10.5 Visualizing and Plotting Volumetric Quantities 10.5.7 Electron Localization Function 10.6 Electric Fields

10.5.8 Electrostatic Potentials

(April 13, 2024)

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

Note: For backwards compatibility with the Q-Chem/Charmm interface, the name IGDESP is equivalent to ESP_GRID.

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 $x,y,z,\phi(x,y,z)$ for each point, where $\phi$ is the ESP.
TYPE:
       INTEGER
DEFAULT:
       -4
OPTIONS:
       $-1$ read grid input via the $plots section of the input deck $-2$ same as the option $-1$ , plus evaluate the ESP of the $external_charges $-3$ same as the option $-1$ but in connection with STATE_ANALYSIS = TRUE. This computes the ESP for all excited-state densities, transition densities, and electron/hole densities. $-4$ No ESP evaluation $0$ 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 10.20 A job that evaluates the electrostatic potential for H ${}_{2}$ 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 electrostatic potential on a line
   1   0.0   0.0
   1   0.0   0.0
  15  -3.0   3.0
   0  0  0  0
   0
$end

The example below evaluates ESP on a plotting grid and generates a cube file, which can be loaded by IQmol to visualize ESP on a molecular surface (e.g. vdW surface or electron density isosurface).

Example 10.21 Calculating the ESP of acetyl chloride on a user-specified grid and generate a cube file as the result.

$molecule
 0 1
 C       0.00000     1.18959     1.29360
 H       0.00000     1.01580     2.37206
 H       0.88291     1.76694     1.00084
 H      -0.88291     1.76694     1.00084
 C       0.00000    -0.13357     0.57945
 O       0.00000    -1.22212     1.05977
 Cl      0.00000     0.06441    -1.23718
$end

$rem
 jobtype  sp
 method   b3lyp
 basis    6-31g(d)
point_group_symmetry False
 scf_convergence  8
 esp_grid  -1
 make_cube_files  true
$end

$plots
 plot the ESP
 50  -4.0  4.0
 50  -5.0  5.0
 50  -5.0  5.0
 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

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. ¹¹²⁹ Simmonett A. C., Gilbert A. T. B., Gill P. M. W.
Mol. Phys.
(2005), 103, pp. 2789. Link 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, set MM_CHARGES = TRUE in the $rem section.

MM_CHARGES

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.

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10.5.8 Electrostatic Potentials