Electron density distribution representation

In representations of electron densities, the presence or lack of boundaries plays a crucial role. A quantum mechanically valid electron density distribution of a molecule cannot have boundaries, nevertheless, artificial electron density representations with actual boundaries provide useful tools of analysis. For these reasons, among the manifold representations of molecular electron densities, manifolds with boundaries play a special role. 

A complete and detailed description of molecular structure includes statements concerning the metric coordinates ) of atomic nuclei supplemented by electron density distribution data. Although a large amount of data is involved, such representation is not particularly suitable for the chemically relevant structural features of molecules. 

Most commonly used is certainly the molecular electrostatic potential. It can be derived from any kind of charge distribution. Usually, the MEP is first calculated on a grid and subsequently transformed to the sphere or Gaussian representation. Quite important is the electron density distribution, which closely models the steric occupancy by a molecule. Other approaches utilize artificial fields for physicochemical properties commonly associated with binding, like a field for the hydrophobicity [193] or H-bonding potential [133,194]. 

Using time-resolved crystallographic experiments, molecular structure is eventually linked to kinetics in an elegant fashion. The experiments are of the pump-probe type. Preferentially, the reaction is initiated by an intense laser flash impinging on the crystal and the structure is probed a time delay. At, later by the x-ray pulse. Time-dependent data sets need to be measured at increasing time delays to probe the entire reaction. A time series of structure factor amplitudes, IF, , is obtained, where the measured amplitudes correspond to a vectorial sum of structure factors of all intermediate states, with time-dependent fractional occupancies of these states as coefficients in the summation. Difference electron densities are typically obtained from the time series of structure factor amplitudes using the difference Fourier approximation (Henderson and Moffatt 1971). Difference maps are correct representations of the electron density distribution. The linear relation to concentration of states is restored in these maps. To calculate difference maps, a data set is also collected in the dark as a reference. Structure factor amplitudes from the dark data set, IFqI, are subtracted from those of the time-dependent data sets, IF,I, to get difference structure factor amplitudes, AF,. Using phases from the known, precise reference model (i.e., the structure in the absence of the photoreaction, which may be determined from... 

A molecule contains a nuclear distribution and an electronic distribution there is nothing else in a molecule. The nuclear arrangement is fully reflected in the electronic density distribution, consequently, the electronic density and its changes are sufficient to derive all information on all molecular properties. Molecular bodies are the fuzzy bodies of electronic charge density distributions consequently, the shape and shape changes of these fuzzy bodies potentially describe all molecular properties. Modern computational methods of quantum chemistry provide practical means to describe molecular electron distributions, and sufficiently accurate quantum chemical representations of the fuzzy molecular bodies are of importance for many reasons. A detailed analysis and understanding of "static" molecular properties such as "equilibrium" structure, and the more important dynamic properties such as vibrations, conformational changes and chemical reactions are hardly possible without a description of the molecule itself that implies a description of molecular bodies. 

The TAE/RECON method, developed by Breneman and co-workers based on Bader s quantum theory of Atoms In Molecules (AIM). The TAB method of molecular electron density reconstruction utilizes a library of integrated atomic basins , as defined by the AIM theory, to rapidly reconstruct representations of molecular electron density distributions and van der Waals electronic surface properties. RECON is capable of rapidly generating 6-31-I-G level electron densities and electronic properties of large molecules, proteins or molecular databases, using TAB reconstruction. A library of atomic charge density fragments has been assembled in a form that allows for the rapid retrieval of the fragments, followed by rapid molecular assembly. Additional details of the method are described elsewhere. ... 

Figure 6.1 A schematic representation of the electron density distribution in d orbitals...

Fig. 1. Perspective drawing of the electron density distribution p(r) of Nj shown with regard to a plane containing the two nuclei (HF/6-31G(d) calculations). In this and the following figures the function value has been cut off above (below) a predetermined value in order to improve the representation...

FIGURE 7.14 A representation of the electron density distribution surrounding the nucleus in the hydrogen atom. It shows a high probability of finding the electron closer to the nucleus. 

Fig. 2. Schematic representation of the centrosymmetric unit cell and its electron density distribution, obtained by stacking of asymmetric membrane vesicles...

The electron density distribution is a four-dimensional function (the number of elearons at a given point (x,y,z)), which is difficult to visually represent. Figures 1 and 2, respectively, show a three-dimensional isoelectronic surface of benzene and a contour plot of the elearon density p(r) in the molecular plane of benzene. Both representations show only gross features of the density. In particular, the total electron density distribution is dominated by the core electrons and appears simply as an aggregate of slightly distorted spheres... 

For each assumed nuclear arrangement Kj of the iterative structure refinement process, an AFDF electron density distribution p(r, Kj) can be calculated, replacing the conventional Gaussian density representations. The least square fit process using AFDF densities consists of the following formal steps, carried out iteratively ... 

Figure 1.4d shows a schematic representation of the electron "cloud in the ground state of the hydrogen atom. The intensity of the shading gives some idea of the electron density. For this case of a single-electron atom, the electron-density distribution is the same as the probability distribution. However, if more electrons are present, the probability distributions for the individual orbitals must be added together to get the net electron-density distribution in the atom. 

The intimate relation between the nuclear distribution and the electronic density distribution is a natural bridge that connects the more conventional, essentially classical, ball-and-stick models, and the more accurate, quantum-chemical electronic density descriptors of molecular shape. It is somewhat surprising that relatively little effort has been devoted to the natural relation between the purely nuclear interactions and the electronic density. In this contribution this connection will be discussed from a specific viewpoint, leading to a 3D representation of molecular shape and to an interpretation of chemical bonding. 

In 1993 Glaser and Choy published a full paper on the electron density distributions (at the RHF/6-31G level and including electron correlation at the MP2(full)/ 6-3IG level) in the heterosubstituted systems XN (X = F, HO, H2N) and compared these systems with methanediazonium ion. The results show that the positive charge on the N()ff)-atom is always larger than that on N(a). The N(a)-atom may even carry a negative charge Unconnected structures of electrophile and dinitrogen must be considered for adequate representation of the density distribution in XNi. ... 

Atomic multipoles can be used as an alternative for atomic point charges,3 " and they are expected to give a better representation of the non-spherical features of the electron density distribution, as found in lone pairs and certain ir-electron densities. For example, optimized crystal structures of acetic acid using atomic multipoles were indeed closer to the experimental structure than those based on atomic point charges. The drawback of this method is that the calculation of the electrostatic term is more CPU-intensive than a point charge model. 

---