The XD Program System and Calculation of Properties Louis J Farrugia Jyväskylä Summer School on...

The XD Program System andCalculation of Properties

Louis J Farrugia

Jyväskylä Summer School on Charge Density August 2007

http://www.westchem.ac.uk/

The XD Program SystemJyväskylä Summer School on Charge Density August 2007

The XD program system is a comprehensive The XD program system is a comprehensive computer program computer program package for multipole refinement, topological analysis of charge package for multipole refinement, topological analysis of charge densities and evaluation of intermolecular energies from densities and evaluation of intermolecular energies from experimental or theoretical structure factors.experimental or theoretical structure factors.

XD uses THREE primary input files :XD uses THREE primary input files :

XD.INP/XD.REXD.INP/XD.RES - contains the refined parametersS - contains the refined parameters

XD.HKLXD.HKL - the reflection data as - the reflection data as FF or or FF22 with sigma's and optional dir cosines with sigma's and optional dir cosines

XD.MASXD.MAS - contains all the program instructions - contains all the program instructions

A. Volkov, P. Macchi, L. J. Farrugia, C. Gatti, P. R. Mallinson, T. Richter, T. Koritsanszky (2006).


modulemodule tasktaskXDINIXDINI importing data to XDimporting data to XD

XDLSMXDLSM least-squares refinementleast-squares refinement

XDGEOMXDGEOM calculation of tables of geometries, calculation of tables of geometries, ADPs, multipolar parameters and ADPs, multipolar parameters and

errorserrors

XFOURXFOUR calculation of Fourier mapscalculation of Fourier maps

XDFFTXDFFT fast Fourier transform programfast Fourier transform program

XDPROPXDPROP calculation of one-electron calculation of one-electron propertiesproperties

XDGRAPHXDGRAPH visualizationvisualization

TOPXDTOPXD full topological analysis of crystal full topological analysis of crystal structuresstructures

The XDINI Program Jyväskylä Summer School on Charge Density August 2007

The XDINI program provides a link between "standard" The XDINI program provides a link between "standard" refinement programs like SHELXL or the standard refinement programs like SHELXL or the standard crystallographic file format (CIF) and the XD program system.crystallographic file format (CIF) and the XD program system.

XDINI reads either SHELX.INS & SHELX.HKL (or XD.CIF & XDINI reads either SHELX.INS & SHELX.HKL (or XD.CIF & XD.FCF) andXD.FCF) andwrites default versions of XD.INP, XD.MAS, XD.HKL.writes default versions of XD.INP, XD.MAS, XD.HKL.

It needs to know (a) format you are using (b) ID name (XD) (c) It needs to know (a) format you are using (b) ID name (XD) (c) the database you wish to use.the database you wish to use. Command lineCommand line XDINI <name> <format> <databank code>XDINI <name> <format> <databank code>

XDINI xd shelx SCM XDINI xd shelx SCM

xd.bnk_RHF_CR: (BANK CR)CHFW Non relativistic wave functions (H-Kr, including ions)Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data Tables, 14, 177-478RDSD E. Clementi and D. L. Raimondi, J. Chem. Phys. 38, 2686-2689 (1963).Analytical Fit : International Tables for Crystallography

xd.bnk_RHF_BBB: (BANK BBB)CHFW Non relativistic wave functions (H-Xe)C. F. Bunge, J. A. Barrientos, A. V. Bunge At. Data Nucl. Data Tables, 53, 113-162 (1993).RDSD E. Clementi and D. L. Raimondi, J. Chem. Phys. 38, 2686-2689 (1963).Analytical Fit : International Tables for Crystallography

xd.bnk_RDF_SCM: (BANK SCM)CHFW Relativistic wave functions (H-Xe, including ions)Z. Su and P. Coppens Acta Cryst., A54, 646 (1998): P. Macchi and P. Coppens Acta Cryst., A57, 656 (2001).RDSD E. Clementi and D. L. Raimondi, J. Chem. Phys. 38, 2686-2689 (1963).Analytical Fit : Su, Z.; Coppens, P. Acta Cryst 1997, A53, 749, Macchi, P.; Coppens, P. Acta Cryst., 2001, A57, 656

Choice of the Databank

xd.bnk_PBE-QZ4P-ZORA: (BANK VM)CHFW Relativistic wave functions (H-Cf) unpublishedRDSD E. Clementi and D. L. Raimondi, J. Chem. Phys. 38, 2686-2689 (1963).Analytical Fit : Macchi, P.; Volkov, A. unpublished


