Electron density electrostatic potential

Figure 3/ for example/ places the lanosterol so as the 3f hydroxyl polar group lies over the propionate side chains. To reduce the complexity of this picture one can now replace the lanosterol structure by a surface canopy to represent the extent of the hydrophobic substrate binding site. There is also the facility to code this surface to signify the electronic properties of the substrates such as their electron density/ electrostatic potential/ or HOMO/LUMO values. Theoretical work of this type is currently suggesting quite remarkable complementarity of electron properties between bound substrates and protein binding sites. (10). 

Tel. 612-683-3688, fax 612-683-3099, e-mail mcole cray.com DGauss for density functional theory calculations with nonlocal, SCF corrections, and geometry optimization. Cadpac 5.0 for ab initio calculations. MNDO90 for semiempirical molecular orbital calculations. A package with a graphics front end for structure input and visualizations of electron density, electrostatic potentials, and molecular orbitals. Silicon Graphics and Macintosh (under X-Windows) networked to a Cray. 

Keywords Tfydrogen bonding electron density electrostatic potential electron localization... 

D. J. Grimwood, I. Bytheway and D. Jayatilaka, Wave functions derived from experiment. V. Investigation of electron densities, electrostatic potentials and electron localization functions for noncentrosymmetric crystals, J. Comp. Chem. 24, 470 83 (2003). 

Projection of molecular features, such as electron density, electrostatic potential, and hydrostatic potential, onto the surface of a sphere has been used successfully by van Geerestein et al. [71]. A small number of surface points are chosen as representative vertices (typically 12 or 20 arranged as an icosahedron or dodecahedron, respectively) that can be used as anchor points for the descriptors. Shape, for instance, can be represented by finding the shortest distance between each vertex and the surface of the molecule. 

The display facilities range from simple descriptors, such as atomic charges, bond orders, and bond strains, to multidimensional energy maps, IR spectra, UV/visible spectra, molecular orbitals, and reactivity surfaces such as electron densities, electrostatic potentials, and Fukui susceptibilities and superdelocalizabilities (electrophilic, radical, and nucleophilic). The presentation-quality figures can be readily cut and pasted into a wide range of desktop publishing applications. 

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. 

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. 

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. 

The mechanism by which electrons interact with crystals is different from that of X-rays. X-rays detect electron density distribution in crystals, while electrons detect electrostatic potential distribution in crystals. Electron crystallography may be used for studying some special problems related to potential distribution such as the oxidation states of atoms in the crystal. 

This chapter introduces a number of useful graphical models, including molecular orbitals, electron densities, spin densities, electrostatic potentials and local ionization potentials, and relates these models both to molecular size and shape and molecular charge distributions. The chapter also introduces and illustrates property maps which simultaneously depict molecular size and shape in addition to a molecular property. Properties include the electrostatic potential, the value of the LUMO, the local ionization potential and the spin density. 

Among the quantities which have proven of value as graphical models are the molecular orbitals, the electron density, the spin density (for radicals and other molecules with unpaired electrons), the electrostatic potential and the local ionization potential. These may all be expressed as three-dimensional functions of the coordinates. One way to display them on a two-dimensional video screen (or on a printed page) is to define a surface of constant value, a so-called isovalue surface or, more simply, isosurface. ... 

This chapter introduces and illustrates isosurface displays of molecular orbitals, electron and spin densities, electrostatic potentials and local ionization potentials, as well as maps of the lowest-unoccupied molecular orbital, the electrostatic and local ionization potentials and the spin density (on top of electron density surfaces). Applications of these models to the description of molecular properties and chemical reactivity and selectivity are provided in Chapter 19 of this guide. 

It is also possible to map a calculated property onto an electron-density surface. Because all three Cartesian coordinates are used to define the points on the surface, the property must be mapped in color, with the colors of the spectrum red-orange-yellow-green-blue representing a range of values. In effect, this is a four-dimensional plot (x, y, z, -i- property mapped). One of the most common plots of this type is the density-electrostatic potential, or density-elpot, plot. The electrostatic potential is determined by placing a unit positive charge at each point... 

The wavefunction allows a calculation of the molecular electron density p(x,y,z). In a way, this is the answer to the question where are the electrons . The electrostatic potential generated by the molecule can be calculated from the density, and this is useful in predicting what a molecule will do when it comes into close contact with another molecule the electrostatic potential is at the origin of control of mutual recognition in molecular complexes and condensed phases, as well as of some directional aspects of reactivity (Section 4.2). 

Visualization options for quantum calculations include both three-dimensional isosurfaces and two-dimensional contour plots for molecular orbitals, total charge density, electrostatic potential, and spin density. The electrostatic potential can be color-mapped onto a three-dimensional charge density isosurface. Isosurface rendering methods include wire mesh, Jorgensen-Salem, transparent and solid surfaces, and Gouraud shaded surfaces. Electronic energy levels, electronic absorption spectra, and vibrational absorption spectra can be displayed. Animation of vibrational modes and display of normal-mode displacement vectors are also available. These features are flexible and allow for user control of most display options. A standard text output file with user-specified print level is also produced on request. 

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 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 ... 

P(r,i) is the pairwise potential, which, depending upon the model, can be considered tc include electrostatic and repulsive contributions. The second term is a function of th< electron density, and varies with the square root, in keeping with the second-momen approximation. The electron density for an afom includes contributions from the neigh bouring atoms as follows ... 

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. 

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