This keyword controls the calculation and plotting of molecular field isosurfaces. Only one isosurface at a time can be generated. For the generation of multiple isosurfaces, the restart specification for the keyword PLOT (Section 4.10.3) can be applied. See the keyword BOX (4.10.7) for the definition of the isosurface boundary.
$<$FIELD$>$ Molecular field specification. The available field acronyms are PSI, RHO, SPIN, LAP, ESP, EFIDS, ELF, ITELF, SGGA, and PRHO in form of PRHOX, PRHOY or PRHOZ. See Table 12 for the acronym meanings. This specification is mandatory, even though the syntax is that of an option!
BASIS The Kohn-Sham density is used for the construction of the isosurface. This is the default.
AUXIS The auxiliary function density is used for the construction of the isosurface. This option is incompatible with the READ option.
LINEAR Linear interpolation scheme for the isosurface construction. This is the default.
BILINEAR Bilinear interpolation scheme for the isosurface construction.
LOGARITHMIC Logarithmic interpolation scheme for the isosurface construction.
BINARY The isosurface is written to the binary file LAT.bin using the VU file format. The VU control file deMon.pie is written, too. This is the default.
ASCII An ascii output of the isosurface is written in the file
TABLE A function table of isosurface coordinates is written in the output file deMon.out.
READ Specifies that an orbital list is read in the body of ISOSURFACE.
ISO=$<$Real$>$ Isosurface value. This specification is mandatory!
TOL=$<$Real$>$ Tolerance for data reduction.
The options AUXIS, BASIS, and READ of the ISOSURFACE keyword are identical in function to the corresponding options of the PLOT keyword (4.10.3). The BINARY option specifies that the isosurface coordinates and connectivities are written to the binary file LAT.bin.

Figure 16: Density isosurface of insulin, left, and the molecular electrostatic potential plotted on top of this isosurface, right.


With the VU control file deMon.pie that is also generated, the isosurface grid can be visualized in VU [41]. It is important to note that the LAT.bin file can be used as an input file for the plotting of a molecular field on the isosurface! For this purpose, that file has to be in the same directory as the deMon.inp file and the POINTS keyword (see Section 4.10.8) must be used to define the isosurface in LAT.bin as plot support. Figure 16 shows the density isosurface of human insulin and the molecular electrostatic potential plotted on top of this isosurface.

With the ASCII option, the ascii file is generated. Here is an example of the data structure of this file:


 VOLUME: .163076E+04
 AREA: .176664E+03

         X               Y               Z
     .312196E+00    -.729474E+00     .105260E+01
     .243158E+00    -.765796E+00     .105260E+01
     .243158E+00    -.729474E+00     .917119E+00

$\vdots$ $\vdots$ $\vdots$
           1          2          3
           4          5          6
           6          7          8

$\vdots$ $\vdots$ $\vdots$

The first line is the file header including the field information (RHO), the isovalue (0.1 a.u.), and the units (ANGSTROM) used for the coordinates, area, and volume data. The NUMBER OF VERTICES value corresponds to the number of interpolation points for the isosurface. The NUMBER OF FACETS is the number of surface elements of the isosurface. The volume (here in Å$^3$) and the surface area (here in Å$^2$) then appear. Note that the volume includes all volume elements with field values below the given threshold. Therefore, the volume of a 0.1 a.u. isosurface of a field with positive and negative values includes all volume elements with positive field values less than 0.1 a.u. and all volume elements with negative field values. The next block lists the coordinates of the interpolation points (here in Å). The last block, entitled CONNECTIVITY, describes the triangulation of the interpolation points. With the option TABLE, the same data as with the ASCII option are written into the file deMon.out.

The options LINEAR, BILINEAR, and LOGARITHMIC specify the interpolation scheme for the construction of the isosurface by use of the marching tetrahedron algorithm [281]. The value of the isosurface is specified with the ISO option. A value in vertical bar delimiters (e.g., $\vert.1\vert$) indicates an absolute isosurface value. It can be used to generate two isosurfaces simultaneously with the same positive and negative threshold (e.g., for molecular orbitals). If the thresholds for the two isosurfaces should be different (e.g., for molecular electrostatic potentials), the two values can be specified as:

ISO = 0.1/-0.05

As noted above, the ISO specification has no default setting and, therefore, is mandatory, despite its syntax as an option! With the TOL option, the amount of data reduction is specified. Allowed values, from $10^{-3}$ to 0.5, specify the severity of the data reduction. A value of $10^{-3}$ indicates no data reduction at all. This is the default. With increasing TOL values, the data reduction increases, thus decreasing the memory requirements and, at the same time, the resolution.

Perturbed density isosurfaces are calculated with respect to the external electric field direction. Thus, the options PRHOX, PRHOY, and PRHOZ generate isosurfaces of the perturbed density originating from an external electric field applied along the $x$-axis, $y$-axis, or $z$-axis, respectively.