The XD.INP Parameter FileJyväskylä Summer School on Charge Density August 2007

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! <<< X D PARAMETER FILE >>> $Revision: 5.39 (Jun 5 2007)$ 24-Jun-06!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!XDPARFILE VERSION 2 XD MODEL 0 0 0 0LIMITS nat 2000 ntx 31 lmx 4 nzz 30 nto 0 nsc 20 ntb 20 nov 2500USAGE 20 0 0 4 0 1 0 0 4 0 0 0 0 0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000E+00 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000O(1) 3 2 13 1 6 2 1 1 0 0 0 0.202009 0.200013 0.479127 1.0000 0.025050 0.012910 0.009490 -0.010960 0.000890 -0.000330 6.0000 0.0000O(2) 3 2 6 2 13 2 1 1 0 0 0 -0.004865 0.031916 0.359431 1.0000 0.023710 0.015640 0.007150 -0.007000 -0.000440 -0.001250 6.0000 0.0000...H(7) 3 2 5 20 19 1 4 4 0 0 0 0.930190 0.964298 0.213487 1.0000 0.024890 0.000000 0.000000 0.000000 0.000000 0.000000 1.0000 0.0000 1 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 2 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 3 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 4 1.200000 1.200000 1.200000 1.200000 1.200000 1.200000 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.117148E+01



<name>



number of atoms



Parameters for atom O(1)



positional parameters



Occupancy - not refinable !



anisotropic thermal parameters U11 U22 U33 U12 U13 U23



multipole parameters - currently only Pv and P00 are present



Kappa parameters



Extinction parameters



Overall scale factor

The XD.HKL Reflection FileJyväskylä Summer School on Charge Density August 2007

XD F^2 NDAT 6 -5 -7 1 1 5.300 0.790 -5 -7 2 1 74.050 2.480 -5 -7 3 1 2.740 1.540 -5 -7 4 1 11.410 10.700 -5 -6 1 1 21.890 1.880 -5 -6 2 1 0.540 1.210 -5 -6 3 1 5.140 0.860 -5 -6 4 1 3.090 1.030 -5 -6 5 1 94.190 2.830 -5 -6 6 1 17.450 13.830 -5 -5 1 1 2.680 1.130...

Data may be presented either as Data may be presented either as FF or or FF22

(NOTE in current version the sigma cutoff is applied BEFORE (NOTE in current version the sigma cutoff is applied BEFORE conversion)conversion)

Several batch scale factors can be refinedSeveral batch scale factors can be refined

Phases may optionally be present (phase angle in radians, NDAT = -Phases may optionally be present (phase angle in radians, NDAT = -7)7)

The XD.MAS Control FileJyväskylä Summer School on Charge Density August 2007

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! <<< X D MASTER FILE >>> $Revision: 5.39 (Jun 5 2007)$ 24-Jun-06!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!TITLE XDCELL 3.6782 7.5991 12.4999 85.662 88.029 84.225WAVE 0.71073CELLSD 0.0003 0.0005 0.0008 0.003 0.003 0.002LATT C PSYMM 1/2+X,1/2-Y,1/2+zBANK SCM!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! MODULE *XDLSMSELECT model 0 2 1 0 based_on F test verbose 1SELECT cycle -1 dampk 1. cmin 0.6 cmax 1. eigcut 1.d-09 convcrit 0.0SAVE deriv lsqmat *cormatSOLVE *inv diag *cond!------------------------------------------------------------------------------SCAT CORE SPHV DEFV 1S 2S 3S 4S 2P 3P 4P 3D 4D 4F 5S 5P 6S 6P 5D 7S 6D 5F DELF' DELF'' NSCTLO CHFW CHFW CSZD 2 -2 0 0 -4 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0110 0.0060 0.580N CHFW CHFW CSZD 2 -2 0 0 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0060 0.0030 0.936C CHFW CHFW CSZD 2 -2 0 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0030 0.0020 0.665H CHFW CHFW CSZD -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0000 0.0000 -0.374END SCAT..

END XDLSM

Divided into sections - one main section and eight other sections Divided into sections - one main section and eight other sections giving commands for the main program modules.giving commands for the main program modules.

