Spartan (software) - Graphical Models

Graphical Models

Graphical models, especially molecular orbitals, electron density, and electrostatic potential maps, are a routine means of molecular visualization in chemistry education.

• Surfaces:
  • Molecular Orbitals (Highest Occupied, Lowest Unoccupied, and others.)
  • Electron Density - The electron density, ρ(r), is a function of the coordinates r, defined such that ρ(r)dr is the number of electrons inside a small volume dr. This is what is measured in an X-ray diffraction experiment. The electron density may be portrayed in terms of an isosurface (an isodensity surface) with the size and shape of the surface being given by the value (or percentage of enclosure) of the electron density.
  • Spin Density - The spin density, ρspin(r), is defined as the difference in electron density formed by electrons of α spin, ρα(r), and the electron density formed by electrons of β spin, ρβ(r). For closed-shell molecules (in which all electrons are paired), the spin density is zero everywhere. For open-shell molecules (in which one or more electrons are unpaired), the spin density indicates the distribution of unpaired electrons. Spin density is an indicator of reactivity of radicals.
  • Van der Waals surface
  • Solvent Accessible surface
  • Electrostatic Potential - The electrostatic potential, ε_p, is defined as the energy of interaction of a positive point charge located at p with the nuclei and electrons of a molecule. A surface for which the electrostatic potential is negative (a negative potential surface) delineates regions in a molecule which are subject to electrophilic attack.
  • Polarization Potential - The polarization potential,ε_p´ is the next term (beyond the electrostatic potential) in the expansion of the energy of interaction of a point positive charge with the nuclei and electrons of a molecule. It provides the energy due to electronic reorganization of the molecule as a result of its interaction with a point positive charge. The sum of the electrostatic and polarization potentials provides a better account of the energy of interaction of a point positive charge than available from the electrostatic potential alone. As evidence, it properly orders the proton affinities of trimethylamine, dimethyl ether and fluoromethane.
• Composite Surfaces (Maps):
  • Electrostatic Potential Map (Electrophilic indicator) - The most commonly employed property map is the electrostatic potential map. This gives the electrostatic potential at locations on a particular surface, most commonly a surface of electron density corresponding to overall molecular size.
  • Local Ionization Potential Map - Is defined as the sum over orbital electron densities, ρi(r) times absolute orbital energies, ∈i, and divided by the total electron density, ρ(r). The local ionization potential reflects the relative ease of electron removal (“ionization”) at any location around a molecule. For example, a surface of “low” local ionization potential for sulfur tetrafluoride demarks the areas which are most easily ionized.
  • LUMO Map (Nucleophilic indicator) - Maps of molecular orbitals may also lead to graphical indicators. For example, the “LUMO map”, wherein the (absolute value) of the lowest-unoccupied molecular orbital (the LUMO) is mapped onto a size surface (again, most commonly the electron density), providing an indication of nucleophilic reactivity.