# 10.5.7 Electrostatic Potentials and Electric Fields

(June 30, 2021)

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: $-3$ 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. $-2$ 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 10.16 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
$end  View output We can also compute the electrostatic potential for the transition density, which can be used, for example, to compute the Coulomb coupling in excitation energy transfer. ESP_TRANS Controls the calculation of the electrostatic potential of the transition density TYPE: LOGICAL DEFAULT: FALSE OPTIONS: TRUE compute the electrostatic potential of the excited state transition density FALSE compute the electrostatic potential of the excited state electronic density RECOMMENDATION: NONE The electrostatic potential is a complicated object and it is not uncommon to model it using a simplified representation based on atomic charges. For this purpose it is well known that Mulliken charges perform very poorly. Several definitions of ESP-derived atomic charges have been given in the literature, however, most of them rely on a least-squares fitting of the ESP evaluated on a selection of grid points. Although these grid points are usually chosen so that the ESP is well modeled in the “chemically important” region, it still remains that the calculated charges will change if the molecule is rotated. Recently an efficient rotationally invariant algorithm was proposed that sought to model the ESP not by direct fitting, but by fitting to the multipole moments. By doing so it was found that the fit to the ESP was superior to methods that relied on direct fitting of the ESP. The calculation requires the traceless form of the multipole moments and these are also printed out during the course of the calculations. To request these multipole-derived charges, set MM_CHARGES = TRUE in the$rem section.

MM_CHARGES
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.

The derivatives of electrostatic potential with respect to positions give electric fields, which is an important physical quantity for studies ranging from vibrational spectroscopy to catalysis. Similar to the case of ESP, Q-Chem can be used to compute the values of E-field on nuclear positions or a given grid, which is also controlled by the $rem variable ESP_GRID. The calculation of electric field is turned on when the value of ESP_EFIELD is greater than 0: ESP_EFIELD Triggers the calculation of ESP and/or E-field at nuclear positions or on a given grid of points TYPE: INTEGER DEFAULT: 0 OPTIONS: 0 Compute ESP only 1 Compute both ESP and electric field 2 Compute electric field only RECOMMENDATION: None Example 10.17 Calculate the electric field on the nuclear positions of a water molecule $molecule
0 1
O    -0.9112629280    1.0922672019    1.0200719528
H    -1.7568362275    1.5186695533    1.2826042030
H    -0.5592940377    1.7449530375    0.3694007293
$end$rem
METHOD       b3lyp
BASIS        cc-pvtz
ESP_GRID     0
ESP_EFIELD   2 ! compute E-field on atomic positions
\$end


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