The XD.MAS Control FileJyväskylä Summer School on Charge Density August 2007

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! <<< X D MASTER FILE >>> $Revision: 5.39 (Jun 5 2007)$ 24-Jun-06!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!TITLE XDCELL 3.6782 7.5991 12.4999 85.662 88.029 84.225WAVE 0.71073CELLSD 0.0003 0.0005 0.0008 0.003 0.003 0.002LATT C PSYMM 1/2+X,1/2-Y,1/2+zBANK SCM!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! MODULE *XDLSMSELECT model 0 2 1 0 based_on F test verbose 1SELECT cycle -1 dampk 1. cmin 0.6 cmax 1. eigcut 1.d-09 convcrit 0.0SAVE deriv lsqmat *cormatSOLVE *inv diag *cond!------------------------------------------------------------------------------SCAT CORE SPHV DEFV 1S 2S 3S 4S 2P 3P 4P 3D 4D 4F 5S 5P 6S 6P 5D 7S 6D 5F DELF' DELF'' NSCTLO CHFW CHFW CSZD 2 -2 0 0 -4 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0110 0.0060 0.580N CHFW CHFW CSZD 2 -2 0 0 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0060 0.0030 0.936C CHFW CHFW CSZD 2 -2 0 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0030 0.0020 0.665H CHFW CHFW CSZD -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0000 0.0000 -0.374END SCAT..

END XDLSM

Everything between MODULE *XDLSM and END XDLSM refers to Everything between MODULE *XDLSM and END XDLSM refers to commands and/or information for the refinement program XDLSM.commands and/or information for the refinement program XDLSM.The *XDLSM indicates that this module isThe *XDLSM indicates that this module is activated activated - a common - a common usage in XDusage in XD

The XDLSM CommandsJyväskylä Summer School on Charge Density August 2007

MODULE *XDLSMSELECT model 0 2 1 0 based_on F test verbose 1SELECT cycle -1 dampk 1. cmin 0.6 cmax 1. eigcut 1.d-09 convcrit 0.0SAVE deriv lsqmat *cormatSOLVE *inv diag *cond!------------------------------------------------------------------------------SCAT CORE SPHV DEFV 1S 2S 3S 4S 2P 3P 4P 3D 4D 4F 5S 5P 6S 6P 5D 7S 6D 5F DELF' DELF'' NSCTLO CHFW CHFW CSZD 2 -2 0 0 -4 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0110 0.0060 0.580N CHFW CHFW CSZD 2 -2 0 0 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0060 0.0030 0.936C CHFW CHFW CSZD 2 -2 0 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0030 0.0020 0.665H CHFW CHFW CSZD -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0000 0.0000 -0.374END SCAT..

END XDLSM

XDLSM is a standard full-matrix least-squares refinement program, XDLSM is a standard full-matrix least-squares refinement program, which can refine on which can refine on FF or or FF22 (based_on F/F^2). (based_on F/F^2). Few sophisticated Few sophisticated features.features.Convergence criterion - refinement stops when I/sig(I) < Convergence criterion - refinement stops when I/sig(I) < convcritconvcrit

The SCAT table defines the scattering model used for each atomic The SCAT table defines the scattering model used for each atomic type.type.The numbers define the occupations of the HF orbitals - negative The numbers define the occupations of the HF orbitals - negative numbers mean that those electrons are defined as the numbers mean that those electrons are defined as the valence valence electronselectrons, otherwise they are assumed to be core. More than one , otherwise they are assumed to be core. More than one entry for a particular element is allowed.entry for a particular element is allowed.

In general, the SCAT table written by the import program XDINI will In general, the SCAT table written by the import program XDINI will be satisfactory for an initial model.be satisfactory for an initial model.

The ATOM TableJyväskylä Summer School on Charge Density August 2007

ATOM ATOM0 AX1 ATOM1 ATOM2 AX2 R/L TP TBL KAP LMX SITESYM CHEMCON

O(1) C(1) X O(1) N(1) Y R 2 1 1 4 m

N(1) C(1) Z N(1) O(1) Y R 2 2 2 4 mm2

C(1) N(1) X C(1) O(1) Y R 2 3 3 4 m

H(1) N(1) Z H(1) C(1) Y R 1 4 4 1 cyl

H(2) N(1) Z H(2) C(1) Y R 1 4 4 1 cyl

H(3) C(1) Z H(3) O(1) Y R 1 4 4 1 cylDUM0 0.0000 0.0000 0.0000END ATOM

The ATOM table defines the The ATOM table defines the local coordinate system local coordinate system used for each used for each atom, as well as identifying the scattering type and Kappa set for atom, as well as identifying the scattering type and Kappa set for that atom. Limits on the multipole expansion, thermal motion that atom. Limits on the multipole expansion, thermal motion description and chemical constraints are also applied here.description and chemical constraints are also applied here.

