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Charge density option in Jana2006. V áclav Pet ř í č ek , Michal Dušek and L ukáš Palatinus Institute of Physics ASCR Praha, Czech Republic.
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Charge density option in Jana2006 Václav Petříček, Michal Dušek and Lukáš Palatinus Institute of Physics ASCR Praha, Czech Republic
Conventional structure analysis is based on the assumption that electrons for each atom are distributed around its central position spherically. Thus all bonding effects are neglected in the conventional model. However interaction of X-rays with the crystal reflects the real density including bond effects and we have a chance to get this information back. But for this data collection is to be made more carefully: • We should try to eliminate effects of ADP to diffracted intensities by reducing the temperature of data collection. Usually we are collecting data at nitrogen temperature. • We should select the best diffracting crystal and measure up to highest possible diffraction angle. • We should preferably make data collection in a full diffraction sphere to reduce s.u.’s of measured intensities. • All correction (LP, absorption, extinction, scaling) should be made very carefully. This is especially important as these correction strongly affects low order data which are so important for detecting chemical bonds.
The following figure shows how valence electrons are contributing to the form factor of the nitrogen atom. Their influence is apparent only for low order data. On the other hand core electrons makes its contribution very flat.
Termination effect The data collection is usually made within a certain sphere of reciprocal space. Depending on the radius of the sphere maps can give more or less details and this sets some limits to what an experiment can get. The termination effect can be predicted from so called shape function which is an Fourier summation of reflection flags which are equal 1 for measured reflection and 0 for not measured one. The real map is than a convolution of the shape function with an ideal map. The higher maximum of sinθ/λ is the more concentrate (δ-like) shape function is and more realistic Fourier maps are. The following figures shows simulation of maps for different (sinθ/λ)max. It starts at (sinθ/λ)max=1.5 and the number of used reflections for each subsequent map is reduced to half.
molecular contours are distinguishable up to the lowest limit • localization of individual atoms difficult (but possible) even for (sinθ/λ)max<0.3Å-1 • the are no additional spurious peaks
Omitting of low order data have different effect • as bonds affects mainly low order data charge density studies are impossible with such a data set • there are some additional spurious peaks in maps
Charge density studies Difference Fourier – After the conventional refinement we can make a Difference Fourier map which should show some residual electron densities. If not there is a little chance that more detailed analysis can give more details.But these maps do not allow to draw more conclusitions as atomic positions are shifted towards bonds.
Charge density studies X-N method – data from X-ray and neutron diffraction combined together to separate the bonding effects from atomic structure. Different approaches: • refinement of the structure with atomic positions fixed to their those we have from neutron diffraction + difference Fourier method • deformation maps – subtraction of neutron density maps from maps made on the base of X-ray data • joint refinement
Charge density studies X-X method – X-ray data collection made up to highest possible diffraction angle. Then atomic positions and ADP’s are refined against high order diffraction data and then this model is used to make deformation maps based on low order data.
Charge density studies Multipole refinement – based on modified structure factor formulas. There are two main approaches Stewart and Hansen- Coppens. N.K.Hansen & P.Coppens, Acta Cryst. (1978). A34, 909-921.Their formalism is used in the MOLLY, XD and also in Jana2000/Jana2006 The first term is a local density connected with core electrons and the second one with valence electrons. Both have still a spherical symmetry. The second term allows spherical redistribution of valence electrons by modifying of two adjustable parameters - and . The third term represents an ashperical term with several adjustable parameters - and .
stand for Slater function and spherical harmonics Slater functions The Fourier transform of the local asperical density leads to an analytical formula for the structure factor: The core and valance form factors for most of chemical elements in different electronic configurations are tabulated: Clementi, E. & Raimondi, D. L. (1963). J. Chem. Phys. 38, 2686–2692. Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data Tables, 14, 177–478.
Interpretation of results Deformation density maps – Form the final density calculated from refined charge density model the idealized spherical model is subtracted. Such a map can show chemical bonds. It can be calculated either by Fourier synthesis or by summation in the direct space. Maps produced by Fourier synthesis are affected by the termination effect. Maps produced by calculation in direct space are less noisy but they are based purely on refined model.
Interpretation of results Topological analysis It make an analysis of the final electron density. There is no need to subtract a core density which can introduce some distortions. The analysis is based on the Bader’s ideas: “ Atoms in Molecules. A Quantum Theory”, R.F.W. Bader, Clarendon, Oxford, 1990 Critical points – Points in which the gradient becomes zero. According to the eigenvalues of the Hessian tensor we can distinguish the following types: There are 4 four possible sign patterns : (- - -), (- - +), (++ -) and (+++) corresponding to a (3,-3) - maximum, (3,-1) , (3,+1) - saddle points and (3,+3) – minimum. The presence of (3,-1) is characteristic for chemical bonds.
Interpretation of results Atomic basin and basin integration Atoms basin is defined a region by Zero-Flux-Surface: Integration of density within atom basins gives a well defined atomic charges.
