Density-electrostatic potential

The model used is the RPM. The average electrostatic potential ifr) at a distance r away from an ion / is related to tire charge density p.(r) by Poisson s equation... 

The atomic scattering factor for electrons is somewhat more complicated. It is again a Fourier transfonn of a density of scattering matter, but, because the electron is a charged particle, it interacts with the nucleus as well as with the electron cloud. Thus p(r) in equation (B1.8.2h) is replaced by (p(r), the electrostatic potential of an electron situated at radius r from the nucleus. Under a range of conditions the electron scattering factor, y (0, can be represented in temis... 

The most elementary mean-field models of electronic structure introduce a potential that an electron at r would experience if it were interacting with a spatially averaged electrostatic charge density arising from the N- 1 remaining electrons ... 

Besides molecular orbitals, other molecular properties, such as electrostatic potentials or spin density, can be represented by isovalue surfaces. Normally, these scalar properties are mapped onto different surfaces see above). This type of high-dimensional visualization permits fast and easy identification of the relevant molecular regions. 

To display properties on molecular surfaces, two different approaches are applied. One method assigns color codes to each grid point of the surface. The grid points are connected to lines chicken-wire) or to surfaces (solid sphere) and then the color values are interpolated onto a color gradient [200]. The second method projects colored textures onto the surface [202, 203] and is mostly used to display such properties as electrostatic potentials, polarizability, hydrophobidty, and spin density. 

The electrostatic potential at a point r, 0(r), is defined as the work done to bring unit positive charge from infinity to the point. The electrostatic interaction energy between a point charge q located at r and the molecule equals The electrostatic potential has contributions from both the nuclei and from the electrons, unlike the electron density, which only reflects the electronic distribution. The electrostatic potential due to the M nuclei is ... 

A cubic lattice is superimposed onto the solute(s) and the surrounding solvent. Values of the electrostatic potential, charge density, dielectric constant and ionic strength are assigned to each grid point. The atomic charges do not usually coincide with a grid point and so the... 

The Poisson equation relates the electrostatic potential ([) to the charge density p. The Poisson equation is... 

Many molecular properties can be related directly to the wave function or total electron density. Some examples are dipole moments, polarizability, the electrostatic potential, and charges on atoms. 

Many functions, such as electron density, spin density, or the electrostatic potential of a molecule, have three coordinate dimensions and one data dimension. These functions are often plotted as the surface associated with a particular data value, called an isosurface plot (Figure 13.5). This is the three-dimensional analog of a contour plot. 

There are ways to plot data with several pieces of data at each point in space. One example would be an isosurface of electron density that has been colorized to show the electrostatic potential value at each point on the surface (Figure 13.6). The shape of the surface shows one piece of information (i.e., the electron density), whereas the color indicates a different piece of data (i.e., the electrostatic potential). This example is often used to show the nucleophilic and electrophilic regions of a molecule. 

FIGURE 13.5 Isosurface plots, (a) Region of negative electrostatic potential around the water molecule. (A) Region where the Laplacian of the electron density is negative. Both of these plots have been proposed as descriptors of the lone-pair electrons. This example is typical in that the shapes of these regions are similar, but the Laplacian region tends to be closer to the nucleus. 

FIGURE 13.6 A plot showing two data values. The shape is an isosurface of the total electron density. The color applied to the surface is based on the magnitude of the electrostatic potential at that point in space. 

The Poisson equation describes the electrostatic interaction between an arbitrary charge density p(r) and a continuum dielectric. It states that the electrostatic potential ([) is related to the charge density and the dielectric permitivity z by... 

Once the job is completed, the UniChem GUI can be used to visualize results. It can be used to visualize common three-dimensional properties, such as electron density, orbital densities, electrostatic potentials, and spin density. It supports both the visualization of three-dimensional surfaces and colorized or contoured two-dimensional planes. There is a lot of control over colors, rendering quality, and the like. The final image can be printed or saved in several file formats. 

Crystal can compute a number of properties, such as Mulliken population analysis, electron density, multipoles. X-ray structure factors, electrostatic potential, band structures, Fermi contact densities, hyperfine tensors, DOS, electron momentum distribution, and Compton profiles. 

The macmolplt graphics package is designed for displaying the output of GAMESS calculations. It can display molecular structures, including an animation of reaction-path trajectories. It also may be used to visualize properties, such as the electron density, orbitals, and electrostatic potential in two or three dimensions. 

Wave functions can be visualized as the total electron density, orbital densities, electrostatic potential, atomic densities, or the Laplacian of the electron density. The program computes the data from the basis functions and molecular orbital coefficients. Thus, it does not need a large amount of disk space to store data, but the computation can be time-consuming. Molden can also compute electrostatic charges from the wave function. Several visualization modes are available, including contour plots, three-dimensional isosurfaces, and data slices. 

The structure of ethylene and the orbital hybridization model for its double bond were presented m Section 2 20 and are briefly reviewed m Figure 5 1 Ethylene is planar each carbon is sp hybridized and the double bond is considered to have a a component and a TT component The ct component arises from overlap of sp hybrid orbitals along a line connecting the two carbons the tt component via a side by side overlap of two p orbitals Regions of high electron density attributed to the tt electrons appear above and below the plane of the molecule and are clearly evident m the electrostatic potential map Most of the reactions of ethylene and other alkenes involve these electrons... 

An sp hybridization model for the carbon-carbon triple bond was developed in Section 2 21 and is reviewed for acetylene in Figure 9 2 Figure 9 3 compares the electrostatic potential maps of ethylene and acetylene and shows how the second tr bond m acetylene causes a band of high electron density to encircle the molecule... 

The electrostatic potential map of benzene (Figure 11 3c) shows regions of high electron density above and below the plane of the ring which is where we expect the most loosely held electrons (the rr electrons) to be In Chapter 12 we will see how this region of high electron density is responsible for the characteristic chemical reactivity of benzene and its relatives... 

An orbital hybridization description of bonding m methylamme is shown m Figure 22 2 Nitrogen and carbon are both sp hybridized and are joined by a ct bond The unshared electron pair on nitrogen occupies an sp hybridized orbital This lone parr IS involved m reactions m which amines act as bases or nucleophiles The graphic that opened this chapter is an electrostatic potential map that clearly shows the concentration of electron density at nitrogen m methylamme... 

You can also plot the electrostatic potential, the total charge density, or the total spin density determined during a semi-empirical or ab initio calculation. This information is useful in determining reactivity and correlating calculational results with experimental data. These examples illustrate uses of these plots ... 

In addition to total energy and gradient, HyperChem can use quantum mechanical methods to calculate several other properties. The properties include the dipole moment, total electron density, total spin density, electrostatic potential, heats of formation, orbital energy levels, vibrational normal modes and frequencies, infrared spectrum intensities, and ultraviolet-visible spectrum frequencies and intensities. The HyperChem log file includes energy, gradient, and dipole values, while HIN files store atomic charge values. 

---