In general, the ATOM table written by the import program XDINI will In general, the ATOM table written by the import program XDINI will be be NOTNOT satisfactory for an initial model. satisfactory for an initial model.

The ATOM TableJyväskylä Summer School on Charge Density August 2007

ATOM ATOM0 AX1 ATOM1 ATOM2 AX2 R/L TP TBL KAP LMX SITESYM CHEMCON

O(1) C(1) X O(1) N(1) Y R 2 1 1 4 m

N(1) C(1) Z N(1) O(1) Y R 2 2 2 4 mm2

C(1) N(1) X C(1) O(1) Y R 2 3 3 4 m

H(1) N(1) Z H(1) C(1) Y R 1 4 4 1 cyl

H(2) N(1) Z H(2) C(1) Y R 1 4 4 1 cyl

H(3) C(1) Z H(3) O(1) Y R 1 4 4 1 cylDUM0 0.0000 0.0000 0.0000END ATOM

O atom m

Formamide HC(=O)NH2

C atom m

N atom mm2

H atom cyl

The KEY TableJyväskylä Summer School on Charge Density August 2007

The KEY table defines The KEY table defines which parameters are to be refinedwhich parameters are to be refined. "0" means . "0" means don't refine and any other entry, usually "1" means refine. The don't refine and any other entry, usually "1" means refine. The layout for the atoms is self explanatory. The XD manual & tutorial layout for the atoms is self explanatory. The XD manual & tutorial gives the order in which the U's and multipole parameters are given.gives the order in which the U's and multipole parameters are given.

In general, the KEY table written by the import program XDINI will be In general, the KEY table written by the import program XDINI will be satisfactory for an initial model, but is the part of the input which satisfactory for an initial model, but is the part of the input which needs changing most.needs changing most.

KEY xyz --U2-- ----U3---- ------U4------- M- -D- --Q-- ---O--- ----H----O(1) 000 000000 0000000000 000000000000000 00 000 00000 0000000 000000000N(1) 000 000000 0000000000 000000000000000 00 000 00000 0000000 000000000C(1) 000 000000 0000000000 000000000000000 00 000 00000 0000000 000000000H(1) 000 000000 0000000000 000000000000000 00 000 00000 0000000 000000000H(2) 000 000000 0000000000 000000000000000 00 000 00000 0000000 000000000H(3) 000 000000 0000000000 000000000000000 00 000 00000 0000000 000000000KAPPA 000000KAPPA 000000KAPPA 000000KAPPA 000000EXTCN 0000000OVTHP 0SCALE 1END KEY

The XDLSM CommandsJyväskylä Summer School on Charge Density August 2007

!GROUP2 atom1 atom2 ...KEEP kappa 1 2 3 4KEEP charge group1!KEEP rigid group1!RESET bond C(1) H(1) 1.09 ...WEIGHT -2.0 .0 .0 .0 .0 0.3333!SWAT g 0.00 U 0.00SKIP obs 0. 1.d10 *sigobs 3. 1.d06 sinthl 0. 2.!PRINT sinthl .0 2. obs 0. 15. delta 0. 10. *del% 80 100 extcn 80. 100. *abssc!EXTCN *iso aniso *type_1 type_2 type_3 distr_g *distr_l msc_0 msc_1DMSDA 1.1 1.8FOUR fmod1 4 2 0 0 fmod2 -1 2 0 0!CON num1 par1/iat1 num2 par2/iat2 ... = num0

In XDLSM (as in all programs) placing an "!" mark as the first In XDLSM (as in all programs) placing an "!" mark as the first character comments out the commands.character comments out the commands.

The KEEP kappa command ensures that the kappa' parameters for The KEEP kappa command ensures that the kappa' parameters for all all ll values valuesof the deformation valence are the sameof the deformation valence are the same

The KEEP charge ensures that the sum of the monopole populations The KEEP charge ensures that the sum of the monopole populations PPvv equals the total valence population. equals the total valence population.

