The first aim of this thesis is the complete renewal of the database with a basis set that extends to elements of the fourth period. Next to including bromine compounds in the database, this will allow homogeneous treatment of all atoms in a metal-organic crys-tal structures by an invariom-like approach and the addition of further attributes to the database.
The renewed database had found its first application in a project to identify metal atoms in coordination compounds.[99] The therein developed method will be the basis for case studies in this thesis on crystal structure pairs from the literature. True isomorphism of the structures to be investigated can in some cases be excluded on the basis of the deposited XRD data. For those cases the application of aspherical scattering factors shall identify which of two possible metals is the correct central atom. Additionally, the method will be tested for cases in which the datasets are not identical but similar, so that the question whether two compounds are indeed isomorphous will be investigated by the invariom-like approach. The influence of inferior data quality on the method will be examined, too.
The second major project of this thesis will depend even more on the renewal of the database. Its aim is the addition of point charges as an attribute that can be transferred via the invariom classification from the invariom database. The development of invariom point charges will be one step towards fully automating force-field parameterization for molecular dynamics[101] simulations of organic molecules. Such molecular-dynamics simulations will allow a correct inclusion of dynamic disorder in crystallographic models. Moreover, point charges facilitate the way to a representation of the electrostatic potential (ESP). Molecular ESPs from invariom point charges will be compared those from other point charges and methods.
The aim of the last project within this thesis will be a pilot study for incorporating a description of the deformation density in models refined with the program Shelxl. This is a meaningful topic, because it became apparent that the change to a more sophisticated and hence more complex program for inclusion of asphericity is a major hindrance for many scientists and therefore limits wider application. Hence only few researches apply invariom scattering factors or similar descriptions of the bonding and lone pair ED. In order to avoid the most complex and error prone part of the multipole modeling, a bond oriented deformation density will be discussed. If the new model’s transferability from the invariom database can be established, the same advantages as for the multipole scattering factor databases will be accessible from the most commonly applied program for structure determination, Shelxl. By improving accessibility, more scientific projects will be able to profit from the invariom database. So the aim of this pilot is to pave the way for a new attribute and thereby another new application of the invariom database.
Overall, the invariom database is renewed, metal atoms in coordination compounds are identified by aspherical scattering factors, invariom point charges are developed and invar-ioms as well as aspherical modeling for Shelxl are investigated. All of these projects either give an example, introduce or prepare the way for new applications of the invariom database.
2.1 Introduction
In order to extend the properties provided by the invariom database to the four attributes listed in Figure 1.7 each model compound needed additional treatment. While multipole populations and distances to hydrogen atoms are present for each model compound, the atomic charges selected as invariom point charges had to be derived from the molecular wave function. The hydrogen ADP (at least the part due to internal vibration) require vibrational frequencies,[102] which can easily be obtained from the Hessian matrix, a side product of geometry optimization. The Hessian matrix includes the derivatives of the energy with respect to changes of atomic coordinates. Analytical determination of those gradients from a self-consistent field (SCF) calculation at a fixed geometry (single-point calculation) would be an alternative. Due to starting the geometry optimization from an already optimized one of another basis set, changes of atomic coordinates were minimal and not too time-consuming. Reoptimizing the geometry with a new basis set and functional yields a consistent treatment for compounds added due to the new basis set like bromine compounds and those already in the database. Therefore, a new geometry optimization was performed for each of the invariom model compounds.
2.1.1 Geometry Optimization
Since the functional B3LYP used so far is old and specific to its implementation in the programGaussian,[103] it was time to change to a more up to date functional. Differences between scattering factors from different functionals are minimal, though. The Minnesota functional M06[104] was developed to cover organic compounds as well as metal-organic coordination compounds. It is as general as B3LYP but more state of the art and in contrast to B3LYP implemented consistently in popular QM programs. M06 is a hybrid meta-exchange correlation functional with 27 % Hartree-Fock (HF) exchange.
The basis set D95++(3df,3pd)[90] only allows the computation of elements up to argon for our database. Moreover, computation of the theoretical structure data does not work for effective core potentials. Hence, a new basis set was required in order to be able to include heavier elements like bromine in the database and enable treatment of metal containing compounds with the same basis set as used in the database. Application of the same basis set as for metal-organic compounds permits homogeneous treatment of metal, ligand and solvent in crystal structures when the metal center is treated by an invariom like approach, but a molecule-specific database.
Ahlrichs et al.[105] introduced a series of new basis sets without effective core potentials for elements up to krypton including transition metals up to zinc in 2003. Two years later two improved versions of these basis sets including slightly more diffuse functions in the
contracted triple-zeta valence basis for second to forth row elements were presented,[106]
with different degrees of polarization. The authors recommended the triple-zeta basis set without extra polarization functions for DFT calculations. Therefore, the def2TZVP basis set was chosen for the new geometry optimizations of the invariom model compounds.
2.1.2 Resolution
Another point of improvement was the resolution of theoretical scattering factors. The half cube of reflection data up to absolute h,k,l values of 40 was increased and cut to a half sphere where h,k,l values reach a maximum of 69 each (Figure 2.1). This way a well defined resolution of 1.15 Å−1 (0.43 Å) was achieved. In principle, a higher resolution would be possible but due to the application in which resolutions higher than 1.15 Å−1 are the exception, it is not considered beneficial. The spherical shape instead of a cube should also allow the same level of information independent of a molecule’s orientation in the theoretical cell.
2.1.3 Scattering factors
Discussions with fellow charge density researchers had raised the interest in different atomic scatting factor tables than those derived from HF Slater-type orbitals (STO) of Clementi and Roetti (CR).[107,108] Therefore, in the refinement of multipole parameters against the new theoretical diffraction data scattering factors derived from STO-Dirac-Fock atomic relativistic wave functions by Su, Coppens and Macchi (SCM)[109,110] were applied. The latter atomic form factors have no physically inadequate constant term in addition to the sum of six resolution dependent functions. For light-atom structures there is no difference between the two options, but for heavier atoms the newer SCM scattering factors provide
Figure 2.1: Additional treatment for every model compound in the database during makeover.
Changes are highlighted in blue while new properties are marked green.
a better fit. An overview of the new model-compound treatment during database renewal is displayed in Figure 2.1.
2.1.4 New compounds
Since the newer basis set allowed more elements, many new model compounds became possible. The inclusion of bromine containing compounds was easily accomplished (see Section 2.2.2) and useful for modeling more organic molecules. Therefore, a systematic investigation of all the halogen compounds in the database allowed the addition of all those model compounds which were necessary to have each of the halogen model compounds with fluorine, chlorine and bromine.