10.6 Electric Fields 10.6 Electric Fields 10.7 Spin and Charge Densities at the Nuclei

10.6.1 Overview

(July 14, 2022)

The derivatives of electrostatic potential (ESP) with respect to positions give electric fields, which is a fundamental physical quantity that has been shown to play an important role in applications ranging from vibrational spectroscopy to molecular and enzyme catalysis. Similar to the case of ESP, Q-Chem is able 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 $>0$ :

ESP_EFIELD

ESP_EFIELD
       Triggers the calculation of ESP and/or electric 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 10.20 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

Q-Chem 6 supports two DFT-based electronic structure methods for the evaluation of electric fields (and also ESPs) arising from a chemical environment (e.g. solvents) at the specific sites of a “probe” molecule (typically at the atomic positions). These methods, whose details are provided in Ref. , involve a partition of the electron density of the entire system into those belonging to the central system and to the environment. The first approach is based on the SPADE partitioning scheme (see Section 11.6.2), ²¹⁹ Claudino D., Mayhall N. J.
J. Chem. Theory Comput.
(2019), 15, pp. 1053. Link which transforms the converged occupied MOs obtained from a standard SCF calculation and then assigns them to different parts of a system. The second approach is based on DFT calculations using absolutely localized molecular orbitals (ALMOs, see Section 12.4), ⁵⁹⁹ Khaliullin R. Z., Head-Gordon M., Bell A. T.
J. Chem. Phys.
(2006), 124, pp. 204105. Link which invokes fragmentation of the supersystem from the beginning and the fragment MOs are then variationally optimized when they are polarized by other fragments. Both of these methods then construct the electron density for the “environment” part of the supersystem ( $\rho_{\mathrm{E}}$ ) using the correspondingly assigned occupied MOs, and the ESP and electric field at a specific site of the central “probe” system can be calculated using the electron density and nuclear charges of the environment. Denoting the embedded central system and its environment as S and E, respectively, the ESP and electric field vector at site $A\in\text{S}$ ( $\phi_{A}$ and $\mathbf{F}_{\!A}$ ) can be evaluated using

\phi_{A}=\sum_{B\in\text{E}}\frac{Z_{B}}{|\mathbf{r}_{A}-\mathbf{r}_{B}|}-% \frac{\rho_{\text{E}}(\mathbf{r})}{|\mathbf{r}_{A}-\mathbf{r}|}\mathrm{d}% \mathbf{r}

(10.23)

and

\mathbf{F}_{\!A}=\bm{\hat{\nabla}}\phi_{A}=\sum_{B\in\text{E}}\frac{Z_{B}(% \mathbf{r}_{A}-\mathbf{r}_{B})}{|\mathbf{r}_{A}-\mathbf{r}_{B}|^{3}}-\int\frac% {\rho_{\text{E}}(\mathbf{r})(\mathbf{r}_{A}-\mathbf{r})}{|\mathbf{r}_{A}-% \mathbf{r}|^{3}}\mathrm{d}\mathbf{r}\;.

(10.24)

The current implementation of these methods requires two Q-Chem jobs to be performed for a single environment ESP and electric field calculation. In the first job, one performs an SCF or SCF-MI calculation and generate the occupied MOs or electron density assigned to the environment; in the second job, the environment MOs or electron density is read in and the ESP and electric fields are calculated using Eqs. (10.23) and (10.24). Note that in the second job, the embedded central system (“probe”) is represented using ghost atoms to probe the nuclear positions; and for SPADE and ALMO the SCF_GUESS for the 2nd job must be READ and READ_DEN, respectively. To evaluate the potential and field at the nuclear positions of the central system, one should set ESP_GRID = 0; for other options (e.g. evaluating the ESP and its gradient on grid points), one should refer to the documentation of “ESP_GRID” in Section 10.5.8.

ALMO_EFIELD

ALMO_EFIELD
       Calculate the environment ESP/E-field using ALMO-based partitioning
TYPE:
       BOOLEAN
DEFAULT:
       FALSE
OPTIONS:
       TRUE In job 1, it saves the electron density for the environment constructed from ALMOs; In job 2, it reads in the electron density (must be together with SCF_GUESS = READ_DEN) FALSE Don’t do ALMO-based ESP/field calculations
RECOMMENDATION:
       Required for both jobs in ALMO-based electric field calculations

ALMO_EFIELD_PROBE_FRGM

ALMO_EFIELD_PROBE_FRGM
       Specify the index of the probe fragment in ALMO-based ESP and electric field calculations
TYPE:
       INTEGER
DEFAULT:
       1
OPTIONS:
       $n$ Specify the $n$ -th fragment as the probe
RECOMMENDATION:
       None

Example 10.21 Using the SPADE partitioning method to calculate the ESP and electric field arising from the environment (the 2nd H ${}_{2}$ O molecule) at the atomic positions of the 1st H ${}_{2}$ O

$molecule
0 1
--
0 1
O  -1.551007  -0.114520   0.000000
H  -1.934259   0.762503   0.000000
H  -0.599677   0.040712   0.000000
--
0 1
O   1.350625   0.111469   0.000000
H   1.680398  -0.373741  -0.758561
H   1.680398  -0.373741   0.758561
$end

$rem
jobtype  sp
method   b3lyp
basis    6-31G(d)
env_method b3lyp
symmetry   false
sym_ignore true
gen_scfman_embed true
spade_partition  true
scf_convergence  8
embedding_early_stop true ! skip the embedded SCF
$end

@@@

$molecule
0 1
@O  -1.551007  -0.114520   0.000000
@H  -1.934259   0.762503   0.000000
@H  -0.599677   0.040712   0.000000
O    1.350625   0.111469   0.000000
H    1.680398  -0.373741  -0.758561
H    1.680398  -0.373741   0.758561
$end

$rem
jobtype sp
method  b3lyp
basis    6-31G(d)
symmetry false
sym_ignore true
scf_guess  read
skip_scfman true ! generate results directly from the MOs read in
esp_grid   0
esp_efield 1 ! compute ESP and E-field on atomic positions
$end

Example 10.22 Using ALMO-based partitioning to calculate the ESP and electric field arising from the environment (the 2nd H ${}_{2}$ O molecule) at the atomic positions of the 1st H ${}_{2}$ O

$molecule
0 1
--
0 1
O  -1.551007  -0.114520   0.000000
H  -1.934259   0.762503   0.000000
H  -0.599677   0.040712   0.000000
--
0 1
O   1.350625   0.111469   0.000000
H   1.680398  -0.373741  -0.758561
H   1.680398  -0.373741   0.758561
$end

$rem
jobtype  sp
method   b3lyp
basis    6-31G(d)
symmetry   false
sym_ignore true
scf_convergence  8
frgm_method   stoll  ! doing SCF-MI (ALMO) calculation
scfmi_mode    1
almo_efield   true   ! save electron density belonging to the 2nd fragment
$end

@@@

$molecule
0 1
@O  -1.551007  -0.114520   0.000000
@H  -1.934259   0.762503   0.000000
@H  -0.599677   0.040712   0.000000
O    1.350625   0.111469   0.000000
H    1.680398  -0.373741  -0.758561
H    1.680398  -0.373741   0.758561
$end

$rem
jobtype sp
method  b3lyp
basis   6-31G(d)
symmetry   false
sym_ignore true
scf_guess  read_den
almo_efield true   ! with read_den, this will read in the density saved in the 1st job
skip_scfman true
esp_grid    0
esp_efield  1  ! compute ESP and E-field on atomic positions
$end

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10.6.1 Overview