The Results of RefinementJyväskylä Summer School on Charge Density August 2007

A set of positional, thermal motion and multipole parameters which A set of positional, thermal motion and multipole parameters which provide the best fit to the data. These parameters can be used to provide the best fit to the data. These parameters can be used to reconstruct and analyse the electron density (do not use Fourier reconstruct and analyse the electron density (do not use Fourier methods).methods).

CAVEATSCAVEATS

1. Because of the complexity of the model, least-squares procedure 1. Because of the complexity of the model, least-squares procedure may notmay notprovide aprovide a unique solution unique solution..2. The refinement of the mutipole parameters may be difficult if the 2. The refinement of the mutipole parameters may be difficult if the structure is non-centrosymmetric, because of correlations between structure is non-centrosymmetric, because of correlations between phases and odd-order multipoles.phases and odd-order multipoles.3. The accuracy of the final parameters depends crucially on the 3. The accuracy of the final parameters depends crucially on the quality of the experimental data. Systematic errors are the worst, quality of the experimental data. Systematic errors are the worst, but even random errors can degrade the results but even random errors can degrade the results

A. El Hauouzi et al (1996) Acta Cryst. A52, 291.C. Lecomte et al (1999) Acta Cryst.A55 1038.

An Interesting Tale ...Jyväskylä Summer School on Charge Density August 2007

In 1992, Howard In 1992, Howard et alet al reported a charge density study on 2-methyl-4- reported a charge density study on 2-methyl-4-nitroaniline (MNA) which showed a threefold enhancement of the molecular nitroaniline (MNA) which showed a threefold enhancement of the molecular dipole moment on crystallisation, to 23D with an error of 8D. Became a dipole moment on crystallisation, to 23D with an error of 8D. Became a classic reference. classic reference.

S. T. Howard et al (1992) J. Chem. Phys. 97, 5616.A. E. Whitten, M. A Spackman et al (2006) J. Phys. Chem. A, 110, 8763.

New results of Whitten, Spackman New results of Whitten, Spackman et alet al in 2006 in 2006 suggest that this result is quite unreasonable. suggest that this result is quite unreasonable. After a very careful data collection and After a very careful data collection and refinement, they estimate that the true result is ~ refinement, they estimate that the true result is ~ 12(1) D, 12(1) D, i.e. i.e. an enhancement of 25-30%. This an enhancement of 25-30%. This result is also close to their theoretical work. The result is also close to their theoretical work. The discrepancies with the previous work is a result of discrepancies with the previous work is a result of unstable refinement of the scale factor and use of unstable refinement of the scale factor and use of anisotropic thermal parameters for the H atoms.anisotropic thermal parameters for the H atoms.

Fourier Maps in XD


Two programs in XDTwo programs in XDXDFFT XDFFT – calculates Fourier over whole unit cell – used for reporting residuals– calculates Fourier over whole unit cell – used for reporting residualsXDFOURXDFOUR – can calculate Fourier in an arbitary plane – useful for investigations – can calculate Fourier in an arbitary plane – useful for investigations

FOUR fmod1 4 2 0 0 fmod2 -1 2 0 0

MODULE *XDFFTSELECT *fobs *fmod1 fmod2 snlmin 0. snlmax 2. sig 3. phase 0.SELECT gridsize 0.2 scale 1. npeak 10 nhole 10 neutron gridf peakfEND XDFFT

MODULE *XDFOURSELECT *fobs *fmod1 fmod2 print snlmin 0. snlmax 2.GRID *3-points perp crystATOM label ato(1) symm 1 trans 0 0 0 *mark on plotATOM label ato(2) symm 1 trans 0 0 0 *mark on plotATOM label ato(3) symm 1 trans 0 0 0 *mark on plotLIMITS xmin -2.0 xmax 2.0 nx 50LIMITS ymin -2.0 ymax 2.0 ny 50LIMITS zmin 0.0 zmax 0.0 nz 1 END XDFOUR

command in XDLSM to write XD.FOU file

XD.FOU contains Fobs and two types of Fcalc based on the models indicated in the FOUR command

Fourier Maps in XD



FOUR fmod1 4 2 0 0 fmod2 -1 2 0 0




fmod1 4 2 0 0 means (a) multipole model up to l = 4 (b) thermal motion up to anisotropic (c) no anomalous dispersion (d) no extinction

