AARHUS UNIVERSITY

1
Analysing the electron density in HBs

• Jacob Overgaard
• University of Aarhus

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What do we want to know about HBs?

• First thing is to locate all HBs HTAB in SHELX,
  XDGEOM or Mercury
• Is the electronic distribution around H
  perturbed?
• Are the bonds covalent or electrostatic?
• Their energetic contribution to the system - Can
  this be calculated from the topological analysis?
• H atomic charges and size - is it H or H(0)?

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Locate the HBs

• Mercury by clicking on the H-bond button.
• Use XDGEOM to calculate the geometries of the
  HBs.
• Does the geometry suggest any anomalities? O-H
  elongated?

4
Visual inspection of the density

• XDFOUR calculates the difference density by
  Fourier summation
• MODULE XDFOUR
• SELECT fobs fmod1 fmod2 print snlmin 0.
  snlmax 1.2
• GRID 3-points perp cryst
• ATOM label C(2) symm 1 trans 0 0 0 mark on plot
  (GIVE THREE ATOMS)

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Visual inspection of the density

• XDPROP can be used to calculate the Laplacian
  distribution
• MODULE XDPROP
• APPLY symm 2 translations 0 0 0 all (INCLUDE
  RELEVANT APPLY COMMANDS)
• PROPERTY rho gradrho d2rho nucpot core valence
  defden esp ef efg
• MAP atoms B(3A) H(3A) O(8) npts 200 stepsize 0.02

Covalent or ionic?
Covalent
Electrostatic?
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Extracting numbers from XD

• Quantitative analysis from a topological analysis
  of the density
• MODULE XDPROP
• APPLY symm 2 translations 0 0 0 all (INCLUDE
  RELEVANT APPLY COMMANDS)
• SELECT numdx esd au verbose 1
• PROPERTY rho gradrho d2rho nucpot core valence
  defden esp ef efg
• CPSEARCH bond H(3A) O(8) (EASIEST TO LIMIT TO THE
  RELEVANT BCPS)
• CPSEARCH bond rmin 0.8 rmax 2.2 (GIVES
  PERHAPS TOO MANY BCPS)
• CPSEARCH bubble O(8) rmin 0.3 rmax 0.5 curv -3
  ncps 3 (FINDS VSCC)
• BPATH ato(1) ato(2) algrithm 2
• Tabulate results
• Bond ?? del2f Rij d1 d2
  Hessian Eigenvalues ?????????
• H(3A)-O(8) 0.371 0.805 1.640 1.128 0.511
  -2.86 -2.51 6.18 0.14

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The density along the HB

• The density and the Laplacian can be plotted
  along the interaction line
• LINE O(8) H(3A) 200

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Quantitative analysis

• Energy densities can be estimated from the
  topological analysis using the expression by
  Abramov

• Based on results from neutron diffraction studies
  and the local virial theorem, Espinosa proposed a
  formula to derive the dissociation energy of a HB

Abramov, Yu. A. Acta Cryst. 1997, A53, 264
Espinosa, E. et al., Chem. Phys. Lett. 1998, 285,
170.
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H and Ehb of HBs

• The previous formulae can be used on the examples

Hbcp -0.61 hartree Å-3 EHB 42.3 kcal mol-1.
Hbcp -0.13 hartree Å-3 EHB 18.1 kcal mol-1.
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Source function from theoretical wavefunctions

• The source function has been described by Carlo
  Gatti.
• Useful in analysis of HBs as a tool to
  discriminate between types What is important is
  the H contribution to the bcp

d(X---O) decreases from left to right

• The trend is that the stronger HBs are followed
  by an increase in the contribution from the H
  atom.

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Source function from XD

• Added in XD2006 is the TOPINT keyword to
  calculate source function contributions to be
  compared to theoretical values.
• SOURCE refpoint 5.673506 2.156185
  2.299098 ! O(1A)-H(1A)
• SOURCE refpoint 9.897701 0.896144
  4.688383 ! O(8) -H(3A)
• SOURCE refpoint 13.550304 2.847093
  0.784550 ! O(1B)-H(1B)
• TOPINT spheres H(2B) 0.256 H(4B) 0.257 ..... (FOR
  ALL ATOMS)
• TOPINT atoms all select N(1B) H(1B)

-contributions to HB2
EXP THEO H3A 6.1 4.9 O8 34.8
35.0 N3A 18.3 21.8 O9 8.4 8.3 N1A 4.3
3.9
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Hydrogen atomic charges

• One could reasonably ask what the integrated
  charge within the H atomic basin is?
• CGEN alim -0.5 1.5 blim -0.5 1.5 clim -0.5 1.5
• ATBP Spheres O(8) 0.806 O(9) 0.824 N(7) 0.867
  C(12) 0.424 C(13) 0.636
• ATBP atoms H(1A) iZFS nvi 100 IRsur 0 IRSav
  Rest Debug Phi 48 Th 36 Rad 120 Accur 1.D-3
• The value of the integrated Laplacian describes
  the accuracy of the integration

q(HX1) 0.60
q(H3A) 0.53 q(H1A) 0.57 q(H1B) 0.57
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Visualise the atomic basin

• The atomic basin can be visualised by the
  command
• ATBP atoms H(1A) iZFS nvi 100 IRsur 0 IRSav
  Rest Debug Phi 48 Th 36 Rad 120 Accur 1.D-3
• VZ3D plot
• files rays.dat
• basins H(1A)
• range default xmi 0. ymi 0. zmi 0. xma 1. yma
  1. zma 1.
• grid default dx 0.05 dy 0.05 dz 0.05 rvec
  default 0.20
• END VZ3D

• Alternatively, the auxiliary program rays2pov
  creates a POV-Ray file for picture creation

H3A
H1A
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Concluding remarks

• As it appears, HBs are characterised by many
  methods, but the following trends should be
  clear
• The strength is intimately related to the D---A
  separation
• The potential energy surface of the H atom can
  have many different looks
• An accurate description of the density requires
  supplementary neutron data
• Covalency is important for the stronger HBs
• HB energies span a wide range strong ones
  contribute significantly
• Topological analysis and derived properties
  provide useful knowledge

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Examples

• Some real time analysis of selected compounds.