11.5 Visualizing and Plotting Orbitals, Densities, and Other Volumetric Data

11.5.6 Electrostatic Potentials

Q-Chem can evaluate electrostatic potentials on a grid of points. Electrostatic potential evaluation is controlled by the $rem variable ESP_GRID.

ESP_GRID
       Controls evaluation of the electrostatic potential on a grid of points. If enabled, the output is in an ASCII file, plot.esp, in the format x,y,z, esp for each point.
TYPE:
       INTEGER
DEFAULT:
       none no electrostatic potential evaluation
OPTIONS:
       -2 same as the option -1, plus evaluate the ESP of the $external_charges -1 read grid input via the $plots section of the input deck 0 Generate the ESP values at all nuclear positions +n read n grid points in bohr from the ASCII file ESPGrid
RECOMMENDATION:
       None

The following example illustrates the evaluation of electrostatic potentials on a grid. Note that IANLTY must also be set to 200.

Example 11.11  A job that evaluates the electrostatic potential for H2 on a 1 by 1 by 15 grid, along the bond axis. The output is in an ASCII file called plot.esp, which lists for each grid point, x, y, z, and the electrostatic potential.

$molecule
   0  1
   H   0.0   0.0   0.35
   H   0.0   0.0  -0.35
$end

$rem
   METHOD     hf
   BASIS      6-31g**
   IANLTY     200
   ESP_GRID     -1
$end

$plots
   plot the HOMO and the LUMO on a line
   1   0.0   0.0
   1   0.0   0.0
  15  -3.0   3.0
   0  0  0  0
   0
$end

We can also compute the electrostatic potential for the transition density, which can be used, for example, to compute the Coulomb coupling in excitation energy transfer.

ESP_TRANS
       Controls the calculation of the electrostatic potential of the transition density
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       TRUE compute the electrostatic potential of the excited state transition density FALSE compute the electrostatic potential of the excited state electronic density
RECOMMENDATION:
       NONE

The electrostatic potential is a complicated object and it is not uncommon to model it using a simplified representation based on atomic charges. For this purpose it is well known that Mulliken charges perform very poorly. Several definitions of ESP-derived atomic charges have been given in the literature, however, most of them rely on a least-squares fitting of the ESP evaluated on a selection of grid points. Although these grid points are usually chosen so that the ESP is well modeled in the “chemically important” region, it still remains that the calculated charges will change if the molecule is rotated. Recently an efficient rotationally invariant algorithm was proposed that sought to model the ESP not by direct fitting, but by fitting to the multipole moments.836 By doing so it was found that the fit to the ESP was superior to methods that relied on direct fitting of the ESP. The calculation requires the traceless form of the multipole moments and these are also printed out during the course of the calculations. To request these multipole-derived charges the following $rem option should be set:

MM_CHARGES
       Requests the calculation of multipole-derived charges (MDCs).
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       TRUE Calculates the MDCs and also the traceless form of the multipole moments
RECOMMENDATION:
       Set to TRUE if MDCs or the traceless form of the multipole moments are desired. The calculation does not take long.