Electron Density Studies of Molecular Crystals

Electron Density Studies of Molecular Crystals 281 table 12.3 Topological Analysis of Theoretical Densities on Strained Ring Molecules... 

Hansen, N. K., Study of the Electron Density Distribution in Molecular Crystals by Analysis of X-ray Diffraction Data Using Non-Spherically Symmetric Scattering Functions, Thesis, University of Arhus, Denmark (1978). 

Second, being quasibound Inside a potential barrier on the perimeter of the molecule, such resonances are localized, have enhanced electron density In the molecular core, and are uncoupled from the external environment of the molecule. This localization often produces Intense, easily studied spectral features, while suppressing non-resonant and/or Rydberg structure and, as discussed more fully below, has a marked Influence on vibrational motion. In addition, localization causes much of the conceptual framework developed for shape resonances In free molecules to apply equally well to photolonlzatlon and electron scattering and to other states of matter such as adsorbed molecules, molecular crystals, and Ionic solids. 

There are four areas of successful investigation electron density studies in molecules, in particular, changes in the orbital occupancy at complexation and substitutions, study of molecular dynamics, in particular, reorientation, rotation of atomic groups, hindered rotation, phase transformation study, revealing and studying defects and mixed crystals investigation. 

The study of electron density distributions resulting from molecular interactions in gas-phase complexes or in molecular crystals, is known [1,2] to facilitate our understanding of the physical mechanisms underlying such interactions. Indeed, the action of these mechanisms is reflected in the interaction density, defined as the difference between the electron density distribution (EDD) of the molecular complex or crystal and that obtained by superimposing the EDDs of free molecules. 

In this paper a method [11], which allows for an a priori BSSE removal at the SCF level, is for the first time applied to interaction densities studies. This computational protocol which has been called SCF-MI (Self-Consistent Field for Molecular Interactions) to highlight its relationship to the standard Roothaan equations and its special usefulness in the evaluation of molecular interactions, has recently been successfully used [11-13] for evaluating Eint in a number of intermolecular complexes. Comparison of standard SCF interaction densities with those obtained from the SCF-MI approach should shed light on the effects of BSSE removal. Such effects may then be compared with those deriving from the introduction of Coulomb correlation corrections. To this aim, we adopt a variational perturbative valence bond (VB) approach that uses orbitals derived from the SCF-MI step and thus maintains a BSSE-free picture. Finally, no bias should be introduced in our study by the particular approach chosen to analyze the observed charge density rearrangements. Therefore, not a model but a theory which is firmly rooted in Quantum Mechanics, applied directly to the electron density p and giving quantitative answers, is to be adopted. Bader s Quantum Theory of Atoms in Molecules (QTAM) [14, 15] meets nicely all these requirements. Such a theory has also been recently applied to molecular crystals as a valid tool to rationalize and quantitatively detect crystal field effects on the molecular densities [16-18]. 

MR is an ensemble of techniques that aims to place and orientate an approximate molecular model in the unit cell of the crystal being studied. This will provide the starting phases needed to calculate the initial electron density map from which the protein model can be built, either manually by iterative use of reconstruction with molecular graphics packages (Jones et al., 1991) followed by refinement (Murshudov et al., 1997), or automatically if diffraction data up to 2.3 Angstroms or better are available (ARP/wARP (Perrakis et al., 2001), Solve/Resolve (Terwilliger, 2003)). 

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