Fourier Maps in XD



FOUR fmod1 4 2 0 0 fmod2 -1 2 0 0




fmod1 –1 2 0 0 means (a) spherical atom model (b) thermal motion up to anisotropic(c) no anomalous dispersion (d) no extinction

Fourier Maps in XD



FOUR fmod1 4 2 0 0 fmod2 -1 2 0 0



*fobs *fmod1 means calculate a difference Fourier with coefficients based on Fcalc from model 1 and Fobs – this map is a full difference Fourier and should be featureless

Fourier Maps in XD


*fobs *fmod1

Residual map

These are very important for checking the quality of data and of the refinement

Contours at 0.05eÅ-3

Fourier Maps in XD


*fobs *fmod2

Experimental deformation map

These are equivalent to the difference maps obtained with a SHELX refinement. Shows the bonding density peaks


Fourier Maps in XD


*fmod1 *fmod2

Dynamic model map

These show the difference between Fcalc (spherical) and Fcalc (multipole).

Similar to experimental deformation map. Does not contain experimental noise, but does contain effects of thermal motion.


XDPROP – calculation of properties


XDPROP performs a number of tasks. The input parameters are the XDPROP performs a number of tasks. The input parameters are the multipolemultipole

populations from the refinement program XDLSM. From these the populations from the refinement program XDLSM. From these the staticstatic

density (and associated properties) can be computed.density (and associated properties) can be computed.

topological analysis topological analysis – finds critical points in scalar field (density or – finds critical points in scalar field (density or Laplacian)Laplacian)

and seaches for bond paths (molecular graph). Graphical display of and seaches for bond paths (molecular graph). Graphical display of gradientgradient

vector plots. Gives the topology of the molecule “extracted” from the vector plots. Gives the topology of the molecule “extracted” from the crystalcrystal

Program TOPXD gives the topology of the crystal.Program TOPXD gives the topology of the crystal.

atomic charges and higher momentsatomic charges and higher moments – these can be calculated in a – these can be calculated in a number ofnumber of

ways, either from the multipole parameters of by numerical ways, either from the multipole parameters of by numerical integration ofintegration of

the derived densitythe derived density

interaction energiesinteraction energies – between two or more fragments of the total – between two or more fragments of the total latticelattice

energyenergy

dd-orbital populations-orbital populations – from multipole parameters – from multipole parameters

Properties are obtained as lists of numbers and also in graphical form Properties are obtained as lists of numbers and also in graphical form (2D and (2D and

3D maps).3D maps).

XDPROP – topological analysis


Concepts of topological analysis Concepts of topological analysis dealtdealt

with in another lecture.with in another lecture.

Shown here is the molecular graph Shown here is the molecular graph for for

formamide, giving the bond paths formamide, giving the bond paths (in(in

gold), the bond critical points (in gold), the bond critical points (in red)red)

and the eigenvectors of the and the eigenvectors of the HessianHessian

(red = major axis, green = minor (red = major axis, green = minor axis axis

of curvature).of curvature).

This POV-Ray picture is producesd This POV-Ray picture is producesd byby

the WinXD GUIthe WinXD GUI

CPSEARCH BOND C(1) H(3)CPSEARCH SHELL O(1) RMIN 1.20 RMAX 1.20 NRAD 1 NANG 15 15 CUT 0.01CPSEARCH POINT 1.2 -0.3 1.3CPSEARCH START xd.cpscpsearch bond rmin 0.9 rmax 1.7BPATH O(1) C(1) ALGRITHM 2BPATH N(1) C(1) ALGRITHM 2BPATH N(1) H(1) ALGRITHM 2BPATH N(1) H(2) ALGRITHM 2BPATH C(1) H(3) ALGRITHM 2

XDPROP – topological analysis


Gradient vector plots show theGradient vector plots show thedivision of the molecule into division of the molecule into

atomicatomicbasinsbasins

Also shows bond paths and bcp’sAlso shows bond paths and bcp’s

ODESOLVE *rk bs eps 1e-6 stepi 0.01TRAJPLT origin atom C(1)TRAJPLT xaxis atom N(1) Xdim1 -2.0 Xdim2 2.5 TRAJPLT yaxis atom H(3) Ydim1 -2.0 Ydim2 2.0TRAJPLT params Circle 0.1 ATrad 0.05 CPrad 0.05 CPgrid 0.1 CPlim 0.01TRAJPLT mark *atoms *labels *bonds *cps *basins hbondsTRAJPLT *plot *plane npath 36 *zcut 0.3 *xytol 0.3 *all select O(1)

