Isovalue surface

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. 

Atomic volumes play an important role in relating physicochemical properties to biological effects. Most atoms in molecules are not entirely bounded by interatomic surfaces and an atomic volume is defined as a measure of the space enclosed by the intersection of the atom s zero-flux surfaces with some outer envelope of the density. The envelope with a value of 0.001 au is generally chosen as this has been shown to yield molecular sizes in good agreement with experimentally assigned van der Waals radii [16, 17]. A related property is the van der Waals surface area, which QTAIM determines by integrating an atom s exposed contribution to a molecule s isovalued surface. 

Figure 1. Symmetry-unique SC orbitalsfor the gas-phase Diels-Alder reaction along the CASSCF(6,6) IRC at IRC -0.6 amu bohr (leftmost column), TS (IRC = 0) and IRC +0.6 amu bohr (rightmost column). Three-dimensional isovalue surfaces, corresponding to / = 0.08, were drawn from virtual reality modelling language (VRML) files produced by MOLDEN [il].

The evolution of the shapes of the SC orbitals with the progress of the cyclohexadiene ring-opening is illustrated by Fig. 5. The symmetry-unique SC orbitals tj/i-ti/s are shown as three-dimensional isovalue surfaces at the cyclohexadiene end of the IRC segment (leftmost column of orbitals), at the TS (central column of orbitals) and at the hexatriene end of the IRC segment (rightmost column of orbitals). The reflections of t /i, tj/2 and /3 in the symmetry plane which is retained throughout this IRC interval, result in /6, /5 and tj/4, respectively. 

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. ... 

Fig. 30.4 o and redox active molecular orbitals (RAMOs) of the 1V54B and 1V540 models of the Cua site in the gas phase. AU isovalue surfaces are set at 0.03 (e/A ). Molecular structures are shown in thin lines... 

Figure 1. Isovalue surfaces of A2FI (p) for (a) tolane, 1, in the absence of an external field, (b) tolane thiolate, 2, in the absence of an external field, (c) tolane thiolate in an external field oriented in cooperation with the electron donation of sulfur (forward bias), and (d) tolane thiolate in an external field oriented in opposition to the electron donation of sulfur(reversebias). A2II (p) = -0.025 au everywhere on these surfaces, and A2n (p)< -0.025 au everywhere within these envelopes. The orientations of the molecules, and the momentum-space axes are as described in the "GettingOriented" section.

Isovalue surfaces of L(r) = 0 for CO (left) and BH3 (right) showing regions of valence-shell charge concentration (VSCC, inside surfaces) and depletion (VSCD, holes) that define the reactive surface and direction of interaction between a Lewis base and a Lewis acid. Adapted from ref [42]. Copyright 1994 Oxford University Press USA. 

Molecular orbitals obtained from ab initio or semiempirical calculations can also be represented by isovalue surfaces (Figures 10 and 11). Visualized HOMOs (highest occupied molecular orbital) and LUMOs (lowest unoccupied molecular orbital) are often used to display reactive pathways of organic molecules. 

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