13.5.4 NEO-PCM‣ 13.5 Nuclear–Electronic Orbital Method ‣ Chapter 13 Specialized Topics ‣ Q-Chem 6.1 User’s Manual

Bulk solvent effects can be directly incorporated into NEO calculations through the application of various implicit solvation models (Section 11.2) within the NEO framework. ¹³¹⁹ Wildman A. et al.
J. Chem. Theory Comput.
(2022), 18, pp. 1340. Link The polarizable continuum model (PCM) constitutes one family of implicit solvation models and itself encompasses several different formulations (i.e., C-PCM ¹²³⁷ Truong T. N., Stefanovich E. V.
Chem. Phys. Lett.
(1995), 240, pp. 253. Link ^, ⁷⁰ Barone V., Cossi M.
J. Phys. Chem. A
(1998), 102, pp. 1995. Link , IEF-PCM ²¹⁵ Chipman D. M.
J. Chem. Phys.
(2000), 112, pp. 5558. Link ^, ¹⁶⁴ Cancès E., Mennucci B.
J. Chem. Phys.
(2001), 114, pp. 4744. Link , SS(V)PE ²¹⁵ Chipman D. M.
J. Chem. Phys.
(2000), 112, pp. 5558. Link , etc.). ⁵⁰⁵ Herbert J. M.
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
(2021), 11, pp. e1519. Link In the PCM approach, the solute molecule is placed in a cavity that is embedded in dielectric continuum solvent, and the cavity surface is discretized into $i$ tesserae grid points. The solvent response is represented by a partial charge $q_{i}$ centered at each tesserae grid point $\mathbf{s}_{i}$ . ¹²²⁵ Tomasi J., Mennucci B., Cammi R.
Chem. Rev.
(2005), 106, pp. 2999. Link

For each SCF iteration, the current electronic and protonic densities, together with the fixed classical nuclei, define the solute’s charge distribution. This charge distribution gives rise to the solute’s electrostatic potential $V_{i}$ at each tesserae grid point:

V_{i}=\sum_{A}\frac{Z_{A}}{\left|\mathbf{R}_{A}-\mathbf{s}_{i}\right|}-\sum_{% \mu\nu}P_{\mu\nu}^{\text{e}}\int d\mathbf{r}_{\text{e}}\frac{\phi_{\mu}^{\text% {e}}\left(\mathbf{r}_{\text{e}}\right)\phi_{\nu}^{\text{e}}\left(\mathbf{r}_{% \text{e}}\right)}{\left|\mathbf{r}_{\text{e}}-\mathbf{s}_{i}\right|}+\sum_{\mu% ^{\prime}\nu^{\prime}}P_{\mu^{\prime}\nu^{\prime}}^{\text{p}}\int d\mathbf{r}_% {\text{p}}\frac{\phi_{\mu^{\prime}}^{\text{p}}\left(\mathbf{r}_{\text{p}}% \right)\phi_{\nu^{\prime}}^{\text{p}}\left(\mathbf{r}_{\text{p}}\right)}{\left% |\mathbf{r}_{\text{p}}-\mathbf{s}_{i}\right|}\;.

(13.44)

The solute electrostatic potential is then used to compute $q_{i}$ using standard PCM methods. Once obtained, the set of tesserae charges is included as an additional one-electron (one-proton) contribution to the electronic (protonic) Fock or analogous Kohn-Sham matrix:


$\displaystyle F^{\text{e},\text{solv}}_{\mu\nu}$	$\displaystyle=F^{\text{e},\text{0}}_{\mu\nu}-\sum_{i}q_{i}\int d\mathbf{r}_{% \text{e}}\frac{\phi_{\mu}^{\text{e}}\left(\mathbf{r}_{\text{e}}\right)\phi_{% \nu}^{\text{e}}\left(\mathbf{r}_{\text{e}}\right)}{\left\|\mathbf{r}_{\text{e}}% -\mathbf{s}_{i}\right\|}$	(13.45a)
$\displaystyle F^{\text{p},\text{solv}}_{\mu^{\prime}\nu^{\prime}}$	$\displaystyle=F^{\text{p},\text{0}}_{\mu^{\prime}\nu^{\prime}}+\sum_{i}q_{i}% \int d\mathbf{r}_{\text{p}}\frac{\phi_{\mu^{\prime}}^{\text{p}}\left(\mathbf{r% }_{\text{p}}\right)\phi_{\nu^{\prime}}^{\text{p}}\left(\mathbf{r}_{\text{p}}% \right)}{\left\|\mathbf{r}_{\text{p}}-\mathbf{s}_{i}\right\|}\;,$	(13.45b)

where $F^{\text{e},\text{0}}_{\mu\nu}$ and $F^{\text{p},\text{0}}_{\mu^{\prime}\nu^{\prime}}$ refer to the gas-phase, electronic (Eq. (13.37a)) and protonic (Eq. (13.37b)) Fock or analagous Kohn-Sham matrix elements, respectively.

NEO-PCM calculations involve iterative, self-consistent convergence of the nuclear-electronic wavefunction in the presence of the dielectric continuum solvent. Both NEO-HF and NEO-DFT PCM energies and analytic gradients are implemented. The calculation can be invoked by setting SOLVENT_METHOD = PCM alongside variables for NEO-SCF (Section 13.5.8) in the $rem input section.

In the simplest approach, the cavity surface is discretized into point charges. However, a more sophisticated approach utilizing Gaussian-smeared charges is also supported. ¹³⁶⁴ York D. M., Karplus M.
J. Phys. Chem. A
(1999), 103, pp. 11060. Link ^, ⁶⁸² Lange A. W., Herbert J. M.
J. Phys. Chem. Lett.
(2010), 1, pp. 556. Link ^, ⁶⁸³ Lange A. W., Herbert J. M.
J. Chem. Phys.
(2010), 133, pp. 244111. Link ^, ⁶⁸⁰ Lange A. W. et al.
Mol. Phys.
(2020), 118, pp. e1644384. Link Selection of these various PCM schemes and related variables can be set in the $pcm and/or $solvent input sections. An example on how to set up a solvated NEO calculation can be found in Section 13.5.9.

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13.5.4 NEO-PCM