability density function (p.d.f.) deviation from Gaussian p.d.f. resulting total p.d.f. Gaussian p.d.f.: f(x) = -1 (2 ) -1/2 exp-x 2 /2 2 ; 3 rd order curve: 0.2xf(x); 4 th order curve: -0.04x 2 f(x) K. Meindl, R. Herbst-Irmer, J. Henn, Acta Cryst. (2010). A66,

46 Influence on U ij 0,035 0, K data U ij (S2) 0,025 0,02 0,015 0,01 harmonic 3 rd order 3 rd and 4 th order 0,005 0 U11 U22 U33 U12 U13 U23

47 Further Structures with Anharmonic Sulfur S. Pillet, M. Souhassou, Y. Pontillon, A. Caneschi, D. Gatteschi, C. Lecomte, New J. Chem., 25, , 2001,

48 Sulfurdiimide R1 = 3.49 % GooF = D. Leusser, J. Henn, N. Kocher, B. Engels, D. Stalke, data:parameter = 50.4 J. Am. Chem. Soc., 126, , 2004.

49 Diimid S 3 rd and 4 th order R1 = 3.27 % GooF = data:parameter = 45.2

50 Triimid Atom Min. resolution sin(theta)/lambda n = 3 n = 4 S(1) C(11) C(13) harmonic R1 = 2.47 % GooF = data:parameter = 84.6

51 Triimid S 3 rd order R1 = 2.46 % GooF = data:parameter = 80.7 S 3 rd and 4 th order R1 = 2.31 % GooF = data:parameter = 75.5 also C11, C13 3 rd order R1 = 2.24 % GooF = data:parameter = 69.5

52 Sulfon harmonic S 3 rd and 4 th order Atom Min. sin(theta)/lambda n = 3 n = 4 S(1) S(2)

53 Sulfin harmonic S 3 rd and 4 th order Atom Min. sin(theta)/lambda n = 3 n = 4 S(1) C(11) C(13) C(21) C(22) C(23) also some C 3 rd order

54 Resolution Dependence Sulfon (sin / ) max = 1.1 Å -1 (sin / ) max = 1.0 Å -1

55 Resolution Dependence 15 K data (sin / ) max = 1.1 Å -1 (sin / ) max = 1.0 Å -1

56 Resolution Dependence 100 K data (sin / ) max = 1.1 Å Å -1 (sin / ) max = 0.9 Å Å Å Å -1

57 Conclusions Anharmonic motion does not seem to be modelled by a multipole refinement Refinement of Anharmonic motion seems to be important for high resolution data sets Refinement of Gram-Charlier coefficients seems to be possible together with multipole refinement Kuh s rule for minimum resolutions seems to be to strict at least for heavier elements like sulfur and phosphorous

58 Acknowledgements Dietmar Stalke Daniel Stern Daniel Kratzert Ulrike Flierler Holger Ott Dirk Leusser Birger Dittrich Christian Hübschle Julian Henn Kathrin Meindl George Sheldrick