XDPROP – calculation of charges


The concept of atomic charges is a central one in chemistry. Unfortunately it The concept of atomic charges is a central one in chemistry. Unfortunately it is a is a

very hazy concept and not one deeply founded in quantum mechanics. It is very hazy concept and not one deeply founded in quantum mechanics. It is onlyonly

through AIM theory that an unambiguous definition of atomic charge has through AIM theory that an unambiguous definition of atomic charge has achieved.achieved.

AIM derived charges are often larger than “chemical intuition” expects and AIM derived charges are often larger than “chemical intuition” expects and this hasthis has

led to considerable criticism.led to considerable criticism.

R. F. W. Bader and C. Matta (2004) J. Phys Chem A. 108, 8385F. L. Hirshfeld (1977). Theor. Chim. Acta, 44, 129

XDPROP provides several ways to calculate net atomic charges:(a) directly from the refined valence populations of the atoms(b) using Hirshfeld’s stockholder’s approach(c) using a fit to the electrostatic potential(d) using Bader’s Quantum Theory of Atoms in Molecules (AIM)

! Atomic/Molecular moments from pseudoatoms :MULTMOM!! Atomic/Molecular from STOCKHOLDER partitioning:STOCKMOM atoms *all select ato(1) ato(2) ...! Atomic charges fitting electrostatic potential:QFIT grid 11 length 7.0 width 1.0 constrain falseCONSTRAIN ato(1) ato(2) ...


XDPROP – electrostatic potentialXDPROP can calculate maps of the electrostatic potential. These may be XDPROP can calculate maps of the electrostatic potential. These may be

used to used to show sites of chemical reactivity.show sites of chemical reactivity.

In general (and always for isolated atoms) the ESP is positive, but on In general (and always for isolated atoms) the ESP is positive, but on chemical bondchemical bond

formation, some areas might achieve a negative potential. One visually formation, some areas might achieve a negative potential. One visually attractiveattractive

way of displaying the ESP is as a colour coded isosurface (usually of the way of displaying the ESP is as a colour coded isosurface (usually of the density). density).


XDPROP – d-orbital populationsThe multipole populations can be directly related to the The multipole populations can be directly related to the dd-orbital populations -orbital populations

in in transition metal compounds. Not unique, but depends on the chosen local transition metal compounds. Not unique, but depends on the chosen local

coordinatecoordinatesystem. Usually best if this system is chosen to correspond to symmetry system. Usually best if this system is chosen to correspond to symmetry

axes (actualaxes (actualor idealised) of the compound. An optimal coordinate system minimises the or idealised) of the compound. An optimal coordinate system minimises the

crosscrosspopulations.populations.

A. Holladay, P. C. Leung & P. Coppens (1983) Acta Cryst. A39, 377J. R. Sabino & P. Coppens (2003). Acta Cryst. A59, 127

Geometry calculations XDGEOM


Geometry calculations carried out using XDGEOM. Uses Geometry calculations carried out using XDGEOM. Uses variance-variance-

covariance matrix covariance matrix xd.covxd.cov (if available) to determine correct (if available) to determine correct su’s for su’s for

derived parameters, derived parameters, distances, angles, torsionsdistances, angles, torsionsProvides • Table of xyz, Uijs, distances, angles, torsions• Tables of multipole parameters• Writes a CIF xd_geo.cif of same (some will be moved to xd_lsm.cif in due time. e.g. xyz, Uijs)

Generally positional parameters (hence interatomic distances, angles) are not very sensitive to model (spherical or multipole), but of course ….Aromatic C-H SHELX (X-ray) 0.96Å neutron 1.083Å

K2SO4 tutorial data set

SHELX XDS-O1 1.4837(4)1.4838(3)S-O2 1.4717(4)1.4716(3)S-O3 1.4830(3)1.4832(2)

The XD Program System and Calculation of Properties Louis J Farrugia Jyväskylä Summer School on...

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Transcript of The XD Program System and Calculation of Properties Louis J Farrugia Jyväskylä Summer School on...